Analysis of Brain Imaging Data

Chapter 1

Abstract

Imaging Data†

imaging and longitudinal measurements.

analysis, multimodal, multi-measurement

1. Introduction

†

3

Atsushi Kawaguchi

Supervised Sparse Components

Analysis with Application to Brain

We propose a dimension-reduction method using supervised (multi-block) sparse (principal) component analysis. The method is first implemented through basis expansion of spatial brain images, and the scores are then reduced through regularized matrix decomposition to produce simultaneous data-driven selections of related brain regions, supervised by univariate composite scores representing linear combinations of covariates. Two advantages of the proposed method are that it identifies the associations between brain regions at the voxel level and that supervision is helpful for interpretation. The proposed method was applied to a study on Alzheimer's disease (AD) that involved using multimodal whole-brain magnetic resonance imaging (MRI) and positron emission tomography (PET). For illustrative purposes, we demonstrate cases of both single- and multimodal brain

Keywords: data-driven approach, dimension reduction, principal component

Recently, multiple neuroimaging data sets per subject have become obtainable due to the remarkable development of imaging techniques such as magnetic resonance imaging (MRI) and positron emission tomography (PET), as well as computer resources and technologies. Vandenberghe and Marsden [1] provide a review on the use of PET and MRI integration technology, such as integrated scanning devices, rather than data analysis. Other modalities such as diffusion MRIs (dMRIs) and functional MRIs (fMRIs) are also useful in collecting brain-related information. These multimodal imaging data sets have the potential to provide rich information about human health and behavior, such as brain function and structure, from different perspectives. From multiple measurements of a single-modal (or multimodal) technique, longitudinal changes in the status and combination of neuro

Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/

wp-content/uploads/how\_to\_apply/ ADNI\_Acknowledgement\_List.pdf

#### Chapter 1

## Supervised Sparse Components Analysis with Application to Brain Imaging Data†

Atsushi Kawaguchi

#### Abstract

We propose a dimension-reduction method using supervised (multi-block) sparse (principal) component analysis. The method is first implemented through basis expansion of spatial brain images, and the scores are then reduced through regularized matrix decomposition to produce simultaneous data-driven selections of related brain regions, supervised by univariate composite scores representing linear combinations of covariates. Two advantages of the proposed method are that it identifies the associations between brain regions at the voxel level and that supervision is helpful for interpretation. The proposed method was applied to a study on Alzheimer's disease (AD) that involved using multimodal whole-brain magnetic resonance imaging (MRI) and positron emission tomography (PET). For illustrative purposes, we demonstrate cases of both single- and multimodal brain imaging and longitudinal measurements.

Keywords: data-driven approach, dimension reduction, principal component analysis, multimodal, multi-measurement

#### 1. Introduction

Recently, multiple neuroimaging data sets per subject have become obtainable due to the remarkable development of imaging techniques such as magnetic resonance imaging (MRI) and positron emission tomography (PET), as well as computer resources and technologies. Vandenberghe and Marsden [1] provide a review on the use of PET and MRI integration technology, such as integrated scanning devices, rather than data analysis. Other modalities such as diffusion MRIs (dMRIs) and functional MRIs (fMRIs) are also useful in collecting brain-related information. These multimodal imaging data sets have the potential to provide rich information about human health and behavior, such as brain function and structure, from different perspectives. From multiple measurements of a single-modal (or multimodal) technique, longitudinal changes in the status and combination of neuro

<sup>†</sup> Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/ wp-content/uploads/how\_to\_apply/ ADNI\_Acknowledgement\_List.pdf

biomarkers can be observed to support the prediction and early diagnosis of disease and the classification of disease subtypes.

obtain undiscovered knowledge. In [29], by using ReliefF [30], features such as the fractional amplitude of low-frequency fluctuations from resting-state fMRIs, segmented gray matter from sMRIs, and fractional anisotropy from dMRIs were extracted. Component analysis based on low-rank approximation is a successful data-driven approach in the fields of not only neuroimaging but also other biological and medical big data analyses, including principal component analysis, partial lease squares, canonical correlation analysis (CCA), independent component analysis (ICA), and nonnegative matrix factorization. These methods are organized into a matrix decomposition framework consisting of score and loading (weight) matrices. The score matrix, with same row length as the number of subjects, is regarded as dimension-reduced data and is suitable for application to statistical models. The weight matrix, with the same column length as the number of features in the imaging data, is regarded as the basis images. All these methods, except for ICA, have a derivation sparse approach with a regularized matrix decomposition to pose small weights to zeros, which helps estimation by avoiding irrelevant information. In addition, the resulting weights can be interpreted to mean that the corresponding features with nonzero weights contribute to the basis image, specifically to produce

Supervised Sparse Components Analysis with Application to Brain Imaging Data

DOI: http://dx.doi.org/10.5772/intechopen.80531

data-driven selections of brain regions related to that component.

network structure by using the PLS.

Section 4.

2. Methods

Ref. [19].

5

These methods also consider another direction in which the application of multimodal imaging data can be extended. Supplementary information from another data set can also be useful for the interpretation of the output. For this purpose, appropriate data fusion or integration techniques are required and are useful for multisite studies. In neuroimaging data analysis, multimodal CCA (mCCA) [31] and mCCA + joint ICA [32] have been developed on the schizophrenia study. Multivariate data fusion approaches were categorized by [33] into asymmetric or symmetric data and blind or semi-blind data in symmetric approach. The asymmetric approach is a regression-type approach and includes specific modalities such as dMRI and electroencephalography. The symmetric approach is a correlation-type approach and allows relationships in both directions. Kawaguchi [19] constructed a risk score for glioblastomas based on MRI data and proposed a two-step dimension-reduction method using a radial basis function-supervised multi-block sparse principal component analysis (SMS-PCA) method. Kawaguchi and Yamashita [34] proposed a more general case including a PLS or CCA framework and applied it to MRI, PET, and SNP data sets. Yoshida et al. [4] analyze imaging and non-imaging data with

In this chapter, we applied SMS-PCA to MRI and PET data sets and a longitudinal MRI data set. One of the key features in the analysis is a multi-block technique which can achieve structural dimension reduction with interpretable parameters (weights for each data set and the possibility of combining them). Although it is not the focus of this chapter, the dimension reduction prior to SMS-PCA is conducted using 3D basis functions. Specifically, our dimension reduction takes place in two steps, and, as described in [35] which applied these techniques to longitudinal study, this two-step approach yields a composite basis function expression with a flexible shape. The organization of this chapter is as follows. Section 2 describes the methodology of the SMS-PCA, which is applied to real data in Section 3. The characteristics of the method, found through its application, are discussed in

We describe the proposed method in this section. The contents are similar to

Multimodal brain imaging analysis is important in brain-related disease studies. Arbabshirani et al. [2] provide many reviews on the subject. Imaging data analysis makes a substantial contribution to the study of mental disorders. Most singlemodal or multimodal imaging studies concern dementia leading to Alzheimer's disease (AD) [3] (around 300 of the AD imaging studies searched in Ref. [2]). Modalities considered in there are structural MRIs (sMRIs), fMRIs, dMRIs, fluorodeoxyglucose PETs, and Amyloid/Tau PETs. In a recent study, Ref. [4] examined sMRI and cerebrospinal fluid (CSF) markers. Magnetoencephalography (MEG) is also useful as AD biomarker, and its localization using sMRI has high accuracy [5]. Schizophrenia is the second most studied disorder after dementia. Shah et al. [6] provide an example of multimodal meta-analysis. For Huntington's disease, white matter is evaluated using dMRI [7]. For mood disorders (depressive disorder and bipolar disorder), Refs. [8, 9] provide a review of the machine learning method. Moeller and Paulus [10] studied the longitudinal prediction of relapse for substance-related disorders using MRI, fMRI, EEG, and PET. Moser et al. [11] studied schizophrenia and bipolar disorder using multimodal imaging data analysis. dMRI is also effective for analyzing these conditions [12]. For developmental disabilities, Ref. [13] investigated volume reductions in attention-deficit hyperactivity disorder (ADHD) with 1713 participants. Aoki et al. [14] reviewed dMRI studies and conducted meta-analysis for ADHD. Li et al. [15] provide a review of imaging studies in autism spectrum disorder. For anxiety disorder, Ref. [16] applied support vector machine (SVM) to multimodal data. They used clinical questionnaires and measured cortisol release, and gray and white matter volumes in subjects with generalized anxiety disorder and major depression and in healthy subjects. Steiger et al. [17] investigated cortical volume, diffusion tensor imaging, and networkbased statistics using multimodal analysis for social anxiety disorder. For borderline personality disorder, Ref. [18] conducted an imaging-based meta-analysis of 10 studies. In cancer research, especially that on glioblastoma multiforme, multimodal imaging analysis is useful for identifying some types of tumors and evaluating patient prognosis (for more details, see [19]). Genome-related data can be regarded as a modality and called imaging genetics when analyzed in combination with imaging data [20].

One important technique for single- and multimodal imaging analysis is prediction, which is useful for the support of disease diagnosis and the selection of treatments [21]. SVM is the most used method not only in neuroimaging but also in the life sciences in high-dimensional data analysis. The random forest method is also useful due to their capability for complex interactions based on the tree model [22, 23]. For multimodal analysis, multiple kernel learning [24] and (multimodal) deep learning [25, 26] have been developed. Janssen et al. [27] reviewed machine learning methods for psychiatric prognosis. Related statistical methodology appeared as multi-omics in bioinformatics, and Ref. [28] reviewed these methods while introducing an R package, mixOmics.

Analysis for such discovery and evaluation is based on the detection of the buried signal in the noise (irrelevant information). Statistical analysis is useful for this purpose; however, it suffers from the ultrahigh dimensional and complex structure of this data, and appropriate dimension reduction is therefore required. Even if a machine learning method is used, appropriate input (feature) should be specified to obtain interpretable results because the method is feasible for highdimensional procedures but not ultrahigh dimensional ones. A region-of-interestbased analysis was the leading approach. In contrast, whole-brain analysis is more informative, and if it is combined with a data-driven approach, it can potentially

#### Supervised Sparse Components Analysis with Application to Brain Imaging Data DOI: http://dx.doi.org/10.5772/intechopen.80531

obtain undiscovered knowledge. In [29], by using ReliefF [30], features such as the fractional amplitude of low-frequency fluctuations from resting-state fMRIs, segmented gray matter from sMRIs, and fractional anisotropy from dMRIs were extracted. Component analysis based on low-rank approximation is a successful data-driven approach in the fields of not only neuroimaging but also other biological and medical big data analyses, including principal component analysis, partial lease squares, canonical correlation analysis (CCA), independent component analysis (ICA), and nonnegative matrix factorization. These methods are organized into a matrix decomposition framework consisting of score and loading (weight) matrices. The score matrix, with same row length as the number of subjects, is regarded as dimension-reduced data and is suitable for application to statistical models. The weight matrix, with the same column length as the number of features in the imaging data, is regarded as the basis images. All these methods, except for ICA, have a derivation sparse approach with a regularized matrix decomposition to pose small weights to zeros, which helps estimation by avoiding irrelevant information. In addition, the resulting weights can be interpreted to mean that the corresponding features with nonzero weights contribute to the basis image, specifically to produce data-driven selections of brain regions related to that component.

These methods also consider another direction in which the application of multimodal imaging data can be extended. Supplementary information from another data set can also be useful for the interpretation of the output. For this purpose, appropriate data fusion or integration techniques are required and are useful for multisite studies. In neuroimaging data analysis, multimodal CCA (mCCA) [31] and mCCA + joint ICA [32] have been developed on the schizophrenia study. Multivariate data fusion approaches were categorized by [33] into asymmetric or symmetric data and blind or semi-blind data in symmetric approach. The asymmetric approach is a regression-type approach and includes specific modalities such as dMRI and electroencephalography. The symmetric approach is a correlation-type approach and allows relationships in both directions. Kawaguchi [19] constructed a risk score for glioblastomas based on MRI data and proposed a two-step dimension-reduction method using a radial basis function-supervised multi-block sparse principal component analysis (SMS-PCA) method. Kawaguchi and Yamashita [34] proposed a more general case including a PLS or CCA framework and applied it to MRI, PET, and SNP data sets. Yoshida et al. [4] analyze imaging and non-imaging data with network structure by using the PLS.

In this chapter, we applied SMS-PCA to MRI and PET data sets and a longitudinal MRI data set. One of the key features in the analysis is a multi-block technique which can achieve structural dimension reduction with interpretable parameters (weights for each data set and the possibility of combining them). Although it is not the focus of this chapter, the dimension reduction prior to SMS-PCA is conducted using 3D basis functions. Specifically, our dimension reduction takes place in two steps, and, as described in [35] which applied these techniques to longitudinal study, this two-step approach yields a composite basis function expression with a flexible shape. The organization of this chapter is as follows. Section 2 describes the methodology of the SMS-PCA, which is applied to real data in Section 3. The characteristics of the method, found through its application, are discussed in Section 4.

#### 2. Methods

We describe the proposed method in this section. The contents are similar to Ref. [19].

biomarkers can be observed to support the prediction and early diagnosis of disease

Multimodal brain imaging analysis is important in brain-related disease studies. Arbabshirani et al. [2] provide many reviews on the subject. Imaging data analysis makes a substantial contribution to the study of mental disorders. Most singlemodal or multimodal imaging studies concern dementia leading to Alzheimer's disease (AD) [3] (around 300 of the AD imaging studies searched in Ref. [2]). Modalities considered in there are structural MRIs (sMRIs), fMRIs, dMRIs, fluorodeoxyglucose PETs, and Amyloid/Tau PETs. In a recent study, Ref. [4] examined sMRI and cerebrospinal fluid (CSF) markers. Magnetoencephalography (MEG) is also useful as AD biomarker, and its localization using sMRI has high accuracy [5]. Schizophrenia is the second most studied disorder after dementia. Shah et al. [6] provide an example of multimodal meta-analysis. For Huntington's disease, white matter is evaluated using dMRI [7]. For mood disorders (depressive disorder and bipolar disorder), Refs. [8, 9] provide a review of the machine learning method. Moeller and Paulus [10] studied the longitudinal prediction of relapse for substance-related disorders using MRI, fMRI, EEG, and PET. Moser et al. [11] studied schizophrenia and bipolar disorder using multimodal imaging data analysis. dMRI is also effective for analyzing these conditions [12]. For developmental disabilities, Ref. [13] investigated volume reductions in attention-deficit hyperactivity disorder (ADHD) with 1713 participants. Aoki et al. [14] reviewed dMRI studies and conducted meta-analysis for ADHD. Li et al. [15] provide a review of imaging studies in autism spectrum disorder. For anxiety disorder, Ref. [16] applied support vector machine (SVM) to multimodal data. They used clinical questionnaires and measured cortisol release, and gray and white matter volumes in subjects with generalized anxiety disorder and major depression and in healthy subjects. Steiger et al. [17] investigated cortical volume, diffusion tensor imaging, and networkbased statistics using multimodal analysis for social anxiety disorder. For borderline personality disorder, Ref. [18] conducted an imaging-based meta-analysis of 10 studies. In cancer research, especially that on glioblastoma multiforme, multimodal imaging analysis is useful for identifying some types of tumors and evaluating patient prognosis (for more details, see [19]). Genome-related data can be regarded as a modality and called imaging genetics when analyzed in combination with

One important technique for single- and multimodal imaging analysis is predic-

tion, which is useful for the support of disease diagnosis and the selection of treatments [21]. SVM is the most used method not only in neuroimaging but also in the life sciences in high-dimensional data analysis. The random forest method is also useful due to their capability for complex interactions based on the tree model [22, 23]. For multimodal analysis, multiple kernel learning [24] and (multimodal) deep learning [25, 26] have been developed. Janssen et al. [27] reviewed machine learning methods for psychiatric prognosis. Related statistical methodology appeared as multi-omics in bioinformatics, and Ref. [28] reviewed these methods

Analysis for such discovery and evaluation is based on the detection of the buried signal in the noise (irrelevant information). Statistical analysis is useful for this purpose; however, it suffers from the ultrahigh dimensional and complex structure of this data, and appropriate dimension reduction is therefore required. Even if a machine learning method is used, appropriate input (feature) should be specified to obtain interpretable results because the method is feasible for highdimensional procedures but not ultrahigh dimensional ones. A region-of-interestbased analysis was the leading approach. In contrast, whole-brain analysis is more informative, and if it is combined with a data-driven approach, it can potentially

and the classification of disease subtypes.

Neuroimaging - Structure, Function and Mind

imaging data [20].

4

while introducing an R package, mixOmics.

#### 2.1 Priory dimension reduction

S ¼ f g s<sup>α</sup> <sup>α</sup>¼1,…,n is the n � N matrix whose column corresponds to the vectorized original image data. As the dimensions for each mth image are the same, we use the same basis function to reduce the dimension from N to q. X ¼ SB is the n � q matrix, where B is the N � q matrix whose jth column corresponds to the vectorized basis function with the jth knot being the center. Note that knots are pre-specified to span the space equally, as shown in Figure 1. In this example, four-pixel equal spanning knots are applied.

#### 2.2 Objective function

Dimension reduction using the basis function is then followed by the SMS-PCA method, considering (sample) correlations based on data values. We consider score t for n � q matrices Xm, where m ¼ 1, 2, …, M with the following multi-block structure:

$$\mathbf{t} = \sum\_{m=1}^{M} b\_{m} \mathbf{X}\_{m} \mathbf{w}\_{m} = \sum\_{m=1}^{M} b\_{m} \mathbf{t}\_{m},\tag{1}$$

where w<sup>m</sup> is the weight vector for the mth sub-block X<sup>m</sup> and bm is the weight for the superblock. Here, it should be noted that the scores in Eq. (1) are referred to as the super scores, whereas t<sup>m</sup> ¼ Xmw<sup>m</sup> is referred to as the block score. Figure 2 schematically describes the score structure for the case of M ¼ 2.

Thus, the super score has a hierarchical structure for each individual and can be used in an application such as the construction of a diagnosis score.

When matrix X<sup>m</sup> is normalized by its columns, the weights w ¼ ð Þ w1; w2; …; w<sup>M</sup> <sup>⊤</sup> and <sup>b</sup> <sup>¼</sup> ð Þ <sup>b</sup>1; <sup>b</sup>2; …; bM <sup>⊤</sup> are estimated by maximizing the function

$$\mathbf{L}(\mathbf{b}, \boldsymbol{\omega}) = (\mathbf{1} - \boldsymbol{\mu})\,\mathbf{t}^{\top}\mathbf{t} + \boldsymbol{\mu}\,\mathbf{t}^{\top}\mathbf{Z} - \sum\_{m=1}^{M} \mathbf{P}\_{\boldsymbol{\lambda}\_{m}}(\boldsymbol{\omega}\_{m}) \tag{2}$$

subject to k k <sup>w</sup><sup>m</sup> <sup>2</sup>

Algorithm for SMS-PCA method.

1. Initialize t with k kt <sup>2</sup> ¼ 1. 2. Repeat until convergence: 2.1. Set <sup>w</sup><sup>e</sup> <sup>m</sup> <sup>¼</sup> <sup>h</sup><sup>λ</sup><sup>m</sup> bmX<sup>⊤</sup>

2.3 Optimization

2.4 Parameter selection

information criterion (BIC):

in wm.

7

Table 1.

Figure 2. Score structure.

<sup>2</sup> <sup>¼</sup> 1 and k k<sup>b</sup> <sup>2</sup>

<sup>w</sup>^ <sup>m</sup> <sup>¼</sup> <sup>w</sup><sup>e</sup> <sup>m</sup>=k k <sup>w</sup><sup>e</sup> <sup>m</sup> <sup>2</sup> ð Þ <sup>m</sup> <sup>¼</sup> <sup>1</sup>; <sup>2</sup>; …; <sup>M</sup> .

b ¼ eb=kebk2.

mtm=t<sup>⊤</sup>

Supervised Sparse Components Analysis with Application to Brain Imaging Data

DOI: http://dx.doi.org/10.5772/intechopen.80531

2.2. Set <sup>t</sup><sup>m</sup> <sup>¼</sup> <sup>X</sup>mw^ <sup>m</sup> and <sup>e</sup>bm <sup>¼</sup> <sup>t</sup><sup>⊤</sup>

m¼1 ^ bmXmw^ <sup>m</sup>.

normalize as ^

2.3. Set <sup>t</sup> <sup>¼</sup> <sup>∑</sup><sup>M</sup>

3. (Deflation step) Set <sup>p</sup><sup>m</sup> <sup>¼</sup> <sup>X</sup><sup>⊤</sup>

<sup>K</sup> component super scores <sup>t</sup>ð Þ<sup>1</sup> ; …; <sup>t</sup>ð Þ <sup>K</sup> with <sup>t</sup>ð Þ<sup>k</sup> <sup>¼</sup> <sup>t</sup>

The optimal value for λ ¼ ð Þ λ1; …; λ<sup>M</sup>

proportion of the supervision, Pλð Þ x is the penalty function, [Pλð Þ¼ x 2λj j x is used in this study], and λ>0 is the regularized parameter that is used to control the sparsity. The larger value of the regularization parameter λ<sup>m</sup> has many nonzero elements

<sup>m</sup>t<sup>m</sup> and <sup>X</sup>^ <sup>m</sup> <sup>¼</sup> <sup>t</sup>mp<sup>⊤</sup>

The algorithm given in Table 1 is used to estimate the weights in Eq. (1) by maximizing L in Eq. (2). The rationality behind this approach is provided in [19]. Note that the deflation step yields multiple components and has several alternatives; that is, through K time iteration for step. 1 to 3 of the algorithm, we can obtain

<sup>2</sup> ¼ 1 with k k� <sup>2</sup> as the L2 norm, where 0≤μ≤1 is the

<sup>m</sup>, and <sup>X</sup><sup>m</sup> <sup>X</sup><sup>m</sup> � <sup>X</sup>^ <sup>m</sup>.

<sup>⊤</sup> �

and

<sup>m</sup>f g ð Þ <sup>1</sup> � <sup>μ</sup> <sup>t</sup> <sup>þ</sup> <sup>μ</sup><sup>Z</sup> � �, where <sup>h</sup>λð Þ¼ <sup>y</sup> signð Þ<sup>y</sup> ð Þ j j <sup>y</sup> <sup>&</sup>gt;<sup>λ</sup> <sup>þ</sup>, and normalize as

<sup>m</sup>f g ð Þ 1 � μ t þ μZ ; then set eb ¼ eb1; eb2; …; ebMÞ

ð Þk <sup>1</sup> ; …;t ð Þk M � � .

<sup>⊤</sup> is selected by minimizing the Bayesian

Figure 1. Dimension reduction via basis function.

Supervised Sparse Components Analysis with Application to Brain Imaging Data DOI: http://dx.doi.org/10.5772/intechopen.80531

#### Figure 2. Score structure.

2.1 Priory dimension reduction

Neuroimaging - Structure, Function and Mind

spanning knots are applied.

2.2 Objective function

w ¼ ð Þ w1; w2; …; w<sup>M</sup>

function

Figure 1.

6

Dimension reduction via basis function.

structure:

S ¼ f g s<sup>α</sup> <sup>α</sup>¼1,…,n is the n � N matrix whose column corresponds to the vectorized original image data. As the dimensions for each mth image are the same, we use the same basis function to reduce the dimension from N to q. X ¼ SB is the n � q matrix, where B is the N � q matrix whose jth column corresponds to the vectorized basis function with the jth knot being the center. Note that knots are pre-specified to span the space equally, as shown in Figure 1. In this example, four-pixel equal

Dimension reduction using the basis function is then followed by the SMS-PCA

bmXmw<sup>m</sup> ¼ ∑

where w<sup>m</sup> is the weight vector for the mth sub-block X<sup>m</sup> and bm is the weight for the superblock. Here, it should be noted that the scores in Eq. (1) are referred to as the super scores, whereas t<sup>m</sup> ¼ Xmw<sup>m</sup> is referred to as the block score. Figure 2

Thus, the super score has a hierarchical structure for each individual and can be

<sup>⊤</sup><sup>t</sup> <sup>þ</sup> <sup>μ</sup> <sup>t</sup>

<sup>⊤</sup><sup>Z</sup> � <sup>∑</sup><sup>M</sup>

M m¼1

bmtm, (1)

<sup>⊤</sup> are estimated by maximizing the

<sup>m</sup>¼<sup>1</sup>P<sup>λ</sup><sup>m</sup> ð Þ <sup>w</sup><sup>m</sup> (2)

method, considering (sample) correlations based on data values. We consider score t for n � q matrices Xm, where m ¼ 1, 2, …, M with the following multi-block

> t ¼ ∑ M m¼1

schematically describes the score structure for the case of M ¼ 2.

<sup>⊤</sup> and <sup>b</sup> <sup>¼</sup> ð Þ <sup>b</sup>1; <sup>b</sup>2; …; bM

Lð Þ¼ b; w ð Þ 1 � μ t

used in an application such as the construction of a diagnosis score. When matrix X<sup>m</sup> is normalized by its columns, the weights


2.1. Set <sup>w</sup><sup>e</sup> <sup>m</sup> <sup>¼</sup> <sup>h</sup><sup>λ</sup><sup>m</sup> bmX<sup>⊤</sup> <sup>m</sup>f g ð Þ <sup>1</sup> � <sup>μ</sup> <sup>t</sup> <sup>þ</sup> <sup>μ</sup><sup>Z</sup> � �, where <sup>h</sup>λð Þ¼ <sup>y</sup> signð Þ<sup>y</sup> ð Þ j j <sup>y</sup> <sup>&</sup>gt;<sup>λ</sup> <sup>þ</sup>, and normalize as <sup>w</sup>^ <sup>m</sup> <sup>¼</sup> <sup>w</sup><sup>e</sup> <sup>m</sup>=k k <sup>w</sup><sup>e</sup> <sup>m</sup> <sup>2</sup> ð Þ <sup>m</sup> <sup>¼</sup> <sup>1</sup>; <sup>2</sup>; …; <sup>M</sup> .

	- normalize as ^ b ¼ eb=kebk2.

$$\text{2.3. Set } \mathbf{t} = \sum\_{m=1}^{M} \hat{b}\_m \mathbf{X}\_m \hat{w}\_m \dots$$

3. (Deflation step) Set <sup>p</sup><sup>m</sup> <sup>¼</sup> <sup>X</sup><sup>⊤</sup> mtm=t<sup>⊤</sup> <sup>m</sup>t<sup>m</sup> and <sup>X</sup>^ <sup>m</sup> <sup>¼</sup> <sup>t</sup>mp<sup>⊤</sup> <sup>m</sup>, and <sup>X</sup><sup>m</sup> <sup>X</sup><sup>m</sup> � <sup>X</sup>^ <sup>m</sup>.

#### Table 1. Algorithm for SMS-PCA method.

subject to k k <sup>w</sup><sup>m</sup> <sup>2</sup> <sup>2</sup> <sup>¼</sup> 1 and k k<sup>b</sup> <sup>2</sup> <sup>2</sup> ¼ 1 with k k� <sup>2</sup> as the L2 norm, where 0≤μ≤1 is the proportion of the supervision, Pλð Þ x is the penalty function, [Pλð Þ¼ x 2λj j x is used in this study], and λ>0 is the regularized parameter that is used to control the sparsity. The larger value of the regularization parameter λ<sup>m</sup> has many nonzero elements

#### 2.3 Optimization

in wm.

The algorithm given in Table 1 is used to estimate the weights in Eq. (1) by maximizing L in Eq. (2). The rationality behind this approach is provided in [19].

Note that the deflation step yields multiple components and has several alternatives; that is, through K time iteration for step. 1 to 3 of the algorithm, we can obtain <sup>K</sup> component super scores <sup>t</sup>ð Þ<sup>1</sup> ; …; <sup>t</sup>ð Þ <sup>K</sup> with <sup>t</sup>ð Þ<sup>k</sup> <sup>¼</sup> <sup>t</sup> ð Þk <sup>1</sup> ; …;t ð Þk M � � .

#### 2.4 Parameter selection

The optimal value for λ ¼ ð Þ λ1; …; λ<sup>M</sup> <sup>⊤</sup> is selected by minimizing the Bayesian information criterion (BIC):

$$\text{BIC}(\lambda) = \log\left(\frac{\sum\_{m=1}^{M} \left\|\hat{\mathbf{X}}\_{m}^{(r)} - \mathbf{X}\_{m}\right\|^{2}}{n\text{M}q}\right) + \frac{\log\left(n\text{M}q\right)}{n\text{M}q} (\neq \text{nonzero elements in } \mathfrak{w}\_{m}),$$

early Alzheimer's disease (AD). We use two types of data set: baseline measurement

Baseline imaging data were collected from 106 subjects with mean ages of 75.2 years for the 54 normal cognitive subjects and 72.9 years for the 27 patients with dementia. This data set was somewhat larger than that of [34] because in this study single-nucleotide polymorphism (SNP) was not considered and subjects with missing SNP data were included. Table 2 summarizes the characteristics of these patients. We consider imaging data from two modalities, MRI X<sup>1</sup> and PET X2, namely, M ¼ 2. The preprocessing method is the same as that used in [34]. For the basis

because of the results of our simulation study. The clinical outcome to supervise is given by Z ¼ 3:17 � CDR þ 0:11 � ADAS13 � 0:57 � MMSE where CDR is the clinical dementia rating score, ADAS13 is the Alzheimer's disease assessment scalecognitive subscale, and MMSE is the mini-mental state examination score. These coefficients were the same as in [34]. The SMSMA method was applied to the data

The original data with dimensions of 2,122,945 (= 121 � 145 � 121) was reduced to 7,162 using the basis functions for each imaging data set. The number of components were selected as 8 for all μ = 0, 0.25, 0.5, 0.75, 1. Figure 3 shows the correlation matrix from the dataset with the binary outcome, AD or Normal, and the

The correlations between the super scores were small except for μ ¼ 1, and for μ ¼ 0, the second component had a high correlation with the outcome. In contrast,

Table 3 shows the results for the multiple logistic regression model with AD or normal as the outcomes and the super scores as predictors for each μ. The numbers

Age (mean [sd]) 75.41 (7.18) 74.93 (4.89) 0.684 PTGENDER = Male (%) 31 (59.6) 36 (66.7) 0.582 APOE4 (%) <0.001

PTEDUCAT (mean [sd]) 14.19 (3.04) 15.89 (2.99) 0.005 CDRSB (mean [sd]) 4.54 (1.73) 0.03 (0.12) <0.001 ADAS11 (mean [sd]) 18.70 (5.63) 6.56 (3.28) <0.001 ADAS13 (mean [sd]) 28.94 (6.30) 10.08 (4.30) <0.001 MMSE (mean [sd]) 23.38 (2.07) 28.87 (1.24) <0.001

Dementia Normal p

for μ>0, the first component had the highest correlation with the outcome.

n 52 54

0 17 (32.7) 39 (72.2) 1 29 (55.8) 13 (24.1) 2 6 (11.5) 2 (3.7)

<sup>3</sup> � <sup>4</sup><sup>2</sup> <sup>p</sup> <sup>¼</sup> <sup>6</sup>:93) equal spacing knots

function, we used four-voxel (therefore, <sup>h</sup> <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffi

ð Þ X1; X2;Z with parameters μ ¼ 0, 0:25, 0:5, and 0:75.

with multimodal MRI and PET images and repeated measuring MRI images.

Supervised Sparse Components Analysis with Application to Brain Imaging Data

3.1 Multimodality

DOI: http://dx.doi.org/10.5772/intechopen.80531

3.1.1 Data

3.1.2 Results

Table 2.

9

Characteristic for data set 1.

resulting super scores for each μ.

where X^ ð Þ<sup>r</sup> <sup>m</sup> <sup>¼</sup> <sup>T</sup>ð Þ<sup>r</sup> <sup>m</sup> Pð Þ<sup>r</sup> <sup>m</sup> with Tð Þ<sup>r</sup> <sup>m</sup> ¼ t ð Þ1 <sup>m</sup> ; …;t ð Þr m h i and <sup>P</sup>ð Þ<sup>r</sup> <sup>m</sup> <sup>¼</sup> <sup>p</sup>ð Þ<sup>1</sup> <sup>m</sup> ; …; pð Þ<sup>r</sup> m � � is obtained from r deflation steps (the projection of X<sup>m</sup> onto the r-dimensional subspace). There are several search strategies for optimization, and these are introduced in the

software options below.

#### 2.5 Software

The statistical software R package msma is provided to implement the method described in Ref. [34] where the SMS-PCA method is a part of the package and the PLS type can also be implemented. The package is available from the Comprehensive R Archive Network (CRAN) at http://CRAN.R-project.org/package=msma. Four-parameter search methods are available. Here, the parameters are λ<sup>m</sup> and the number of components. The "simultaneous" method identifies the number of components by searching the regularized parameters in each component. The "regpara1st" method identifies the regularized parameters by fixing the number of components and then searching for the number of components with the selected regularized parameters. The "ncomp1st" method identifies the number of components with a regularized parameter of 0 and then searches for the regularized parameters with the selected number of components. The "regparaonly" method searches for the regularized parameters with a fixed number of components.

In this chapter, the "ncomp1st" method was applied with nonzero sparsity when the number of components was selected because, in our experience, the BIC value suffered from the high dimensionality of the data. The basic R code for this method is as follows:

tuneparams = optparasearch(X=X, Z=Z, search.method="ncomp1st", maxpct4ncomp=0.5, muX=0.5)

where the argument maxpct4ncomp = 0.5 means that 0:5 λmax is used as the regularized parameter when the number of components is searched and where λmax is the maximum of the regularized parameters among the possible candidates. In order to obtain the final fit result with optimized parameters, the following code should be implemented:

fit1 = msma(X=X, Z=Z, comp=tuneparams\$optncomp, lambdaX=tuneparams \$optlambdaX, lambdaY=tuneparams\$optlambdaY, muX = 0.5)

For more details, please see the package manual.

#### 3. Application

In this section, we apply the SMS-PCA described in the previous section to real data. The data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). The ADNI was launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner, MD. The primary goal of ADNI has been to test whether serial magnetic resonance imaging (MRI), positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment (MCI) and

early Alzheimer's disease (AD). We use two types of data set: baseline measurement with multimodal MRI and PET images and repeated measuring MRI images.

#### 3.1 Multimodality

#### 3.1.1 Data

BICð Þ¼ λ log

where X^ ð Þ<sup>r</sup>

2.5 Software

is as follows:

maxpct4ncomp=0.5, muX=0.5)

should be implemented:

3. Application

8

software options below.

∑<sup>M</sup> <sup>m</sup>¼<sup>1</sup> <sup>X</sup>^ ð Þ<sup>r</sup>

Neuroimaging - Structure, Function and Mind

<sup>m</sup> Pð Þ<sup>r</sup>

0

B@

<sup>m</sup> <sup>¼</sup> <sup>T</sup>ð Þ<sup>r</sup>

� � �

<sup>m</sup> � X<sup>m</sup>

nMq

<sup>m</sup> with Tð Þ<sup>r</sup>

� � � 2

<sup>m</sup> ¼ t ð Þ1 <sup>m</sup> ; …;t ð Þr m h i

ponents by searching the regularized parameters in each component. The

tuneparams = optparasearch(X=X, Z=Z, search.method="ncomp1st",

\$optlambdaX, lambdaY=tuneparams\$optlambdaY, muX = 0.5)

For more details, please see the package manual.

where the argument maxpct4ncomp = 0.5 means that 0:5 λmax is used as the regularized parameter when the number of components is searched and where λmax is the maximum of the regularized parameters among the possible candidates. In order to obtain the final fit result with optimized parameters, the following code

fit1 = msma(X=X, Z=Z, comp=tuneparams\$optncomp, lambdaX=tuneparams

In this section, we apply the SMS-PCA described in the previous section to real

data. The data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). The ADNI was launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner, MD. The primary goal of ADNI has been to test whether serial magnetic resonance imaging (MRI), positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment (MCI) and

from r deflation steps (the projection of X<sup>m</sup> onto the r-dimensional subspace). There are several search strategies for optimization, and these are introduced in the

The statistical software R package msma is provided to implement the method described in Ref. [34] where the SMS-PCA method is a part of the package and the PLS type can also be implemented. The package is available from the Comprehensive R Archive Network (CRAN) at http://CRAN.R-project.org/package=msma. Four-parameter search methods are available. Here, the parameters are λ<sup>m</sup> and the number of components. The "simultaneous" method identifies the number of com-

"regpara1st" method identifies the regularized parameters by fixing the number of components and then searching for the number of components with the selected regularized parameters. The "ncomp1st" method identifies the number of components with a regularized parameter of 0 and then searches for the regularized parameters with the selected number of components. The "regparaonly" method searches for the regularized parameters with a fixed number of components.

In this chapter, the "ncomp1st" method was applied with nonzero sparsity when the number of components was selected because, in our experience, the BIC value suffered from the high dimensionality of the data. The basic R code for this method

1

CA <sup>þ</sup> log ð Þ nMq

and Pð Þ<sup>r</sup>

<sup>m</sup> <sup>¼</sup> <sup>p</sup>ð Þ<sup>1</sup>

nMq ð Þ # nonzero elements in <sup>w</sup><sup>m</sup> ,

<sup>m</sup> ; …; pð Þ<sup>r</sup> m � � is obtained

> Baseline imaging data were collected from 106 subjects with mean ages of 75.2 years for the 54 normal cognitive subjects and 72.9 years for the 27 patients with dementia. This data set was somewhat larger than that of [34] because in this study single-nucleotide polymorphism (SNP) was not considered and subjects with missing SNP data were included. Table 2 summarizes the characteristics of these patients.

We consider imaging data from two modalities, MRI X<sup>1</sup> and PET X2, namely, M ¼ 2. The preprocessing method is the same as that used in [34]. For the basis function, we used four-voxel (therefore, <sup>h</sup> <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>3</sup> � <sup>4</sup><sup>2</sup> <sup>p</sup> <sup>¼</sup> <sup>6</sup>:93) equal spacing knots because of the results of our simulation study. The clinical outcome to supervise is given by Z ¼ 3:17 � CDR þ 0:11 � ADAS13 � 0:57 � MMSE where CDR is the clinical dementia rating score, ADAS13 is the Alzheimer's disease assessment scalecognitive subscale, and MMSE is the mini-mental state examination score. These coefficients were the same as in [34]. The SMSMA method was applied to the data ð Þ X1; X2;Z with parameters μ ¼ 0, 0:25, 0:5, and 0:75.

#### 3.1.2 Results

The original data with dimensions of 2,122,945 (= 121 � 145 � 121) was reduced to 7,162 using the basis functions for each imaging data set. The number of components were selected as 8 for all μ = 0, 0.25, 0.5, 0.75, 1. Figure 3 shows the correlation matrix from the dataset with the binary outcome, AD or Normal, and the resulting super scores for each μ.

The correlations between the super scores were small except for μ ¼ 1, and for μ ¼ 0, the second component had a high correlation with the outcome. In contrast, for μ>0, the first component had the highest correlation with the outcome.

Table 3 shows the results for the multiple logistic regression model with AD or normal as the outcomes and the super scores as predictors for each μ. The numbers


Table 2. Characteristic for data set 1.

Figure 3. Correlations between super scores.

of 5% statistically significant components were 3, 4, 3, 3, and 0 for μ = 0, 0.25, 0.5, 0.75, and 1, respectively. The minimum numbers of nonzero subweights were 552, 581, 574, 523, and 1075, respectively.

Figure 4 shows the reconstructed subweights Bw<sup>1</sup> and Bw<sup>2</sup> for the MRI and PET data, respectively, overlying a structural brain image shown for the most correlated components with the binary outcome from each of μ ¼ 0, 0:5, 0:75, and 1. The images for μ ¼ 0:25 were similar to those of μ ¼ 0:5, 0:75 and are not shown here.

Figure 5 shows the reconstructed subweights Bw<sup>1</sup> and Bw<sup>2</sup> overlying a structural brain image and bar plots for the super-weights (right bottom) in the case of μ ¼ 0:5 for all components.

In each component, the negative and positive sides are represented. These can be interpreted by looking at the sign of the super-weight. Most cases remain on one side of 0 (positive or negative), except for components 5 to 8. The super-weights are similar between MRI and PET.

A 10-fold cross validated ROC analysis (Figure 6A) was conducted to evaluate the diagnostic probabilities estimated from the multivariable logistic regression mode whose coefficients and p-values are shown in Table 3. For comparison, the single modalities, MRI (Figure 6B) and PET (Figure 6C), were also analyzed.

In the case of the multimodal MRI and PET (Figure 6A), μ ¼ 1 had the highest AUC value (0.984) following by μ ¼ 0:75 (AUC = 0.880). In the case of the singlemodal MRI (Figure 6B), all values were below the AUC values of the multimodal case. In the case of the single-modal PET (Figure 6C), μ ¼ 1 and 0:75 outperformed the multimodal case, and the other values (μ ¼ 0, 0:25, and 0:5) did not.

#### 3.2 Multi-measurements

#### 3.2.1 Data

The second data set was a collection of repeated measured imaging data from 68 patients with mild cognitive impairment (MCI). There were two groups, the conversion to dementia MCI (cMCI) group and the stable MCI (not converted to dementia, sMCI) group. MRI data measured at four time points were used. For the cMCI group, the four time points were just before diagnosis of conversion.

μ = 0.00

11

Estimate

comp1

comp2

comp3

comp4

comp5

comp6

comp7

comp8

Table 3. Results for

multivariable

 logistic regression analysis.

 0.0336

 0.2517

 0.0446

 0.0891

 0.0505 0.0228

 0.3804

 0.0636

 0.0510 0.0226

 0.3816

 0.0619

 0.0535 0.0218

 0.3904

 0.0549

0.0364

 0.0900

 0.0396

 0.0320

 0.0403

 0.0715

 0.0425

 0.0658

0.0424

 0.0228

 0.0452

 0.0432

 0.0430

 0.0203

 0.0431

 0.0206

0.0072

 0.6126

 0.0037

 0.7953

 0.0044

 0.7583

 0.0064

 0.6574

0.0621

 0.0001

 0.0180

 0.0923

 0.0180

 0.0920

 0.0181

 0.0952

 0.0882

 <0.0001

 0.0460

 0.0030

 0.0458

 0.0031

 0.0451

 0.0039

0.0210

 0.0615

 0.0827

 <0.0001

 0.0832

 <0.0001

 0.0857

 <0.0001

 4.287 2.555 4.633 1.827 3.905 4.994

 0.9984

0.9988

0.9987

0.9995

Supervised Sparse Components Analysis with Application to Brain Imaging Data

0.9989

 Pr(>|z|)

 Estimate

 Pr(>|z|)

 Estimate

 Pr(>|z|)

 Estimate

 Pr(>|z|)

 Estimate

 Pr(>|z|)

0.9982

μ = 0.25

μ = 0.50

μ = 0.75

μ = 1

DOI: http://dx.doi.org/10.5772/intechopen.80531


Supervised Sparse Components Analysis with Application to Brain Imaging Data DOI: http://dx.doi.org/10.5772/intechopen.80531

> Table 3.

Results for multivariable logistic regression analysis.

of 5% statistically significant components were 3, 4, 3, 3, and 0 for μ = 0, 0.25, 0.5, 0.75, and 1, respectively. The minimum numbers of nonzero subweights were 552,

Figure 4 shows the reconstructed subweights Bw<sup>1</sup> and Bw<sup>2</sup> for the MRI and PET data, respectively, overlying a structural brain image shown for the most correlated components with the binary outcome from each of μ ¼ 0, 0:5, 0:75, and 1. The images for μ ¼ 0:25 were similar to those of μ ¼ 0:5, 0:75 and are not shown here. Figure 5 shows the reconstructed subweights Bw<sup>1</sup> and Bw<sup>2</sup> overlying a structural brain image and bar plots for the super-weights (right bottom) in the case of

In each component, the negative and positive sides are represented. These can be interpreted by looking at the sign of the super-weight. Most cases remain on one side of 0 (positive or negative), except for components 5 to 8. The super-weights

A 10-fold cross validated ROC analysis (Figure 6A) was conducted to evaluate the diagnostic probabilities estimated from the multivariable logistic regression mode whose coefficients and p-values are shown in Table 3. For comparison, the single modalities, MRI (Figure 6B) and PET (Figure 6C), were also analyzed.

In the case of the multimodal MRI and PET (Figure 6A), μ ¼ 1 had the highest AUC value (0.984) following by μ ¼ 0:75 (AUC = 0.880). In the case of the singlemodal MRI (Figure 6B), all values were below the AUC values of the multimodal case. In the case of the single-modal PET (Figure 6C), μ ¼ 1 and 0:75 outperformed

The second data set was a collection of repeated measured imaging data from 68 patients with mild cognitive impairment (MCI). There were two groups, the conversion to dementia MCI (cMCI) group and the stable MCI (not converted to dementia, sMCI) group. MRI data measured at four time points were used. For the cMCI group, the four time points were just before diagnosis of conversion.

the multimodal case, and the other values (μ ¼ 0, 0:25, and 0:5) did not.

581, 574, 523, and 1075, respectively.

Neuroimaging - Structure, Function and Mind

μ ¼ 0:5 for all components.

Correlations between super scores.

Figure 3.

3.2 Multi-measurements

3.2.1 Data

10

are similar between MRI and PET.

Figure 5. Sub- and super-weights for all components of μ ¼ 0:5.

For the sMCI group, the four time points were from the baseline for the entire period of the study. Groups were matched for age, gender, and intracranial volume. Table 4 summarizes the characteristics of these patients at baseline (at the first image observation).

selected was 6 for μ ¼ 0, 0:25, 0:5, 0:75 and 4 for μ ¼ 1. Table 5 shows the results for the multiple logistic regression model with cMCI or sMCI as the outcomes and the super scores as the predictors for each μ. The numbers of 5% statistically significant components were 2, 3, 3, 3, and 2 for μ ¼ 0, 0:25, 0:5, 0:75; 1, respectively. The minimum numbers of nonzero subweights were 724, 736, 749, 753, and 852,

Results for cross-validated ROC analysis for (A) MRI and PET, (B) MRI, and (C) PET.

Supervised Sparse Components Analysis with Application to Brain Imaging Data

DOI: http://dx.doi.org/10.5772/intechopen.80531

n 34 34

0 12 (35.3) 22 (64.7) 1 18 (52.9) 11 (32.4) 2 4 (11.8) 1 (2.9)

Age (mean [sd]) 76.06 (5.94) 75.91 (5.90) 0.922 PTGENDER = 2 (%) 10 (29.4) 10 (29.4) 1.000 APOE4 (%) 0.040

PTEDUCAT (mean [sd]) 16.15 (3.06) 15.50 (2.86) 0.371 CDRSB (mean [sd]) 1.76 (1.07) 1.32 (0.73) 0.051 ADAS11 (mean [sd]) 12.09 (3.49) 9.40 (4.08) 0.005 ADAS13 (mean [sd]) 19.65 (4.31) 15.93 (6.10) 0.005 MMSE (mean [sd]) 26.71 (1.71) 27.88 (1.70) 0.006

cMCI sMCI p

A tenfold cross validated ROC analysis (Figure 7) was conducted to evaluate the diagnostic probabilities estimated from the multivariable logistic regression mode

For comparison, the single-modal analysis for each time point was conducted. The fourth time point (MRI4), which is closest to the MCI conversion diagnosis time, had the highest AUC values, and these were higher than the multimodal

Figure 9 shows the first component subweights, Bw<sup>m</sup> (m ¼ 1, 2, 3, 4), for the four time points for μ ¼ 0 and 0.5. In the case of μ ¼ 0:5, the hippocampus area was

related to the components, and in the case of μ ¼ 0, the parietal lobe was.

whose coefficients and p-values are shown in Table 5.

respectively.

Table 4.

Characteristic for data set 2.

Figure 6.

values (Figure 8).

13

For imaging data processing, we used the VBM8 toolbox. For the basis function, we used four-voxel equal spacing knots, as in the first study in the previous section. The clinical outcome is given by Z ¼ 0:44 � CDR þ 0:12 � ADAS13 � 0:11� MMSE: The coefficients were different from those in the first study because the target population was different.

#### 3.2.2 Results

The original data with dimensions of 2,122,945 (=121 � 145 � 121) was reduced to 7162 using basis functions for each imaging data set. The number of components Supervised Sparse Components Analysis with Application to Brain Imaging Data DOI: http://dx.doi.org/10.5772/intechopen.80531

Figure 6.

Results for cross-validated ROC analysis for (A) MRI and PET, (B) MRI, and (C) PET.


#### Table 4.

For the sMCI group, the four time points were from the baseline for the entire period of the study. Groups were matched for age, gender, and intracranial volume. Table 4 summarizes the characteristics of these patients at baseline (at the first

For imaging data processing, we used the VBM8 toolbox. For the basis function, we used four-voxel equal spacing knots, as in the first study in the previous section. The clinical outcome is given by Z ¼ 0:44 � CDR þ 0:12 � ADAS13 � 0:11� MMSE: The coefficients were different from those in the first study because the

The original data with dimensions of 2,122,945 (=121 � 145 � 121) was reduced to 7162 using basis functions for each imaging data set. The number of components

image observation).

3.2.2 Results

12

Figure 5.

Figure 4. Subweights.

target population was different.

Sub- and super-weights for all components of μ ¼ 0:5.

Neuroimaging - Structure, Function and Mind

Characteristic for data set 2.

selected was 6 for μ ¼ 0, 0:25, 0:5, 0:75 and 4 for μ ¼ 1. Table 5 shows the results for the multiple logistic regression model with cMCI or sMCI as the outcomes and the super scores as the predictors for each μ. The numbers of 5% statistically significant components were 2, 3, 3, 3, and 2 for μ ¼ 0, 0:25, 0:5, 0:75; 1, respectively. The minimum numbers of nonzero subweights were 724, 736, 749, 753, and 852, respectively.

A tenfold cross validated ROC analysis (Figure 7) was conducted to evaluate the diagnostic probabilities estimated from the multivariable logistic regression mode whose coefficients and p-values are shown in Table 5.

For comparison, the single-modal analysis for each time point was conducted. The fourth time point (MRI4), which is closest to the MCI conversion diagnosis time, had the highest AUC values, and these were higher than the multimodal values (Figure 8).

Figure 9 shows the first component subweights, Bw<sup>m</sup> (m ¼ 1, 2, 3, 4), for the four time points for μ ¼ 0 and 0.5. In the case of μ ¼ 0:5, the hippocampus area was related to the components, and in the case of μ ¼ 0, the parietal lobe was.



Results for multivariable logistic regression analysis. Figure 7.

Figure 8.

Figure 9.

15

Subweights for all time points for μ ¼ 0 and 0.5.

Subweights for times 1 and 4.

Results for cross validated ROC analysis.

Supervised Sparse Components Analysis with Application to Brain Imaging Data

DOI: http://dx.doi.org/10.5772/intechopen.80531

Supervised Sparse Components Analysis with Application to Brain Imaging Data DOI: http://dx.doi.org/10.5772/intechopen.80531

Figure 7. Results for cross validated ROC analysis.

Figure 8.

Subweights for times 1 and 4.

Figure 9. Subweights for all time points for μ ¼ 0 and 0.5.

μ = 0.00

14

Estimate

comp1

comp2

comp3

comp4

comp5

comp6

Table 5. Results for

multivariable

 logistic regression analysis.

0.0203

 0.1617

 0.0077

 0.6205

 0.0074

 0.6313

 0.0078

 0.6139

 0.0001

 0.9963

 0.0458

 0.0022

 0.0460

 0.0021

 0.0469

 0.0019

0.0333

 0.0042

0.0125

 0.1481

 0.0083

 0.1714

 0.0198 0.0093

0.0073

 0.4505

 0.1410

 0.0195 0.0073

 0.4490

 0.0215

 0.0196 0.0070

 0.4709

 0.0214

 0.0172 0.0157

 0.5288

 0.2833

 0.0199

 0.0095

 0.1298

 0.0097

 0.1240

 0.0359

 0.0049

0.0132

 0.0139

 0.0142

 0.0215

 0.0142

 0.0212

 0.0143

 0.0204

 0.0331

 0.0018

 Pr(>|z|)

 Estimate

 Pr(>|z|)

 Estimate

 Pr(>|z|)

 Estimate

 Pr(>|z|)

 Estimate

 Pr(>|z|)

μ = 0.25

μ = 0.50

μ = 0.75

μ = 1

Neuroimaging - Structure, Function and Mind

5. Conclusion

DOI: http://dx.doi.org/10.5772/intechopen.80531

Acknowledgements

Conflict of interest

None declared.

17

analysis.

Although there is room for improvement in this method, this study showed reasonable results when the method was applied to the dementia study. In conclusion, this data-driven approach would be helpful for exploratory neuroimaging data

Supervised Sparse Components Analysis with Application to Brain Imaging Data

This study was supported in part by the Intramural Research Grant (27-8) for Neurological and Psychiatric Disorders of NCNP. For this research work, we used the supercomputer of ACCMS, Kyoto University. Data collection and sharing for this project were funded by the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense Award Number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer's Association; Alzheimer's Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd. and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer's Therapeutic Research Institute at the University of Southern California. ADNI data are disseminated by the Laboratory of

Neuro Imaging at the University of Southern California.

Figure 10. Super-weights.

Figure 10 shows the corresponding super-weights. This result should be carefully interpreted. For time 4, the sparsest block weights were obtained, and thus the weight values were larger than those of times 1 to 3, which were balanced by the small super-weight. As a result, the super score for this component has the mean value of the block scores.

#### 4. Discussion

In this chapter, the SMS-PCA method was introduced and applied to multiple measured neuroimaging data sets. The first data set consisted of two different types of images, MRI and PET. The second data set consisted of repeated MRI measurements (the same type of image). These imaging data have many voxels per person which were reduced using the basis function prior to conducting the SMS-PCA. The multi-block feature of the SMS-PCA also caused further reduction in each block, and their summary was obtained in the super level where the weights were the relationship and the scores were used in the prediction model.

One of the key features in the SMS-PCA is that it is supervised and its proportion to (self) variance is parametrized by μ. In each study, the impact of μ was studied. The case of μ ¼ 1 resulted in only supervision, that is, only the correlation between the score and the outcome, without the variance of the score. As in an original PCA, maximizing the variance of the score corresponds to μ ¼ 0, and the correlated variables (voxels) have relatively high weights for each component. Thus, the messy maps for the block weights overlaying the brain in the case of μ ¼ 1 were reasonable. In both applications, because μ ¼ 0:25, 0:5, and 0:75 had similar results, a possible large value in μ<1, or the median value μ ¼ 0:5 with a trade-off, can be selected as optimal.

Repeated measured imaging data analysis was studied in [35] which reduced the imaging dimensions using basis functions but did this independent for each image. In contrast, in this study, the correlation between measurements at different time points is considered. That is, simultaneous temporal and spatial correlation was considered. This approach was limited by the need that the number of images for each individual be the same, and this will be improved in future work. In addition, the method introduced in this chapter can incorporate modalities such as network models which would need to summarize the information into the component. This research is in progress.

Supervised Sparse Components Analysis with Application to Brain Imaging Data DOI: http://dx.doi.org/10.5772/intechopen.80531

#### 5. Conclusion

Although there is room for improvement in this method, this study showed reasonable results when the method was applied to the dementia study. In conclusion, this data-driven approach would be helpful for exploratory neuroimaging data analysis.

#### Acknowledgements

Figure 10 shows the corresponding super-weights. This result should be carefully interpreted. For time 4, the sparsest block weights were obtained, and thus the weight values were larger than those of times 1 to 3, which were balanced by the small super-weight. As a result, the super score for this component has the mean

In this chapter, the SMS-PCA method was introduced and applied to multiple measured neuroimaging data sets. The first data set consisted of two different types of images, MRI and PET. The second data set consisted of repeated MRI measurements (the same type of image). These imaging data have many voxels per person which were reduced using the basis function prior to conducting the SMS-PCA. The multi-block feature of the SMS-PCA also caused further reduction in each block, and their summary was obtained in the super level where the weights were the

One of the key features in the SMS-PCA is that it is supervised and its proportion to (self) variance is parametrized by μ. In each study, the impact of μ was studied. The case of μ ¼ 1 resulted in only supervision, that is, only the correlation between the score and the outcome, without the variance of the score. As in an original PCA, maximizing the variance of the score corresponds to μ ¼ 0, and the correlated variables (voxels) have relatively high weights for each component. Thus, the messy maps for the block weights overlaying the brain in the case of μ ¼ 1 were reasonable. In both applications, because μ ¼ 0:25, 0:5, and 0:75 had similar results, a possible large value in μ<1, or the median value μ ¼ 0:5 with a trade-off, can be

Repeated measured imaging data analysis was studied in [35] which reduced the imaging dimensions using basis functions but did this independent for each image. In contrast, in this study, the correlation between measurements at different time points is considered. That is, simultaneous temporal and spatial correlation was considered. This approach was limited by the need that the number of images for each individual be the same, and this will be improved in future work. In addition, the method introduced in this chapter can incorporate modalities such as network models which would need to summarize the information into the component. This

relationship and the scores were used in the prediction model.

value of the block scores.

Neuroimaging - Structure, Function and Mind

4. Discussion

Figure 10. Super-weights.

selected as optimal.

research is in progress.

16

This study was supported in part by the Intramural Research Grant (27-8) for Neurological and Psychiatric Disorders of NCNP. For this research work, we used the supercomputer of ACCMS, Kyoto University. Data collection and sharing for this project were funded by the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense Award Number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer's Association; Alzheimer's Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd. and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer's Therapeutic Research Institute at the University of Southern California. ADNI data are disseminated by the Laboratory of Neuro Imaging at the University of Southern California.

#### Conflict of interest

None declared.

Neuroimaging - Structure, Function and Mind

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Supervised Sparse Components Analysis with Application to Brain Imaging Data

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Atsushi Kawaguchi† Faculty of Medicine, Saga University, Saga, Japan

\*Address all correspondence to: akawa@cc.saga-u.ac.jp

† For the Alzheimer's Disease Neuroimaging Initiative

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Supervised Sparse Components Analysis with Application to Brain Imaging Data DOI: http://dx.doi.org/10.5772/intechopen.80531

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18

Atsushi Kawaguchi†

Faculty of Medicine, Saga University, Saga, Japan

Neuroimaging - Structure, Function and Mind

provided the original work is properly cited.

\*Address all correspondence to: akawa@cc.saga-u.ac.jp

For the Alzheimer's Disease Neuroimaging Initiative

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

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[29] Meng X, Jiang R, Lin D, et al. Predicting individualized clinical measures by a generalized prediction framework and multimodal fusion of MRI data. NeuroImage. 2017;145: 218-229

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[30] Stokes ME, Visweswaran S. Application of a spatially-weighted relief algorithm for ranking genetic predictors of disease. BioData Mining. 2012;5:20

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classification of neuroimaging data in Alzheimer's disease: A systematic review. Frontiers in Aging Neuroscience. 2017;9:329

[23] Dimitriadis SI, Liparas D. How random is the random forest? Random forest algorithm on the service of structural imaging biomarkers for Alzheimer's disease: From Alzheimer's disease neuroimaging initiative (ADNI)

database. Neural Regeneration Research. 2018;13:962-970

98-110

[24] Ahmed OB, Benois-Pineau J, Allard M, et al. Recognition of Alzheimer's disease and mild cognitive impairment with multimodal image-derived biomarkers and multiple kernel learning. Neurocomputing. 2017;220:

[25] Vieira S, Pinaya WH, Mechelli A. Using deep learning to investigate the neuroimaging correlates of psychiatric and neurological disorders: Methods and

Biobehavioral Reviews. 2017;74:58-75

[26] Shen D, Wu G, Suk HI. Deep learning in medical image analysis. Annual Review of Biomedical Engineering. 2017;19:221-248

[27] Janssen RJ, Mourão-miranda J, Schnack HG. Making individual prognoses in psychiatry using neuroimaging and machine learning. Biological Psychiatry: Cognitive Neuroscience and Neuroimaging. 2018

[28] Rohart F, Gautier B, Singh A, Lê Cao KA. mixOmics: An R package for 'omics feature selection and multiple data integration. PLoS Computational Biology. 2017;13:e1005752

[29] Meng X, Jiang R, Lin D, et al. Predicting individualized clinical measures by a generalized prediction framework and multimodal fusion of MRI data. NeuroImage. 2017;145:

218-229

applications. Neuroscience &

[15] Li D, Karnath HO, Xu X. Candidate biomarkers in children with autism spectrum disorder: A review of MRI studies. Neuroscience Bulletin. 2017;33:

[16] Hilbert K, Lueken U, Muehlhan M, Beesdo-Baum K. Separating generalized anxiety disorder from major depression using clinical, hormonal, and structural MRI data: A multimodal machine learning study. Brain and Behavior: A Cognitive Neuroscience Perspective.

[17] Steiger VR, Brühl AB, Weidt S, et al. Pattern of structural brain changes in social anxiety disorder after cognitive

longitudinal multimodal MRI study. Molecular Psychiatry. 2017;22:1164-1171

[18] Schulze L, Schmahl C, Niedtfeld I. Neural correlates of disturbed emotion processing in borderline personality disorder: A multimodal meta-analysis. Biological Psychiatry. 2016;79:97-106

[19] Kawaguchi A. Supervised dimension reduction methods for brain tumor image data analysis. In: Matsui S, Crowley J, editors. Frontiers of

Biostatistical Methods and Applications

[20] Shen L, Thompson PM, Potkin SG, et al. Genetic analysis of quantitative phenotypes in AD and MCI: Imaging, cognition and biomarkers. Brain Imaging and Behavior. 2014;8:183-207

[21] Stephan KE, Schlagenhauf F, Huys QJM, et al. Computational neuroimaging strategies for single patient predictions.

[22] Sarica A, Cerasa A, Quattrone A. Random forest algorithm for the

NeuroImage. 2017;145:180-199

20

in Clinical Oncology. Singapore: Springer; 2017. pp. 401-412

behavioral group therapy: A

2018;59:193-202

219-237

2017;7:e00633

[31] Correa NM, Adali T, Li YO, Calhoun VD. Canonical correlation analysis for data fusion and group inferences: Examining applications of medical imaging data. IEEE Signal Processing Magazine. 2010;27:39-50

[32] Sui J, He H, Pearlson GD, et al. Three-way (N-way) fusion of brain imaging data based on mCCA+jICA and its application to discriminating schizophrenia. NeuroImage. 2013;66: 119-132

[33] Calhoun VD, Sui J. Multimodal fusion of brain imaging data: A key to finding the missing link(s) in complex mental illness. Biological Psychiatry: Cognitive Neuroscience and Neuroimaging. 2016;1:230-244

[34] Kawaguchi A, Yamashita F. Supervised multiblock sparse multivariable analysis with application to multimodal brain imaging genetics. Biostatistics. 2017;18:651-665

[35] Kawaguchi A. Diagnostic probability modeling for longitudinal structural brain MRI data analysis. In: Truong KY, editor. Statistical Techniques for Neuroscientists. Boca Raton, Florida: CRC Press; 2016. pp. 361-374

**23**

**1. Introduction**

**Chapter 2**

Spectroscopy

clinical and social applications of fNIRS.

*Toshinori Kato*

**Abstract**

Vector-Based Approach for

the Detection of Initial Dips

Using Functional Near-Infrared

Functional near-infrared spectroscopy (fNIRS) is a non-invasive method for the detection of local brain activity using changes in the local levels of oxyhemoglobin (oxyHb) and deoxyhemoglobin (deoxyHb). Simultaneous measurement of the levels of oxyHb and deoxyHb is an advantage of fNIRS over other modalities. This review provides a historical description of the physiological problems involved in the accurate identification of local brain activity using fNIRS. The need for improved spatial and temporal identification of local brain activity is described in terms of the physiological challenges of task selection and placement of probes. In addition, this review discusses challenges with data analysis based on a single index, advantages of the simultaneous analysis of multiple indicators, and recently established composite indicators. The vector-based approach provides quantitative imaging of the phase and intensity contrast for oxygen exchange responses in a time series and may detect initial dips related to neuronal activity in the skull. The vector plane model consists of orthogonal vectors of oxyHb and deoxyHb. Initial dips are hemodynamic reactions of oxyHb and deoxyHb induced by increased oxygen consumption in the early tasks of approximately 2–3 seconds. The new analytical concept of fNIRS, able to effectively detect initial dips, may extend further the

**Keywords:** functional near-infrared spectroscopy, fNIRS, initial dip, phase, vectorbased analysis, cerebral oxygen exchange, COE, oxyhemoglobin, deoxyhemoglobin

Functional near-infrared spectroscopy (fNIRS) is a non-invasive method for the detection of brain activity using changes in the local levels of oxyhemoglobin (oxyHb), deoxyhemoglobin (deoxyHb), and total hemoglobin (total Hb) [1]. fNIRS imposes fewer physical restrictions on patients compared with positron emission tomography (PET) or functional magnetic resonance imaging (fMRI), allowing investigators to measure and analyze cerebral circulation and metabolism while the patient walks or moves his/her upper body. Recently, studies showed that brain activity during rehabilitation [2] and car driving [3–6] may also be measured using fNIRS. In 1991, the first study of fNIRS utilizing localized changes in the levels

#### **Chapter 2**

## Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared Spectroscopy

*Toshinori Kato*

### **Abstract**

Functional near-infrared spectroscopy (fNIRS) is a non-invasive method for the detection of local brain activity using changes in the local levels of oxyhemoglobin (oxyHb) and deoxyhemoglobin (deoxyHb). Simultaneous measurement of the levels of oxyHb and deoxyHb is an advantage of fNIRS over other modalities. This review provides a historical description of the physiological problems involved in the accurate identification of local brain activity using fNIRS. The need for improved spatial and temporal identification of local brain activity is described in terms of the physiological challenges of task selection and placement of probes. In addition, this review discusses challenges with data analysis based on a single index, advantages of the simultaneous analysis of multiple indicators, and recently established composite indicators. The vector-based approach provides quantitative imaging of the phase and intensity contrast for oxygen exchange responses in a time series and may detect initial dips related to neuronal activity in the skull. The vector plane model consists of orthogonal vectors of oxyHb and deoxyHb. Initial dips are hemodynamic reactions of oxyHb and deoxyHb induced by increased oxygen consumption in the early tasks of approximately 2–3 seconds. The new analytical concept of fNIRS, able to effectively detect initial dips, may extend further the clinical and social applications of fNIRS.

**Keywords:** functional near-infrared spectroscopy, fNIRS, initial dip, phase, vectorbased analysis, cerebral oxygen exchange, COE, oxyhemoglobin, deoxyhemoglobin

#### **1. Introduction**

Functional near-infrared spectroscopy (fNIRS) is a non-invasive method for the detection of brain activity using changes in the local levels of oxyhemoglobin (oxyHb), deoxyhemoglobin (deoxyHb), and total hemoglobin (total Hb) [1]. fNIRS imposes fewer physical restrictions on patients compared with positron emission tomography (PET) or functional magnetic resonance imaging (fMRI), allowing investigators to measure and analyze cerebral circulation and metabolism while the patient walks or moves his/her upper body. Recently, studies showed that brain activity during rehabilitation [2] and car driving [3–6] may also be measured using fNIRS. In 1991, the first study of fNIRS utilizing localized changes in the levels

of oxyHb and deoxyHb was conducted by Kato and his colleagues at the National Center of Neurology and Psychiatry, Tokyo, Japan [1].

This study was the first to demonstrate that the activation of Hb in the human brain during photic stimuli was associated with increased levels of oxyHb, deoxyHb, and total Hb in the visual cortex. Of note, the measurements in the prefrontal cortex did not show clinically meaningful changes in the levels of these three indices. The original fNIRS technique was able to detect local activation of the brain during a task that is stronger than the signals during rest, by placing pairs of probes 2.5 cm apart on the scalp over the targeted cortex [7–9].

Thus, fNIRS solved the problem of oxygenation monitoring in NIRS [10, 11]. The measurement of targeted temporal changes in task-related activation markedly reduced data noise from the blood flow in the scalp at rest and from artifact-related bodily movement. Nowadays, more than 25 years later, statistical processing and mapping of changes in the levels of hemoglobin measured by fNIRS are used for the evaluation of brain activity.

The advantage of fNIRS over fMRI and other modalities is the ability to simultaneously and independently measure the levels of oxyHb and deoxyHb. Combined, these data may be used as indices reflecting changes in both blood volume and oxygenation.

However, the temporal resolution of fNIRS is fairly low on a 40–100 ms scale, compared with the underlying neural activity which is spanning from 1 to 3 ms of action potential firing and can be recorded extracranially using magnetoencephalography (MEG). MEG can be sensitive on subcortical activity in a case of large extent of activated neuronal assembly and spatial extent of activated cortical assembly [12, 13].

In slow voluntary movements of the self-paced index finger, the activity of the sensorimotor area was detected before 4.5 seconds of the pre-movement using electroencephalography (EEG) [14]. Consistent with the findings of EEG, early deoxygenation of 3–4 seconds prior to the movement of the finger was observed in the sensorimotor area using fNIRS [15]. Presently, research on simultaneous measurements using fNIRS and EEG is becoming an effective means of brain-computer interface [16].

In addition, a disadvantage of fNIRS is the low spatial resolution (5–10 mm) of the activation mapping of the cortical surface compared with those obtained from fMRI and PET. Research combining the use of fNIRS, fMRI, and MEG for source localization is currently ongoing [17]. These combination studies have advantages in temporal and spatial mapping of brain function.

A response involving increased and decreased levels of oxyHb and deoxyHb, respectively, has been considered the model of canonical activation in numerous studies utilizing fNIRS. However, the actual frequency of the occurrence of canonical activation, the most suitable index or indices for the differentiation between the center of activation and the surrounding area, and the associated degree of probability remain to be investigated. Following canonical activation, the rates of change in the levels of oxyHb and deoxyHb are not constant and may differ according to the task. Wylie et al. [18] performed a qualitative differentiation between two types of canonical activation according to the increase/decrease in the levels of total Hb. The investigators of that study identified four additional patterns of increase and decrease in the levels of oxyHb, deoxyHb, and total Hb that do not correspond to canonical activation.

Presently, the detection of the spatiotemporal characteristics of brain activity using fNIRS remains suboptimal. This fundamental limitation in evaluating brain activity may lead to misdiagnosis. fNIRS research is particularly challenging in the prefrontal cortex, responsible for complex higher functions. In areas of the brain

**25**

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared…*

with clear localization of cerebral function (i.e., primary motor or visual cortices), it is possible to verify the accuracy of fNIRS data. However, in the human prefrontal cortex, there is currently no clear understanding of the localization of the more complex functions, and thus, the verification of the reliability of fNIRS data in this

Studies have attempted to bolster the reliability of fNIRS in the prefrontal cortex

by comparing data obtained from fNIRS and fMRI [19, 20]. However, because the mechanisms differ between the two modalities [21–24], even if conformity is found between fMRI and fNIRS data, the reliability of the results is not necessarily increased. Several problems have been pointed out. Considerable attention is required when analyzing with the index of oxyHb alone. In the prefrontal region, task-dependent data noise in the oxyHb response (increased levels) resulting from skin blood flow has been reported [25, 26]. In 2011, an article criticized the use of NIRS in the clinical diagnosis of psychiatric disorders as being insufficiently supported by scientific evidence [27]. In mental illness studies, the actual localization of increases in the levels of oxyHb is not clear [28], and therefore, measurements of

Furthermore, analytical challenges in the field of fNIRS have been reported. This review introduces new composite functional indices incorporating ratios of changes in the levels of oxyHb and deoxyHb, along with a novel vector-based fNIRS method [29, 30]. This vector-based approach can be used to visually and quantitatively evaluate combinations of changes in the levels of oxyHb and deoxyHb as new indices. It was useful to classify variations in the levels of hemoglobin in response to neural activity, using combinations of changes in the levels of hemoglobin. It was effective especially when the signal change is small such as initial dips. Initial dips are the hemodynamic reactions of oxyHb and deoxyHb induced by increased oxygen consumption in the early tasks of approximately 2–3 seconds [31, 32]. The vector-based approach could improve the sensitivity of fNIRS in the detection of brain activity both temporally and spatially through recognition of the initial dips

In addition, this review discusses challenges with data analysis based on a single index, advantages of the simultaneous analysis of multiple indicators, and recently

Prior to the development of fNIRS, NIRS was used mainly for monitoring cerebral oxygenation. Changes in tissue oxygen saturation are accompanied by simultaneous changes in cerebral blood volume. Using NIRS, Jöbsis [37] reported hypocapnia and a reduction in cerebral blood volume during human hyperventilation. In addition, NIRS was used to prevent hypoxia through monitoring newborn and premature infants [10, 11]. Of note, NIRS had also been used to investigate the

In 1990, Takashima et al. [41] used NIRS to examine patients with probes placed

5 cm apart from each other. This study was based on the original concept of the research conducted by Jöbsis [29]. The results of this study showed reductions in the levels of oxyHb, deoxyHb, and total Hb in the prefrontal area during hyperventilation. Until 1990, research on NIRS did not target the specific localized brain function of the cerebral cortex. The technique was merely used to observe changes in the levels of hemoglobin (task-related and at rest), without specific spatial identification. Hypocapnia is known to cause global changes in the scalp and the entire brain. Hence, the changes reported during hyperventilation did not constitute proof of

oxyHb levels cannot be linked to a specific brain activity.

from the skull to hemodynamic responses [33–36].

established composite indicators.

**2. NIRS until 1990**

brains of animals [38–40].

*DOI: http://dx.doi.org/10.5772/intechopen.80888*

area remains a challenge.

#### *Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared… DOI: http://dx.doi.org/10.5772/intechopen.80888*

with clear localization of cerebral function (i.e., primary motor or visual cortices), it is possible to verify the accuracy of fNIRS data. However, in the human prefrontal cortex, there is currently no clear understanding of the localization of the more complex functions, and thus, the verification of the reliability of fNIRS data in this area remains a challenge.

Studies have attempted to bolster the reliability of fNIRS in the prefrontal cortex by comparing data obtained from fNIRS and fMRI [19, 20]. However, because the mechanisms differ between the two modalities [21–24], even if conformity is found between fMRI and fNIRS data, the reliability of the results is not necessarily increased. Several problems have been pointed out. Considerable attention is required when analyzing with the index of oxyHb alone. In the prefrontal region, task-dependent data noise in the oxyHb response (increased levels) resulting from skin blood flow has been reported [25, 26]. In 2011, an article criticized the use of NIRS in the clinical diagnosis of psychiatric disorders as being insufficiently supported by scientific evidence [27]. In mental illness studies, the actual localization of increases in the levels of oxyHb is not clear [28], and therefore, measurements of oxyHb levels cannot be linked to a specific brain activity.

Furthermore, analytical challenges in the field of fNIRS have been reported. This review introduces new composite functional indices incorporating ratios of changes in the levels of oxyHb and deoxyHb, along with a novel vector-based fNIRS method [29, 30]. This vector-based approach can be used to visually and quantitatively evaluate combinations of changes in the levels of oxyHb and deoxyHb as new indices. It was useful to classify variations in the levels of hemoglobin in response to neural activity, using combinations of changes in the levels of hemoglobin. It was effective especially when the signal change is small such as initial dips. Initial dips are the hemodynamic reactions of oxyHb and deoxyHb induced by increased oxygen consumption in the early tasks of approximately 2–3 seconds [31, 32]. The vector-based approach could improve the sensitivity of fNIRS in the detection of brain activity both temporally and spatially through recognition of the initial dips from the skull to hemodynamic responses [33–36].

In addition, this review discusses challenges with data analysis based on a single index, advantages of the simultaneous analysis of multiple indicators, and recently established composite indicators.

#### **2. NIRS until 1990**

*Neuroimaging - Structure, Function and Mind*

evaluation of brain activity.

oxygenation.

assembly [12, 13].

interface [16].

canonical activation.

temporal and spatial mapping of brain function.

Center of Neurology and Psychiatry, Tokyo, Japan [1].

probes 2.5 cm apart on the scalp over the targeted cortex [7–9].

of oxyHb and deoxyHb was conducted by Kato and his colleagues at the National

brain during photic stimuli was associated with increased levels of oxyHb, deoxyHb, and total Hb in the visual cortex. Of note, the measurements in the prefrontal cortex did not show clinically meaningful changes in the levels of these three indices. The original fNIRS technique was able to detect local activation of the brain during a task that is stronger than the signals during rest, by placing pairs of

This study was the first to demonstrate that the activation of Hb in the human

Thus, fNIRS solved the problem of oxygenation monitoring in NIRS [10, 11]. The measurement of targeted temporal changes in task-related activation markedly reduced data noise from the blood flow in the scalp at rest and from artifact-related bodily movement. Nowadays, more than 25 years later, statistical processing and mapping of changes in the levels of hemoglobin measured by fNIRS are used for the

The advantage of fNIRS over fMRI and other modalities is the ability to simultaneously and independently measure the levels of oxyHb and deoxyHb. Combined, these data may be used as indices reflecting changes in both blood volume and

However, the temporal resolution of fNIRS is fairly low on a 40–100 ms scale, compared with the underlying neural activity which is spanning from 1 to 3 ms of action potential firing and can be recorded extracranially using magnetoencephalography (MEG). MEG can be sensitive on subcortical activity in a case of large extent of activated neuronal assembly and spatial extent of activated cortical

In slow voluntary movements of the self-paced index finger, the activity of the sensorimotor area was detected before 4.5 seconds of the pre-movement using electroencephalography (EEG) [14]. Consistent with the findings of EEG, early deoxygenation of 3–4 seconds prior to the movement of the finger was observed in the sensorimotor area using fNIRS [15]. Presently, research on simultaneous measurements using fNIRS and EEG is becoming an effective means of brain-computer

In addition, a disadvantage of fNIRS is the low spatial resolution (5–10 mm) of the activation mapping of the cortical surface compared with those obtained from fMRI and PET. Research combining the use of fNIRS, fMRI, and MEG for source localization is currently ongoing [17]. These combination studies have advantages in

A response involving increased and decreased levels of oxyHb and deoxyHb, respectively, has been considered the model of canonical activation in numerous studies utilizing fNIRS. However, the actual frequency of the occurrence of canonical activation, the most suitable index or indices for the differentiation between the center of activation and the surrounding area, and the associated degree of probability remain to be investigated. Following canonical activation, the rates of change in the levels of oxyHb and deoxyHb are not constant and may differ according to the task. Wylie et al. [18] performed a qualitative differentiation between two types of canonical activation according to the increase/decrease in the levels of total Hb. The investigators of that study identified four additional patterns of increase and decrease in the levels of oxyHb, deoxyHb, and total Hb that do not correspond to

Presently, the detection of the spatiotemporal characteristics of brain activity using fNIRS remains suboptimal. This fundamental limitation in evaluating brain activity may lead to misdiagnosis. fNIRS research is particularly challenging in the prefrontal cortex, responsible for complex higher functions. In areas of the brain

**24**

Prior to the development of fNIRS, NIRS was used mainly for monitoring cerebral oxygenation. Changes in tissue oxygen saturation are accompanied by simultaneous changes in cerebral blood volume. Using NIRS, Jöbsis [37] reported hypocapnia and a reduction in cerebral blood volume during human hyperventilation. In addition, NIRS was used to prevent hypoxia through monitoring newborn and premature infants [10, 11]. Of note, NIRS had also been used to investigate the brains of animals [38–40].

In 1990, Takashima et al. [41] used NIRS to examine patients with probes placed 5 cm apart from each other. This study was based on the original concept of the research conducted by Jöbsis [29]. The results of this study showed reductions in the levels of oxyHb, deoxyHb, and total Hb in the prefrontal area during hyperventilation. Until 1990, research on NIRS did not target the specific localized brain function of the cerebral cortex. The technique was merely used to observe changes in the levels of hemoglobin (task-related and at rest), without specific spatial identification.

Hypocapnia is known to cause global changes in the scalp and the entire brain. Hence, the changes reported during hyperventilation did not constitute proof of

#### **Figure 1.**

*Changes in the levels of HbO2 (oxyhemoglobin, oxyHb), HbR (deoxyhemoglobin, deoxyHb), and HbO2 + HbR (total hemoglobin, total Hb) with neck compression [40]. Comparisons between tasks had been reported at that time, unlike responses derived from specific cortical activity.*

functional local brain activity. These early studies of hyperventilation suggested that blood volume was reduced in the region supplied by the external carotid artery, which distributes blood mainly to the scalp and muscles outside the skull. In brain death, in spite of the absence of blood flow through the internal carotid artery, the blood flow distribution through the external carotid artery remains unimpaired an observation known as "the finding of the hollow skull" [42]. Early data obtained using NIRS data were affected by this blood flow from areas of the scalp supplied by the external carotid artery and the veins.

In addition, probes placed in the prefrontal area of seven healthy patients in a task of pressure for 1 minute on the jugular vein reported increases in the levels of oxyHb, deoxyHb, and total Hb [41]. These results were consistent with those obtained from an animal study (**Figure 1** [40]), indicating task-related hemodynamic changes prior to 1990. Importantly, the presence of a task does not differentiate fNIRS from NIRS.

Until 1990, NIRS had not been considered a tool for the identification of specific cortical activity. In the usage of NIRS at the time, there was no technique that data could be obtained selectively from a site on the cortex located directly under a site sandwiched between irradiation and detection probes, let alone evidence of brain activity. The near-infrared light paths and the range and depth of irradiation were unknown. Moreover, the influence of factors such as the external carotid artery was undeniable. Early NIRS did not associate changes in the levels of Hb with localized brain activity and was unable to clearly distinguish between signals derived from the external carotid artery or the veins and those derived from the cortex.

#### **3. Conception and first experiment of fNIRS in 1991**

fNIRS was developed in 1991 [1, 7–9, 31] as a functional imaging method using NIRS to detect local brain activity accurately. This was achieved by identifying changes in the levels of Hb in different areas of the brain at rest and during a task. It was necessary to initially demonstrate that NIRS was able to detect localized brain activity to establish fNIRS. The selection of an experimental task and the settings of the probe were the key factors in this process. In the search for a task, lesion studies and PET studies were reviewed to identify a small part of the brain that could be clearly stimulated and measured from the frontal lobe. A multifocal increase in regional cerebral blood flow (CBF) had been reported in a mental arithmetic task in the frontal lobe [43]. Furthermore, mental arithmetic tasks to induce an autonomic

**27**

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared…*

nerve stimulus had been used to show the possibility of blood volume changes in the region supplied by the external carotid artery [44, 45]. Dyscalculia was not sufficiently localized, because it occurs in multiple sites of the frontal and temporal

The cerebral metabolic rate of oxygen (CMRO2) was shown to increase by approximately 10% in a study using thinking tasks [47]. However, when compared with that observed at rest, this change in regional cerebral blood volume (CBV) was not significant. Exercise tasks produced side effects from movement of the probes and systemic circulation. In addition, a PET study had shown that blood flow increased in both the primary motor area of the frontal lobe and the nearby supplemental motor areas [48]. Overall, the confirmation of localization in the frontal lobe was challenging. The primary auditory cortex is located inside the Sylvian fissure, and there was no certainty that near-infrared light would be able to reach

In summary, an experiment designed to confirm that localization was possible

3.It should avoid the region supplied by the external carotid artery (possibility

6.It should not target brain activity from the frontal or temporal lobes (possibil-

According to these conditions, a suitable task would be one that stimulates the primary visual cortex, located in the occipital lobe and supplied with blood mostly from the posterior cerebral artery. An earlier study had reported an increase in CBF in the visual cortex with a task of 7.8 Hz photic stimulation [49]. A major question at that point was the following: "What kind of response in terms of local Hb levels would be obtained in a photic stimulation experiment using NIRS?" Other, more practical problems included the use of external light with the NIRS equipment and the irradiation of the stimulus light to the patient wearing the probes. However, these problems were resolved during the experiment. As shown by PC darkness in **Figure 2**, the

In 1991, the time course of responses arising from changes in the local levels of oxyHb, deoxyHb, and total Hb remained unknown. Therefore, it was necessary to perform measurements on different sites that would demonstrate brain activity and a null response. It was thought that the detection of varied responses from different sites in response to a given stimulus could demonstrate the localization of function. In the actual experiment, photic stimulation (8 Hz) was delivered using a photosonic stimulator (Nihon Kohden Co., Japan) from the front and at the height of the patient's line of sight for 5 minutes. As **Figure 2** shows, the activation observed in the visual cortex during the photic stimulus was associated with increased levels of oxyHb, deoxyHb (slightly), and total Hb. No changes were observed in the

*DOI: http://dx.doi.org/10.5772/intechopen.80888*

the site and reflect back to produce meaningful data.

using fNIRS required a task meeting the following conditions:

1.It should not stimulate the autonomous nervous system.

2.It should not induce global activation of the brain.

4.It should not involve pressure on the carotid artery.

7.It should induce brain activity within a well-defined site.

influence of extraneous light could be eliminated in actual experiments.

of changes in the volume of blood).

5.It should not require bodily motion.

ity of movement of the scalp or muscles).

lobes from injury, etc. [46].

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared… DOI: http://dx.doi.org/10.5772/intechopen.80888*

nerve stimulus had been used to show the possibility of blood volume changes in the region supplied by the external carotid artery [44, 45]. Dyscalculia was not sufficiently localized, because it occurs in multiple sites of the frontal and temporal lobes from injury, etc. [46].

The cerebral metabolic rate of oxygen (CMRO2) was shown to increase by approximately 10% in a study using thinking tasks [47]. However, when compared with that observed at rest, this change in regional cerebral blood volume (CBV) was not significant. Exercise tasks produced side effects from movement of the probes and systemic circulation. In addition, a PET study had shown that blood flow increased in both the primary motor area of the frontal lobe and the nearby supplemental motor areas [48]. Overall, the confirmation of localization in the frontal lobe was challenging. The primary auditory cortex is located inside the Sylvian fissure, and there was no certainty that near-infrared light would be able to reach the site and reflect back to produce meaningful data.

In summary, an experiment designed to confirm that localization was possible using fNIRS required a task meeting the following conditions:


7.It should induce brain activity within a well-defined site.

According to these conditions, a suitable task would be one that stimulates the primary visual cortex, located in the occipital lobe and supplied with blood mostly from the posterior cerebral artery. An earlier study had reported an increase in CBF in the visual cortex with a task of 7.8 Hz photic stimulation [49]. A major question at that point was the following: "What kind of response in terms of local Hb levels would be obtained in a photic stimulation experiment using NIRS?" Other, more practical problems included the use of external light with the NIRS equipment and the irradiation of the stimulus light to the patient wearing the probes. However, these problems were resolved during the experiment. As shown by PC darkness in **Figure 2**, the influence of extraneous light could be eliminated in actual experiments.

In 1991, the time course of responses arising from changes in the local levels of oxyHb, deoxyHb, and total Hb remained unknown. Therefore, it was necessary to perform measurements on different sites that would demonstrate brain activity and a null response. It was thought that the detection of varied responses from different sites in response to a given stimulus could demonstrate the localization of function.

In the actual experiment, photic stimulation (8 Hz) was delivered using a photosonic stimulator (Nihon Kohden Co., Japan) from the front and at the height of the patient's line of sight for 5 minutes. As **Figure 2** shows, the activation observed in the visual cortex during the photic stimulus was associated with increased levels of oxyHb, deoxyHb (slightly), and total Hb. No changes were observed in the

*Neuroimaging - Structure, Function and Mind*

the external carotid artery and the veins.

*that time, unlike responses derived from specific cortical activity.*

ate fNIRS from NIRS.

**Figure 1.**

functional local brain activity. These early studies of hyperventilation suggested that blood volume was reduced in the region supplied by the external carotid artery, which distributes blood mainly to the scalp and muscles outside the skull. In brain death, in spite of the absence of blood flow through the internal carotid artery, the blood flow distribution through the external carotid artery remains unimpaired an observation known as "the finding of the hollow skull" [42]. Early data obtained using NIRS data were affected by this blood flow from areas of the scalp supplied by

*Changes in the levels of HbO2 (oxyhemoglobin, oxyHb), HbR (deoxyhemoglobin, deoxyHb), and HbO2 + HbR (total hemoglobin, total Hb) with neck compression [40]. Comparisons between tasks had been reported at* 

In addition, probes placed in the prefrontal area of seven healthy patients in a task of pressure for 1 minute on the jugular vein reported increases in the levels of oxyHb, deoxyHb, and total Hb [41]. These results were consistent with those obtained from an animal study (**Figure 1** [40]), indicating task-related hemodynamic changes prior to 1990. Importantly, the presence of a task does not differenti-

Until 1990, NIRS had not been considered a tool for the identification of specific cortical activity. In the usage of NIRS at the time, there was no technique that data could be obtained selectively from a site on the cortex located directly under a site sandwiched between irradiation and detection probes, let alone evidence of brain activity. The near-infrared light paths and the range and depth of irradiation were unknown. Moreover, the influence of factors such as the external carotid artery was undeniable. Early NIRS did not associate changes in the levels of Hb with localized brain activity and was unable to clearly distinguish between signals derived from

fNIRS was developed in 1991 [1, 7–9, 31] as a functional imaging method using NIRS to detect local brain activity accurately. This was achieved by identifying changes in the levels of Hb in different areas of the brain at rest and during a task. It was necessary to initially demonstrate that NIRS was able to detect localized brain activity to establish fNIRS. The selection of an experimental task and the settings of the probe were the key factors in this process. In the search for a task, lesion studies and PET studies were reviewed to identify a small part of the brain that could be clearly stimulated and measured from the frontal lobe. A multifocal increase in regional cerebral blood flow (CBF) had been reported in a mental arithmetic task in the frontal lobe [43]. Furthermore, mental arithmetic tasks to induce an autonomic

the external carotid artery or the veins and those derived from the cortex.

**3. Conception and first experiment of fNIRS in 1991**

**26**

#### **Figure 2.**

*Changes in the levels of oxyhemoglobin (oxyHb), deoxyhemoglobin (deoxyHb), total hemoglobin (total Hb), Cyt (Cytochromeaa3), and PC darkness (photon counting darkness) measured over the occipital surface (above) and the frontal surface (below) prior to, during, and after photic stimulation in a healthy adult. Background noise from extraneous light was monitored as PC darkness. The data show spatial (site-dependent) and temporal (task on/off) differences in response [7, 8].*

prefrontal cortex following photic stimulation. These findings demonstrated that fNIRS is able to detect spatial and temporal information (i.e., different hemodynamic responses), depending on the site and the presence or absence of stimulation.

Today, fNIRS is widely used for tasks or in environments difficult for other modalities. Although the above list of requirements for task selection may seem outdated, the first four conditions are still required to distinguish between local activity and global change. The difference between local activity and global changes is still determined by the presence or absence of a response, limitation to a specific site, and dependence on the duration of the task.

#### **4. Probe placement on the skull**

A fundamental part for fNIRS is probe placement. As **Figure 3A** shows, Jöbsis [37] used infrared transillumination and optical computed tomography (CT) to create images of blood flow distribution at rest corresponding to brain structures. He estimated the optical path length of the human head to be 13.3 cm [37]. In addition, he stated that an interprobe distance of ≥4.25 cm would allow the detection of data from the brain tissue rather than the scalp (**Figure 3B** [50]). Although the diffused and reflected light used today had already replaced infrared transillumination, subsequent research on cerebral oxygenation monitoring [41] continued to use this setting (distance between probes ≥4.25 cm).

During the design of the first investigation using fNIRS, MRI showed that the distance between the scalp and the primary visual cortex was <1 cm in neonates and <2 cm in adults and demonstrated the gentle curvature of the skull [51]. The shape of the skull permitted further reduction in the distance between the probes (**Figure 3C**) and improved the detection of activity in the cerebral cortex.

In the study, placement of the probes 5 cm apart revealed only a slight increase in the levels of oxyHb. When the distance between the probes was shortened to 4 cm, the increase in the levels of oxyHb became more pronounced. At an interprobe distance of 2.5 cm, a transient dip in the levels of oxyHb was observed. This effect occurred simultaneously with the initiation of the stimulus, followed promptly by an

**29**

**Figure 3.**

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared…*

increase in the levels of oxyHb, faster peak latency, and a post-stimulus undershoot in oxyHb. At an interprobe distance of 1.0–1.5 cm, there was either no response at all or the total amounts of Hb remained unchanged while small mirror-image changes were observed, namely an increase and decrease in the levels of oxyHb and deoxyHb, respectively. These mirror-image changes may have been derived from either the scalp (where metabolism does not increase) or from vascular changes in the veins on the surface of the brain. From these findings, it was established that an

*(A) Conceptual schema of optical computed tomography performed by Jöbsis illustrated on a magnetic resonance imaging (MRI) image (revision from [37]). (B) Relationship between the signal intensity of hemoglobin and the distance between the light entry and exit locations, using the reflectance technique according to the origin of the reflected light (revision from [50]). (C) Conceptual schema of functional near-infrared spectroscopy illustrated on the same MRI image. (D) Relationship between the activation-related* 

*change in the levels of hemoglobin and the distance between the light source and detector [31].*

Based on this empirical hypothesis, the area on the scalp corresponding to the visual cortex that can be covered with two probes was considered to be 1.0 × 2.5 cm, as identified through sagittal MRI. Each pair of emitter and receptor probes was placed 2.5 cm apart vertically to prevent data noise from activity in the secondary visual cortex and the large vein running vertically through the sagittal sinus. The movement of the probes outward by 1.0 cm impaired the detection of response in the pilot study. Thus, pairs of probes (channels) were placed within 1.0 cm of the target in the horizontal direction to ensure accuracy. This adjustment permitted the investigators to develop the concept of functional resolution (in this case 1.0 × 2.5 cm) for the identification of the precise area of response. The original NIRS apparatus used (NIRO 1000, Hamamatsu Photonics K.K., Japan), shown in **Figure 4**, had only two channels and 5-mm diameter optical fibers for the emission

The concept that the spatial resolution of fNIRS should be determined by the anatomy of the cerebral cortex and the range in which a response occurs was developed from this early research. To establish the desired resolution, the distance

interprobe distance of 2.5 cm provided the most robust results (**Figure 3D**).

and reception of light with 8 × 8 mm contact surfaces.

*DOI: http://dx.doi.org/10.5772/intechopen.80888*

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared… DOI: http://dx.doi.org/10.5772/intechopen.80888*

#### **Figure 3.**

*Neuroimaging - Structure, Function and Mind*

prefrontal cortex following photic stimulation. These findings demonstrated that fNIRS is able to detect spatial and temporal information (i.e., different hemodynamic responses), depending on the site and the presence or absence of stimulation. Today, fNIRS is widely used for tasks or in environments difficult for other modalities. Although the above list of requirements for task selection may seem outdated, the first four conditions are still required to distinguish between local activity and global change. The difference between local activity and global changes is still determined by the presence or absence of a response, limitation to a specific

*Changes in the levels of oxyhemoglobin (oxyHb), deoxyhemoglobin (deoxyHb), total hemoglobin (total Hb), Cyt (Cytochromeaa3), and PC darkness (photon counting darkness) measured over the occipital surface (above) and the frontal surface (below) prior to, during, and after photic stimulation in a healthy adult. Background noise from extraneous light was monitored as PC darkness. The data show spatial (site-dependent) and* 

A fundamental part for fNIRS is probe placement. As **Figure 3A** shows, Jöbsis [37] used infrared transillumination and optical computed tomography (CT) to create images of blood flow distribution at rest corresponding to brain structures. He estimated the optical path length of the human head to be 13.3 cm [37]. In addition, he stated that an interprobe distance of ≥4.25 cm would allow the detection of data from the brain tissue rather than the scalp (**Figure 3B** [50]). Although the diffused and reflected light used today had already replaced infrared transillumination, subsequent research on cerebral oxygenation monitoring [41] continued to use

During the design of the first investigation using fNIRS, MRI showed that the distance between the scalp and the primary visual cortex was <1 cm in neonates and <2 cm in adults and demonstrated the gentle curvature of the skull [51]. The shape of the skull permitted further reduction in the distance between the probes

In the study, placement of the probes 5 cm apart revealed only a slight increase in the levels of oxyHb. When the distance between the probes was shortened to 4 cm, the increase in the levels of oxyHb became more pronounced. At an interprobe distance of 2.5 cm, a transient dip in the levels of oxyHb was observed. This effect occurred simultaneously with the initiation of the stimulus, followed promptly by an

(**Figure 3C**) and improved the detection of activity in the cerebral cortex.

site, and dependence on the duration of the task.

this setting (distance between probes ≥4.25 cm).

**4. Probe placement on the skull**

*temporal (task on/off) differences in response [7, 8].*

**Figure 2.**

**28**

*(A) Conceptual schema of optical computed tomography performed by Jöbsis illustrated on a magnetic resonance imaging (MRI) image (revision from [37]). (B) Relationship between the signal intensity of hemoglobin and the distance between the light entry and exit locations, using the reflectance technique according to the origin of the reflected light (revision from [50]). (C) Conceptual schema of functional near-infrared spectroscopy illustrated on the same MRI image. (D) Relationship between the activation-related change in the levels of hemoglobin and the distance between the light source and detector [31].*

increase in the levels of oxyHb, faster peak latency, and a post-stimulus undershoot in oxyHb. At an interprobe distance of 1.0–1.5 cm, there was either no response at all or the total amounts of Hb remained unchanged while small mirror-image changes were observed, namely an increase and decrease in the levels of oxyHb and deoxyHb, respectively. These mirror-image changes may have been derived from either the scalp (where metabolism does not increase) or from vascular changes in the veins on the surface of the brain. From these findings, it was established that an interprobe distance of 2.5 cm provided the most robust results (**Figure 3D**).

Based on this empirical hypothesis, the area on the scalp corresponding to the visual cortex that can be covered with two probes was considered to be 1.0 × 2.5 cm, as identified through sagittal MRI. Each pair of emitter and receptor probes was placed 2.5 cm apart vertically to prevent data noise from activity in the secondary visual cortex and the large vein running vertically through the sagittal sinus.

The movement of the probes outward by 1.0 cm impaired the detection of response in the pilot study. Thus, pairs of probes (channels) were placed within 1.0 cm of the target in the horizontal direction to ensure accuracy. This adjustment permitted the investigators to develop the concept of functional resolution (in this case 1.0 × 2.5 cm) for the identification of the precise area of response. The original NIRS apparatus used (NIRO 1000, Hamamatsu Photonics K.K., Japan), shown in **Figure 4**, had only two channels and 5-mm diameter optical fibers for the emission and reception of light with 8 × 8 mm contact surfaces.

The concept that the spatial resolution of fNIRS should be determined by the anatomy of the cerebral cortex and the range in which a response occurs was developed from this early research. To establish the desired resolution, the distance between the probes and the distance between the channels should be controlled independently. The more recently available multichannel fNIRS devices have become essential for the localization of brain activity. Unless the interchannel distance is changed depending on whether the measurement target is deep or wide from the scalp, the likelihood of detecting a localized response is reduced. In newborns, the distance between the brain and the surface of the cortex is <1 cm [51, 52]. Thus, in infants, the distance between probes should be shortened to 1–2 cm [53], rather than being set at 2.5 cm apart [7–9, 54]. The 3-cm apart matrix array of probes commonly used in recent years [55, 56] cannot necessarily provide results corresponding to the actual distribution of brain function in usage not considering age and head size. Spatial identification may not be performed effectively when a probe "hat" with probes arranged without reference to the anatomy of the brain/scalp is used. Registration markers and MRI should be used to determine the localization of probe placement for each individual.

In late 1992, Hoshi and Tamura [57] reported findings from research using task-related NIRS. The investigators reported a calculation task which stimulated the autonomic nervous system with an interprobe distance of 4 cm. This protocol did not meet the requirements for either task selection or probe settings described earlier in this review, and thus, the method is not considered fNIRS. Villringer et al. [58] selected probe positions on the scalp with interprobe distances ranging from 4 to 7 cm. In 1993, Chance et al. [59] also performed the task-related NIRS experiments from the frontal skull. However, they were unable to demonstrate localization. Advances in techniques for the improvement of spatial resolution continued. The spatial resolution of the 3 cm2 probe arrangement failed to provide detailed information regarding responses in the cortex [60]. Highly selective probe arrangements for establishing high-density measurement points have been reported (e.g., one with 10-mm channel interval and 25-mm probe interval [31, 32], and one with a center probe and surrounding probes [61]). Structural MRI has been used to evaluate the distance between the brain and the scalp [62]. Moreover, a method using diffuse optical tomography for removing signals on the scalp has been reported [63–65].

Of note, fNIRS has also been used in animal studies. The results have shown that measurement of fNIRS indices from the scalp with an interprobe distance of 4 and 8 mm was possible in the brain of rats [66] and cats, respectively. As **Figure 5** shows, using fNIRS (ETG-100, Hitachi Medical Co., Tokyo, Japan), an initial dip was able to

#### **Figure 4.**

*The NIRO 1000 (Hamamatsu Photonics K.K., Japan) used in the first functional near-infrared spectroscopy experiment [7–9].*

**31**

**Figure 5.**

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared…*

measure hemoglobin indices in the visual cortex during photic stimulation from outside the skull of a cat. In particular, the fNIRS response pattern to photic stimulation was identical between the cat and the human brains [67, 68]. These animal studies suggested that it was possible to use fNIRS for the detection of activity in a 1–2 mm

*Time series data of hemodynamic response showing an initial dip in the levels of total hemoglobin decreased through stimulation using light in the cat brain. A thick black line indicates stimulation using light.*

Numerous current fNIRS devices measure the levels of oxyHb, deoxyHb, and total Hb independently. A new challenge is that spatiotemporal characteristics may vary in functional brain imaging depending on the index used, and this problem has not been widely recognized or studied. In 1991, Kato et al. reported increases in the levels of oxyHb, deoxyHb (slight), and total Hb in the primary visual cortex during photic stimulation. Subsequent studies using fMRI and fNIRS reported increases and decreases in the levels of oxyHb and deoxyHb, respectively, in motor and visual tasks [69–71]. These results were accepted as typical fNIRS responses and have been

Nowadays, atypical responses are mostly ignored and left unexplained. There is a widespread tendency, hypothesized patterns of hemoglobin reaction in advance and those that are not hypothesized reaction types tend to be statistically excluded from the analysis data without being insufficiently examined [72]. In response to this trend, recent studies also have processed statistically and mapped independently the observed increase and decrease in the levels of oxyHb [73, 74] and deoxyHb [75, 76], respectively. Even in studies using rats, their analysis may be

However, evaluation of brain activity using a single hemoglobin index is contrary to the physiological mechanisms involved, ignoring the fact that hemodynamic responses include both blood volume and oxygenation. The distinction between blood volume and oxygenation, applying to fNIRS and fMRI [23, 24], has

**5. Brain function indices and oxygen responses in capillaries**

*DOI: http://dx.doi.org/10.5772/intechopen.80888*

region of the targeting cortex from the scalp.

corroborated by numerous fNIRS studies [1].

performed using only oxyHb [77].

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared… DOI: http://dx.doi.org/10.5772/intechopen.80888*

**Figure 5.**

*Neuroimaging - Structure, Function and Mind*

localization of probe placement for each individual.

spatial resolution of the 3 cm2

between the probes and the distance between the channels should be controlled independently. The more recently available multichannel fNIRS devices have become essential for the localization of brain activity. Unless the interchannel distance is changed depending on whether the measurement target is deep or wide from the scalp, the likelihood of detecting a localized response is reduced. In newborns, the distance between the brain and the surface of the cortex is <1 cm [51, 52]. Thus, in infants, the distance between probes should be shortened to 1–2 cm [53], rather than being set at 2.5 cm apart [7–9, 54]. The 3-cm apart matrix array of probes commonly used in recent years [55, 56] cannot necessarily provide results corresponding to the actual distribution of brain function in usage not considering age and head size. Spatial identification may not be performed effectively when a probe "hat" with probes arranged without reference to the anatomy of the brain/scalp is used. Registration markers and MRI should be used to determine the

In late 1992, Hoshi and Tamura [57] reported findings from research using task-related NIRS. The investigators reported a calculation task which stimulated the autonomic nervous system with an interprobe distance of 4 cm. This protocol did not meet the requirements for either task selection or probe settings described earlier in this review, and thus, the method is not considered fNIRS. Villringer et al. [58] selected probe positions on the scalp with interprobe distances ranging from 4 to 7 cm. In 1993, Chance et al. [59] also performed the task-related NIRS experiments from the frontal skull. However, they were unable to demonstrate localization. Advances in techniques for the improvement of spatial resolution continued. The

tion regarding responses in the cortex [60]. Highly selective probe arrangements for establishing high-density measurement points have been reported (e.g., one with 10-mm channel interval and 25-mm probe interval [31, 32], and one with a center probe and surrounding probes [61]). Structural MRI has been used to evaluate the distance between the brain and the scalp [62]. Moreover, a method using diffuse optical tomography for removing signals on the scalp has been reported [63–65]. Of note, fNIRS has also been used in animal studies. The results have shown that measurement of fNIRS indices from the scalp with an interprobe distance of 4 and 8 mm was possible in the brain of rats [66] and cats, respectively. As **Figure 5** shows, using fNIRS (ETG-100, Hitachi Medical Co., Tokyo, Japan), an initial dip was able to

*The NIRO 1000 (Hamamatsu Photonics K.K., Japan) used in the first functional near-infrared spectroscopy* 

probe arrangement failed to provide detailed informa-

**30**

**Figure 4.**

*experiment [7–9].*

*Time series data of hemodynamic response showing an initial dip in the levels of total hemoglobin decreased through stimulation using light in the cat brain. A thick black line indicates stimulation using light.*

measure hemoglobin indices in the visual cortex during photic stimulation from outside the skull of a cat. In particular, the fNIRS response pattern to photic stimulation was identical between the cat and the human brains [67, 68]. These animal studies suggested that it was possible to use fNIRS for the detection of activity in a 1–2 mm region of the targeting cortex from the scalp.

#### **5. Brain function indices and oxygen responses in capillaries**

Numerous current fNIRS devices measure the levels of oxyHb, deoxyHb, and total Hb independently. A new challenge is that spatiotemporal characteristics may vary in functional brain imaging depending on the index used, and this problem has not been widely recognized or studied. In 1991, Kato et al. reported increases in the levels of oxyHb, deoxyHb (slight), and total Hb in the primary visual cortex during photic stimulation. Subsequent studies using fMRI and fNIRS reported increases and decreases in the levels of oxyHb and deoxyHb, respectively, in motor and visual tasks [69–71]. These results were accepted as typical fNIRS responses and have been corroborated by numerous fNIRS studies [1].

Nowadays, atypical responses are mostly ignored and left unexplained. There is a widespread tendency, hypothesized patterns of hemoglobin reaction in advance and those that are not hypothesized reaction types tend to be statistically excluded from the analysis data without being insufficiently examined [72]. In response to this trend, recent studies also have processed statistically and mapped independently the observed increase and decrease in the levels of oxyHb [73, 74] and deoxyHb [75, 76], respectively. Even in studies using rats, their analysis may be performed using only oxyHb [77].

However, evaluation of brain activity using a single hemoglobin index is contrary to the physiological mechanisms involved, ignoring the fact that hemodynamic responses include both blood volume and oxygenation. The distinction between blood volume and oxygenation, applying to fNIRS and fMRI [23, 24], has been a subject of controversy. This remains an unresolved problem common to all brain functional imaging research based on hemodynamic responses. The beginning of this argument can be traced back to Roy and Sherrington, who in 1890 proposed neurovascular coupling. Changes in oxygenation and blood volume in the capillaries reflect neuronal activity. However, as Roy and Sherrington noted, these data were not derived from the capillaries [78].

The first to report the quantification of CBF using Fick's law (i.e., subtracting the value of the veins from that of arteries, in units of per 100 g per minute) were Kety et al. [79]. Increases in CBF, calculated without taking the capillaries into account, show a positive correlation with increasing CMRO2 [80]. Based on slight increases in CMRO2 observed following an increase in CBF [81], a coupling model of a positive correlation between CBF and CMRO2 [82, 83] was used widely to evaluate vascular response. Changes in CBF were used as a substitute for changes in oxygen metabolism. It is likely that this trend also affected fNIRS and led to the independent analysis of the levels of oxyHb, as performed today. Recent waveforms of increases in the levels of oxyHb closely resemble the waveforms of increases in blood flow reported by Roy and Sherrington in 1890. After more than 120 years, the interpretation of neurovascular coupling has not advanced considerably. Roy and Sherrington had foresight in their interpretation related to blood flow, but they did not observe cerebral oxygen metabolism.

Although the capillary transit time in humans is reported to be <10 seconds [84], PET sampling times are markedly longer. For this reason, PET data include changes in CBF in the capillaries related to oxygen exchange, coupled with the additional component of the delayed increase in CBF in the veins not accompanied by oxygen exchange. Using PET, a dissociation between CMRO2 and CBF has been reported [85, 86]. Using fMRI, signals have been shown to remain unaltered during

#### **Figure 6.**

*Schematic diagram of the possible hemodynamic responses occurring simultaneously with neural activity (revision from [31]). In (A), oxygen demand is increased by neural activity, and consequently, transient deoxygenation increases in the capillaries (oxyhemoglobin [HbO2] → hemoglobin [Hb] + oxygen [O2]). In a site with little neural activity (B), minimal amounts of oxygen enter the cells and even during a task, increased levels of oxyHb from the artery pass through the capillaries, bypassing the cells (HbO2 → HbO2). This response—increased and decreased levels of oxyHb and deoxyHb, respectively—has been recognized as typical activation. In actuality, according to the variation in the amount of oxygen exchange due to neural activity (C), a mixed response combining these two responses must also be present. These responses, differing according to the strength of oxygen exchange, are likely to be distributed among different sites, depending on the strength of neural activity at each site. Because the blood flows from (A), (B), and (C) are further mixed in the large veins, the data may not provide specific spatial information if responses are measured at longer sampling times than the capillary transit time.*

**33**

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared…*

the capillary transit time [87]. In other words, there is a need to move beyond the simplistic interpretation of neurovascular coupling, which predicts an increase in the levels of oxyHb and blood flow in response to neural activity. **Figure 6** shows the relationship between neural activity and hemodynamic response schematically. fNIRS is able to measure the levels of oxyHb and deoxyHb at the same time. Therefore, it is a useful tool to solve this serious problem of simultaneously measuring cerebral blood flow and cerebral oxygen metabolism which are faced by brain researchers for over 120 years. Future fNIRS research should distinguish between changes in blood volume and oxygenation occurring simultaneously with brain activity in the analysis of hemodynamic responses. In addition, it is necessary to re-evaluate activity-based hemodynamic responses using modalities such as EEG and MEG. Research involving event-related optical signals [87] and invasive optical measurements [88, 89] has been unable to distinguish between oxygenation and blood volume. OxyHb and deoxyHb are involved in both oxygenation and blood volume. Thus, it may not be possible to evaluate brain activity based exclusively on

Currently, an experimental protocol termed block task design, employing tasks that continue for ≥10 seconds (longer than the capillary transit time), is being used in many fNIRS studies. The reason for this is that the peak latency of oxyHb is generally 10 seconds (occasionally longer) from the initiation of a task. The use of this method in fNIRS studies has followed from its use in fMRI and PET research, where the low temporal resolution of the modality justifies the use of a block design. When a task requires a longer period of time corresponding to a block design or the task requires a certain amount of time to elapse for observation, the selection of a block design protocol in research using fNIRS, providing higher temporal resolution, is appropriate. With fNIRS, there is no need to repeat cognitive tasks involving factors such as perception, recognition, or judgment for prolonged time to obtain a sufficiently strong peak response in oxyHb levels. A block design including many task components does not clarify the correspondence between each task component and spatiotemporal local brain activity. Studies have also analyzed post-task time periods [90, 91]. However, the data from these studies lacked simultaneity with local brain activity and were unable to temporally and spatially identify local brain activity. Although EEG shows high simultaneity between data and brain activity, it is characterized by poor spatial resolution. In this respect, if the spatial resolution of fNIRS can be set from the standpoint of functional resolution as described earlier, its high temporal resolution may be valuable for event-related measurements. The initial dip, which is early deoxygenation in event-related experiments, is a highly accurate spatial indicator of neural activity [92]. In studies using optical intrinsic signals (OIS), increase in the levels of deoxyHb occurring prior to slow increases in the levels of oxyHb or total Hb has also been considered to be an index of increased oxygen metabolism [88, 93–97]. The absence of a correspondence (spatial or temporal) between increases in early deoxygenation and blood volume was also shown in a human study using invasive optical imaging [98]. Kato et al. [67, 68, 99, 100] conducted the first fNIRS study measuring initial dips appearing in fNIRS signals from the motor, visual, and language areas. Subsequently, the initial

*DOI: http://dx.doi.org/10.5772/intechopen.80888*

the measurement of the levels of oxyHb.

dip was observed in several fNIRS studies [18, 32–36, 101].

It has been suggested that this early increase in the levels of deoxyHb may arise from a transient increase in the consumption of oxygen in tissues [102, 103]. It has been obvious that this deoxyHb increase is useful as a precise indicator of brain

**6. Detection of initial dips**

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared… DOI: http://dx.doi.org/10.5772/intechopen.80888*

the capillary transit time [87]. In other words, there is a need to move beyond the simplistic interpretation of neurovascular coupling, which predicts an increase in the levels of oxyHb and blood flow in response to neural activity. **Figure 6** shows the relationship between neural activity and hemodynamic response schematically.

fNIRS is able to measure the levels of oxyHb and deoxyHb at the same time. Therefore, it is a useful tool to solve this serious problem of simultaneously measuring cerebral blood flow and cerebral oxygen metabolism which are faced by brain researchers for over 120 years. Future fNIRS research should distinguish between changes in blood volume and oxygenation occurring simultaneously with brain activity in the analysis of hemodynamic responses. In addition, it is necessary to re-evaluate activity-based hemodynamic responses using modalities such as EEG and MEG.

Research involving event-related optical signals [87] and invasive optical measurements [88, 89] has been unable to distinguish between oxygenation and blood volume. OxyHb and deoxyHb are involved in both oxygenation and blood volume. Thus, it may not be possible to evaluate brain activity based exclusively on the measurement of the levels of oxyHb.

#### **6. Detection of initial dips**

*Neuroimaging - Structure, Function and Mind*

data were not derived from the capillaries [78].

not observe cerebral oxygen metabolism.

been a subject of controversy. This remains an unresolved problem common to all brain functional imaging research based on hemodynamic responses. The beginning of this argument can be traced back to Roy and Sherrington, who in 1890 proposed neurovascular coupling. Changes in oxygenation and blood volume in the capillaries reflect neuronal activity. However, as Roy and Sherrington noted, these

The first to report the quantification of CBF using Fick's law (i.e., subtracting the value of the veins from that of arteries, in units of per 100 g per minute) were Kety et al. [79]. Increases in CBF, calculated without taking the capillaries into account, show a positive correlation with increasing CMRO2 [80]. Based on slight increases in CMRO2 observed following an increase in CBF [81], a coupling model of a positive correlation between CBF and CMRO2 [82, 83] was used widely to evaluate vascular response. Changes in CBF were used as a substitute for changes in oxygen metabolism. It is likely that this trend also affected fNIRS and led to the independent analysis of the levels of oxyHb, as performed today. Recent waveforms of increases in the levels of oxyHb closely resemble the waveforms of increases in blood flow reported by Roy and Sherrington in 1890. After more than 120 years, the interpretation of neurovascular coupling has not advanced considerably. Roy and Sherrington had foresight in their interpretation related to blood flow, but they did

Although the capillary transit time in humans is reported to be <10 seconds [84], PET sampling times are markedly longer. For this reason, PET data include changes in CBF in the capillaries related to oxygen exchange, coupled with the additional component of the delayed increase in CBF in the veins not accompanied by oxygen exchange. Using PET, a dissociation between CMRO2 and CBF has been reported [85, 86]. Using fMRI, signals have been shown to remain unaltered during

*Schematic diagram of the possible hemodynamic responses occurring simultaneously with neural activity (revision from [31]). In (A), oxygen demand is increased by neural activity, and consequently, transient deoxygenation increases in the capillaries (oxyhemoglobin [HbO2] → hemoglobin [Hb] + oxygen [O2]). In a site with little neural activity (B), minimal amounts of oxygen enter the cells and even during a task, increased levels of oxyHb from the artery pass through the capillaries, bypassing the cells (HbO2 → HbO2). This response—increased and decreased levels of oxyHb and deoxyHb, respectively—has been recognized as typical activation. In actuality, according to the variation in the amount of oxygen exchange due to neural activity (C), a mixed response combining these two responses must also be present. These responses, differing according to the strength of oxygen exchange, are likely to be distributed among different sites, depending on the strength of neural activity at each site. Because the blood flows from (A), (B), and (C) are further mixed in the large veins, the data may not provide specific spatial information if responses are measured at longer sampling times* 

**32**

*than the capillary transit time.*

**Figure 6.**

Currently, an experimental protocol termed block task design, employing tasks that continue for ≥10 seconds (longer than the capillary transit time), is being used in many fNIRS studies. The reason for this is that the peak latency of oxyHb is generally 10 seconds (occasionally longer) from the initiation of a task. The use of this method in fNIRS studies has followed from its use in fMRI and PET research, where the low temporal resolution of the modality justifies the use of a block design. When a task requires a longer period of time corresponding to a block design or the task requires a certain amount of time to elapse for observation, the selection of a block design protocol in research using fNIRS, providing higher temporal resolution, is appropriate. With fNIRS, there is no need to repeat cognitive tasks involving factors such as perception, recognition, or judgment for prolonged time to obtain a sufficiently strong peak response in oxyHb levels. A block design including many task components does not clarify the correspondence between each task component and spatiotemporal local brain activity. Studies have also analyzed post-task time periods [90, 91]. However, the data from these studies lacked simultaneity with local brain activity and were unable to temporally and spatially identify local brain activity. Although EEG shows high simultaneity between data and brain activity, it is characterized by poor spatial resolution. In this respect, if the spatial resolution of fNIRS can be set from the standpoint of functional resolution as described earlier, its high temporal resolution may be valuable for event-related measurements.

The initial dip, which is early deoxygenation in event-related experiments, is a highly accurate spatial indicator of neural activity [92]. In studies using optical intrinsic signals (OIS), increase in the levels of deoxyHb occurring prior to slow increases in the levels of oxyHb or total Hb has also been considered to be an index of increased oxygen metabolism [88, 93–97]. The absence of a correspondence (spatial or temporal) between increases in early deoxygenation and blood volume was also shown in a human study using invasive optical imaging [98]. Kato et al. [67, 68, 99, 100] conducted the first fNIRS study measuring initial dips appearing in fNIRS signals from the motor, visual, and language areas. Subsequently, the initial dip was observed in several fNIRS studies [18, 32–36, 101].

It has been suggested that this early increase in the levels of deoxyHb may arise from a transient increase in the consumption of oxygen in tissues [102, 103]. It has been obvious that this deoxyHb increase is useful as a precise indicator of brain

activity, but against the background that this increase in deoxyHb has been difficult to detect. For example, there is the case of less likely early deoxyHb increase depend on factors such as the type of task or the use of anesthesia [92]. A minimal and very localized increase may be attributed to imprecise fNIRS probe settings (i.e., missing the center of activity) or masking due to a strong increase in blood flow in the veins compromising detection.

With fMRI, what was reported previously as an early increase in the levels of deoxyHb was observed as an "initial dip" [21, 104, 105]. However, fMRI does not differentiate between oxyHb and deoxyHb. In addition, the relationship between increases or decreases in the levels of oxyHb and the increase in the levels of deoxyHb has not been investigated.

The more recently developed vector-based NIRS method [29, 30] is able to measure initial dips characterized by the canonical dip pattern showing increased deoxyhemoglobin, as well as several different hemoglobin patterns corresponding to differences in the degree of oxygen metabolism [32]. This method has permitted the reproducible measurement of hypoxic–ischemic initial dips (i.e., decreased levels of oxyHb) [34–36]. The initial dip at which the level of deoxyHb increases and the reaction where oxyHb increases after 2–3 seconds do not necessarily occur at the same site. Moreover, research on the intersection of these responses is limited, leading investigators to select one of the two responses (i.e., the typical oxyHb response or the initial dip) for the evaluation of brain activity. This serious problem may arise from the lack of quantification of brain activity. Indeed, the results of the evaluation of laterality in the language area [106, 107] may differ depending on the index used [108]. In addition, investigation of the relationship between eventrelated oxyHb and deoxyHb responses, especially those within seconds from neural activity, in previous fNIRS studies has been limited.

#### **7. Composite indices derived from vector analysis**

An advantage of fNIRS over other modalities is the simultaneous measurement of the levels of oxyHb and deoxyHb. However, this advantage leads to the following question: What do the various possible combinations of oxyHb, deoxyHb, and total Hb mean? Early fNIRS lacked a quantitative integrated theory for the interpretation of combinations of hemoglobin indices from multiple channels. Kato [29, 30] developed a quantitative method of analysis of the ratios between changes in the levels of oxyHb (ΔO) and deoxyHb (ΔD) to differentiate between oxygenation and blood volume.

This technique uses a two-dimensional vector plane on which vector tracks generated by task-related changes in cerebral blood volume (ΔCBV) and change in cerebral oxygen exchange (ΔCOE) are quantitatively classified into eight "phases." This provides a visible graphical display of information concerning hemodynamic responses (**Figure 7**). This vector-based approach is able to calculate the angle *k*, determining the phase of the response, and the intensity of response *L*. Subsequently, these may be used as indices of vector-based brain activity.

**Figure 7** shows an orthogonal vector coordinate plane defined by the ΔO and ΔD axes. Rotating this vector plane 45° counterclockwise results in an orthogonal vector coordinate plane defined by the ΔCBV and ΔCOE axes. For ΔCOE, a positive value indicates hypoxic change from ΔCOE = 0, whereas a negative value indicates hyperoxic change. The relationships among these four axes are described by the following square matrix:

$$
\begin{pmatrix}
\Delta \mathcal{O} + \Delta \mathcal{D} \\
\end{pmatrix} = \begin{pmatrix}
\mathbf{1} & \mathbf{1} \\
\end{pmatrix} \begin{pmatrix}
\Delta \mathcal{O} \\
\Delta \mathcal{D}
\end{pmatrix} = \begin{pmatrix}
\Delta \mathcal{C} \mathcal{B} V \\
\Delta \mathcal{C} \mathcal{D}
\end{pmatrix} \tag{1}
$$

**35**

**Figure 7.**

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared…*

Expansion of these shows ΔCBV and ΔCOE representing blood volume and

The scalar *L*, drawn from the origin to the coordinates of an arbitrary point on the vector plane, indicates the amplitude of a vector, reflecting the amount of

The angle *k*, indicating the phase, is defined by the following equation:

A vector on the polar coordinate plane contains the four Hb indices (i.e., ΔO, ΔD, ΔCBV, and ΔCOE). The relationships between the four Hb vectors (**Figure 7**) are defined by the equations shown earlier in this section: Eqs. (1) and (2) define hemoglobin changes; Eq. (5) defines the scalar *L*; and Eq. (6) defines the angle *k*, which determines the phase of a vector. Earlier evaluations of brain activity were

change in Hb. *L* can be described by the following equation:

*Functional near-infrared spectroscopy vector plane. Revised from [29, 30].*

(2)

(3)

(4)

(5)

(6)

*DOI: http://dx.doi.org/10.5772/intechopen.80888*

oxygenation, respectively:

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared… DOI: http://dx.doi.org/10.5772/intechopen.80888*

$$
\begin{pmatrix} \Delta O\\ \Delta D \end{pmatrix} = \frac{1}{2} \begin{pmatrix} 1 & -1\\ 1 & 1 \end{pmatrix} \begin{pmatrix} \Delta CBV\\ \Delta COE \end{pmatrix} \tag{2}
$$

Expansion of these shows ΔCBV and ΔCOE representing blood volume and oxygenation, respectively:

$$
\Delta \mathbf{CBV} = \frac{1}{\sqrt{2}} (\Delta \mathbf{D} + \Delta \mathbf{O}) \tag{3}
$$

$$
\Delta \mathbf{COE} = \frac{1}{\sqrt{2}} (\Delta \mathbf{D} - \Delta \mathbf{O}) \tag{4}
$$

The scalar *L*, drawn from the origin to the coordinates of an arbitrary point on the vector plane, indicates the amplitude of a vector, reflecting the amount of change in Hb. *L* can be described by the following equation:

$$L = \sqrt{(\Delta O)^2 + (\Delta D)^2} = \frac{1}{\sqrt{2}}\sqrt{(\Delta D - \Delta O)^2 + (\Delta D + \Delta O)^2}$$

$$= \frac{1}{\sqrt{2}}\sqrt{(\Delta COE)^2 + (\Delta CBV)^2} \tag{5}$$

The angle *k*, indicating the phase, is defined by the following equation:

$$k = \text{ } \space Arc \, \text{ } \space \tan\left(\frac{\Delta D}{\Delta O}\right) = \space \space Arc \, \space \tan\left(\frac{\Delta COE}{\Delta CBV}\right) + \space \space 45^{\circ} \quad \{-135^{\circ} \not\leq k \; \space \& 225^{\circ}\} \quad \{6\}$$

A vector on the polar coordinate plane contains the four Hb indices (i.e., ΔO, ΔD, ΔCBV, and ΔCOE). The relationships between the four Hb vectors (**Figure 7**) are defined by the equations shown earlier in this section: Eqs. (1) and (2) define hemoglobin changes; Eq. (5) defines the scalar *L*; and Eq. (6) defines the angle *k*, which determines the phase of a vector. Earlier evaluations of brain activity were

**Figure 7.** *Functional near-infrared spectroscopy vector plane. Revised from [29, 30].*

(1)

*Neuroimaging - Structure, Function and Mind*

compromising detection.

deoxyHb has not been investigated.

activity, in previous fNIRS studies has been limited.

**7. Composite indices derived from vector analysis**

activity, but against the background that this increase in deoxyHb has been difficult to detect. For example, there is the case of less likely early deoxyHb increase depend on factors such as the type of task or the use of anesthesia [92]. A minimal and very localized increase may be attributed to imprecise fNIRS probe settings (i.e., missing the center of activity) or masking due to a strong increase in blood flow in the veins

With fMRI, what was reported previously as an early increase in the levels of deoxyHb was observed as an "initial dip" [21, 104, 105]. However, fMRI does not differentiate between oxyHb and deoxyHb. In addition, the relationship between increases or decreases in the levels of oxyHb and the increase in the levels of

The more recently developed vector-based NIRS method [29, 30] is able to measure initial dips characterized by the canonical dip pattern showing increased deoxyhemoglobin, as well as several different hemoglobin patterns corresponding to differences in the degree of oxygen metabolism [32]. This method has permitted the reproducible measurement of hypoxic–ischemic initial dips (i.e., decreased levels of oxyHb) [34–36]. The initial dip at which the level of deoxyHb increases and the reaction where oxyHb increases after 2–3 seconds do not necessarily occur at the same site. Moreover, research on the intersection of these responses is limited, leading investigators to select one of the two responses (i.e., the typical oxyHb response or the initial dip) for the evaluation of brain activity. This serious problem may arise from the lack of quantification of brain activity. Indeed, the results of the evaluation of laterality in the language area [106, 107] may differ depending on the index used [108]. In addition, investigation of the relationship between eventrelated oxyHb and deoxyHb responses, especially those within seconds from neural

An advantage of fNIRS over other modalities is the simultaneous measurement of the levels of oxyHb and deoxyHb. However, this advantage leads to the following question: What do the various possible combinations of oxyHb, deoxyHb, and total Hb mean? Early fNIRS lacked a quantitative integrated theory for the interpretation of combinations of hemoglobin indices from multiple channels. Kato [29, 30] developed a quantitative method of analysis of the ratios between changes in the levels of oxyHb (ΔO) and deoxyHb (ΔD) to differentiate between oxygenation and blood volume. This technique uses a two-dimensional vector plane on which vector tracks generated by task-related changes in cerebral blood volume (ΔCBV) and change in cerebral oxygen exchange (ΔCOE) are quantitatively classified into eight "phases." This provides a visible graphical display of information concerning hemodynamic responses (**Figure 7**). This vector-based approach is able to calculate the angle *k*, determining the phase of the response, and the intensity of response *L*. Subsequently, these may be used as indices of vector-based brain activity.

**Figure 7** shows an orthogonal vector coordinate plane defined by the ΔO and ΔD axes. Rotating this vector plane 45° counterclockwise results in an orthogonal vector coordinate plane defined by the ΔCBV and ΔCOE axes. For ΔCOE, a positive value indicates hypoxic change from ΔCOE = 0, whereas a negative value indicates hyperoxic change. The relationships among these four axes are described by the

**34**

following square matrix:

based on signal intensity, without the concept of a phase. However, this method describes all the possible combinations of responses through eight phases on the vector plane. In addition, particular patterns of physiological responses are presented in a highly visual manner. This method provides a quantitative measure of oxygen metabolism, offering the advantage of measurements expressed in units of degrees. Moreover, measurements are determined from ratios of change rather than the actual extent of change in the levels of Hb.

#### **8. Interpretation of initial dips using the vector-based approach**

The angle *k* shows a positive value in the phases of initial dip occurrence. Previously, the initial dip was regarded as an indication of increased oxygen consumption. However, it was not possible to evaluate the strength of the initial dip or the possibility of different kinds of initial dips. Yoshino and Kato [32] classified initial dips in the language area by phase according to their particular combinations of ΔO, ΔD, ΔCBV, and ΔCOE.


Regarding oxygen metabolism, responses in the dip phases may indicate stronger brain activity than those in the non-dip phases. It is necessary to verify the strongest dip phases during the evaluation of the regulation between the oxygenation axis (ΔCOE) and the blood volume axis (ΔCBV) in the vector plane. The typical response corresponds to Phases −1 and − 2, interpreted as brain activity with a low degree of oxygen exchange. The responses in other phases should be evaluated in the same manner and the frequency of their occurrence should be investigated based on phase classifications. The percentage of dips in Wernicke's area in Phases 1 and 2 was low (total: 15–21%). However, in Phases 4 and 5, this percentage was higher (total: 62–68%) [32]. Differences in the frequency of phase depending on the brain site and the task may have different physiological implications. The ratio between the decrease and increase in the levels of deoxyHb and oxyHb, respectively, in a typical response is not constant. The quantitative values of the phase angle *k* may be used to investigate such differences in typical responses.

In **Figure 8**, time course data for previously reported initial dips are reproduced on a vector plane using the vector-based technique. **Figure 8A** and **8B** show two different types of dip in different phases, depending on the observed change in the ΔCBV. In both fMRI and OIS, the canonical initial dip has been considered to be a response

**37**

**Figure 8.**

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared…*

induced by increased levels of deoxyHb. **Figure 8B** shows an fNIRS initial dip (an increased ΔD accompanying a decreased ΔO), indicating Phase 4 [18, 32, 67, 68]. Recently, fNIRS was used to observe this new type of initial dip in primates [109]. As shown in **Figure 8A**, if this canonical initial dip detected by Malonek and Grinvald using OIS [94] corresponds to that of fMRI [95, 104], this would mean that the a blood oxygenation level-dependent (BOLD) signal from fMRI was able to differentiate between Phase 1, as a signal decrease, and Phase −1, as a signal increase. However, Phase 1 is an increased ΔCBV dip, in which ΔCOE decreases while the levels of deoxyHb increase. Thus, there is a discrepancy between the results from the two modalities. A theory bridging fNIRS and fMRI has been proposed, suggesting that a BOLD signal influenced by changes in ΔCBV closely resembles an increase in the levels of oxyHb [24]. In this model, the fMRI signal in the increased ΔCBV phase depends on the observed change in ΔO (not ΔD). Theoretically, this change may be considered to be a BOLD signal increase rather than a dip. Indeed, the use of the vector plane may explain the fact that the OIS

*4, followed by rotation in a counterclockwise direction into Phase −1 and subsequently into Phase 1.*

*Two kinds of initial dips [32]. Representative patterns of two types of initial dips when data from (A) and (B) were converted into vectors on a vector plane. (A) In a study using optical intrinsic signals, ΔD increased during the early part of a task [94]. The vector in this time course is in Phase 1 during the initial dip and subsequently progresses into Phase −1, indicating a typical response. (A) Initially, the vector is in Phase 1 and subsequently rotates in a clockwise direction into Phase −2. (B) The vector initially rotates in a clockwise direction into Phase* 

In present, initial dips could be reliably detected with OIS [92–97] and fNIRS [31–36, 109]. On the other hand, the occurrence of the initial dip in fMRI has been doubted and its mechanism is still controversial [21–24, 105]. Logothetis et al. [86] reported a period of latency, when the increase in the BOLD signal was flat for a few seconds at the beginning of the task. This shows the difficulty in detecting changes in phases during passage through the capillaries from those in the BOLD

initial dip does not correspond to that of fMRI.

*DOI: http://dx.doi.org/10.5772/intechopen.80888*

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared… DOI: http://dx.doi.org/10.5772/intechopen.80888*

#### **Figure 8.**

*Neuroimaging - Structure, Function and Mind*

the actual extent of change in the levels of Hb.

which ΔO decreases and ΔCBV increases.

of ΔO, ΔD, ΔCBV, and ΔCOE.

an initial dip.

ΔCBV decreases.

based on signal intensity, without the concept of a phase. However, this method describes all the possible combinations of responses through eight phases on the vector plane. In addition, particular patterns of physiological responses are presented in a highly visual manner. This method provides a quantitative measure of oxygen metabolism, offering the advantage of measurements expressed in units of degrees. Moreover, measurements are determined from ratios of change rather than

**8. Interpretation of initial dips using the vector-based approach**

The angle *k* shows a positive value in the phases of initial dip occurrence. Previously, the initial dip was regarded as an indication of increased oxygen

consumption. However, it was not possible to evaluate the strength of the initial dip or the possibility of different kinds of initial dips. Yoshino and Kato [32] classified initial dips in the language area by phase according to their particular combinations

• Phases 1 through 5 on the vector plane were dip phases, showing increases in ΔD or ΔCOE; the presence of an event-related vector in these phases defined

0 < ΔCOE<ΔCBV) are canonical dips [79], in which both ΔD and ΔO increase.

ΔCBV<0 < ΔCOE) are hypoxic–ischemic dips, in which ΔCOE increases and

• Phases −1 through −3 are non-dip phases, in which ΔD and ΔCOE decrease.

In **Figure 8**, time course data for previously reported initial dips are reproduced on a vector plane using the vector-based technique. **Figure 8A** and **8B** show two different types of dip in different phases, depending on the observed change in the ΔCBV. In both fMRI and OIS, the canonical initial dip has been considered to be a response

Regarding oxygen metabolism, responses in the dip phases may indicate stronger brain activity than those in the non-dip phases. It is necessary to verify the strongest dip phases during the evaluation of the regulation between the oxygenation axis (ΔCOE) and the blood volume axis (ΔCBV) in the vector plane. The typical response corresponds to Phases −1 and − 2, interpreted as brain activity with a low degree of oxygen exchange. The responses in other phases should be evaluated in the same manner and the frequency of their occurrence should be investigated based on phase classifications. The percentage of dips in Wernicke's area in Phases 1 and 2 was low (total: 15–21%). However, in Phases 4 and 5, this percentage was higher (total: 62–68%) [32]. Differences in the frequency of phase depending on the brain site and the task may have different physiological implications. The ratio between the decrease and increase in the levels of deoxyHb and oxyHb, respectively, in a typical response is not constant. The quantitative values of the phase angle *k* may be used to investigate such differences in typical

• Phase 1 (0 < ΔD < ΔO, ΔCOE<0 < ΔCBV) and Phase 2 (0 < ΔO < ΔD,

• Phase 3 (ΔO < 0 < ΔD, 0 < ΔCBV<ΔCOE) is a hypoxic-hyperemic dip, in

• Phase 4 (ΔO < 0 < ΔD, ΔCBV<0 < ΔCOE) and Phase 5 (ΔO < ΔD < 0,

**36**

responses.

*Two kinds of initial dips [32]. Representative patterns of two types of initial dips when data from (A) and (B) were converted into vectors on a vector plane. (A) In a study using optical intrinsic signals, ΔD increased during the early part of a task [94]. The vector in this time course is in Phase 1 during the initial dip and subsequently progresses into Phase −1, indicating a typical response. (A) Initially, the vector is in Phase 1 and subsequently rotates in a clockwise direction into Phase −2. (B) The vector initially rotates in a clockwise direction into Phase 4, followed by rotation in a counterclockwise direction into Phase −1 and subsequently into Phase 1.*

induced by increased levels of deoxyHb. **Figure 8B** shows an fNIRS initial dip (an increased ΔD accompanying a decreased ΔO), indicating Phase 4 [18, 32, 67, 68]. Recently, fNIRS was used to observe this new type of initial dip in primates [109].

As shown in **Figure 8A**, if this canonical initial dip detected by Malonek and Grinvald using OIS [94] corresponds to that of fMRI [95, 104], this would mean that the a blood oxygenation level-dependent (BOLD) signal from fMRI was able to differentiate between Phase 1, as a signal decrease, and Phase −1, as a signal increase. However, Phase 1 is an increased ΔCBV dip, in which ΔCOE decreases while the levels of deoxyHb increase. Thus, there is a discrepancy between the results from the two modalities. A theory bridging fNIRS and fMRI has been proposed, suggesting that a BOLD signal influenced by changes in ΔCBV closely resembles an increase in the levels of oxyHb [24]. In this model, the fMRI signal in the increased ΔCBV phase depends on the observed change in ΔO (not ΔD). Theoretically, this change may be considered to be a BOLD signal increase rather than a dip. Indeed, the use of the vector plane may explain the fact that the OIS initial dip does not correspond to that of fMRI.

In present, initial dips could be reliably detected with OIS [92–97] and fNIRS [31–36, 109]. On the other hand, the occurrence of the initial dip in fMRI has been doubted and its mechanism is still controversial [21–24, 105]. Logothetis et al. [86] reported a period of latency, when the increase in the BOLD signal was flat for a few seconds at the beginning of the task. This shows the difficulty in detecting changes in phases during passage through the capillaries from those in the BOLD

signal. Of note, the sensitivity of fMRI declines at detecting activities with high oxygen consumption. During early research on the combination of fMRI and fNIRS [9, 110], the concept of phases had not been introduced and the differences between these methods were not understood clearly.

Collectively, research has shown that these two modalities are physiologically inconsistent in their sensitivity to the initial dip, with significant differences between them. Moreover, animal studies have demonstrated the variation of ratios between changes in the levels of deoxyHb and oxyHb occurring simultaneously with neural activity (i.e., diversity of phase) [103, 109]. Using the concept of phases, it is also possible to re-evaluate the results of a previous fNIRS study [8] (**Figure 2**) and confirm that the results indicate Phase 1 in areas where oxygen consumption is high or in the time zone. The vector-based evaluation was able to show a short initial dip and sustained oxygen metabolism because the period of the task was long in this study. On the other hand, investigations that followed this previous study [8] may have evaluated the intensity of brain activity only (similar to *L*) in the Phase −1 and −2 typical responses.

#### **9. Quantification of brain activity in time series**

Local brain activity was quantified for the first time in 1993 using continuouswave fNIRS, by substituting optical differential path length factors [8]. At that time, mmol∙mm (or mmol∙cm) was commonly used as the unit expressing the degree of change in the levels of Hb, taking the differential path length factor as 1 [111, 112]. The phase angle k expresses oxygen metabolism quantitatively in degrees. This offers the advantage of being independent of the actual levels of Hb. **Figure 9** shows image displays from a verbal task [29, 30]. Local increases in the angle *k* were detected in Broca's area (channel 4) and the surrounding area during the task, with almost no change observed in ΔCBV. Thus, the use of the angle *k* may permit the high-sensitivity detection of local brain activity occurring simultaneously with a task (regardless of the duration of the task) that has been undetected in previous studies against the background of slow hemodynamic change. On the other hand, intensity (*L*) is strongest in channels 4 and 5 during and after the task, respectively. After the task, the angle *k* decreases approaching zero. These findings indicate the variable behavior of different indices in spatiotemporal imaging. In the past, the differences in spatiotemporal imaging had been largely ignored, with researchers focusing exclusively on typical responses. The differences in local brain activity of this kind were equally ignored, particularly when they occurred simultaneously with short tasks.

It has been shown that vector-based NIRS is able to quantitatively evaluate differences in the oxygen load in the prefrontal cortex arising from different breathing routes (**Figure 10** [113]). In that study, although there were no significant differences in *L*, differences in the time series of the angle *k* were apparent between nasal and mouth breathing. This may have potentially useful practical applications, such as the provision of an earlier and more reliable diagnosis of a patient's habitual breathing route compared with a patient interview. The use of an index combining both deoxyHb and oxyHb may lead to new interpretations of previous fNIRS data. Previous brain imaging studies have been based on the intensity of response.

In usage of this vector-based approach, it may not be possible to obtain the correct phase value by conventional data processing. For example, if the deoxyHb and oxyHb data are processed independently (e.g., when normalization or statistical parametric mapping has been performed on only the oxyHb data) [114], this will change the ratios, and there is a risk that the values of k will be distorted.

**39**

**Figure 10.**

**Figure 9.**

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared…*

In addition, a method of baseline correction, in which linear regression connecting the pre- and post-task period is used to emphasize the typical response, is available [115]. This may affect the angle *k* and *L* (intensity of response). By moving forward with quantitative analysis of this kind—designed to clarify differences between oxygenation and blood volume while taking care to avoid distortion from the initial processing of the data—fNIRS will be able to meet the challenges of

*P < 0.1) [113].*

*Spatiotemporal imaging of cerebral oxygen exchange for a verbal task [29, 30]. (A) Channel positions. Broca's area corresponds to channel 4. (B) Pink shows the duration of word listening (average 1.2 seconds) and blue shows the duration of word repetition (average 1.1 seconds). For ΔCBV, red indicates positive vector changes, whereas black indicates negative vector changes. For the angle k, black indicates k = 0, whereas red indicates the maximum angle k (180°). For L, black indicates 0, whereas red indicates the peak value. (C) Time courses of hemoglobin components and their two dimensional vector coordinates. Oxyhemoglobin (OxyHb; red), deoxyhemoglobin (deoxyHb; blue), and total hemoglobin (total Hb; yellow). Arbitrary unit (a.u.).*

quantitatively and accurately identifying localized brain activity.

*Time courses of the angle k for nasal and mouth breathing (\*\*P < 0.05; \**

*DOI: http://dx.doi.org/10.5772/intechopen.80888*

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared… DOI: http://dx.doi.org/10.5772/intechopen.80888*

#### **Figure 9.**

*Neuroimaging - Structure, Function and Mind*

Phase −1 and −2 typical responses.

between these methods were not understood clearly.

**9. Quantification of brain activity in time series**

signal. Of note, the sensitivity of fMRI declines at detecting activities with high oxygen consumption. During early research on the combination of fMRI and fNIRS [9, 110], the concept of phases had not been introduced and the differences

Collectively, research has shown that these two modalities are physiologically

Local brain activity was quantified for the first time in 1993 using continuouswave fNIRS, by substituting optical differential path length factors [8]. At that time, mmol∙mm (or mmol∙cm) was commonly used as the unit expressing the degree of change in the levels of Hb, taking the differential path length factor as 1 [111, 112]. The phase angle k expresses oxygen metabolism quantitatively in degrees. This offers the advantage of being independent of the actual levels of Hb. **Figure 9** shows image displays from a verbal task [29, 30]. Local increases in the angle *k* were detected in Broca's area (channel 4) and the surrounding area during the task, with almost no change observed in ΔCBV. Thus, the use of the angle *k* may permit the high-sensitivity detection of local brain activity occurring simultaneously with a task (regardless of the duration of the task) that has been undetected in previous studies against the background of slow hemodynamic change. On the other hand, intensity (*L*) is strongest in channels 4 and 5 during and after the task, respectively. After the task, the angle *k* decreases approaching zero. These findings indicate the variable behavior of different indices in spatiotemporal imaging. In the past, the differences in spatiotemporal imaging had been largely ignored, with researchers focusing exclusively on typical responses. The differences in local brain activity of this kind were equally

ignored, particularly when they occurred simultaneously with short tasks.

change the ratios, and there is a risk that the values of k will be distorted.

It has been shown that vector-based NIRS is able to quantitatively evaluate differences in the oxygen load in the prefrontal cortex arising from different

breathing routes (**Figure 10** [113]). In that study, although there were no significant differences in *L*, differences in the time series of the angle *k* were apparent between nasal and mouth breathing. This may have potentially useful practical applications, such as the provision of an earlier and more reliable diagnosis of a patient's habitual breathing route compared with a patient interview. The use of an index combining both deoxyHb and oxyHb may lead to new interpretations of previous fNIRS data. Previous brain imaging studies have been based on the intensity of response.

In usage of this vector-based approach, it may not be possible to obtain the correct phase value by conventional data processing. For example, if the deoxyHb and oxyHb data are processed independently (e.g., when normalization or statistical parametric mapping has been performed on only the oxyHb data) [114], this will

inconsistent in their sensitivity to the initial dip, with significant differences between them. Moreover, animal studies have demonstrated the variation of ratios between changes in the levels of deoxyHb and oxyHb occurring simultaneously with neural activity (i.e., diversity of phase) [103, 109]. Using the concept of phases, it is also possible to re-evaluate the results of a previous fNIRS study [8] (**Figure 2**) and confirm that the results indicate Phase 1 in areas where oxygen consumption is high or in the time zone. The vector-based evaluation was able to show a short initial dip and sustained oxygen metabolism because the period of the task was long in this study. On the other hand, investigations that followed this previous study [8] may have evaluated the intensity of brain activity only (similar to *L*) in the

**38**

*Spatiotemporal imaging of cerebral oxygen exchange for a verbal task [29, 30]. (A) Channel positions. Broca's area corresponds to channel 4. (B) Pink shows the duration of word listening (average 1.2 seconds) and blue shows the duration of word repetition (average 1.1 seconds). For ΔCBV, red indicates positive vector changes, whereas black indicates negative vector changes. For the angle k, black indicates k = 0, whereas red indicates the maximum angle k (180°). For L, black indicates 0, whereas red indicates the peak value. (C) Time courses of hemoglobin components and their two dimensional vector coordinates. Oxyhemoglobin (OxyHb; red), deoxyhemoglobin (deoxyHb; blue), and total hemoglobin (total Hb; yellow). Arbitrary unit (a.u.).*

**Figure 10.** *Time courses of the angle k for nasal and mouth breathing (\*\*P < 0.05; \* P < 0.1) [113].*

In addition, a method of baseline correction, in which linear regression connecting the pre- and post-task period is used to emphasize the typical response, is available [115]. This may affect the angle *k* and *L* (intensity of response). By moving forward with quantitative analysis of this kind—designed to clarify differences between oxygenation and blood volume while taking care to avoid distortion from the initial processing of the data—fNIRS will be able to meet the challenges of quantitatively and accurately identifying localized brain activity.

#### **10. Conclusion**

The precise detection of local brain activity was the original purpose of fNIRS. Nowadays, because of the vector-based approach, investigators can measure initial dips from the scalp. Progress has been achieved in the quantitative detection of local brain activity and the development of spatiotemporal imaging. However, some fNIRS studies are actually task-related studies using NIRS, never intended for the spatial localization of brain function. This together with other factors has introduced doubts regarding the validity of fNIRS. The historical background described earlier in this review may be useful as we attempt to erase these doubts and improve the spatial and temporal accuracy of fNIRS. Studies are warranted to examine the physiological significance of the different combinations of changes in the levels of the different Hb and changes in the characteristics of mapping depending on the selection of indices.

Local brain activity induces local oxygen consumption and demand for oxygen supply. Further research is required to investigate the relationship between the consumption of oxygen and the spatial distribution of oxygen supply accompanying local brain activity. The indices angle *k* and *L*, indicating the phase of hemoglobin response and its intensity, respectively, are new indices for the detection of local brain activity. In addition, the simultaneous measurement of composite indices of this kind may improve the detection of local brain activity. The application of methods for the simultaneous evaluation of these composite indicators is one of the challenges for future research on the new fNIRS method.

#### **Author details**

Toshinori Kato Department of Brain Environmental Research, KatoBrain Co., Ltd., Tokyo, Japan

\*Address all correspondence to: kato@katobrain.com

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**41**

10.3141/2518-03

*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared…*

cerebral blood flow by means of nearinfrared spectroscopy. Comprehensive research report concerning medical care for children (people) with disabilities. Japan. Ministry of Health & Welfare.

[8] Kato T, Kamei A, Takashima S, Ozaki T. Human visual cortical function during photic stimulation monitoring by means of near-infrared spectroscopy. Journal of Cerebral Blood Flow and Metabolism. 1993;**13**:516-520. PMID: 8478409 DOI: 10.1038/jcbfm.1993.66

[9] Kato T, Takashima S, Kamada K, Kishibayashi J, Sunohara N, Ozaki T.

spectroscopy in the human functional

Advantage of near-infrared

MR imaging in brain. In: 12th Annual Scientific Meeting of the Society of Magnetic Resonance in Medicine. Proceedings of the International Society for Magnetic Resonance in Medicine. New York; Aug 14-20 1993;**1993**(S3):1409. https://onlinelibrary.wiley.com/doi/ epdf/10.1002/mrmp.22419930308

[10] Wyatt JS, Cope M, Delpy DT, Wray S, Reynolds EO. Quantification

[11] Togari H. Noninvasive cerebral blood volume monitoring in premature infants. Journal of

Clinical and Experimental Medicine.

localization of the earliest visual activity in the occipital cortex. Medical & Biological Engineering & Computing. 2011;**49**(5):545-554. DOI: 10.1007/

[12] Golubic SJ, Susac A, Grilj V, Ranken D, Huonker R, Haueisen J, et al. Size matters: MEG empirical and simulation study on source

haemodynamics in sick newborn infants by near infrared spectrophotometry.

of cerebral oxygenation and

Lancet. 1986;**2**:1063-1066

1987;**142**:907-909

s11517-011-0764-9

1992:179-181

*DOI: http://dx.doi.org/10.5772/intechopen.80888*

[1] Ferrari M, Quaresima V. A brief review on the history of human functional near-infra-red spectroscopy (fNIRS) development and fields of application. NeuroImage. 2012;**63**:921-935. DOI: 10.1016/j. neuroimage.2012.03.049

[2] Mihara M, Miyai I. Review of functional near-infrared spectroscopy in neurorehabilitation. Neurophotonics.

2016;**3**:031414. DOI: 10.1117/1.

[3] Yoshino K, Oka N, Yamamoto K, Takahashi H, Kato T. Functional brain imaging using near infrared spectroscopy during actual driving on an expressway. Frontiers in Human Neuroscience. 2013;**7**:882. DOI: 10.3389/ fnhum.2013.00882. eCollection 2013.

[4] Yoshino K, Oka N, Yamamoto K, Takahashi H, Kato T. Correlation of prefrontal cortical activation with changing vehicle speeds in actual driving: A vector-based functional nearinfrared spectroscopy study. Frontiers in Human Neuroscience. 2013;**7**:895. DOI:

[5] Oka N, Yoshino K, Yamamoto K, Takahashi H, Li S, Sugimachi T, et al. Greater activity in the frontal cortex on left curves: A vector-based fNIRS study of left and right curve driving. PLoS One. 2015;**10**(5):e0127594. DOI:

10.3389/fnhum.2013.00895

10.1371/journal.pone.0127594

[6] Orino Y, Yoshino K, Oka N, Yamamoto K, Takahashi H, Kato T. Brain activity involved in vehicle velocity changes in a sag vertical curve on an expressway: Vector-based functional near-infrared spectroscopy study. Journal of the Transportation Research Board. 2015;**2518**:18-26. DOI:

[7] Takashima S, Kato T, Hirano S, Mito T. Observation of activation in local

NPh.3.3.031414

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*Vector-Based Approach for the Detection of Initial Dips Using Functional Near-Infrared… DOI: http://dx.doi.org/10.5772/intechopen.80888*

#### **References**

*Neuroimaging - Structure, Function and Mind*

The precise detection of local brain activity was the original purpose of fNIRS. Nowadays, because of the vector-based approach, investigators can measure initial dips from the scalp. Progress has been achieved in the quantitative detection of local brain activity and the development of spatiotemporal imaging. However, some fNIRS studies are actually task-related studies using NIRS, never intended for the spatial localization of brain function. This together with other factors has introduced doubts regarding the validity of fNIRS. The historical background described earlier in this review may be useful as we attempt to erase these doubts and improve the spatial and temporal accuracy of fNIRS. Studies are warranted to examine the physiological significance of the different combinations of changes in the levels of the different Hb and changes in the characteristics of mapping depending on the

Local brain activity induces local oxygen consumption and demand for oxygen supply. Further research is required to investigate the relationship between the consumption of oxygen and the spatial distribution of oxygen supply accompanying local brain activity. The indices angle *k* and *L*, indicating the phase of hemoglobin response and its intensity, respectively, are new indices for the detection of local brain activity. In addition, the simultaneous measurement of composite indices of this kind may improve the detection of local brain activity. The application of methods for the simultaneous evaluation of these composite indicators is one of the

**10. Conclusion**

selection of indices.

**40**

**Author details**

Toshinori Kato

provided the original work is properly cited.

\*Address all correspondence to: kato@katobrain.com

challenges for future research on the new fNIRS method.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Department of Brain Environmental Research, KatoBrain Co., Ltd., Tokyo, Japan

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[2] Mihara M, Miyai I. Review of functional near-infrared spectroscopy in neurorehabilitation. Neurophotonics. 2016;**3**:031414. DOI: 10.1117/1. NPh.3.3.031414

[3] Yoshino K, Oka N, Yamamoto K, Takahashi H, Kato T. Functional brain imaging using near infrared spectroscopy during actual driving on an expressway. Frontiers in Human Neuroscience. 2013;**7**:882. DOI: 10.3389/ fnhum.2013.00882. eCollection 2013.

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[7] Takashima S, Kato T, Hirano S, Mito T. Observation of activation in local

cerebral blood flow by means of nearinfrared spectroscopy. Comprehensive research report concerning medical care for children (people) with disabilities. Japan. Ministry of Health & Welfare. 1992:179-181

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onlinelibrary.wiley.com/doi/ epdf/10.1002/mrmp.22419920303

1993;**8**:237-241

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onlinelibrary.wiley.com/doi/ epdf/10.1002/mrmp.22419920303

*Neuroimaging - Structure, Function and Mind*

[97] Jones M, Berwick J, Johnston D, Mayhew J. Concurrent optical imaging spectroscopy and laser-doppler flowmetry: The relationship between blood flow, oxygenation, and volume in rodent barrel cortex. NeuroImage.

Echo-planar imaging mirrors previous optical imaging using intrinsic signals. Magnetic Resonance in Medicine. 1995,

[105] Hu X, Yacoub E. The story of the initial dip in fMRI. NeuroImage.

[106] Watanabe E, Maki A, Kawaguchi F, Takashiro K, Yamashita Y, Koizumi H, et al. Non-invasive assessment of language dominance with near-infrared spectroscopic mapping. Neuroscience

[107] Bisconti S, Di Sante G, Ferrari M, Quaresima V. Functional near-infrared spectroscopy reveals heterogeneous patterns of language lateralization over frontopolar cortex. Neuroscience

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Letters. 1998;**256**:49-52

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JBO.17.5.056005

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[109] Zaidi AD, Birbaumer N, Fetz E, Logothetis N, Sitaram R. The hemodynamic initial-dip consists of both volumetric and oxymetric changes correlated to localized spiking activity. bioRxiv.2018. https:// www.biorxiv.org/content/biorxiv/ early/2018/02/22/259895.full.pdf

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[98] Suh M, Bahar S, Mehta A, Schwartz T. Blood volume and hemoglobin oxygenation response following electrical stimulation of human cortex.

2001;**13**:1002-1015

1999;**9**(6):S430

1999;**9**(6):S1025

2003;**20**:479-488

2001;**306**:106-110

2004;**7**:919-920

NeuroImage. 2006;**31**:66-75

[99] Kato T, Endo A, Fukumizu M, Furusho J, Takashima S, Kawaguchi F, et al. Single finger movement trial using human functional nearinfraredgraphy (fNIR). NeuroImage.

[100] Kato T, Yamashita Y, Maki A, Yamamoto T, Koizumi H. Temporal behavior of human functional nearinfraredgraphy (fNIR) using singleword speaking trial. NeuroImage.

[101] Jasdzewski G, Strangman G, Wagner J, Kwong KK, Poldrack RA, Boas DA. Differences in the hemodynamic response to event-related motor and visual paradigms as measured by nearinfrared spectroscopy. NeuroImage.

[102] Ances BM, Buerk DG, Greenberg JH, Detre JA. Temporal dynamics of the partial pressure of brain tissue oxygen during functional forepaw stimulation

[103] Thompson J, Peterson M, Freeman R. High-resolution neurometabolic coupling revealed by focal activation of visual neurons. Nature Neuroscience.

[104] Menon RS, Ogawa S, Hu X, Strupp JS, Andersen P, Ugurbil K. BOLD based functional MRI at 4 Tesla includes a capillary bed contribution:

in rats. Neuroscience Letters.

**48**

[111] Hirano S, Hasegawa M, Kamei A, Ozaki T, Takashima S. Responses of cerebral blood volume and oxygenation to carotid ligation and hypoxia in young rabbits: Near-infrared spectroscopy study. Journal of Child Neurology. 1993;**8**:237-241

[112] Kamei A, Ozaki T, Takashima S. Monitoring of the intracranial hemodynamics and oxygenation during and after hyperventilation in newborn rabbits with near-infrared spectroscopy. Pediatric Research. 1994;**35**:334-338

[113] Sano M, Sano S, Oka N, Yoshino K, Kato T. Increased oxygen load in the prefrontal cortex from mouth breathing: A vector-based near-infrared spectroscopy study. Neuroreport. 2013;**24**(17):935-940. DOI: 10.1097/ WNR.0000000000000008

[114] Ye JC, Tak S, Jang KE, Jung JW, Jang JD. NIRS-SPM: Statistical parametric mapping for nearinfrared spectroscopy. NeuroImage. 2009;**44**:428-447

[115] Tsujimoto S, Yamamoto T, Kawaguchi H, Koizumi H, Sawaguchi T. Prefrontal cortical activation associated with working memory in adults and preschool children: An event-related optical topography study. Cerebral Cortex. 2004;**14**:703-712

Chapter 3

in fMRI

Yongxia Zhou

Abstract

detection.

detection

51

1. Introduction

Application of ICA and Dynamic

The emphasis of this work is on developing novel data-processing techniques to achieve a higher spatiotemporal resolution in dynamic functional magnetic resonance imaging (fMRI). Due to partial volume effects, a pixel in fMRI may contain signals from a mixture of micro- and macrovasculature, with very different temporal characteristics. This mixture effect provides a way to separate microvasculature from macrovasculature in fMRI. A multi-component model representing a mixture of many reference functions is used to fit the time course of pixels in fMRI. The results suggest that it may be possible to separate the micro- and macrovasculature fractional contributions to pixels by this approach. Compared to the classical singlecomponent model, the multi-component model fits the measured fMRI time course with a higher correlation coefficient and also detects voxels with low latencies more efficiently. Spatial independent component analysis (ICA) as a preprocessing step is implemented to remove major physiological noise and artifacts. The results of mixture model fitting after ICA cleaning show better results for microvasculature

Keywords: fMRI microvasculature, ICA, dynamic mixture model, neuronal

Functional magnetic resonance imaging (fMRI) is the most widely used modality to map brain function because it can be easily implemented, is noninvasive, and has a relatively high spatial resolution. The dynamic fMRI signal change is regulated by the local changes in cerebral blood flow (CBF), cerebral blood volume (CBV), and blood oxygenation. CBF studies have suggested that a local increase in oxygen delivery beyond metabolic demand occurs in active cerebral tissue, which results in a higher concentration of oxygenated blood and a decrease in deoxyhemoglobin concentration within the microvasculature of metabolically active brain regions. Due to the four unpaired electrons, deoxyhemoglobin maintains a larger observed magnetic susceptibility effect and is paramagnetic relative to oxyhemoglobin and the surrounding brain tissue. The decrement in this paramagnetic substance in the activated brain leads to an increase in the local magnetic homogeneity and reduces

Mixture Model to Identify

Microvasculature Activation

#### Chapter 3

## Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI

Yongxia Zhou

#### Abstract

The emphasis of this work is on developing novel data-processing techniques to achieve a higher spatiotemporal resolution in dynamic functional magnetic resonance imaging (fMRI). Due to partial volume effects, a pixel in fMRI may contain signals from a mixture of micro- and macrovasculature, with very different temporal characteristics. This mixture effect provides a way to separate microvasculature from macrovasculature in fMRI. A multi-component model representing a mixture of many reference functions is used to fit the time course of pixels in fMRI. The results suggest that it may be possible to separate the micro- and macrovasculature fractional contributions to pixels by this approach. Compared to the classical singlecomponent model, the multi-component model fits the measured fMRI time course with a higher correlation coefficient and also detects voxels with low latencies more efficiently. Spatial independent component analysis (ICA) as a preprocessing step is implemented to remove major physiological noise and artifacts. The results of mixture model fitting after ICA cleaning show better results for microvasculature detection.

Keywords: fMRI microvasculature, ICA, dynamic mixture model, neuronal detection

#### 1. Introduction

Functional magnetic resonance imaging (fMRI) is the most widely used modality to map brain function because it can be easily implemented, is noninvasive, and has a relatively high spatial resolution. The dynamic fMRI signal change is regulated by the local changes in cerebral blood flow (CBF), cerebral blood volume (CBV), and blood oxygenation. CBF studies have suggested that a local increase in oxygen delivery beyond metabolic demand occurs in active cerebral tissue, which results in a higher concentration of oxygenated blood and a decrease in deoxyhemoglobin concentration within the microvasculature of metabolically active brain regions. Due to the four unpaired electrons, deoxyhemoglobin maintains a larger observed magnetic susceptibility effect and is paramagnetic relative to oxyhemoglobin and the surrounding brain tissue. The decrement in this paramagnetic substance in the activated brain leads to an increase in the local magnetic homogeneity and reduces

dephasing of spins. This increases the T2\* contrast in the activated brain and results in increases of MR signal relative to the resting state. A fast MRI data acquisition sequence known as the echo-planar imaging (EPI) sequence is commonly used to acquire fMRI signals. The physiological contributors to the fMRI signal changes include the blood-oxygenation-level-dependent (BOLD) and in-flow effects such as the increase in local CBF and arterial oxygenation. The signal in the functional area reflects the local changes in the CBF and oxygen consumption rate due to the task or stimulus [1]. And finally, the quantitative fMRI image indicates the spatiotemporal mapping of the hemodynamic in response to a given task at specific brain areas.

a higher field at 7 T was used to increase the relative contribution of

DOI: http://dx.doi.org/10.5772/intechopen.79222

large veins using intensity, phase, and temporal delay as features [17].

culature mixtures within one voxel.

2. Methods

53

2.1 Experiment

microcomponent to the BOLD signal. In spin-echo fMRI [14], large vessel contributions were suppressed because the 180° radiofrequency (RF) pulse in spin-echo (SE) sequence refocused the dephasing effect of the static field inhomogeneity around large vessels. A fast response that may be attributed to an increased oxygen consumption had been observed [15, 16]. This fast dip might be more sensitive to microvasculature. Also, previous approaches to separate the microvasculature have relied upon post-processing techniques that utilize the fact that the phase of the MR signal often reflects the presence of larger vessels in a voxel [17, 18]. Thus, larger vessels could be removed in the frequency domain or K-space. Our group has presented a study of segmenting fMRI pixels into microvasculature, venules, and

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI

Independent component analysis (ICA) was first applied to fMRI in 1998 by McKeown et al. using INFORMAX [19] and has been shown to be superior to principle component analysis (PCA) in determining the spatial and temporal extents of task-related activation. ICA can also be used to identify the nontaskrelated components, such as physiological noise and movement artifacts. Initially, ICA methods assumed that the sources were naturally occurring sources and mostly had a super-Gaussian probability density function. Later on, the super-Gaussian assumption was expanded to a combination of super-Gaussian and sub-Gaussian distribution assuming that the source distribution was either sub-Gaussian or super-Gaussian [20]. Recently, a mixture density model for the sources has been proposed that enables the unknown sources to have a flexible density distribution [21]. The advantages of ICA over PCA, the correlation of spatial ICA and temporal ICA to fMRI, and some other issues have been discussed in many papers for the past decade [22, 23]. In this study, ICA is implemented as an advanced preprocessing step in fMRI activation detection to remove artifacts by identifying and then removing some unrelated noisy components. ICA can also be used to identify temporally independent sources by implementing temporal ICA to fMRI signals within the region of interest (ROI). Sources identified by temporal ICA provide extra information regarding the segmentation of microvasculature and macrovas-

Temporal characteristics of the BOLD response had been investigated by using a series of time-shifted reference functions [7, 24]. A better localization of the activated sites and temporal relationships among different brain regions within selected clusters of activated voxels was achieved using this dynamic correlation method. But this dynamic fitting used only a one-reference function at a time. Our method is to use a multi-component model representing a mixture of many vascular components to account for partial volume effect within one voxel [25, 26]. Because of physiological and random noises in the fMRI signal, the multiple components fitting of the dynamic mixture model can be further improved with both spatial and temporal ICA methods to improve SNR. Our purpose is to implement dynamic fitting in the proposed mixture model to account for different temporal characteristics of vascular components and to improve SNR with ICA integration for better

To test the methodology, an Institutional Review Board (IRB)-approved human

study was conducted with fMRI on two normal subjects aged 25 and 40 years.

microvasculature detections and a higher spatiotemporal resolution.

The coupling between the BOLD hemodynamic effect and the underlying neuronal activity has been studied and emphasized recently [2–4]. The first question is whether the BOLD effect can reflect neuronal activation. Experiments have been done with both animals and humans to verify that the BOLD contrast directly reflects the neural responses elicited by a stimulus [5, 6]. The second question is how the BOLD signal reflects the underlying neuronal activation. The exact nature of the neurovascular coupling is not known yet. The studies by Logothetis suggest that the BOLD signal is more likely to reflect the input and local neuronal processing in a given area [5], whose weighted average of dendro-somatic components is measured as the local field potential (LFP). However, because of the slow-brain hemodynamics and the draining effects of vessels and veins, the BOLD activation detected in fMRI is temporally delayed and spatially blurred from the actual site of neuronal activation. The third question is then how to detect the neuronal activations from fMRI. Because of the unknown nature of the neurovascular coupling, how to detect neuronal activation remains an open question. Since neuronal activation originates in tissue subserved by the microvasculature, the detected microvasculature will be co-localized or at least closer to neuronal activation.

The fMRI BOLD effect originates within the microvasculature but also spreads into veins that drain blood from the activated brain tissue. And fMRI-based BOLD contrast consists mainly of activations in the microvasculature, large venules, and draining veins [7–10]. Because the BOLD signal is largely contaminated by the signals in large veins and noise, extracting earlier microvasculature activation is difficult and several issues need to be resolved. One major problem is the compounding effects from the physiological cardiac and respiratory noise, random noise, and also the contamination of head and vessel motion artifacts [11]. The percentage signal changes triggered by the stimuli typically is 1–10% in 1.5–3 T scanners [7]. Averaging scans for all events can improve signal-to-noise ratio (SNR) in fMRI by canceling random noise. Low-pass and high-pass filtering for the data can also improve SNR by removing the slow physiological processes such as subject habituation, learning or fatigue, subject motion, machine calibration drift, and scan-to-scan baseline variability [12]. However, artifacts in fMRI are often correlated with the signal of interest. Thus, classical average and filtering methods are not very effective. Noise-removing methods that are based on the intrinsic structure of the measured signals are more effective.

Another challenge is the partial volume effect (PVE) within one fMRI voxel. Because of the relatively large size of the voxel at the scale of mm compared to the size of veins and microvasculature, a mixture of micro- and macrovasculatures is present in the activated voxel with different temporal characteristics. Since the actual site of neuronal activity could be masked by signals from macrovasculature, a technique to separate micro- and macrovasculature within a voxel would be of great significance to fMRI to improve spatial specificity as well.

The vascular contributions to the BOLD signal depend on magnetic field strength as well as on data acquisition methods. Many previous works have been done to enhance the detection of microvasculature. In Chen and Ugurbil [13],

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI DOI: http://dx.doi.org/10.5772/intechopen.79222

a higher field at 7 T was used to increase the relative contribution of microcomponent to the BOLD signal. In spin-echo fMRI [14], large vessel contributions were suppressed because the 180° radiofrequency (RF) pulse in spin-echo (SE) sequence refocused the dephasing effect of the static field inhomogeneity around large vessels. A fast response that may be attributed to an increased oxygen consumption had been observed [15, 16]. This fast dip might be more sensitive to microvasculature. Also, previous approaches to separate the microvasculature have relied upon post-processing techniques that utilize the fact that the phase of the MR signal often reflects the presence of larger vessels in a voxel [17, 18]. Thus, larger vessels could be removed in the frequency domain or K-space. Our group has presented a study of segmenting fMRI pixels into microvasculature, venules, and large veins using intensity, phase, and temporal delay as features [17].

Independent component analysis (ICA) was first applied to fMRI in 1998 by McKeown et al. using INFORMAX [19] and has been shown to be superior to principle component analysis (PCA) in determining the spatial and temporal extents of task-related activation. ICA can also be used to identify the nontaskrelated components, such as physiological noise and movement artifacts. Initially, ICA methods assumed that the sources were naturally occurring sources and mostly had a super-Gaussian probability density function. Later on, the super-Gaussian assumption was expanded to a combination of super-Gaussian and sub-Gaussian distribution assuming that the source distribution was either sub-Gaussian or super-Gaussian [20]. Recently, a mixture density model for the sources has been proposed that enables the unknown sources to have a flexible density distribution [21]. The advantages of ICA over PCA, the correlation of spatial ICA and temporal ICA to fMRI, and some other issues have been discussed in many papers for the past decade [22, 23]. In this study, ICA is implemented as an advanced preprocessing step in fMRI activation detection to remove artifacts by identifying and then removing some unrelated noisy components. ICA can also be used to identify temporally independent sources by implementing temporal ICA to fMRI signals within the region of interest (ROI). Sources identified by temporal ICA provide extra information regarding the segmentation of microvasculature and macrovasculature mixtures within one voxel.

Temporal characteristics of the BOLD response had been investigated by using a series of time-shifted reference functions [7, 24]. A better localization of the activated sites and temporal relationships among different brain regions within selected clusters of activated voxels was achieved using this dynamic correlation method. But this dynamic fitting used only a one-reference function at a time. Our method is to use a multi-component model representing a mixture of many vascular components to account for partial volume effect within one voxel [25, 26]. Because of physiological and random noises in the fMRI signal, the multiple components fitting of the dynamic mixture model can be further improved with both spatial and temporal ICA methods to improve SNR. Our purpose is to implement dynamic fitting in the proposed mixture model to account for different temporal characteristics of vascular components and to improve SNR with ICA integration for better microvasculature detections and a higher spatiotemporal resolution.

#### 2. Methods

#### 2.1 Experiment

To test the methodology, an Institutional Review Board (IRB)-approved human study was conducted with fMRI on two normal subjects aged 25 and 40 years.

dephasing of spins. This increases the T2\* contrast in the activated brain and results in increases of MR signal relative to the resting state. A fast MRI data acquisition sequence known as the echo-planar imaging (EPI) sequence is commonly used to acquire fMRI signals. The physiological contributors to the fMRI signal changes include the blood-oxygenation-level-dependent (BOLD) and in-flow effects such as the increase in local CBF and arterial oxygenation. The signal in the functional area reflects the local changes in the CBF and oxygen consumption rate due to the task or stimulus [1]. And finally, the quantitative fMRI image indicates the spatiotemporal mapping of the hemodynamic in response to a given task at specific brain areas. The coupling between the BOLD hemodynamic effect and the underlying neuronal activity has been studied and emphasized recently [2–4]. The first question is whether the BOLD effect can reflect neuronal activation. Experiments have been done with both animals and humans to verify that the BOLD contrast directly reflects the neural responses elicited by a stimulus [5, 6]. The second question is how the BOLD signal reflects the underlying neuronal activation. The exact nature of the neurovascular coupling is not known yet. The studies by Logothetis suggest that the BOLD signal is more likely to reflect the input and local neuronal processing in a given area [5], whose weighted average of dendro-somatic components is measured as the local field potential (LFP). However, because of the slow-brain hemodynamics and the draining effects of vessels and veins, the BOLD activation detected in fMRI is temporally delayed and spatially blurred from the actual site of neuronal activation. The third question is then how to detect the neuronal activations from fMRI. Because of the unknown nature of the neurovascular coupling, how to detect neuronal activation remains an open question. Since neuronal activation originates in tissue subserved by the microvasculature, the detected microvas-

Neuroimaging - Structure, Function and Mind

culature will be co-localized or at least closer to neuronal activation.

of the measured signals are more effective.

52

significance to fMRI to improve spatial specificity as well.

The fMRI BOLD effect originates within the microvasculature but also spreads into veins that drain blood from the activated brain tissue. And fMRI-based BOLD contrast consists mainly of activations in the microvasculature, large venules, and draining veins [7–10]. Because the BOLD signal is largely contaminated by the signals in large veins and noise, extracting earlier microvasculature activation is difficult and several issues need to be resolved. One major problem is the

compounding effects from the physiological cardiac and respiratory noise, random noise, and also the contamination of head and vessel motion artifacts [11]. The percentage signal changes triggered by the stimuli typically is 1–10% in 1.5–3 T scanners [7]. Averaging scans for all events can improve signal-to-noise ratio (SNR) in fMRI by canceling random noise. Low-pass and high-pass filtering for the data can also improve SNR by removing the slow physiological processes such as subject habituation, learning or fatigue, subject motion, machine calibration drift, and scan-to-scan baseline variability [12]. However, artifacts in fMRI are often correlated with the signal of interest. Thus, classical average and filtering methods are not very effective. Noise-removing methods that are based on the intrinsic structure

Another challenge is the partial volume effect (PVE) within one fMRI voxel. Because of the relatively large size of the voxel at the scale of mm compared to the size of veins and microvasculature, a mixture of micro- and macrovasculatures is present in the activated voxel with different temporal characteristics. Since the actual site of neuronal activity could be masked by signals from macrovasculature, a technique to separate micro- and macrovasculature within a voxel would be of great

The vascular contributions to the BOLD signal depend on magnetic field strength as well as on data acquisition methods. Many previous works have been done to enhance the detection of microvasculature. In Chen and Ugurbil [13],

A 480-volume of event-related EPI was acquired on a GE 1.5 T LX system from two continuous slices (i.e., two images per volume) through the visual cortex. The stimulus was a reversing checkerboard flashing with a 2-Hz frequency for 2 s every 20 s. The pulse repetition time TR = 275 ms, effective echo time TE = 45 ms, 45° flip angle, 64 � 128 acquisition matrix, and 20 � 40 cm field of view. A total of seven events were acquired.

#### 2.2 Model

A multi-component reference function with a variable latency and a variable time separation between adjacent components was fitted to the time course of each voxel within the visual cortex, as shown in Eq. (1)

$$y(t) = \sum\_{i=1}^{N} a\_i s\_i(t) + n \Rightarrow Y = \text{SA} + n, t = \mathbf{1}, \dots, T \tag{1}$$

Recently, a first-order Taylor approximation for the temporal derivative of the

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI

ðÞ)t y tðÞ¼ β1r tðÞþ β2r

•

•

ð Þþt n tð Þ

ð Þt is the temporal derivative of the

δð Þ t � Ttrial (7)

�ð Þ� <sup>δ</sup>2=τ<sup>2</sup> ð Þ <sup>t</sup>�τ<sup>2</sup> (8)

(5)

ð6Þ

reference function is used to estimate the delay of the fMRI response and the latency difference in different regions [29, 30]. Assuming that there is a slight time delay T<sup>0</sup> between the reference function and the measurement, the delay T<sup>0</sup> can be

•

reference function. Both are used as two basis functions in a GLM. The betaparameters β<sup>1</sup> and β<sup>2</sup> are estimated using the GLM algorithm. In case of a dualcomponent model, the derivative of only one component or the derivatives of both

After the mixture coefficients are estimated for any combination of two (or more) different reference functions, the combination of the two-reference functions that has the minimum fitting error or a maximum correlation coefficient with regard to the original time course of each voxel is the estimate of the two compo-

To account for the relatively small microvasculature signal compared to veins at 1.5 T, a weighting factor can be used to estimate the relative fractions of micro- and macrovasculature inside a voxel from the fitted coefficients. For two components, assume is the estimate of fraction coefficient from each component in one voxel using NNLS method, and is the weighting factor for each component. Then, the percentage contribution of each component in this

In Eq. (2), each component comes from a reference function with certain latencies. The reference function mimicking the BOLD response is represented by the convolution of the stimuli function and the hemodynamic response function

HRF is the brain response to an impulse stimulus and is modeled as the differ-

trial

�ð Þ� <sup>δ</sup>1=τ<sup>1</sup> ð Þ <sup>t</sup>�τ<sup>1</sup> � <sup>c</sup> � <sup>t</sup>

τ2 <sup>δ</sup><sup>2</sup> e

(HRF), assuming that the brain response is linear to the input (7)

τ1 <sup>δ</sup><sup>1</sup> e

ence between two gamma functions as in Eq. (8) [31]

h t<sup>ð</sup> ; <sup>τ</sup>1; <sup>τ</sup>2; <sup>δ</sup>1; <sup>δ</sup>2Þ ¼ <sup>t</sup>

r tðÞ¼ h tð Þ∗I tð Þ,I tðÞ¼ ∑

estimated as listed in Eq. (5)

DOI: http://dx.doi.org/10.5772/intechopen.79222

components are tested.

nents with different latencies.

voxel is computed as in Eq. (6)

2.4 Simulation

55

y tðÞ¼ a � r tð Þþ � T<sup>0</sup> n tð Þ

r tð Þ � T<sup>0</sup> ≈ r tðÞ� T<sup>0</sup> � r

where r tð Þ is a one-reference function and r

) a ≈ β1, T<sup>0</sup> ≈ β2=β<sup>1</sup>

where y is the normalized time course of a voxel, n is fMRI noise, N is the number of component, si is the ith component, ai is the contributions or the mixture coefficient of si in y,T is the number of time points in the time course.

Each vascular component is modeled by a reference function with a latency parameter (2):

$$S\_{T \times N}(t; N) = [X\_1(t - T\_1), X\_2(t - T\_2), \dots, X\_N(t - T\_N)] \tag{2}$$

where X(t) is the reference function to best represent BOLD response, and Ti is the latency parameter for the ith component to account for delay. Since latency is the most important and influential parameter in dynamic fitting, a dual-component model was investigated in this chapter for simplicity.

#### 2.3 Estimation algorithm

Assuming the noise in fMRI is Gaussian white noise and the components (or mixtures) can be explicitly modeled by a series of reference functions, there are several ways to estimate the mixture coefficient and the latency of each component.

A non-negative least square (NNLS) solver [27] can be used to estimate the contribution coefficients of each component after normalizing both the time course and the components. At each iteration, only the column of S where the associated entry of A > 0 was used for least square estimation as in Eq. (3)

$$\mathcal{A}\_{\rm NN}^{(i)} = \mathbb{S}\_{\rm J}^{+} \mathbf{Y}, \ J = \left\{ j | \mathbb{A}\_{\rm j}^{(i-1)} = \mathbf{0} \right\} \tag{3}$$

If the non-negative constraint is removed from the estimation, then a standard minimum norm method can be used to estimate the contribution coefficients of each component. The model falls in the general linear model (GLM) fitting problem [28]. Thus, the estimation of the coefficient and hypothesis testing for the estimation can be done using Eq. (4)

$$\begin{aligned} A\_{GLM} &= \left(\mathbb{S}^T \mathbb{S}\right)^{-1} \mathbb{S}^T \cdot Y\\ A\_{GLM} &\sim \mathcal{N}\left(\mathbb{S}^+ Y, \sigma\_n^{-2} \cdot \left(\mathbb{S}^T \mathbb{S}\right)^{-1}\right) \end{aligned} \tag{4}$$

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI DOI: http://dx.doi.org/10.5772/intechopen.79222

Recently, a first-order Taylor approximation for the temporal derivative of the reference function is used to estimate the delay of the fMRI response and the latency difference in different regions [29, 30]. Assuming that there is a slight time delay T<sup>0</sup> between the reference function and the measurement, the delay T<sup>0</sup> can be estimated as listed in Eq. (5)

$$\begin{aligned} y(t) &= a \cdot r(t - T\_0) + n(t) \\ r(t - T\_0) &\approx r(t) - T\_0 \cdot \dot{r}(t) \Rightarrow y(t) = \beta\_1 r(t) + \beta\_2 \dot{r}(t) + n(t) \\ \Rightarrow a &\approx \beta\_1, \ T\_0 \approx \beta\_2 / \beta\_1 \end{aligned} \tag{5}$$

where r tð Þ is a one-reference function and r • ð Þt is the temporal derivative of the reference function. Both are used as two basis functions in a GLM. The betaparameters β<sup>1</sup> and β<sup>2</sup> are estimated using the GLM algorithm. In case of a dualcomponent model, the derivative of only one component or the derivatives of both components are tested.

After the mixture coefficients are estimated for any combination of two (or more) different reference functions, the combination of the two-reference functions that has the minimum fitting error or a maximum correlation coefficient with regard to the original time course of each voxel is the estimate of the two components with different latencies.

To account for the relatively small microvasculature signal compared to veins at 1.5 T, a weighting factor can be used to estimate the relative fractions of micro- and macrovasculature inside a voxel from the fitted coefficients. For two components, assume is the estimate of fraction coefficient from each component in one voxel using NNLS method, and is the weighting factor for each component. Then, the percentage contribution of each component in this voxel is computed as in Eq. (6)

$$P\_1 = \sqrt{(1 + \frac{\mathcal{A}\_1}{\mathcal{A}\_2} \cdot \frac{F\_2}{F\_1})}, P\_2 = 1 - P\_1 \tag{6}$$

#### 2.4 Simulation

A 480-volume of event-related EPI was acquired on a GE 1.5 T LX system from two continuous slices (i.e., two images per volume) through the visual cortex. The stimulus was a reversing checkerboard flashing with a 2-Hz frequency for 2 s every 20 s. The pulse repetition time TR = 275 ms, effective echo time TE = 45 ms, 45° flip angle, 64 � 128 acquisition matrix, and 20 � 40 cm field of view. A total of seven

A multi-component reference function with a variable latency and a variable time separation between adjacent components was fitted to the time course of each

where y is the normalized time course of a voxel, n is fMRI noise, N is the number of component, si is the ith component, ai is the contributions or the mixture

Each vascular component is modeled by a reference function with a latency

where X(t) is the reference function to best represent BOLD response, and Ti is the latency parameter for the ith component to account for delay. Since latency is the most important and influential parameter in dynamic fitting, a dual-component

Assuming the noise in fMRI is Gaussian white noise and the components (or mixtures) can be explicitly modeled by a series of reference functions, there are several ways to estimate the mixture coefficient and the latency of each component. A non-negative least square (NNLS) solver [27] can be used to estimate the contribution coefficients of each component after normalizing both the time course and the components. At each iteration, only the column of S where the associated

<sup>þ</sup>Y, J ¼ jjAj

If the non-negative constraint is removed from the estimation, then a standard minimum norm method can be used to estimate the contribution coefficients of each component. The model falls in the general linear model (GLM) fitting problem [28]. Thus, the estimation of the coefficient and hypothesis testing for the estima-

<sup>S</sup><sup>T</sup> � <sup>Y</sup>

ð Þ <sup>i</sup>�<sup>1</sup> <sup>¼</sup> <sup>0</sup> n o

<sup>2</sup> � STS � ��<sup>1</sup> � � (4)

(3)

ST�<sup>N</sup>ð Þ¼ t; N ½ � X1ð Þ t � T<sup>1</sup> ;X2ð Þ t � T<sup>2</sup> ; ⋯;XNð Þ t � TN (2)

coefficient of si in y,T is the number of time points in the time course.

aisiðÞþt n ) Y ¼ SA þ n, t ¼ 1, ⋯T (1)

voxel within the visual cortex, as shown in Eq. (1)

model was investigated in this chapter for simplicity.

entry of A > 0 was used for least square estimation as in Eq. (3)

AGLM <sup>¼</sup> STS � ��<sup>1</sup>

AGLM � N SþY; σ<sup>n</sup>

Að Þ<sup>i</sup> NN ¼ SJ

y tðÞ¼ ∑ N i¼1

Neuroimaging - Structure, Function and Mind

events were acquired.

2.2 Model

parameter (2):

2.3 Estimation algorithm

tion can be done using Eq. (4)

54

In Eq. (2), each component comes from a reference function with certain latencies. The reference function mimicking the BOLD response is represented by the convolution of the stimuli function and the hemodynamic response function (HRF), assuming that the brain response is linear to the input (7)

$$r(t) = h(t) \* I(t), \\ I(t) = \sum\_{trial} \delta(t - T\_{trial}) \tag{7}$$

HRF is the brain response to an impulse stimulus and is modeled as the difference between two gamma functions as in Eq. (8) [31]

$$h(t; \tau\_1, \tau\_2, \delta\_1, \delta\_2) = \left(\frac{t}{\tau\_1}\right)^{\delta\_1} e^{-(\delta\_1/\tau\_1)\cdot(t-\tau\_1)} - c \cdot \left(\frac{t}{\tau\_2}\right)^{\delta\_2} e^{-(\delta\_2/\tau\_2)\cdot(t-\tau\_2)}\tag{8}$$

where τ<sup>1</sup> controls the rising time to peak, τ<sup>2</sup> controls the peak time of the undershoot, δ1, δ<sup>2</sup> determine the dispersion of the two peaks, and c controls the influence of the undershoot.

Firstly, the influences of the HRF parameters τ1, τ2, δ1, δ2, c and the reference function latency parameter T<sup>0</sup> were studied. These parameters were in the range of as listed in the study:

2.5 ICA denoise preprocessing

DOI: http://dx.doi.org/10.5772/intechopen.79222

several groups [32, 33].

in the following way (9):

XN�<sup>V</sup> <sup>¼</sup> <sup>W</sup>�<sup>1</sup>

where W�<sup>1</sup>

W�<sup>1</sup>

57

f ¼ 1=TR ¼ 3:64 Hz.

To improve the fitting using the multi-component model, spatial ICA (SICA) was implemented first to improve SNR. Temporal ICA (TICA) had also been applied to the cleaned data within a region of interest to extract the possible intrinsic temporally independent sources. TICA has also been used on functional MRI by

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI

In SICA, the assumption is that all the intrinsic spatial independent components are mixed temporally and measured at different time (which has the same meaning as "channel"). In order for spatial ICA to work, the measured fMRI EPI 2D or 3D image will be transformed to 1D vector in the same order at each time. The whole fMRI data are formulated as a 2D matrix: Xij, i ¼ 1, 2, ⋯, N; j ¼ 1, 2, ⋯, V. N is the number of EPI volumes and V is the number of voxels in each volume. Assuming SM�<sup>V</sup> are the M independent components, the independent components are mixed

> M m¼1

Xi <sup>¼</sup> Xi1, Xi2, <sup>⋯</sup>, XiV� <sup>0</sup>

In order to get a good estimation of unmixing matrix and source components, the number of samples or voxel number (V) and the number of sources (M) should satisfy <sup>V</sup>≥M<sup>∗</sup>ð Þ <sup>M</sup> <sup>þ</sup> <sup>1</sup> <sup>=</sup>2. The number of sources should not exceed the number of channels: M≤N [19]. In the ICA algorithm, the number of sources by default is set to be the number of channels (time points in case of spatial ICA and voxel number in case of temporal ICA). The source numbers are usually very large and can increase the computational complexity and lead to unstable solution [21]. One way to solve this problem is to estimate the number of sources (or model order) using

In this chapter, we used PCA to estimate the number of the sources (M) in the data based on the eigen decomposition of the covariance matrix of the data. The number of components is estimated to maintain >95% of non-zero eigenvalues [33] to contain a majority of data information. After PCA preprocessing, the data that maintain the first M largest components were used for the spatial ICA decomposition using the ICA INFORMAX software [35]. The unmixing matrix and indepen-

Three features are extracted for each independent component (IC) in order to select the artifacts components: (1) Spatial ICA map obtained by superimposing activated voxels on the anatomy for the ith IC, Si, i ¼ 1, 2, ⋯, 30. Each IC is scaled

The active voxels are selected such that j j Z ≥ 1:96 corresponds to statistical p = 0.05. (2) The associated time course of the spatial IC. Based on Eq. (9), the contribution of the ith IC to the original data is the ith column of the mixing matrix W�<sup>1</sup>

ð Þ :; i is called the associated time course for the ith IC, and it reflects the temporal pattern of this source. The correlation coefficient (CC) and the statistical P-value between the associated time course of sources and the single-shifted reference function are also calculated. (3) The power spectrum density (PSD) function for the associated time course for the ith component with sampling frequency

the probability PCA such as Bayesian information criterion (BIC) [34].

dent components are obtained as the output.

by the variance after removing mean: Zij <sup>¼</sup> Sij� mi

W�<sup>1</sup>

<sup>N</sup>�<sup>M</sup> is the mixing matrix and WN�<sup>M</sup> is called the unmixing matrix.

im � Si, i ¼ 1, 2, ⋯, N

<sup>σ</sup><sup>i</sup> , i ¼ 1, 2, ⋯, 30; j ¼ 1, 2, ⋯, 480.

(9)

ð Þ :; i .

<sup>N</sup>�<sup>M</sup> � SM�<sup>V</sup> ) Xi ¼ ∑

τ<sup>1</sup> ¼ 3:4 : 7:4, δ<sup>1</sup> ¼ 5 : 7, τ<sup>2</sup> ¼ 12, δ<sup>2</sup> ¼ 2δ1, c ¼ 0:35, T<sup>0</sup> ¼ �10 : 10 [24]. Then, the reference function with all these parameters was fitted to one time course in the activated brain. The correlation coefficient between time course and the reference function as a function of shape parameter δ<sup>1</sup> and delay parameter τ<sup>1</sup> at one latency parameter T<sup>0</sup> is used as a criterion for optimization, similar to the dictionary-based finger-printing method. Except for the latency parameter T0, all the other parameters of HRF are found to have a minor influence on the correlation coefficient, and thus, only the latency parameter is used as a variable for each reference function in this work. And HRF parameters are the same as in SPM software τ<sup>1</sup> ¼ 5:4, τ<sup>2</sup> ¼ 12, δ<sup>1</sup> ¼ 6, δ<sup>2</sup> ¼ 12, c ¼ 0:35 [28].

Secondly, a Monte-Carlo study was conducted to test the fitting algorithm and to study the influence of noise on the latency estimations. The simulated time course was a mixture of one- or two-reference functions at different latencies from a series of reference functions. The mixture coefficient Wi, i ¼ 1, 2 of each reference function (or component) had a uniform distribution of Wi � U½ � 0; 1 . A Gaussian white noise was added to the mixed time course with different SNR. The latencies of the components were estimated by different GLM and NNLS with or without derivative algorithms. The sampling step for the reference functions was dt ¼ 105 ms in the case studied based on maximal temporal resolution that fMRI could achieve. The process of adding random Gaussian noise to the mixture of one or two components with a random uniform coefficient was repeated 1000 times for each SNR. The SNRs were tested at level from 1 to 10, 20, and infinite which is noise-free. The results were obtained for a traditional one-reference function condition and a mixture of two-reference function condition.

For the simulated time course coming from one-reference function case, the tested algorithms are GLM method for one component and one derivative (i.e., two basis functions), GLM method with only one component, and NNLS method with only one component. The results show that the estimation is unbiased for both NNLS and GLM methods for all SNRs, and the standard deviation (STD) for the estimation is relatively small (less than 100 ms) for both methods at SNR larger than 3. For the GLM plus the derivative component method, the estimation error is non-zero for larger SNR. This is because the method uses the first-order derivative as an approximation, assuming that the delay is very small and the assumption is not always valid. The result is consistent with Hensen [29]. So only, the GLM and the NNLS without derivative were tested for the mixture of two components.

For the case in which the simulated time course came from two mixed reference functions, the latency of first component and separation of the two reference functions were estimated. First, only the latency of the first component was estimated and the separation of the two reference functions was initialized and fixed. Then, the separation of the two reference functions is also set as a variable. The Monte-Carlo simulation shows that both fixed and variable separations between two reference functions give a small bias in the estimation of latency as a function of SNR in case of mixture fitting. However, the NNLS estimation algorithm produces smaller bias than GLM. Also, a variable separation gives a higher STD than a fixed separation for latency estimation. Therefore, NNLS with a fixed separation is used for this work.

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI DOI: http://dx.doi.org/10.5772/intechopen.79222

#### 2.5 ICA denoise preprocessing

where τ<sup>1</sup> controls the rising time to peak, τ<sup>2</sup> controls the peak time of the undershoot, δ1, δ<sup>2</sup> determine the dispersion of the two peaks, and c controls the

Firstly, the influences of the HRF parameters τ1, τ2, δ1, δ2, c and the reference function latency parameter T<sup>0</sup> were studied. These parameters were in the range of

τ<sup>1</sup> ¼ 3:4 : 7:4, δ<sup>1</sup> ¼ 5 : 7, τ<sup>2</sup> ¼ 12, δ<sup>2</sup> ¼ 2δ1, c ¼ 0:35, T<sup>0</sup> ¼ �10 : 10 [24]. Then, the reference function with all these parameters was fitted to one time course in the activated brain. The correlation coefficient between time course and the reference function as a function of shape parameter δ<sup>1</sup> and delay parameter τ<sup>1</sup> at one latency parameter T<sup>0</sup> is used as a criterion for optimization, similar to the dictionary-based finger-printing method. Except for the latency parameter T0, all the other parameters of HRF are found to have a minor influence on the correlation coefficient, and thus, only the latency parameter is used as a variable for each reference function in

Secondly, a Monte-Carlo study was conducted to test the fitting algorithm and to study the influence of noise on the latency estimations. The simulated time course was a mixture of one- or two-reference functions at different latencies from a series of reference functions. The mixture coefficient Wi, i ¼ 1, 2 of each reference function (or component) had a uniform distribution of Wi � U½ � 0; 1 . A Gaussian white noise was added to the mixed time course with different SNR. The latencies of the components were estimated by different GLM and NNLS with or without derivative algorithms. The sampling step for the reference functions was dt ¼ 105 ms in the case studied based on maximal temporal resolution that fMRI could achieve. The process of adding random Gaussian noise to the mixture of one or two components with a random uniform coefficient was repeated 1000 times for each SNR. The SNRs were tested at level from 1 to 10, 20, and infinite which is noise-free. The results were obtained for a traditional one-reference function condition and a mix-

For the simulated time course coming from one-reference function case, the tested algorithms are GLM method for one component and one derivative (i.e., two basis functions), GLM method with only one component, and NNLS method with only one component. The results show that the estimation is unbiased for both NNLS and GLM methods for all SNRs, and the standard deviation (STD) for the estimation is relatively small (less than 100 ms) for both methods at SNR larger than 3. For the GLM plus the derivative component method, the estimation error is non-zero for larger SNR. This is because the method uses the first-order derivative as an approximation, assuming that the delay is very small and the assumption is not always valid. The result is consistent with Hensen [29]. So only, the GLM and the NNLS without derivative were tested for the mixture of two components.

For the case in which the simulated time course came from two mixed reference

functions, the latency of first component and separation of the two reference functions were estimated. First, only the latency of the first component was estimated and the separation of the two reference functions was initialized and fixed. Then, the separation of the two reference functions is also set as a variable. The Monte-Carlo simulation shows that both fixed and variable separations between two reference functions give a small bias in the estimation of latency as a function of SNR in case of mixture fitting. However, the NNLS estimation algorithm produces smaller bias than GLM. Also, a variable separation gives a higher STD than a fixed separation for latency estimation. Therefore, NNLS with a fixed separation is used

this work. And HRF parameters are the same as in SPM software

τ<sup>1</sup> ¼ 5:4, τ<sup>2</sup> ¼ 12, δ<sup>1</sup> ¼ 6, δ<sup>2</sup> ¼ 12, c ¼ 0:35 [28].

ture of two-reference function condition.

for this work.

56

influence of the undershoot.

Neuroimaging - Structure, Function and Mind

as listed in the study:

To improve the fitting using the multi-component model, spatial ICA (SICA) was implemented first to improve SNR. Temporal ICA (TICA) had also been applied to the cleaned data within a region of interest to extract the possible intrinsic temporally independent sources. TICA has also been used on functional MRI by several groups [32, 33].

In SICA, the assumption is that all the intrinsic spatial independent components are mixed temporally and measured at different time (which has the same meaning as "channel"). In order for spatial ICA to work, the measured fMRI EPI 2D or 3D image will be transformed to 1D vector in the same order at each time. The whole fMRI data are formulated as a 2D matrix: Xij, i ¼ 1, 2, ⋯, N; j ¼ 1, 2, ⋯, V. N is the number of EPI volumes and V is the number of voxels in each volume. Assuming SM�<sup>V</sup> are the M independent components, the independent components are mixed in the following way (9):

$$X\_{N \times V} = W^{-1}\_{N \times M} \cdot \mathbb{S}\_{M \times V} \Rightarrow X\_i = \sum\_{m=1}^{M} W^{-1}\_{im} \cdot \mathbb{S}\_{ii} \qquad i = \mathtt{1, 2, \cdots, N} \tag{9}$$

$$X\_i = \begin{bmatrix} X\_{i1}, X\_{i2}, \cdots, X\_{iV} \end{bmatrix}^{\prime}$$

where W�<sup>1</sup> <sup>N</sup>�<sup>M</sup> is the mixing matrix and WN�<sup>M</sup> is called the unmixing matrix.

In order to get a good estimation of unmixing matrix and source components, the number of samples or voxel number (V) and the number of sources (M) should satisfy <sup>V</sup>≥M<sup>∗</sup>ð Þ <sup>M</sup> <sup>þ</sup> <sup>1</sup> <sup>=</sup>2. The number of sources should not exceed the number of channels: M≤N [19]. In the ICA algorithm, the number of sources by default is set to be the number of channels (time points in case of spatial ICA and voxel number in case of temporal ICA). The source numbers are usually very large and can increase the computational complexity and lead to unstable solution [21]. One way to solve this problem is to estimate the number of sources (or model order) using the probability PCA such as Bayesian information criterion (BIC) [34].

In this chapter, we used PCA to estimate the number of the sources (M) in the data based on the eigen decomposition of the covariance matrix of the data. The number of components is estimated to maintain >95% of non-zero eigenvalues [33] to contain a majority of data information. After PCA preprocessing, the data that maintain the first M largest components were used for the spatial ICA decomposition using the ICA INFORMAX software [35]. The unmixing matrix and independent components are obtained as the output.

Three features are extracted for each independent component (IC) in order to select the artifacts components: (1) Spatial ICA map obtained by superimposing activated voxels on the anatomy for the ith IC, Si, i ¼ 1, 2, ⋯, 30. Each IC is scaled by the variance after removing mean: Zij <sup>¼</sup> Sij� mi <sup>σ</sup><sup>i</sup> , i ¼ 1, 2, ⋯, 30; j ¼ 1, 2, ⋯, 480. The active voxels are selected such that j j Z ≥ 1:96 corresponds to statistical p = 0.05. (2) The associated time course of the spatial IC. Based on Eq. (9), the contribution of the ith IC to the original data is the ith column of the mixing matrix W�<sup>1</sup> ð Þ :; i . W�<sup>1</sup> ð Þ :; i is called the associated time course for the ith IC, and it reflects the temporal pattern of this source. The correlation coefficient (CC) and the statistical P-value between the associated time course of sources and the single-shifted reference function are also calculated. (3) The power spectrum density (PSD) function for the associated time course for the ith component with sampling frequency f ¼ 1=TR ¼ 3:64 Hz.

To clean the data, the noise independent components are removed by setting the associated columns of the noise components in the mixing matrix to be zero. Data are reconstructed from the possible signal components as shown in Eq. (10)

$$\begin{aligned} X\_{V \times N} &= W^{-1}\_{V \times M} \cdot \mathbb{S}\_{M \times N} \Rightarrow \tilde{X}\_i = \sum\_{m=1}^{M} \tilde{W}^{-1}\_{im} \cdot \mathbb{S}\_{i\flat} \quad i = 1, 2, \cdots, V\\ \tilde{W}^{-1}(:,j) &= 0, \quad \text{if } j \in noise; \quad \tilde{W}^{-1}(:,k) = W^{-1}(:,k), \text{ otherwise} \end{aligned} \tag{10}$$

#### 3. Results and discussion

#### 3.1 Microvasculature estimation before ICA cleaning

Microvasculature estimation based on the methods described was applied to the original data and the data after ICA cleaning. The histogram of voxels was detected as a function of latency in steps of TR = 275 ms for the single component (Figure 1). The histogram was fitted by a Gaussian distribution with the estimated mean and standard deviation. Since pixels containing mostly microvasculature would have a shorter latency among all detected voxels, the time separation from the peak of the Gaussian to its baseline on the left side would be a reasonable estimate of the time separation between the micro- and macrocomponents. The peak level was 22 (number of pixels) and Gaussian baseline is chosen at 10% of peak level which was 2.2. These correspond to indexes of 20 and 12, respectively, in units of TR. Therefore, a separation of 8\*TR = 2.2 s was selected between the components of the twocomponent model.

contribution from the earlier component. These voxels are likely to contain a microvasculature component. The relative fractional contribution of these components in the 34 voxels is shown in Figure 3b. Figure 3c shows the distribution of voxels indexed with a high latency (after 15 shown in Figure 2) likely to be veins. The relative contributions of the two components in these voxels are plotted in Figure 3d. In Figure 3c, a large vein structure can be seen that may contain a mixture of two macrovasculature components. In Figure 3a, the microvasculature estimated in the V5 region (marked by circle) is in gray matter, though a couple of pixels are likely to be macrovasculature and thus contain two vascular components as shown in Figure 3b. For macrovasculature voxels estimated in Figure 3c, since there might still be two vascular components (venules and veins) with different latencies, the fractional contributions shown in Figure 3d were not equally distrib-

Results of mixture model for microvasculature estimation. (a) Voxels corresponding to indexes up to 15 in Figure 2, (b) Fractional contributions from microvasculature (blue line) and macro-vasculature(green line). (c) Voxels corresponding to indexes after 15 in Figure 2. (d) Fractional contributions from two components in

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI

DOI: http://dx.doi.org/10.5772/intechopen.79222

To further improve the mixture model, ICA is used as a preprocessing operation for denoising. PCA was used to estimate the number of the sources, and the number of components was chosen to be 30 (Figure 4) that contains ≥95% data variation and information. After PCA preprocessing, the data that maintain the first 30 largest components were used for the spatial ICA decomposition using the ICA

Figure 5 shows the features of a one-source component. The first row is the spatial map of the 15th IC. V1, V2, and V5, expected to be activated, can be seen in the spatial map. The second row is the associated time course and the averaged time courses of original data. The associated time course matches well with the averaged original time course. The correlation coefficient between the associated time course and the reference function is 0.4 with P < 0.0001. The third row is the PSD of the associated time course shown in the unit of Hz. Since the stimulus is presented every 20 s, the corresponding frequency is 1/20 s = 0.05 Hz. The peak at 0.05 Hz can be seen in the PSD; however, there are also some large peaks around 0.1 Hz and lower frequencies that may come from the alias of the physiological noise. This component is mostly likely to be task-related based on the high CC of 0.4 and a distinct peak at 0.05 Hz in PSD. Figures 6 and 7 show two examples of components

uted as in Figure 3b.

Figure 3.

the macrovasculature.

INFORMAX software.

59

3.2 Microvasculature estimation after ICA cleaning

Figure 2 shows the histogram of dual-component models using separation time = 2.2 s. The histogram is a combination of two Gaussian distributions. The latency boundary of micro- and macrovascular classes is chosen based on the separation between two classes. The vertical line at �15 shows the separation boundary (Figure 2).

Figure 3a shows the voxels (numbering 34) localized from fitting indexes 2–15 with earlier latency (latency up to 15, Figure 2) and has >50% fractional

Figure 1.

Histogram showing the number of voxels as a function of latency (each point in X-axis is 275-ms unit) for best fitting time of a one-component model.

Figure 2.

Histogram showing the number of voxels as a function of latency for best fitting time for a dual-component model.

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI DOI: http://dx.doi.org/10.5772/intechopen.79222

Figure 3.

To clean the data, the noise independent components are removed by setting the associated columns of the noise components in the mixing matrix to be zero. Data are reconstructed from the possible signal components as shown in Eq. (10)

W~ �<sup>1</sup>

Microvasculature estimation based on the methods described was applied to the original data and the data after ICA cleaning. The histogram of voxels was detected as a function of latency in steps of TR = 275 ms for the single component (Figure 1). The histogram was fitted by a Gaussian distribution with the estimated mean and standard deviation. Since pixels containing mostly microvasculature would have a shorter latency among all detected voxels, the time separation from the peak of the Gaussian to its baseline on the left side would be a reasonable estimate of the time separation between the micro- and macrocomponents. The peak level was 22 (number of pixels) and Gaussian baseline is chosen at 10% of peak level which was 2.2. These correspond to indexes of 20 and 12, respectively, in units of TR. Therefore, a separation of 8\*TR = 2.2 s was selected between the components of the two-

Figure 2 shows the histogram of dual-component models using separation time = 2.2 s. The histogram is a combination of two Gaussian distributions. The latency boundary of micro- and macrovascular classes is chosen based on the separation between two classes. The vertical line at �15 shows the separation boundary

Figure 3a shows the voxels (numbering 34) localized from fitting indexes 2–15

Histogram showing the number of voxels as a function of latency (each point in X-axis is 275-ms unit) for best

Histogram showing the number of voxels as a function of latency for best fitting time for a dual-component

with earlier latency (latency up to 15, Figure 2) and has >50% fractional

ð Þ¼ :; <sup>k</sup> <sup>W</sup>�<sup>1</sup>

im � Si, i ¼ 1, 2, ⋯, V

ð Þ :; k , otherwise

(10)

M m¼1

<sup>V</sup>�<sup>M</sup> � SM�<sup>N</sup> ) <sup>X</sup><sup>~</sup> <sup>i</sup> <sup>¼</sup> <sup>∑</sup>

ð Þ¼ :; <sup>j</sup> <sup>0</sup>, if <sup>j</sup> <sup>∈</sup> noise; <sup>W</sup><sup>~</sup> �<sup>1</sup>

Neuroimaging - Structure, Function and Mind

3.1 Microvasculature estimation before ICA cleaning

XV�<sup>N</sup> <sup>¼</sup> <sup>W</sup>�<sup>1</sup>

3. Results and discussion

W~ �<sup>1</sup>

component model.

(Figure 2).

Figure 1.

Figure 2.

model.

58

fitting time of a one-component model.

Results of mixture model for microvasculature estimation. (a) Voxels corresponding to indexes up to 15 in Figure 2, (b) Fractional contributions from microvasculature (blue line) and macro-vasculature(green line). (c) Voxels corresponding to indexes after 15 in Figure 2. (d) Fractional contributions from two components in the macrovasculature.

contribution from the earlier component. These voxels are likely to contain a microvasculature component. The relative fractional contribution of these components in the 34 voxels is shown in Figure 3b. Figure 3c shows the distribution of voxels indexed with a high latency (after 15 shown in Figure 2) likely to be veins. The relative contributions of the two components in these voxels are plotted in Figure 3d. In Figure 3c, a large vein structure can be seen that may contain a mixture of two macrovasculature components. In Figure 3a, the microvasculature estimated in the V5 region (marked by circle) is in gray matter, though a couple of pixels are likely to be macrovasculature and thus contain two vascular components as shown in Figure 3b. For macrovasculature voxels estimated in Figure 3c, since there might still be two vascular components (venules and veins) with different latencies, the fractional contributions shown in Figure 3d were not equally distributed as in Figure 3b.

#### 3.2 Microvasculature estimation after ICA cleaning

To further improve the mixture model, ICA is used as a preprocessing operation for denoising. PCA was used to estimate the number of the sources, and the number of components was chosen to be 30 (Figure 4) that contains ≥95% data variation and information. After PCA preprocessing, the data that maintain the first 30 largest components were used for the spatial ICA decomposition using the ICA INFORMAX software.

Figure 5 shows the features of a one-source component. The first row is the spatial map of the 15th IC. V1, V2, and V5, expected to be activated, can be seen in the spatial map. The second row is the associated time course and the averaged time courses of original data. The associated time course matches well with the averaged original time course. The correlation coefficient between the associated time course and the reference function is 0.4 with P < 0.0001. The third row is the PSD of the associated time course shown in the unit of Hz. Since the stimulus is presented every 20 s, the corresponding frequency is 1/20 s = 0.05 Hz. The peak at 0.05 Hz can be seen in the PSD; however, there are also some large peaks around 0.1 Hz and lower frequencies that may come from the alias of the physiological noise. This component is mostly likely to be task-related based on the high CC of 0.4 and a distinct peak at 0.05 Hz in PSD. Figures 6 and 7 show two examples of components

#### Figure 4.

SVD decomposition of fMRI data. Cutoff horizontal line was chosen to discard less than 5% data variation with the corresponding number of components at 30.

#### Figure 5.

Representative result of one component from spatial ICA that is task related. (a) Spatial map of the 15th IC. V1, V2, and V5, expected to be activated, can be seen in the spatial map. (b) Associated time course (red) and the averaged time courses of original data (blue). The associated time course matches well with the averaged original time course. The correlation coefficient between the associated time course and the reference function is 0.4. (c) Power spectrum density (PSD) of the associated time course shown in the unit of Hz. Since the stimulus is presented every 20 s, the corresponding frequency is 1/20 s = 0.05 Hz as seen with the large peak in the spectrum.

attributed to physiological noise. For instance, the source that is most likely from the heart-beating with a dominant peak in 1.2 Hz is shown in Figure 6, and the source that is from breathing and heart beating activation in the ventricles with distinct frequencies at 0.27 and 1.2 Hz as in Figure 7. Figure 8 demonstrates an example of the motion artifact component. The associated time course shows a gradual drift along time. This component is likely to be movement-based lowfrequency drift. The activations have a "ring-like" spatial distribution that is coming from head movement.

Eight noise components were identified based on the three features, and data

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI

were reconstructed by removing these components. We applied both multicomponent model and TICA to the original data and the data after ICA cleaning to the visual cortex. Dynamic mixture model was used to fit the data after ICA cleaning. The same time separation, 2.2 s, of "before ICA" was used for "after ICA"

Another noisy component from both breathing and heart beating with distinct frequencies at 0.27 (from

fitting.

61

Figure 7.

breathing) and 1.2 Hz (from heart beating).

Figure 6.

One noisy component from heart beating.

DOI: http://dx.doi.org/10.5772/intechopen.79222

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI DOI: http://dx.doi.org/10.5772/intechopen.79222

Figure 6. One noisy component from heart beating.

#### Figure 7.

attributed to physiological noise. For instance, the source that is most likely from the heart-beating with a dominant peak in 1.2 Hz is shown in Figure 6, and the source that is from breathing and heart beating activation in the ventricles with distinct frequencies at 0.27 and 1.2 Hz as in Figure 7. Figure 8 demonstrates an example of the motion artifact component. The associated time course shows a gradual drift along time. This component is likely to be movement-based lowfrequency drift. The activations have a "ring-like" spatial distribution that is coming

Representative result of one component from spatial ICA that is task related. (a) Spatial map of the 15th IC. V1, V2, and V5, expected to be activated, can be seen in the spatial map. (b) Associated time course (red) and the averaged time courses of original data (blue). The associated time course matches well with the averaged original time course. The correlation coefficient between the associated time course and the reference function is 0.4. (c) Power spectrum density (PSD) of the associated time course shown in the unit of Hz. Since the stimulus is presented every 20 s, the corresponding frequency is 1/20 s = 0.05 Hz as seen with the large peak in the

SVD decomposition of fMRI data. Cutoff horizontal line was chosen to discard less than 5% data variation with

from head movement.

Figure 4.

Figure 5.

spectrum.

60

the corresponding number of components at 30.

Neuroimaging - Structure, Function and Mind

Another noisy component from both breathing and heart beating with distinct frequencies at 0.27 (from breathing) and 1.2 Hz (from heart beating).

Eight noise components were identified based on the three features, and data were reconstructed by removing these components. We applied both multicomponent model and TICA to the original data and the data after ICA cleaning to the visual cortex. Dynamic mixture model was used to fit the data after ICA cleaning. The same time separation, 2.2 s, of "before ICA" was used for "after ICA" fitting.

Figure 8. Result of motion artifact component from spatial ICA.

#### Figure 9.

Histogram showing the number of voxels as a function of latency for best fitting time for a dual-component model after ICA cleaning.

Figure 9 shows the histogram of a dual-component model using component separation time = 2.2 s after ICA cleaning. The separation of micro- and macrovascular classes was 12. The shape of the Gaussian distribution is narrowed compared to Figure 2 before ICA. This is because ICA has removed the noisy voxels and thus the distribution is less Gaussian.

increased from 34 to 50 (50%) after ICA. The regions marked by a circle in Figure 10 identified microvasculature in V5 region on the left side which was

Correlation coefficient (CC) before ICA (blue) and after ICA (red). Average CC of all voxels improved 70%

Results of microvasculature estimation after ICA cleaning. (a) Voxels corresponding to indexes up to 13 in Figure 9. (b) Fractional contributions from micro- and macrovasculature. (c) Voxels corresponding to indexes

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI

after 13 in Figure 9. (d) Fractional contributions from two components in the macrovasculature.

nents in the macrovasculature are different with venules and veins.

3.4 Comparison microvasculature estimation with temporal ICA

ent types of temporally independent components.

For all the estimated microvasculature, the fractional contribution coefficients of two components after ICA (Figure 10b) are the same, suggesting all the voxels are in the microvasculature. The fractional contribution coefficients of two compo-

We have implemented further temporal ICA to the data after spatial ICA cleaning in the cluster that has a higher correlation (≥0.3) to the reference function. The assumption is that the concurrent active voxels may still be mixed with differ-

The number of components was set to be 10 based on the PCA of the cleaned data within the activated cluster. There is an associated spatial map for each temporal component that reflects the spatial contribution of the component. The spatial

map of each temporal IC is shown in Figure 12. Compared to the micro and macrovasculature images, temporal IC #9 and IC #1 in Figure 12 have activation patterns similar to the macrovasculature image in Figure 10c, while the spatial map

missed by the estimation before ICA.

after ICA compared to original fitting without ICA denoising.

DOI: http://dx.doi.org/10.5772/intechopen.79222

Figure 10.

Figure 11.

63

Figure 10a shows the voxels (numbering 50) localized from low latency (up to 12, Figure 4) and has >50% fractional contribution from the earlier component. These voxels are likely to contain a microvasculature component. Figure 10b shows the relative fractional contribution of these components. Figure 10c shows the distribution of voxels indexed with a high latency (after 12 in Figure 9) likely to be veins. The relative contributions of two components in these later voxels are plotted in Figure 10d.

#### 3.3 Comparison of results before and after spatial ICA

The average correlation coefficient for the fitting after ICA cleaning has increased around 70% compared to the original fitting (Figure 11). The number of voxels at an earlier latency (up to 15 in Figure 2 and up to 12 in Figure 9) also increased. The number of voxels that are most likely to be microvasculature has

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI DOI: http://dx.doi.org/10.5772/intechopen.79222

Figure 10.

Results of microvasculature estimation after ICA cleaning. (a) Voxels corresponding to indexes up to 13 in Figure 9. (b) Fractional contributions from micro- and macrovasculature. (c) Voxels corresponding to indexes after 13 in Figure 9. (d) Fractional contributions from two components in the macrovasculature.

#### Figure 11.

Figure 9 shows the histogram of a dual-component model using component

Histogram showing the number of voxels as a function of latency for best fitting time for a dual-component

macrovascular classes was 12. The shape of the Gaussian distribution is narrowed compared to Figure 2 before ICA. This is because ICA has removed the noisy voxels

Figure 10a shows the voxels (numbering 50) localized from low latency (up to 12, Figure 4) and has >50% fractional contribution from the earlier component. These voxels are likely to contain a microvasculature component. Figure 10b shows the relative fractional contribution of these components. Figure 10c shows the distribution of voxels indexed with a high latency (after 12 in Figure 9) likely to be veins. The relative contributions of two components in these later voxels are plotted

The average correlation coefficient for the fitting after ICA cleaning has increased around 70% compared to the original fitting (Figure 11). The number of voxels at an earlier latency (up to 15 in Figure 2 and up to 12 in Figure 9) also increased. The number of voxels that are most likely to be microvasculature has

separation time = 2.2 s after ICA cleaning. The separation of micro- and

and thus the distribution is less Gaussian.

Result of motion artifact component from spatial ICA.

Neuroimaging - Structure, Function and Mind

3.3 Comparison of results before and after spatial ICA

in Figure 10d.

62

Figure 8.

Figure 9.

model after ICA cleaning.

Correlation coefficient (CC) before ICA (blue) and after ICA (red). Average CC of all voxels improved 70% after ICA compared to original fitting without ICA denoising.

increased from 34 to 50 (50%) after ICA. The regions marked by a circle in Figure 10 identified microvasculature in V5 region on the left side which was missed by the estimation before ICA.

For all the estimated microvasculature, the fractional contribution coefficients of two components after ICA (Figure 10b) are the same, suggesting all the voxels are in the microvasculature. The fractional contribution coefficients of two components in the macrovasculature are different with venules and veins.

#### 3.4 Comparison microvasculature estimation with temporal ICA

We have implemented further temporal ICA to the data after spatial ICA cleaning in the cluster that has a higher correlation (≥0.3) to the reference function. The assumption is that the concurrent active voxels may still be mixed with different types of temporally independent components.

The number of components was set to be 10 based on the PCA of the cleaned data within the activated cluster. There is an associated spatial map for each temporal component that reflects the spatial contribution of the component. The spatial map of each temporal IC is shown in Figure 12. Compared to the micro and macrovasculature images, temporal IC #9 and IC #1 in Figure 12 have activation patterns similar to the macrovasculature image in Figure 10c, while the spatial map

Temporal ICA decomposition in the activated regions could overcome these problems with good spatial correspondence results between temporal ICA and mixture models. One limitation is that temporal independent assumption might not be fully

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI

In conclusion, we had used two new methods (i.e., ICA and dynamic mixture model) to improve microvasculature detection in fMRI that is closer to true neuronal activation and therefore improve the specificity of the fMRI microvasculature detection in both functional and structural ways [38]. Further integration and validation with other modalities such as EEG and PET are warranted in the near future. Further imaging of the full dynamic spatiotemporal multi-parametric functional and neurophysiological profile including BOLD microvasculature activation, couplings between BOLD and CBF/CBV, between BOLD, and oxygen extraction/

The authors thank Dr. Singh and colleagues for their help on this work.

Departments of Radiology and Biomedical Engineering, University of Southern

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

California and Columbia University, Los Angeles, CA, USA

Address all correspondence to: yongxia.zhou@yahoo.com

provided the original work is properly cited.

satisfied in fMRI data since hemodynamic responses evolve with time [29].

metabolism [39] are expected in the near future [40].

4. Conclusion

DOI: http://dx.doi.org/10.5772/intechopen.79222

Acknowledgements

Author details

Yongxia Zhou

65

Figure 12. Ten associated maps of temporal independent components (IC) identified by TICA.

of temporal IC #10 and IC #4 has similar distributions with the microvasculature image in Figure 10a.

#### 3.5 Discussion

We have described a novel multiple-component model that takes into consideration vascular mixtures in the fMRI BOLD signal and partial volume effect and developed methods to estimate the contribution of each component. Experimental studies have shown that compared to the traditional single-component model, our method achieves a better match to the original time courses of fMRI and thus reduces the fitting errors. Another advantage of the method is that it allows us to estimate microvasculature. The microvasculature is closer to the site of neuronal activation and validated with the temporal ICA method, as expected [36]. Spatial ICA has been used as a preprocessing step in the mixture model to remove noise and improve the microvasculature detection with a higher CC and more voxels with lower latencies detected. The spatial and temporal distributions of all these noisy components were consistent with the results of other studies [32, 34, 37].

We use a series of reference functions to model the brain vascular components. Compared to the classical single-component model, the multi-component model fits the measured fMRI time course with a higher correlation coefficient and also detects voxels with low latencies more efficiently. Different vascular components will have different HRF shapes. Therefore, how the brain vascular components can be modeled more accurately needs to be investigated in the future. Also, the multiple reference functions are not orthogonal to each other; some de-correlation methods can be further implemented to improve the robustness of the fitting.

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI DOI: http://dx.doi.org/10.5772/intechopen.79222

Temporal ICA decomposition in the activated regions could overcome these problems with good spatial correspondence results between temporal ICA and mixture models. One limitation is that temporal independent assumption might not be fully satisfied in fMRI data since hemodynamic responses evolve with time [29].

#### 4. Conclusion

In conclusion, we had used two new methods (i.e., ICA and dynamic mixture model) to improve microvasculature detection in fMRI that is closer to true neuronal activation and therefore improve the specificity of the fMRI microvasculature detection in both functional and structural ways [38]. Further integration and validation with other modalities such as EEG and PET are warranted in the near future. Further imaging of the full dynamic spatiotemporal multi-parametric functional and neurophysiological profile including BOLD microvasculature activation, couplings between BOLD and CBF/CBV, between BOLD, and oxygen extraction/ metabolism [39] are expected in the near future [40].

#### Acknowledgements

The authors thank Dr. Singh and colleagues for their help on this work.

### Author details

of temporal IC #10 and IC #4 has similar distributions with the microvasculature

Ten associated maps of temporal independent components (IC) identified by TICA.

We have described a novel multiple-component model that takes into consideration vascular mixtures in the fMRI BOLD signal and partial volume effect and developed methods to estimate the contribution of each component. Experimental studies have shown that compared to the traditional single-component model, our method achieves a better match to the original time courses of fMRI and thus reduces the fitting errors. Another advantage of the method is that it allows us to estimate microvasculature. The microvasculature is closer to the site of neuronal activation and validated with the temporal ICA method, as expected [36]. Spatial ICA has been used as a preprocessing step in the mixture model to remove noise and improve the microvasculature detection with a higher CC and more voxels with lower latencies detected. The spatial and temporal distributions of all these noisy

We use a series of reference functions to model the brain vascular components. Compared to the classical single-component model, the multi-component model fits the measured fMRI time course with a higher correlation coefficient and also detects voxels with low latencies more efficiently. Different vascular components will have different HRF shapes. Therefore, how the brain vascular components can be modeled more accurately needs to be investigated in the future. Also, the multiple reference functions are not orthogonal to each other; some de-correlation methods can be further implemented to improve the robustness of the fitting.

components were consistent with the results of other studies [32, 34, 37].

image in Figure 10a.

Neuroimaging - Structure, Function and Mind

3.5 Discussion

64

Figure 12.

Yongxia Zhou Departments of Radiology and Biomedical Engineering, University of Southern California and Columbia University, Los Angeles, CA, USA

Address all correspondence to: yongxia.zhou@yahoo.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### References

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[31] Glover H. Deconvolution of impulse response in event-related BOLD fMRI.

[32] Biswal BB, Ulmer JL. Blind source separation of multiple signal sources of fMRI data sets using independent component analysis. Journal of

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[34] Beckmann M, Smith SM.

Probabilistic independent component analysis for functional magnetic

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Magazine. 2002;(1):44-57

2473-2475

Application of ICA and Dynamic Mixture Model to Identify Microvasculature Activation in fMRI

15:83-97

593-606

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1706-1708

[19] McKeown MJ, Makeig S, Brown GB, Jung TB, Kindermann SS, Bell AJ, Sejnowski TJ. Analysis of fMRI data by blind separation into independent spatial components. Human Brain

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[21] Jeong J. Localization of brain alpha activity using independent component analysis in fMRI and EEG, Doctor of Philosophy Dissertation. USC; 2002

Sejnowski TJ. Independent component analysis of functional MRI: What is signal and what is noise? Current Opinion in Neurobiology. 2003;13(5):

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Component Analysis and Blind Source

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[13] Chen W, Ugurbil K. High spatial resolution functional magnetic resonance imaging at very-highmagnetic field. Topics in Magnetic Resonance Imaging. 1999;10(1):63-78

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Section 2

Functional Brain Imaging

Section 2
