**2.1 fMRI preprocessing**

The preprocessing of fMRI data is necessary since there are non-neural noises in the signal. There are openly available toolboxes to carry out preprocessing, such as Statistical Parametric Mapping (SPM), FMRIB Software Library (FSL), and Data Processing Assistant for Resting-State fMRI (DPARSF)[8]. Common preprocessing procedures begin by removing the first 10 time points to let the subject be familiar with the scanning environment. Since the scanning of fMRI data within a repetition period (2s) is done in a slice-by-slice manner, the exact collection time of the first slice and the last slice has a time difference. To correct this difference, a procedure called slice timing correction needs to be performed. Then the head motion is corrected so that each voxel corresponds to the same brain location in the scanning series.

For group analysis, the data of different subjects need to be co-registered or normalized to the Montreal Neurological Institute (MNI) standard space. The data then undergoes smoothing using a Gaussian filter with a specified full-width-halfmaximum (FWHM) value. After that, the linear trend in the signal is removed and nuisance covariates, such as white matter, cerebral spinal fluid (CSF), and global signal, are regressed out. At last, the data are filtered to keep signals within 0.01- 0.08 Hz, since signals within this frequency range are reported to reflect spontaneous neural activities.

Although numerous preprocessing steps have been developed, there is still no consensus on the standard fMRI data preprocessing pipeline. The controversy is centered on the nuisance covariates regression, especially global signal regression (GSR)[9] and white matter signal regression [10]. Other researchers tried to optimize the preprocessing across multiple outcome measures [11], for low-frequency fluctuation analysis [12] and specific patients, such as stroke patients [13]. We have also investigated how the choices of preprocessing parameters and steps influence statistical analysis results [14]. The preprocessing of fMRI data remains to be a complex but important research topic.

#### **2.2 Node definition**

The most basic node definition is the voxel in a 3D fMRI image. Each voxel within the brain can be treated as a node and the constructed voxel-based network covers the whole brain. However, since the spatial resolution of fMRI is relatively high (2mm–4mm), the number of voxels is rather large (around the magnitude of 100,000) and the constructed network requires huge computation power for further analysis. Researchers have proposed specialized methods, such as the Parallel Graph-theoretical Analysis (PAGANI) toolkit to accelerate the processing of voxel-based whole-brain networks [15].

On the other hand, the nodes of the brain network can be defined as regions in the brain. The preprocessed data of voxels within a region are averaged spatially as the signal related to this node. The region can be specified manually by drawing regions of interest (ROI). Independent component analysis (ICA) can also reveal the component region but requires specifying parameters, such as the number of components. Both methods require human intervention and depend heavily on expert knowledge.

We proposed a fuzzy node definition method in Ref. [16] for tumor-brain, named "Spatial-Neighborhood and Functional-Correlation (SNFC)" based on fuzzy connectedness. It is a self-adapting method where the network was divided into functional connection and spatial adjacency. In the SNFC method, fuzzy connectedness between two voxels acts as a measurement to decide if they belong to the same node. Each voxel in the brain could be mapped into two feature spaces—structure feature space *S* and correlation feature space *C* . Let *i k*, *s* represent the spatial relationship between voxel *<sup>i</sup> v* and voxel *<sup>k</sup> v* , acting as a judgment of the neighboring relationship. *i k*, *c* is the correlation coefficient between the BOLD signal of *<sup>i</sup> v* and *<sup>k</sup> v* . The features of structural space *S* guarantee the principle of the spatial neighborhood and the features of correlation space *C* ensure the principle of consistency. Fuzzy connectedness between two voxels could be defined as the following:

$$F\mathbf{C}\_{\iota,k} = \mathfrak{s}\_{\iota,k} \cdot \mathfrak{c}\_{\iota,k} \tag{1}$$

If *FC T i k*, > , then *<sup>i</sup> v* and *<sup>k</sup> v* belong to the same node, where *T* is the correlation threshold determining whether the correlation of two voxels is strong enough to be in the same node.

The nodes can also be defined using regions in the brain atlas to avoid the subjective error caused by human intervention and enable automatic processing for large cohorts of data. The most known brain atlas is the Brodmann atlas, created by the German anatomist Korbinian Brodmann based on cytoarchitecture [17]. Another popular brain parcellation is the Automated Anatomical Labeling (AAL) atlas [18]. The AAL atlas focuses on brain structure and the finer partition of certain cortices was proposed in AAL2 [19] and AAL3 [20]. Apart from structure, the brain atlas derived from diffusion and functional data is getting more attention. The Brainnetome Atlas was proposed based on DTI data with fine-grained parcellation [21]. Researchers also developed functional atlas, such as the Atlas of Intrinsic Connectivity of Homotopic Areas (AICHA) that considered the homolog of regions in both hemispheres [22]. The above-defined network is called a region-based wholebrain network. We can also construct networks within a region. In this scenario, the voxels are defined as nodes, and the network only consists of voxels within a region. The constructed network is called a voxel-based local network, representing

*Resting-State Brain Network Analysis Methods and Applications DOI: http://dx.doi.org/10.5772/intechopen.104827*

the topology within certain regions. We proposed a multilevel brain network joint analysis method on voxel-based whole-brain networks, voxel-based local networks as well as region-based whole-brain networks (**Figure 2**) [23].

Node definition has a fundamental influence on the topology of the brain network. Different atlas parcels the cerebrum and cerebellum based on different information, and it plays a key role in linking physiological regions to abstract brain network nodes. However, similar to the preprocessing of fMRI data, there is no gold standard for the node definition. Several researches have been carried out to investigate the effect of node definition on network analysis [24], resting-state networks [25], and the topology of both functional networks [26] and structural networks [27]. It is still an open question and needs more thorough research.

## **2.3 Static and dynamic functional connectivity**

Edges in brain networks are represented by the connectivity between nodes. One of the most common connectivity measures is functional connectivity (FC). In 1995, Biswal et al firstly reported the correlation of intrinsic low-frequency BOLD signal fluctuation under resting-state and since then, multiple efforts have been devoted to FC analysis [1, 3]. Functional connectivity is commonly defined as the Pearson correlation between the BOLD signal of spatially distant regions. In recent years, researchers realized that FC ignores the dynamics of neural activity and developed dynamic functional connectivity (DFC) or Chronnectome [28–30]. The research on DFC is becoming popular and has attracted lots of attention.

Technically speaking, FC or static functional connectivity (SFC) is calculated using the whole time series, whereas DFC utilizes a sliding time window and the correlation of signals within the window is calculated. The window then moves from the beginning of the BOLD signal to the end, with a pre-defined step size. As a result, the connectivity shows dynamic fluctuations as the window slides, and each scanning session is associated with a series of brain networks, or a dynamic brain network. In

**Figure 2.** *Construction of multilevel functional brain networks.*

contrast, there is only one static network related to the scanning session. The network is usually represented by a graph adjacency matrix, which is a square symmetric matrix and the (*i j*, ) value equals the connection of node *i* to node *j* . For a dynamic network, there is a time axis along with the adjacency matrix.

There are two major parameters regarding DFC calculation—the window length and the sliding step size. With a longer window length, the dynamics of neural activity might be averaged out while a shorter window length can capture transient signal changes. The step size controls the temporal resolution of DFC. Normally it is specified as several TRs. We investigated the optimal window width by using the smallworld property as criteria [31]. Node degree distribution has exponential truncated power-law in the small-world network, and the normal human brain network shows a strong small-world property. The reasonable window width range was verified on both SNFC-based and voxel-based whole-brain networks. Results show that the smallest window width is 200 seconds and 260 seconds for normal subjects and brain tumor patients, respectively. Leonardi et al also studied the theory between window length and filter cut-off frequency during preprocessing [32]. Apart from the two window parameters, the shape of the sliding window is another concern. The rectangular window is the simplest solution, but other choices such as tapered window exist. Mokhtari et al also proposed a modulated rectangular (mRect) window to reduce spectral modulations [33].

We also proposed a dynamic network analysis method for enlarging the training samples required by an unsupervised learning classification algorithm [34], such as a classical backpropagation neural network classifier containing a hidden layer. It reached the optimal accuracy of 100% for classifying glioma patients and normal subjects.

Despite controversies, DFC has been used to investigate diseases, such as schizophrenia [35], post-traumatic stress disorder (PTSD) [36], Parkinson's Disease [37], and autism [38]. It has also been applied to lifespan studies [39] and cognitive research [40]. From either a methodological or application view, the research on DFC is still insufficient.

## **2.4 Directed connectivity**

As the definition implies, both SFC and DFC contain no directional information. Effective connectivity (EC) can measure the directional influence of one region toward another area by calculating the causal relationships between time series. Commonly adopted EC estimation methods are structural equation modeling (SEM) [41], dynamic causal modeling (DCM) [42], and Granger causality analysis (GCA) [43, 44]. The computation cost becomes unacceptable for SEM and DCM as the number of nodes increases [43]. Several amendments have been proposed to reduce the computation requirement of DCM recently [45, 46], but the model complexity is still challenging for clinical applications. We proposed a method based on convergent cross-mapping (CCM) that can reflect the interactions between regions in a dynamic, nonlinear, and deterministic way, which is not covered by GCA [47]. The method overview, together with the extended network-based statistic, is shown in **Figure 3**.

CCM was originally developed to detect causality in complex ecosystems [48]. It acts as a complement to GCA as CCM assumes the system to be deterministic and dynamical, while GCA works for a stochastic system and requires separability. In GCA, if removing X decreases the predictability of Y, it can be deduced that X causes

#### **Figure 3.**

*CCM-based directed connectivity estimation and extended network-based statistic method.*

Y, and in a brain network scenario, there is a directed connection from X to Y. On the other hand, in deterministic dynamic systems where CCM was developed, we can measure how well Y can estimate X to determine the causal relationship from X to Y, which then determines the directed connectivity strength from X to Y. The procedure of estimating X using Y is called cross-mapping. CCM is also applicable under situations where separability is not guaranteed. GCA, on the other hand, may produce erroneous results [49]. As for the brain, it is a dynamic system whose functional organization is poorly understood [50]. Utilizing CCM to estimate directed connectivity between regions could facilitate the investigation of brain activity as well as enable novel clinical applications.
