A Computerized Approach for Morphological Analysis of the Corpus Callosum C. Davatzikos, M. Vaillant, S.M. Resnick, J.L. Prince, S. Letovsky, and R.N.

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1 A Computerized Approach for Morphological Analysis of the Corpus Callosum Chris Davatzikos, Marc Vaillant, Susan M. Resnick, Jerry L. Prince, Stanley Letovsky, and R. Nick Bryan Aliations: Chris Davatzikos, Ph.D., Marc Vaillant, B.Sc., Stanley Letovsky, Ph.D., R. Nick Bryan, M.D., Ph.D.: Neuroimaging Laboratory Department of Radiology and Radiological Science The Johns Hopkins University School of Medicine Baltimore, MD Susan M. Resnick, Ph.D.: Laboratory of Personality and Cognition Gerontology Research Center National Institute on Aging Baltimore, MD Jerry L. Prince, Ph.D.: Image Analysis and Communications Laboratory Department of Electrical and Computer Engineering The Johns Hopkins University Baltimore, MD Correspond to: Chris Davatzikos Division of Neuroradiology The Johns Hopkins University School of Medicine 600 N. Wolfe Street, Baltimore, MD Tel Fax: Short Title: Morphological Analysis of the Corpus Callosum. Submitted for Publication: This paper is submitted to the Journal of Computer Assisted Tomography. Financial Support Statement: This work has been supported in part by the NIH grant No1-AG

2 A Computerized Approach for Morphological Analysis of the Corpus Callosum C. Davatzikos, M. Vaillant, S.M. Resnick, J.L. Prince, S. Letovsky, and R.N. Bryan Abstract Purpose. A new technique for analyzing the morphology of the corpus callosum is presented, and it is applied to a group of elderly subjects. Methods. The proposed approach normalizes subject data into the Talairach 2 space using an elastic deformation transformation. The properties of this transformation are used as a quantitative description of the callosal shape with respect to the Talairach atlas, which is treated as a standard. In particular, a deformation function measures the enlargement/shrinkage associated with this elastic deformation. Inter-subject comparisons are made by comparing deformation functions. Results. This technique was applied to eight male and eight female subjects. Based on the average deformation functions of each group, the posterior region of the female corpus callosum was found to be larger than its corresponding region in the males. The average callosal shape of each group was also found, demonstrating visually the callosal shape dierences between the two groups in this sample. Conclusion. The proposed methodology utilizes the full resolution of the data, rather than relying on global descriptions such as area measurements. The application of this methodology to an elderly group indicated sex-related dierences in the callosal shape and size. Key Words: Image Analysis, Corpus Callosum, Image Registration, Morphological Analysis, Brain.

3 A Computerized Approach for Morphological Analysis of the Corpus Callosum 3 C. Davatzikos 1, M. Vaillant 1, S.M. Resnick 2, J.L. Prince 3;1, S. Letovsky 1, and R.N. Bryan 1 1 Department of Radiology, Johns Hopkins University School of Medicine 2 National Institute on Aging 3 Department of Electrical and Computer Engineering, Johns Hopkins University I. Introduction The inuences of sex and handedness on variability in the size of the corpus callosum remain controversial. Following initial reports that the posterior fth of the corpus callosum, the splenium, is larger in women compared with men [1], a number of investigators failed to replicate this nding. While the initial ndings and subsequent extensions to other samples [2, 3] were based on autopsy samples, investigations which reported no signicant sex dierences in splenial size were based on magnetic resonance imaging [4]{[7], as well as autopsy samples [8, 9, 10]. Similarly, reports of dierences in callosal size between right and left- handers have yielded inconsistent results, with some investigators reporting larger midsagittal areas for left compared with right handers [10, 6] and others reporting no signicant eects of handedness [11]. It has been suggested that the diversity of methods for quantifying the size of the corpus callosum and its subdivisions is a major factor in the discrepant ndings across studies. Due to these methodological dierences, results of

4 4 dierent investigations cannot always be directly compared. More importantly, most methodologies (e.g. [12, 4, 6, 2, 13, 5, 14]) depend largely on the curvature of the corpus callosum, which varies dramatically across subjects (Fig. 4). Therefore, the reported results do not necessarily reect actual dierences in the size of the subregions of the corpus callosum, but are unavoidably aected by the callosal shape. In fact, Allen et al. [4] were unable to replicate sex dierences in the size of the splenium, but found signicant dierences in corpus callosum shape, consistent with a more bulbous splenium in females. In this paper we propose a new quantitative approach for studying the size and shape of the corpus callosum, which reduces the eect of variability in the callosal shape on size measurements. Our methodology is based on a spatial normalization procedure, which transforms images into a common reference system bringing them into correspondence with a template image. In the study presented in this paper we have used the Talairach-Tournoux atlas [15] as a template. However, we demonstrate that our analysis is independent from the particular image used as the template. Associated with the Talairach atlas is a coordinate system, which divides the brain into 1,056 partitions and has been widely used as a standard reference system for localizing brain anatomical regions. In the proposed methodology, a map between the Talairach space and the subject space is obtained using a registration algorithm which is based on an elastic warping of the Talairach atlas. Associated with this warping is a deformation function, which is dened at each point of the corpus callosum of the atlas, and which reects the size dierence between an innitesimal region around a point in the Talairach space and its corresponding innitesimal region in the subject space [16, 17]. The size of an arbitrary region of the corpus callosum is obtained by integrating

5 5 the deformation function within its corresponding region in the Talairach space. This normalization procedure reduces the eect of the shape variability on size measurements, and provides a common reference system for intersubject comparisons. Moreover, it takes advantage of the full data resolution since it is based on a point-wise morphological description, as opposed to the existing methodologies [1, 6, 5, 10] which are based on region of interest area measurements. Finally, as shown in Section II, our methodology provides a means for obtaining population averages of the shape of the corpus callosum. The primary purpose of this paper is to present a new morphometric tool. However, in order to demonstrate its utility in investigating sex dierences in the corpus callosum, we applied it to two groups of right-handed subjects 8 men and 8 women. Comparison of the male and female groups revealed considerable sex dierences. Most notably, the posterior part of the corpus callosum was larger in the female group than in the male group, despite the fact that the average total cross-sectional area of the corpus callosum was larger in men. This analysis, which needs to be replicated on a larger sample, indicates a possible sex-related anatomical variability of the corpus callosum and is consistent with prior studies suggesting greater splenial area in females compared with males [1]. It has been suggested that the larger splenial area in females may reect greater connectivity between the posterior part of the two hemispheres in females than in males and might contribute to the more symmetric representation of cognitive function in women and conversely, greater hemispheric specialization in men.

6 6 II. Materials and Methods Subjects The subjects were 8 male and 8 female participants in the Baltimore Longitudinal Study of Aging (BLSA) [18]. All were right-handers, as determined by the 10-item Edinburgh Inventory [19]. Subjects were between 62 and 84 years of age. Mean ages and standard deviations for men and women were, respectively, and years. Magnetic Resonance (MR) Imaging MR scans were acquired volumetrically on a GE Signa 1.5 Tesla scanner, using the SPGR acquisition protocol (TR=35ms, TE=5ms, ip angle = 45 o, pixel size=0.94mm0.94mm). The volumetric images were then resliced parallel to the AP-PC plane, correcting for roll, yaw, and pitch. A 0.94mm thick midsagittal slice was extracted from the resliced data on an ISG workstation (ISG Corporation, Toronto, Canada). Quantitative Procedures In this section we present a brief description of our registration method, which is used to derive a map between the Talairach space and the subject space. We then explain how the resulting map is used to describe the local characteristics of the callosal size of a subject, and we describe our methodology for obtaining population averages of the shape of the corpus callosum. Finally, we conclude by addressing the issue of the dependency of our analysis on the selection of the particular atlas, and we show that, in principle, any atlas can be used instead of Talairach's as the template in our deformation analysis. Atlas/MR Registration. Our registration procedure is comprised of two stages. In the rst stage the boundary points of the corpus callosum are

7 7 extracted through seeded region growing [20], in the midsagittal image of a subject and in the Talairach atlas midsagittal image 1. An active contour algorithm [21, 22] is then applied to both boundaries. The active contour is an elastic string, which is initialized at a conguration surrounding the corpus callosum and deforms toward the boundary of the corpus callosum under the presence of an external force eld described in detail in [21]. After a series of elastic deformations, the active contour balances on the boundary of the corpus callosum. Figure 1 shows four instances of the deformation of an active contour toward the boundary of the corpus callosum of one of the subjects. The active contour algorithm is a key step in our approach because it results in a mathematical description, or parametrization [23], of the callosal boundary. Based on this parametrization, the curvature function along the boundary of the corpus callosum, which reects its shape characteristics, is determined for the midsagittal image of each subject. This procedure is also performed for the midsagittal atlas image. Finally, we nd the circular shift of the boundary of the corpus callosum in the MR image that brings its curvature function in best agreement with the curvature function of the boundary of the corpus callosum in the atlas image. This circular shift brings homologous regions of the callosal boundary into correspondence. In the second stage of our registration procedure an elastic warping is applied to the atlas image bringing it into registration with the MR image. This warping is obtained by rst deforming the boundary of the corpus callosum of the atlas toward that in the MR image, resulting in overlapping boundaries. The body of the corpus callosum in the atlas is then deformed elastically like a rubber sheet, following the deformation of its boundary (see [24, 25] for 1 The Talairach atlas was photographed using a high resolution camera and was stored in digital format.

8 8 details). Deformation Function. The warping applied to the corpus callosum in this registration procedure is reected in the deformation function, denoted by d(u; v), which is dened at each point (u; v) of the corpus callosum of the atlas. If the point (u; v) of the Talairach space is mapped to the point (U(u; v); V (u; v)) in the subject space (see Fig. 2), then d(u; v) is dened by d(u; v) = det (r(u(u; v); V (u; v))) ; (1) where r denotes the gradient of a vector function and det() denotes the determinant of a matrix. The deformation function d(u; v) measures the stretching or shrinking which brings the atlas into registration with a subject. In particular, from the principles of continuum mechanics [26], if d(u; v) > 1 at a point (u; v), then an innitesimal area around (u; v) expands as a result of the atlas warping. Similarly, if d(u; v) < 1, then a local shrinking around (u; v) occurs. Consider now a region R in the subject space. Let R a be its corresponding region in the Talairach space. These regions are related by the map (U(u; v); V (u; v)), as follows: The area, A, of R is given by [26] R = [ (u;v)2r a (U(u; v); V (u; v)) : (2) A = Z Z R a d(u; v)dudv : (3) Note that, since dudv is the area of an innitesimal region in the Talairach space, d(u; v) is a local scaling factor representing area enlargement/shrinkage in the neighborhood of (u; v) with respect to the Talairach atlas (see Fig. 2). Therefore, d(u; v) is a means for quantifying the size of the corpus callosum and its subregions by using the Talairach atlas as metric.

9 9 Now consider a region of interest, R a, in the Talairach space. Consider also two particular subjects, referred to as Subject 1 and Subject 2. Let R1 and R2 be the regions in the corpus callosum of Subject 1 and Subject 2, respectively, to which R a is mapped through the warping transformations (U 1 (u; v); V 1 (u; v)) and (U 2 (u; v); V 2 (u; v)) (see Equation (2)). Let also A1 and A2 be the areas of R1 and R2. Then from (3) we deduce that A1 A2 = Z Z R Z Z a d 1 (u; v)dudv ; (4) d 2 (u; v)dudv R a where d 1 (u; v) and d 2 (u; v) are the deformation functions of Subject 1 and Subject 2, respectively. Equation (4) shows that the deformation function is a means for quantifying inter-subject variability of the size of the corpus callosum, on a region of interest basis. Population Analyses. Based on the Talairach space normalization, qualitative and quantitative population comparisons can be readily made. Specifically, let (U 1 (u; v); V 1 (u; v)); ; (U N (u; v); V N (u; v)) be the maps from the corpus callosum of the atlas to the corpus callosum of each of the N subjects of a population. Let, also, U p (u; v) and V p (u; v) be the average of the N functions U 1 ; ; U N and V 1 ; ; V N, respectively: U p (u; v) = 1 N V p (u; v) = 1 N NX U i (u; v) ; i=1 NX V i (u; v) : i=1 (5a) (5b) Then the average corpus callosum C p of that population is dened as the collection of the points where the atlas corpus callosum points are mapped: C p = [ (u;v)2c a (U p (u; v); V p (u; v)) ; (6)

10 10 where C a is the collection of points belonging to the corpus callosum of the atlas. Let p (u; v) be the point-wise mean of the deformation function of the population: p (u; v) = 1 NX d i (u; v) ; (7) N i=1 where d 1 (u; v); ; d N (u; v) are the deformation functions of the N subjects (see Equation (1)). Then the dierence between two populations, denoted with subscripts 1 and 2, can be measured for each callosal region as an eect size dened as [27] e(u; v) = p1(u; v)? p2 (u; v) (u; v) ; (8) where (u; v) is the point-wise standard deviation of the two populations combined, and is given by (u; v) = vu u t 1 N t? 1 N X t (d i (u; v)? (u; v)) 2 : (9) i=1 Here, N t is the total number of subjects in the two populations and (u; v) is the mean deformation function of the two populations combined and is given by an expression analogous to (7). We will use the eect size as a measure of the statistical signicance of our experimental results in Section III. Impact of the Template. In our analysis up to now we have used the Talairach atlas as template for the deformation analysis. In principle, any other midsagittal image can be used as template, without aecting our analysis. Specically, let U(u; v) = (U(u; v); V (u; v)) be the map from Atlas 1 to a subject (see Fig. 3), and let the corresponding deformation function be d(u; v) (see Equation (1)). Let, also, T(u; v) be the map from Atlas 1 to Atlas 2, and let s(u; v) be the corresponding deformation function. Finally, let U 0 (T(u; v)) be the map from Atlas 2 to the same subject, and d 0 (T(u; v))

11 11 be the corresponding deformation function. Assuming that U(; ), T(; ), and U 0 (; ) map homologous points to each other, the following is true: U(u; v) = U 0 (T(u; v)) : From the principles of mathematical analysis it then follows that ru = ru 0 rt ; which together with (1) yields d(u; v) = d 0 (T(u; v))s(u; v) : (10) Now consider two populations having average deformation functions p1 (u; v) and p2 (u; v), respectively, with respect to Atlas 1, which are given by (7). Let, also, (u; v) be the point-wise standard deviation of the two populations combined. Finally, let the average deformation functions and the combined standard deviation of these populations with respect to Atlas 2 be 0 (T(u; v)), p1 0 p2 (T(u; v)), and 0 (T(u; v)). Multiplying the numerator and denominator of (8) by 1=s(u; v) we get e(u; v) = 1 s(u; v) p1(u; v)? 1 s(u; v) p2(u; v) 1 s(u; v) (u; v) : (11) From Equations (7), (9), and (10) it readily follows that 0 p1 (T(u; v)) = 1 s(u; v) p1(u; v) ; 0 p2 (T(u; v)) = 1 s(u; v) p2(u; v) ; 0 (T(u; v)) = 1 (u; v) : s(u; v) (12c) (12a) (12b) From (12), (11), and (8) we conclude that e 0 (T(u; v)) = e(u; v) ;

12 12 which implies the invariance of population comparisons to the selection of the atlas 2. A key assumption in the development above is that the warping transformation maps homologous points to each other. In practice there are deviations from this assumption, due to registration errors. These errors, however, are fairly small, since the matching of the callosal boundaries yields a good matching of the body of the corpus callosum, as well. Moreover, the inherent smoothness of the elastic transformation results in smoothly varying deformation functions, and therefore it reduces the eect of registration errors since neighboring points (e.g. the points U(u; v) and U 0 (T(u; v)) in Fig. 3) have very similar deformation functions. This is bolstered by experimental evidence provided in the following section. III. Results These procedures were applied to the 8 men and 8 women described in Section II. The boundaries of the corpus callosum were extracted in the midsagittal MR images of the 16 subjects through seeded region growing, using an ISG workstation (ISG, Toronto, Canada). The points where the region growing terminated dened the boundary of the corpus callosum. The active contour algorithm was applied to each MR image, as described in Section II. In all subjects, the active contour was initialized at a circular conguration of radius 100 pixels surrounding the corpus callosum, as in Fig. 1a, and allowed to converge. Fig. 4 shows the nal curves, which the active contour converged to after a sequence of deformations. 2 We note that the actual values of p 1 (; ), p 2 (; ), and (; ) depend on the particular atlas used as template, since they measure size relative to the atlas.

13 13 Using the elastic registration method described in Section II, the Talairach atlas midsagittal image (Figure 42 in [15]) was then warped to each of the 16 MR images separately, resulting in the warped atlas images shown in Fig. 5. The deformation functions (see Equation (1)) were then calculated for each of the 16 subjects and are shown in Fig. 6. In this gure the deformation functions are displayed as grey scale images superimposed on the shape of the corpus callosum of the Talairach atlas, with image brightness being proportional to the expansion of the atlas 3. Specically, the darker a region of a subject appears in Fig. 6, the more contraction the atlas underwent when registered to the MR image of that subject, and therefore the smaller this region is in the MR image relative to the atlas. The point-wise mean deformation functions were then calculated for the male subjects and for the female subjects using Equation (7); these are displayed in Fig. 7. In Fig. 8 we show the regions in which the mean deformation function of the female group was larger than the mean deformation function of the male group. Figure 8 reveals that the posterior part of the corpus callosum was larger in the female group than in the male group. Moreover, in most other regions the average male corpus callosum was larger than the female one. Although this result indicates size dierences of the corpus callosum between the male and the female subjects, it is biased by the fact that the male subjects that participated in this study had larger corpora callosa than the female subjects. To eliminate this bias we calculated the total cross-sectional area of the corpus callosum of each subject. The mean total callosal area was found to be mm 2 for the male group and mm 2 for the female group. The mean deformation functions were then normalized by the total area, so that the integral of d(u; v) was the same for the two groups. 3 All deformation functions were scaled for display purposes.

14 14 This is equivalent to scaling the original MR images so that the average total callosal area is the same for both groups, and equal to 550.5mm 2. The points where the normalized mean female deformation was larger than the mean male deformation are shown in Fig. 9. Fig. 9 shows that in addition to the splenium, a portion of the isthmus appears relatively larger, on average, in females compared with males. However, only the sex dierence in the splenium had a signicant eect size, as shown in Figs. 10a, 10b, and 10c where the points having eect size greater than 1, 0.75, and 0.5, respectively, are shown in white. In our next experiment we determined the average corpus callosum for each of the two groups, using Equation (6). The result is shown in Fig. 11, and it qualitatively veries our quantitative analysis. Specically, the posterior part of the corpus callosum appears to be more bulbous in females, as opposed to the rest of the corpus callosum which appears to be larger in males. In order to demonstrate the invariance of inter-subject comparisons to the specic template used as the atlas, we used the midsagittal MR images of two dierent subjects as templates: one female, shown in Fig. 12a, and one male, shown in Fig. 12b. None of these subjects was within the group of 16 studied here. The experiments described above were repeated for these two new templates. The regions with eect sizes greater than 1, 0.75, and 0.5, using Fig. 12a as template, are shown in white in Fig. 13. Figure 13 shows a very similar result to the one obtained using Talairach's atlas as template. The average male and female callosal shapes are shown in Fig.14, revealing very similar dierences between the two groups. Finally, we used Fig. 12b as template, and repeated the analysis. The regions with eect sizes greater than 1, 0.75, and 0.5, are shown in white in

15 15 Fig. 15. Figure 15 also shows a very similar result to the one obtained using the other two templates. The average male and female callosal shapes for this template are shown in Fig.16. IV. Discussion In this work we developed a new approach for quantifying the shape of the corpus callosum, based on the Talairach space normalization and on the measurement of a deformation function resulting from the registration of the Talairach atlas with subject images. This technique was tested by comparing a group of male with a group of female subjects. The proposed approach can potentially overcome several limitations of previously described methods for quantifying the size of the corpus callosum. In particular, instead of dividing the corpus callosum into a number of discrete regions (see e.g. [14, 1, 6]), our approach results in a continuous deformation function which reveals local dierences between the corpora callosa of dierent subjects. Inter-subject comparisons of any region of the corpus callosum can be readily obtained by integrating the deformation function in that region. Moreover, if advances in the imaging techniques make available information on the internal structure of the corpus callosum at the resolution of the callosal bers, in addition to the shape of its boundary, our method can readily incorporate such information by imposing additional constraints on the elastic transformation, which will match not only the callosal boundary points, but certain callosal bers as well. Using the Talairach atlas, or any other template, in our analysis provides a common reference system for population studies, which can potentially eliminate the variability in methodologies for dividing the corpus callosum.

16 16 Using the spatial normalization described in this paper, a division of the corpus callosum of any population is obtained in a uniform way for all subjects by dividing the corpus callosum in the atlas and mapping this division to each subject through the functions U(u; v) and V (u; v). We have also demonstrated the utility of spatial normalization in dening average shapes for populations. The average corpus callosum of each group was found by averaging U(u; v) and V (u; v), as opposed to averaging the MR images which can result in fuzzy average shapes [28, 29]. The shape variability of the corpus callosum of a population in our approach is reected in the standard deviation of the normalizing functions U(u; v) and V (u; v), rather than in the fuzziness of the average image. By comparing the average deformations of the male and female groups, we demonstrated that the male corpus callosum in this sample of elderly subjects was larger overall by 6.7%, except for its posterior part which was larger in the female group. In particular the area in the posterior corpus callosum shown in white in Fig. 8 was larger by 9.3% in the females. It should be stressed that the magnitude of the sex dierence was comparable to the point-wise standard deviation of the deformation functions. However, the remarkable dierence between this region and the rest of the corpus callosum, and the fact that the region in which this dierence was observed was a large and contiguous region suggests an anatomical dierence between men and women in this sample. These ndings, which are based on a small sample, require replication in a larger series of subjects and should be extended to younger subjects to assess the generalizability of the sex dierence across age groups. Our results are consistent with previous reports on this topic which state that the splenial region in the corpus callosum is relatively larger in adult

17 17 females than in adult males [1, 2, 6]. Previous reports diering from our results may be explained by methodological or population dierences [6]. Though the statistical power of our study is limited by the small number of subjects, our new methodology partially osets this problem; based on a point-wise morphological representation of the callosal shape, our approach minimizes the partial volume errors, which are large in previous, arbitrary ROI methods. Several methodological issues of our approach also need to be further investigated and rened in future work. In particular, in addition to the deformation function, other properties of the elastic warping of the atlas can be measured, such as strain. These properties reect not only size characteristics, but shape characteristics as well, since they reect angular warping in addition to growth or shrinkage. References [1] C. de Lacoste-Utamsing and R.L. Holloway. Sexual dimorphism in the human corpus callosum. Science, 216:1431{1432, [2] M.C. de Lacoste, R.L. Holloway, and D.J. Woodward. Sex dierences in the fetal corpus callosum. Human Neurobiology, 5:93{96, [3] R.L. Holloway, P.J. Anderson, R. Defendini, and C. Harper. Sexual dimorphism of the human corpus callosum from three independent samples: relative size of the corpus callosum. American Journal of Physical Anthropology, 92:481{498, [4] L.S. Allen, M.F. Richey, Y.M. Chai, and R.A. Gorski. Sex dierences in the corpus callosum of the living human being. The Journal of Neuroscience, 11:933{942, [5] W. Byne, R. Bleier, and L. Houston. Variations in human corpus callosum do not predict gender: a study using magnetic resonance imaging. Behavioral Neuroscience, 102:222{227, [6] M. Habib, D. Gayraud, A. Oliva, J. Regis, G. Salamon, and R. Khalil. Eects of handedness and sex on the morphology of the corpus callosum: a study with brain magnetic resonance imaging. Brain and Cognition, 16:41{61, 1991.

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20 20 (a) (b) (c) (d) Figure 1: A sequence of an active contour deformation toward the corpus callosum boundary: (a) initial conguration, (b) and (c) two intermediate deformations, (d) nal conguration after convergence. The active contour was attracted by the callosal boundary which was extracted in a preprocessing step using seeded region growing. Figure 2: A point (u; v) in the Talairach space is mapped to the point (U; V ) = (U(u; v); V (u; v)) in the subject space via the elastic transformation. During this transformation, an innitesimal area dudv around each point (u; v) is mapped to an area equal to d(u; v)dudv. Therefore, the deformation function d(u; v) quanties the local expansion/contraction resulting from this mapping.

21 21 Atlas 1 Atlas 2 (u,v) T(u,v) Subject U(u,v) U (T(u,v)) Figure 3: The invariance of the deformation analysis to the particular atlas used as template. Assuming a perfect registration, U 0 (T(u; v)) = U(u; v), and the results of the deformation analysis using Atlas 1 as template are identical to the results using Atlas 2 as template.

22 22 (a) (b) Figure 4: The nal active contour congurations for (a) the male group and (b) the female group.

23 23 (a) (b) Figure 5: The transformed Talairach atlas midsagittal image for (a) the male group and (b) the female group.