**5. Probabilistic atlases**

Probabilistic atlases depict the normal range in size, shape, and topographical location of individual cortical or subcortical structures from many subjects. The rationale behind the idea is that the neuroanatomy of a select single subject's brain cannot cover the pronounced

 *Cytoarchitectonic 3D contours of red nucleus (NR or RN, in red), subthalamic nucleus (STh in gray), and substantia nigra (in white) merged to the MRI from the same brain. PC in this case is the abbreviation for pedunculi cerebri. The question concerning the hypointense region in MRI antero-lateral to red nucleus is* 

By combining both technologies, fundamental questions on post-mortem delay, appropriate fixation and neuroimagaing/neuropathological correlations could be addressed (Grinberg

The salient feature of this methodological approach to an atlas on the human basal ganglia is the post-mortem in situ MRI-scanning of the brain and the histological processing of the brain to generate serial 400 µm thick Nissl-stained sections. This protocol greatly facilitates cytoarchitectonic delineation of cortical and subcortical grey matter, compensation for shrinkage, and deformation and co-registration of high-resolution Nissl-stained sections

Compelling results of match (red nucleus) and mismatch (subthalamic nucleus) of Nissl-

The images are imported to software tools and warped to the original MRI scans, following nonlinear and linear correction protocols developed by the team and yet to be published. Three-dimensional cytoarchitectonic contours can then be compared to the original scans.All the illustrations presented in this chapter were made using our own material and techniques.

Probabilistic atlases depict the normal range in size, shape, and topographical location of individual cortical or subcortical structures from many subjects. The rationale behind the idea is that the neuroanatomy of a select single subject's brain cannot cover the pronounced

*presently being studied in detail, applying this method to additional cases* 

stained sections with the MRI-boundaries are depicted in Fig. 5.

Fig. 5. Cytoarchitecture x MRI

with MRI scans.

**5. Probabilistic atlases** 

et al., 2008, 2009; Teipel et al. 2008).

anatomic variability. Consequently, errors in diagnosis and neurosurgical interventions impend on generalizing interrelationships of a single brain. Probabilistic maps can include features such as cytoarchitecture, chemoarchitecture, blood flow distributions, metabolic rates, behavioral and pathologic correlates, electrophysiologic tissue characteristics and others (Mazziota, 1995). Some previously described atlases list probabilistic features (Andrew et al., 1969; Afshar et al., 1978; Krauth et al*.,* 2010). In this paragraph, special focus will be on probabilistic atlases not classified in previous sections.

#### **5.1 A probabilistic atlas and reference system for the human brain: International consortium for Brain Mapping (ICBM)(Mazziotta et al., 2001)**

Through an International Consortium for Brain Mapping (ICBM) a data set that includes 7000 subjects between the ages of eighteen and ninety years and including 342 mono- and dizygotic twins has been collected.

Data on each subject include detailed demographic, clinical, behavioral, and imaging information. DNA has been collected for genotyping from 5800 subjects. A component of the program uses post-mortem tissue to determine the probabilistic distribution of microscopic cyto- and chemoarchitectural regions in the human brain. This can be combined with macroscopic information about structure and function derived from subjects *in vivo*, providing the an opportunity to gain meaningful insights into the concordance or discordance in micro- and macroscopic structure and function (Mazziota et al., 2001).

#### **5.2 A probabilistic functional atlas of the human subthalamic nucleus (Nowinski et al., 2004)**

The concept of probabilistic functional atlas (PFA) was introduced by Nowinski. His idea is to overcome limitations of the current electronic stereotactic brain atlases, such as anatomical nature, spatial sparseness, inconsistency, and lack of population information. The PFA is an algorithm that converts the coordinates of the neurologically most effective contacts into probabilistic functional maps, taking into account the geometry of a stimulating electrode and the patient's anatomy. Nowinski published the use of this algorithm to build an atlas of the subthalamic nucleus and of the ventrointermediate thalamic nucleus (VIM) (Nowinski et al., 2004, 2006).

This paper introduces a method for generation and validation of a probabilistic functional brain atlas of subcortical structures from electrophysiological and neuroimaging data. The method contains three major steps: (1) acquisition of pre-, intra-, and postoperative multimodal data; (2) selection of an accurate data set for atlas generation; and (3) generation of the atlas from the selected data set. The method is here applied to construct the probabilistic functional atlas of the human subthalamic nucleus from data collected during surgical treatment of 184 patients with Parkinson's disease. It is based on preoperative X-ray ventriculography imaging, intraoperative electrophysiological measurements and X-ray imaging, and postoperative neurological assessment. This method can be used to build PFAs from other regions, as the next work from 2006 did.

#### **5.3 A probabilistic functional atlas of the VIM nucleus constructed from pre-, intraand postoperative electrophysiological and neuroimaging data acquired during the surgical treatment of Parkinson's disease patients (Nowinski et al, 2006)**

This work addresses construction of the PFA for the ventrointermediate nucleus (PFA-VIM). The PFA-VIM is constructed from pre-, intra- and postoperative electrophysiological and

Review of Printed and Electronic Stereotactic Atlases of the Human Brain 165

(Fischer et al., 1973; Kato, 1939; Lagerlöf & Torgersruud, 1934; Stevenson, 1923; Treff & Kraus, 1960; Tutsch-Bauer, 1979 as cited in Quester & Schröder, 1997). This "positive formalin effect" (Schremmer, 1967 as cited in Quester & Schröder, 1997) is higher for lower formalin concentrations (Flatau, 1897; Treff and Kraus, 1960 as cited in Quester & Schröder, 1997).The results from Quester and Schröder (1997) confirm that local shrinkage and correction factors have to be determined for each area of interest owing to the heterogeneous constitution of the

Embedding, sectioning, staining and mounting are likewise sources of tissue distortion. Each of these factors deforms the histological slice either in a homogeneous (linear distortion) or heterogeneous (nonlinear distortion) fashion. For example, the gray and the white matter have a differential staining shrinkage (Simmons & Swanson 2009; Kretschmann et al., 1982). In Schaltenbrand's study from 1977 (Schaltenbrand &Wahren, 1977) the average shrinkage rate for different applied methods was variable. Embedding in paraffin led to an average shrinkage of 30%, while celloidin shrank the tissue in 20%, wax in 5% and freezing in 1%. For this reason they chose freezing as method, but they noticed that when freezing is used there is no embedding material to hold the tissue together, causing

In order to correct all these confounding factors, it is mandatory to know the precise volume and shape of the tissue prior to processing. Spiegel and Wycis used fiducial markers to guide them. Many years later, the fiducial concept was resumed by Yelnik et al. (2007), but with the great technological improvement of having the specimen scanned in a MRI scanner before the brain was removed. High-resolution post-mortem imaging provides important information about the volume and form of the brain before being processed (Pfefferbaum et.al, 2004) and it can be used to correct and align histological slices. In 1952 these corrections were performed by photographic manipulation, and within the following years this was the standard procedure. In 1987 Yoshida (Yoshida, 1987) focused on extracting a three-dimensional volume from the great histological slices obtained by Schaltenbrand and Bailey (Schaltenbrand & Bailey, 1959). In the following years, other authors created threedimensional atlases based on the most-consulted printed atlases, using computational technology (Nowinski et al.,1997; St-Jean et al.,1998; Nowinski & Belov, 2003; Ganser et al., 2004; Carballo-Barreda et al., 2007). However, some inaccuracies on the original atlases led to great 3D inconsistencies (Nieman et al., 1994; Nowinski et al., 2006a, 2006b).The orthogonal plates from the Talairach & Tournoux atlas are not consistent and as a result a given point in the stereotactic space may have up to three different labels. Another example is that 3D structures reconstructed from the Schaltenbrand and Wahren atlas from 1977 are often distorted and sometimes have unrealistic shapes (Nowinski et al., 1997). To overcome this, some techniques were developed. Nowinski in 1997 (Nowinski et al., 1997) opted to correct by manual correction of rotation and overlay-plate mis-registrations; however, the inherent inconsistencies from the original templates could not be corrected. St-Jean in 1998 (St-Jean et al., 1998) addressed the problem first by performing an interpolation of the 2D contours using Hermite polynomials to achieve a 3D representation of the structures. The second step was registering the atlas volume to an MRI reference volume, the Colin27 (average of 27 scans from the same subject). This was made by identifying 250 homologous landmarks at the atlas and at the MRI and then applying the Brookstein thin-plate spline approach to warp them. As a result, the Colin27 was a labeled 3D volume based on the Schaltenbrand & Wahren atlas and could be warped to a given patient MRI with better accuracy. In 2003, Nowinski (Nowinski & Belov, 2003) added structures to the original templates to improve 3D consistency, and developed algorithms to reformat the atlas to the

parts to become dislodged and float around, especially those close to the surface.

individual cerebral structures.

neuroimaging data acquired during the surgical treatment of Parkinson's disease patients. The data contains the positions of the chronically implanted electrodes and their best contacts. For each patient, the intercommissural distance, height of the thalamus, and width of the third ventricle were measured. An algorithm was developed to convert these data into the PFA-VIM, and to present them on axial, coronal, and sagittal planes and in 3D. The PFA-VIM gives a spatial distribution of the best contacts, and its probability is proportional to best contact concentration in a given location. The region with the highest probability corresponds to the best target. The authors content that the PFA-VIM atlas overcomes several limitations of the current anatomical atlases, and can improve targeting of thalamotomies and thalamic stimulations.

#### **6. Discussion**

Inserting electrodes and needles without direct visual control into a hermetically closed space, filled with complex and vital structures, sounds at the first sight at least dangerous. Stereotactic interventions allow a tiny margin of error, since coagulation of the wrong nucleus or finding a big vessel inadvertently with a small opening on the skull may result in immediate death or irreparable neurological damage. Mechanical devices were developed (Horsley & Clarke, 1908) to give the neurosurgeons the precision that their hands will never achieve. A version of the stereotaxic apparatus created by Horsley and Clarke was adapted by Spiegel and Wycsis to perform such procedures in humans. At that time, they realized that safe intracerebral navigation with minor side effects necessitates a precise brain map. In 1952 these authors published the first stereotactic atlas of the human brain, objecting that functional stereotactic neurosurgery ''requires an exact preoperative calculation of the electrode position, and such a calculation depends on two conditions: (1) determination of a reference point by means of an X-ray picture taken under definite standard conditions, and (2) an exact knowledge of the position of the area to be destroyed in relation to the reference point. Thus . . . a stereotaxic atlas of the human brain is presented" (Spiegel &Wycis, 1952).Today, highresolution images from the brain are possible; however, some important target regions are still hidden, and others are so far not subject to a precise morpho-functional delineation.

#### **6.1 Correcting tissue processing-induced errors**

The rationale for a stereotactic atlas is to unravel the position of certain brain regions that we cannot directly see with the current image technologies from the patient's cerebrum. In 1952, Spiegel and Wycis had to project their atlas into an X-ray picture. Today, we can count on much more refined images of the human central nervous system, like 3.0T MRI. As we will discuss later, even this detailed picture is not enough to show all the structures we are aiming to reach. Histological methods still supply the standard tools for identification of deep brain structures, be they neurons or fiber tracts. Conventional histology is applied to thin slices of brain tissue obtained from a diseased subject. The tissue is most often submitted to a formalin fixation (Yelnik et al., 2009).The processing of the nervous system leads to transformations in its size and form since the moment of death. Formalin fixation and other chemical reactions cause several volumetric changes in the nervous tissue. The changes in cerebral tissue due to fixation have been studied since the late 1960s (Bauchot, 1967) and the reliability of dimensions of formalin-fixed brains as well (Small & Peterson, 1982). The effects of formaldehyde on the human cerebrum have been described to result in a maximum increase in weight and volume between the first and fifth day, which decreases during the following weeks and months

neuroimaging data acquired during the surgical treatment of Parkinson's disease patients. The data contains the positions of the chronically implanted electrodes and their best contacts. For each patient, the intercommissural distance, height of the thalamus, and width of the third ventricle were measured. An algorithm was developed to convert these data into the PFA-VIM, and to present them on axial, coronal, and sagittal planes and in 3D. The PFA-VIM gives a spatial distribution of the best contacts, and its probability is proportional to best contact concentration in a given location. The region with the highest probability corresponds to the best target. The authors content that the PFA-VIM atlas overcomes several limitations of the current anatomical atlases, and can improve targeting of

Inserting electrodes and needles without direct visual control into a hermetically closed space, filled with complex and vital structures, sounds at the first sight at least dangerous. Stereotactic interventions allow a tiny margin of error, since coagulation of the wrong nucleus or finding a big vessel inadvertently with a small opening on the skull may result in immediate death or irreparable neurological damage. Mechanical devices were developed (Horsley & Clarke, 1908) to give the neurosurgeons the precision that their hands will never achieve. A version of the stereotaxic apparatus created by Horsley and Clarke was adapted by Spiegel and Wycsis to perform such procedures in humans. At that time, they realized that safe intracerebral navigation with minor side effects necessitates a precise brain map. In 1952 these authors published the first stereotactic atlas of the human brain, objecting that functional stereotactic neurosurgery ''requires an exact preoperative calculation of the electrode position, and such a calculation depends on two conditions: (1) determination of a reference point by means of an X-ray picture taken under definite standard conditions, and (2) an exact knowledge of the position of the area to be destroyed in relation to the reference point. Thus . . . a stereotaxic atlas of the human brain is presented" (Spiegel &Wycis, 1952).Today, highresolution images from the brain are possible; however, some important target regions are still

hidden, and others are so far not subject to a precise morpho-functional delineation.

The rationale for a stereotactic atlas is to unravel the position of certain brain regions that we cannot directly see with the current image technologies from the patient's cerebrum. In 1952, Spiegel and Wycis had to project their atlas into an X-ray picture. Today, we can count on much more refined images of the human central nervous system, like 3.0T MRI. As we will discuss later, even this detailed picture is not enough to show all the structures we are aiming to reach. Histological methods still supply the standard tools for identification of deep brain structures, be they neurons or fiber tracts. Conventional histology is applied to thin slices of brain tissue obtained from a diseased subject. The tissue is most often submitted to a formalin fixation (Yelnik et al., 2009).The processing of the nervous system leads to transformations in its size and form since the moment of death. Formalin fixation and other chemical reactions cause several volumetric changes in the nervous tissue. The changes in cerebral tissue due to fixation have been studied since the late 1960s (Bauchot, 1967) and the reliability of dimensions of formalin-fixed brains as well (Small & Peterson, 1982). The effects of formaldehyde on the human cerebrum have been described to result in a maximum increase in weight and volume between the first and fifth day, which decreases during the following weeks and months

**6.1 Correcting tissue processing-induced errors** 

thalamotomies and thalamic stimulations.

**6. Discussion** 

(Fischer et al., 1973; Kato, 1939; Lagerlöf & Torgersruud, 1934; Stevenson, 1923; Treff & Kraus, 1960; Tutsch-Bauer, 1979 as cited in Quester & Schröder, 1997). This "positive formalin effect" (Schremmer, 1967 as cited in Quester & Schröder, 1997) is higher for lower formalin concentrations (Flatau, 1897; Treff and Kraus, 1960 as cited in Quester & Schröder, 1997).The results from Quester and Schröder (1997) confirm that local shrinkage and correction factors have to be determined for each area of interest owing to the heterogeneous constitution of the individual cerebral structures.

Embedding, sectioning, staining and mounting are likewise sources of tissue distortion. Each of these factors deforms the histological slice either in a homogeneous (linear distortion) or heterogeneous (nonlinear distortion) fashion. For example, the gray and the white matter have a differential staining shrinkage (Simmons & Swanson 2009; Kretschmann et al., 1982). In Schaltenbrand's study from 1977 (Schaltenbrand &Wahren, 1977) the average shrinkage rate for different applied methods was variable. Embedding in paraffin led to an average shrinkage of 30%, while celloidin shrank the tissue in 20%, wax in 5% and freezing in 1%. For this reason they chose freezing as method, but they noticed that when freezing is used there is no embedding material to hold the tissue together, causing parts to become dislodged and float around, especially those close to the surface.

In order to correct all these confounding factors, it is mandatory to know the precise volume and shape of the tissue prior to processing. Spiegel and Wycis used fiducial markers to guide them. Many years later, the fiducial concept was resumed by Yelnik et al. (2007), but with the great technological improvement of having the specimen scanned in a MRI scanner before the brain was removed. High-resolution post-mortem imaging provides important information about the volume and form of the brain before being processed (Pfefferbaum et.al, 2004) and it can be used to correct and align histological slices. In 1952 these corrections were performed by photographic manipulation, and within the following years this was the standard procedure. In 1987 Yoshida (Yoshida, 1987) focused on extracting a three-dimensional volume from the great histological slices obtained by Schaltenbrand and Bailey (Schaltenbrand & Bailey, 1959). In the following years, other authors created threedimensional atlases based on the most-consulted printed atlases, using computational technology (Nowinski et al.,1997; St-Jean et al.,1998; Nowinski & Belov, 2003; Ganser et al., 2004; Carballo-Barreda et al., 2007). However, some inaccuracies on the original atlases led to great 3D inconsistencies (Nieman et al., 1994; Nowinski et al., 2006a, 2006b).The orthogonal plates from the Talairach & Tournoux atlas are not consistent and as a result a given point in the stereotactic space may have up to three different labels. Another example is that 3D structures reconstructed from the Schaltenbrand and Wahren atlas from 1977 are often distorted and sometimes have unrealistic shapes (Nowinski et al., 1997). To overcome this, some techniques were developed. Nowinski in 1997 (Nowinski et al., 1997) opted to correct by manual correction of rotation and overlay-plate mis-registrations; however, the inherent inconsistencies from the original templates could not be corrected. St-Jean in 1998 (St-Jean et al., 1998) addressed the problem first by performing an interpolation of the 2D contours using Hermite polynomials to achieve a 3D representation of the structures. The second step was registering the atlas volume to an MRI reference volume, the Colin27 (average of 27 scans from the same subject). This was made by identifying 250 homologous landmarks at the atlas and at the MRI and then applying the Brookstein thin-plate spline approach to warp them. As a result, the Colin27 was a labeled 3D volume based on the Schaltenbrand & Wahren atlas and could be warped to a given patient MRI with better accuracy. In 2003, Nowinski (Nowinski & Belov, 2003) added structures to the original templates to improve 3D consistency, and developed algorithms to reformat the atlas to the

Review of Printed and Electronic Stereotactic Atlases of the Human Brain 167

This system was not really easy to employ, so they and others have developed simpler and more useful ones. Talairach could prove a good and consistent relationship between the AC-PC line (and its derivative planes) with the deep brain nuclei (Talairach et al., 1957). This would change the standard for intracerebral localization. In their 1988 work Talairach & Tournoux present the proportional grid system, which permits the transformation of the

These deformations can be performed using different strategies, as landmark-based

The most widely used system to adapt a brain atlas to the individual anatomy of a living subject is the proportional system of Talairach. It relies primarily on the AC-PC distance, i.e., the length between the anterior and posterior commissural points, well-identifiable on a ventriculography or a mid-sagittal section of a MRI acquisition. The user has just to measure the AC-PC distance in the living brain and to adapt the antero-posterior length of the atlas to that of the brain. The proportional system of Talairach is a reliable system, although it is inhomogeneous since the adaptation along the antero-posterior dimension is based upon two deep brain ventricular landmarks, whereas adaptation along the medio-lateral and infero superior dimensions depends on the overall size of the cerebral cortex. This is due to the fact that with ventriculography, internal landmarks are less clear along these dimensions the height of the

deformation methods or automatic deformations based on registration algorithms.

thalamus and width of the third ventricle are the best possible landmarks (Yelnik, 2009).

important, as it directly influences the quality of the atlas-to-patient result.

data, performing a Talairach transformation.

**6.3 Do we need new atlases?** 

An automatic registration algorithm is based on the comparison of features (grey-level values, points, lines, graphs, etc.) present in the two images to be registered. The algorithm is defined by three main characteristics: the similarity measure, the space of allowed deformations (the number of degrees-of-freedom (DoF) of the deformation, e.g., 6 DoF for a 3D rigid transform), and the optimization method that is used. Deformations can be very constrained (limited number of DoF), e.g., linear scaling (7 DoF) or not, like elastic, fluid, or even free-form deformations. These last types of deformations are often referred to as morphing or warping transforms. The choice of the most adequate deformation type is

Chakravarty, in 2009, has studied and compared the "atlas to patient warping techniques"(Chakravarty et al., 2009) describing and comparing the linear, piece-wise linear and nonlinear techniques. These are automatic developed algorithms, although in the piecewise technique, twelve different landmarks must be identified on both atlas and patient

Chakravarty resumes the most typically used methods to warp the atlas to patient MRI data in two. The first is matching the anatomical structures directly from the atlas to the same structures seen in pre-operative scans (Ganser et al., 2004; Nowinski et al., 2000; Xu & Nowinski, 2001 as cited in Chakravarty et al., 2009). The second method starts with a set of anatomical atlas contours, pre-aligned to an MRI template. A transformation is then estimated between the template MRI and patient's MRI. Once this template-to patient transformation is estimated, the transformation is then applied to the anatomical atlas contours, thus customizing it to patient's anatomy (Bardinet et al., 2005; Chakravarty et al., 2005; D'Haese et al., 2005; Sanchez Castro et al., 2006; Yelnik et al., 2007as cited in Chakravarty et al., 2009).

Currently, magnetic resonance imaging is the method of choice for anatomic delineation of the brain. Its noninvasive nature allied to the possibility of unlimited repetition provides the

models to fit individual variability.

intercommissural plane. In 2004, Ganser presented an algorithm to align and reconstruct three-dimensionally the Talairach and Tournoux atlas (Ganser et al., 2004). The authors therefore used the coronal plates and improved the spatial resolution by interpolating additional cross-sections between each pair of adjacent original plates. After processing the images with Delauney tetrahedrization of the object using the Nuages algorithm, smoothing the shapes by applying a spatial low pass convolution filter, extracting the surface representation of the object with the marching cubes algorithm (Lorensen and Cline, 1987 as cited in Ganser et al., 2004), and reducing the number of vertices by applying the polygon reduction algorithm proposed by Melax (Melax, 1998 as cited in Ganser et al., 2004), they obtained a better 3D surface from the Talairach and Tournoux atlas. The lateral symmetry of the brain gives rise to a high redundancy in brain cross-sections, for which reason Talairach and Tournoux drew only one hemisphere in detail. They exploited this symmetry for further reduction of data as well: They have only processed the right hemisphere of the atlas and mirrored it at the midsagittal plane to the left side.

Even with all the mathematical treatment and computation of the images, the 3D atlases based on the classical 2D atlases did not fully satisfy the functional neurosurgeon's needs. Therefore, three groups started building three-dimensional atlases based on own histological preparations, so they could cut and prepare the slices using modern technique.

Even with new methods, the slices continue to suffer linear and nonlinear transformations by the fixation and processing techniques. The Canadian group (Chakravarty et al., 2006) used a previously presented nonlinear transforming algorithm (ANIMAL-Automated Nonlinear Image Matching and Anatomical Labeling) to register and align slice-to-slice together to build a contiguous 3D histological volume. The French group (Yelnik et al., 2007) used MRI scans from the same subject and slice-to-slice alignment (crioblock corregistered to cryosections, Nissl, immunostained, T1 and T2 MRI images) to build the coherent volume. The corresgistration was made with software tools (TTS, YAv++ and BALADIN) through an intensity-based block-matching approach. The Swiss group (Krauth et al., 2010) calculated the distortion index of the tissue by measuring the ICL distance in MRI *in vivo*  and *in vitro,* and comparing it with the ICL distance from the processed tissue. They extrapolated the results to the stacks in which no MRI was performed.

In fact, the use of MRI scans as parameter to align and correct tissue processing linear and nonlinear transformations is the gold standard at the moment; however, the methods so far used to readapt the histological slices into their original volume and form can be further developed to allow exact correlations between histology, immunostaining, and image.

The next challenging part of the process is how to adapt this histological 3D coherent volume obtained to a given patient.

#### **6.2 Warping the atlas to the patient**

As soon as we have consistent, validated, three-dimensional surfaces, we have to fit them into the patient's brain. Therefore, reliable (and visible in both atlas and patient image) reference points are needed to transform the atlas into the living brain ( 3 '3 transform). In the early 1950s, pneumoencephalography and ventriculography permitted the visualization of some intraventricular landmarks as the pineal gland calcification, habenular calcification, and ventricular landmarks (AC and PC). Based on this, Spiegel and Wyics developed the first intracerebral coordinate system used in their atlas. An imaginary line connecting the center of the PC with the pontomedullary sulcus at the posterior border of the pons (PO) defined the CP-PO line.

intercommissural plane. In 2004, Ganser presented an algorithm to align and reconstruct three-dimensionally the Talairach and Tournoux atlas (Ganser et al., 2004). The authors therefore used the coronal plates and improved the spatial resolution by interpolating additional cross-sections between each pair of adjacent original plates. After processing the images with Delauney tetrahedrization of the object using the Nuages algorithm, smoothing the shapes by applying a spatial low pass convolution filter, extracting the surface representation of the object with the marching cubes algorithm (Lorensen and Cline, 1987 as cited in Ganser et al., 2004), and reducing the number of vertices by applying the polygon reduction algorithm proposed by Melax (Melax, 1998 as cited in Ganser et al., 2004), they obtained a better 3D surface from the Talairach and Tournoux atlas. The lateral symmetry of the brain gives rise to a high redundancy in brain cross-sections, for which reason Talairach and Tournoux drew only one hemisphere in detail. They exploited this symmetry for further reduction of data as well: They have only processed the right hemisphere of the atlas and

Even with all the mathematical treatment and computation of the images, the 3D atlases based on the classical 2D atlases did not fully satisfy the functional neurosurgeon's needs. Therefore, three groups started building three-dimensional atlases based on own histological preparations, so they could cut and prepare the slices using modern technique. Even with new methods, the slices continue to suffer linear and nonlinear transformations by the fixation and processing techniques. The Canadian group (Chakravarty et al., 2006) used a previously presented nonlinear transforming algorithm (ANIMAL-Automated Nonlinear Image Matching and Anatomical Labeling) to register and align slice-to-slice together to build a contiguous 3D histological volume. The French group (Yelnik et al., 2007) used MRI scans from the same subject and slice-to-slice alignment (crioblock corregistered to cryosections, Nissl, immunostained, T1 and T2 MRI images) to build the coherent volume. The corresgistration was made with software tools (TTS, YAv++ and BALADIN) through an intensity-based block-matching approach. The Swiss group (Krauth et al., 2010) calculated the distortion index of the tissue by measuring the ICL distance in MRI *in vivo*  and *in vitro,* and comparing it with the ICL distance from the processed tissue. They

In fact, the use of MRI scans as parameter to align and correct tissue processing linear and nonlinear transformations is the gold standard at the moment; however, the methods so far used to readapt the histological slices into their original volume and form can be further developed to allow exact correlations between histology, immunostaining, and image. The next challenging part of the process is how to adapt this histological 3D coherent

As soon as we have consistent, validated, three-dimensional surfaces, we have to fit them into the patient's brain. Therefore, reliable (and visible in both atlas and patient image) reference points are needed to transform the atlas into the living brain ( 3 '3 transform). In the early 1950s, pneumoencephalography and ventriculography permitted the visualization of some intraventricular landmarks as the pineal gland calcification, habenular calcification, and ventricular landmarks (AC and PC). Based on this, Spiegel and Wyics developed the first intracerebral coordinate system used in their atlas. An imaginary line connecting the center of the PC with the pontomedullary sulcus at the posterior border

mirrored it at the midsagittal plane to the left side.

volume obtained to a given patient.

**6.2 Warping the atlas to the patient** 

of the pons (PO) defined the CP-PO line.

extrapolated the results to the stacks in which no MRI was performed.

This system was not really easy to employ, so they and others have developed simpler and more useful ones. Talairach could prove a good and consistent relationship between the AC-PC line (and its derivative planes) with the deep brain nuclei (Talairach et al., 1957). This would change the standard for intracerebral localization. In their 1988 work Talairach & Tournoux present the proportional grid system, which permits the transformation of the models to fit individual variability.

These deformations can be performed using different strategies, as landmark-based deformation methods or automatic deformations based on registration algorithms.

The most widely used system to adapt a brain atlas to the individual anatomy of a living subject is the proportional system of Talairach. It relies primarily on the AC-PC distance, i.e., the length between the anterior and posterior commissural points, well-identifiable on a ventriculography or a mid-sagittal section of a MRI acquisition. The user has just to measure the AC-PC distance in the living brain and to adapt the antero-posterior length of the atlas to that of the brain. The proportional system of Talairach is a reliable system, although it is inhomogeneous since the adaptation along the antero-posterior dimension is based upon two deep brain ventricular landmarks, whereas adaptation along the medio-lateral and infero superior dimensions depends on the overall size of the cerebral cortex. This is due to the fact that with ventriculography, internal landmarks are less clear along these dimensions the height of the thalamus and width of the third ventricle are the best possible landmarks (Yelnik, 2009).

An automatic registration algorithm is based on the comparison of features (grey-level values, points, lines, graphs, etc.) present in the two images to be registered. The algorithm is defined by three main characteristics: the similarity measure, the space of allowed deformations (the number of degrees-of-freedom (DoF) of the deformation, e.g., 6 DoF for a 3D rigid transform), and the optimization method that is used. Deformations can be very constrained (limited number of DoF), e.g., linear scaling (7 DoF) or not, like elastic, fluid, or even free-form deformations. These last types of deformations are often referred to as morphing or warping transforms. The choice of the most adequate deformation type is important, as it directly influences the quality of the atlas-to-patient result.

Chakravarty, in 2009, has studied and compared the "atlas to patient warping techniques"(Chakravarty et al., 2009) describing and comparing the linear, piece-wise linear and nonlinear techniques. These are automatic developed algorithms, although in the piecewise technique, twelve different landmarks must be identified on both atlas and patient data, performing a Talairach transformation.

Chakravarty resumes the most typically used methods to warp the atlas to patient MRI data in two. The first is matching the anatomical structures directly from the atlas to the same structures seen in pre-operative scans (Ganser et al., 2004; Nowinski et al., 2000; Xu & Nowinski, 2001 as cited in Chakravarty et al., 2009). The second method starts with a set of anatomical atlas contours, pre-aligned to an MRI template. A transformation is then estimated between the template MRI and patient's MRI. Once this template-to patient transformation is estimated, the transformation is then applied to the anatomical atlas contours, thus customizing it to patient's anatomy (Bardinet et al., 2005; Chakravarty et al., 2005; D'Haese et al., 2005; Sanchez Castro et al., 2006; Yelnik et al., 2007as cited in Chakravarty et al., 2009).

#### **6.3 Do we need new atlases?**

Currently, magnetic resonance imaging is the method of choice for anatomic delineation of the brain. Its noninvasive nature allied to the possibility of unlimited repetition provides the

Review of Printed and Electronic Stereotactic Atlases of the Human Brain 169

The authors would like to thank all the members of the team participating on the São Paulo-Würzburg collaborative project and their representatives: Dr. Lea T. Grinberg, Dr.Wilson Jacob Filho, Prof. Dr. Manoel Jacobsen Teixeira, Prof. Dr. Edson Amaro Jr, and Prof. Dr.

The author, Eduardo Joaquim Lopes Alho, has a scholarship for doctoral studies in the Julius-Maximilian Universität Würzburg, supported by the Brazilian agency CAPES in

Special thanks also to Bruna Barbosa Teodoro Felix, and to David Rochester for reviewing

Afshar, F.; Watkins, E. S. & Yap, J. C. (1978). *Stereotaxic atlas of the human brainstem and* 

Andrade-Souza, Y. M.; Schwalb, J. M.; Hamani, C.; Hoque, T.; Saint-Cyr, J. & Lozano, A. M.

Andrew, J. & Watkins, E. S. (1969). *A stereotaxic atlas of the human thalamus and adjacent* 

Ballester, M. A. G.; Zisserman, A. P. & Brady, M. (2002). Estimation of the partial volume

Benabid, A. L.; Pollak, P.; Koudsie, A.; Benazzouz, A.; Piallat, B.; Krack, P.; Limousin, P. & Le Bas, J. F. (2001). Deep Brain stimulation for Parkinson's disease. *AdvNeurol,* 86, 405-412 Bauchot, R. (1967). Les modifications du poidencephalique au cours de la fixation*. J* 

Caire, F.; Ouchchane, L.; Coste, J.; Gabrillargues, J.; Derost, P.; Ulla, M.; Durif, F. &Lemaire, J. J.

Chakravarty, M. M.; Bertrand, G.; Hodge, C. P.; Sadikot, A. F. & Collins, D. L. (2006). The

Chakravarty, M. M.; Sadikot, A. F.; Germann, J.; Hellier, P.; Bertrand, G. & Collins, D. L.

Coffey, R. J. (2009).Printed Stereotactic Atlases, Review, In:*Textbook of Stereotactic and* 

Dormont, D.; Ricciardi, K. G.; Tandé, D.; Parain, K.; Menuel, C.; Galanaud, D.; Navarro, S.;

funcionales guiadas por imágenes. *Neurocirugía,* 18, 478-484

Neurosurgical Applications. *Human Brain Mapping,* 30, 3574-3595

Atlas Data. *AJNR Am J Neuroradiol,* 25, 1516-1523

(2009). Subthalamic Nucleus Location: Relationships between Stereotactic AC-PC-Based Diagrams and MRI Anatomy-Based Contours. *Stereotact Funct Neurosurg,* 87, 337-347 Carballo-Barreda, M.; Rodríguez-Rojas, R.; Torres-Montoya, A. & López-Flores, G. (2007).

Atlas computarizado para la planificación de neurocirugías estereotácticas

creation of a brain atlas for image guided neurosurgery using serial histological

(2009). Comparison of Piece-Wise Linear, Linear, and Nonlinear Atlas-to-Patient Warping Techniques: Analysis of the Labeling of Subcortical Nuclei for Functional

*Functional Neurosurgery,* Lozano, AM, Gildenberg, PL, and Tasker, RR, pp. 347-372,

Cornu, P.; Agid, Y. & Yelnik, J. (2004). Is the Subthalamic Nucleus Hypointense on T2-Weighted Images? A Correlation Study Using MR Imaging and Stereotactic

(2005). Comparison of 2-dimensional magnetic resonance imaging and 3-planar reconstruction methods for targeting the subthalamic nucleus in Parkinson disease.

**9. Acknowledgment** 

Carlos Augusto Pascualucci.

the chapter.

**10. References** 

cooperation with the German agency DAAD .

*SurgNeurol,* 63, 357, pp. 363

*Hirnforsch*, 253-283

data. *NeuroImage,* 30, 359-376

Springer, Berlin/Heidelberg

*cerebellar nuclei,* Raven Press, New York

*structures,*Williams and Wilkins, Baltimore

effect in MRI. *Medical Image Analysis,* 6, 389-405

option of *in vivo* applications for clinical purposes and basic science research with quite comfortable accessibility. Volumetric and multi-sequence acquisitions of MRI images supply different sets of data, for instance, macroscopic anatomy, differentiation of gray and white matter, detection of iron deposits, fiber tracking, spectroscopy, BOLD effect in addition to the possibility of re-slicing and generating 3D reconstructions of the brain. It is even possible to differentiate the cortical layers in MRI (Fatterpekar et al., 2002). However, the protocol used to achieve this definition was a 9.4 T machine and each specimen was submitted to an overnight acquisition time of 14 hours and 17 minutes. This is not possible in living patients, not only because of the long acquisition time, but also due to movement artifacts including breathing. The subthalamic nucleus is a good example for this discussion, because it is an important target to place electrodes in Deep Brain Stimulation (DBS) for treatment of Parkinson's disease, (Limousin et al., 1995; Benabid et al., 2001; Hamani et al*.*, 2004) dystonia and epilepsy, and obsessive-compulsive disorders (Mallet et al., 2002).The real limits of STh within the hypointense image in the region lateral to the red nucleus is still matter of debate (Littlechild et al., 2003; Pollo et al., 2003; Dormont et al., 2004 ;Andrade-Souza et al., 2005 ; Sather & Patil, 2007; Stancanello et al., 2008; Kitajima et al., 2008;Caire et al., 2009; Vertinsky et al., 2009).The problem seems bigger if we consider that most neurosurgery services use 1.5 to 3.0 T magnetic fields in MRI acquisition. Although MRI images have improved in recent years, no sharp limits are really observed. Additionally, the iron content of the nucleus is unevenly distributed, predominating in its anterior aspects. We cannot forget as well the artifacts such as partial volume effect that distort the images and blur the nuclear outlines when we target small volumes (Ballester et al., 2002). On the other hand, the pioneer experiences of the first atlases based in brain histology have recently obtained substantial improvement with the addition of new staining techniques, imunohistochemestry specific to different subcellular and membrane structures of neurons and glial cells, and the development of softwares and algorithms to warp and correct the errors induced by tissue processing, all of which have made it more reliable and precise. Functional neurosurgery is aimed at functional targets, but these functional units are linked to an anatomical substrate. If we can in the future overlap the cytoarchitecture, intraoperative electrophysiology, and high-resolution functional images, we will surely be able to better understand the function and structure relationship and propose new treatments for diseases that have seemed hopeless until now .
