Keywords: Structural MRI, Fetal imaging, tensor based morphometry, directional growth modeling, brain development

2.1. Deformation Direction Vector (DDV)

The principal deformation direction can be obtained from the principal component of the Jacobian matrix at each voxel. In order to avoid stability issues associated with eigen analysis of any Jacobian matrix, we leverage the polar decomposition property ofJ [12] to compute the primary deformation direction indirectly. At each voxel, the Jacobian matrix, being a second order tensor, can be separated into a rotational and a strain component [31].

whereR is the orthogonal, rotation tensor such thatR⁻¹ =R^T and det(R) = + 1.S andS′ are symmetric, positive definite tensors known as the right and left stretch tensors respectively.S andS′ are related byS′ = RSR^T. The stretch tensors can be computed from the following relationship

C andC′ are known as the right and left Cauchy-Green tensors (CGT), respectively.

As illustratedFigure 1, this decomposition is analogous to first stretching the voxel byS and then rotating it byR to realize the deformation [8]. Therefore, the direction of deformation, is computed by extracting the principal eigenvector of strain (e) fromS, and rotating this byR yields the DDV. Here, we would like to emphasize thate only specifies the principal direction of strain and not the direction of the complete deformation. For each subject, we compute a DDV map (DDV at each voxel), which is used to analyze local changes in directionality.

2.2. Principal Growth Direction (PGD)

In scalar TBM, the definition of volume change is well understood, i.e. undeformed voxels have a Jacobian determinant of 1 and any deviation from this value is considered as change. For directional properties, such a distinct baseline does not exist. To establish a baseline, we make use of the DDV map for each subject which provides orientation information specific to each subject at any given location. As described inEquation 5, PGD at a voxel is defined as the DDV (of a single subject) which has the least circular distance [28] from DDVs of all the other (N–1) subjects.

The PGD map gives us a baseline which can be used along with the results from the directional TBM in Section 2.1 to interpret how the directionality of growth changes with age and development. Therefore, we propose to first compute the most common growth direction at each tissue location across the population being studied and then analyze how directional growth is varying with respect to this direction at each location.

If a PGD cannot be clearly established, i.e. the eigenvalues are not well-separated at many locations, the study can be done on each of the 3 directions separately. Three deformation direction maps are formed and are studied individually. After being tested individually, the three significance maps are combined using an OR method or the fisher test.

4.1. Fetal subjects and image acquisition

The following experiments were performed using 40 clinical scans of 38 fetuses at gestational ages (GA) ranging from 20.57 to 27.86 weeks GA, estimated by last menstrual period. The mothers were referred for MRI of the fetal brain due to questionable findings on prenatal ultrasound, a prior abnormal pregnancy, or volunteered for scans as part of studies at UCSF. All women had normal fetal MRI. The subject population contains 19 females and 19 males. The mean delivery age was 39.3 weeks GA (37.4 – 41.57 weeks GA). The imaging study has IRB approval and complies with NIH human subject guidelines. Clinical MR imaging was performed on a 1.5T scanner (GE Healthcare, Milwaukee,WI) using an eight-channel torso phased-array coil. Multiple stacks of single-shot fast spin- echo (SSFSE) T2 weighted slice images (in plane pixel size of 0.5 mm × 0.5 mm, thickness 3 mm, no gap) were obtained in the approximately axial, sagittal and coronal planes with respect to the fetal brain. All slice images were acquired in an interleaved manner to reduce saturation of spins in adjacent slices. The MR sequence parameters (repetition time TR = 3000 – 9000ms, echo time TE = 91 ms) were originally designed for clinical scans. To account and correct for spontaneous fetal movement during scanning, all image slices in the slice stacks of a subject were registered using the slice intersection motion correction (SIMC) technique [21] and reconstructed into 3D volumes with isotropic voxel size of 0.5 mm. The SIMC method has been validated using 100 synthesized datasets and 45 clinically acquired datasets. The method has shown to recover fetal motion between slice acquisitions of up to 15 mm of translation and 30 degrees of rotation with subvoxel accuracy. The 3D volume was reconstructed by gradient weighted Gaussian averaging, where voxels were selectively weighted by the acquisition quality and compounded into a 3D volume that is consistent with each of the 2D slices.

4.2. Automatic tissue segmentation

Using manual segmentations of 30 subjects, we created a spatiotemporal atlas of MR intensity, tissue probability, and shape of the fetal brain [14]. Using this atlas, a synthetic age-specific MR intensity template and an age-specific tissue probability map were generated for all 40 subjects used in this study. Each subject MRI was aligned to the age-matched MR template using a sequence of global linear registrations driven by maximization of the correlation coefficient between the age synthesized MRI and subject MRI intensities [41], followed by multiple elastic deformations driven by maximization of mutual information [46] within a fixed mask. Based on the inverse of the estimated spatial transformation, the age-matched tissue probability map was aligned with the subject MRI and used as a source of spatial priors for automatic atlas-based expectation-maximization (EM) segmentations of developing brain tissues [15]. The reconstructed volumes were automatically segmented into regions of the cortical plate (CP); subplate (SP), intermediate zone (IZ), and deep gray nuclei (DG); germinal matrix (GMAT); and ventricles (VENT) (Figure 7b)).

4.3. Groupwise registration

Deformation based morphometric brain studies require that all subject anatomies be spatially aligned so as to bring subject anatomies into the same anatomical coordinate system. For fetal morphometric studies, the optimal registration method should be template-free to avoid introducing a shape bias in the significant range of anatomies being studied. To this end, we used an unbiased groupwise registration method to coalign the tissue maps of the subjects being studied [34]. The registration method simultaneously estimates an unbiased, minimum deformation population average and diffeo-morphic transformation to each of the subjects being studied.

Fetal MR registration presents a few unique challenges which were addressed as follows:

Changing tissue contrast The developing fetal brain exhibits significant MR tissue contrast change with age. In order to avoid the possibility of bias introduced by such changing contrasts, we took the approach of aligning tissue label maps derived from automated segmentation, rather than aligning the raw MR image values directly.

Transient tissue types The fetal anatomy also contains transient tissue types that change in volume across age groups; specifically regions of GMAT and subplate are more visible on MRI in the beginning of this period (20 wks GA) but not visible in many brain regions later in the developmental period (27 weeks GA). The inconsistent tissue boundaries would introduce artifactual deformations between anatomies as the algorithm attempts to account for the missing tissue classes in older anatomies. In order to compute meaningful diffeomorphic transformations between the anatomies, we combine the tissue classes to exclude inconsistent tissue boundaries. This was achieved by combining the transient tissue classes, corresponding to the germinal matrix, the intermediate zone, subplate, and subcortical gray matter, into a not cortical plate (NCP) tissue label (Figure 7b).

The groupwise registration is initialized with a linear registration of the NCP region of every subject to a single, average NCP tissue map [15]. The registration then estimates a set of unbiased, dense field deformations that minimize the mean square difference between the tissue label maps (CP, NCP, VENT) of each subject to the current average tissue label map (CP, NCP, VENT) for the group. Using an iterative gradient descent optimization, the squared difference in tissue labels between the current average and each individual’s tissue map is summed over each tissue class, then minimized with respect to the displacement vector at each voxel. To ensure spatially differentiable mappings, a multi-level, Gaussian smoothing [42] [29] operator was used to regularize the deformation fields during alignment. A 2 mm Gaussian kernel was used at the first level to capture larger-scale shape differences and then a 1 mm Gaussian kernel was used to capture the smaller-scale and more local shape changes. A composition of a sequence of two of these diffeomorphic mappings, each characterized by a vector field of displacements (Figure 7c), from the average anatomy to each subject was estimated. The regularization factors were chosen experimentally so to enforce numerically diffeomorphic mapping during registration.

In order to validate the accuracy of the registration process, we used a subset of subjects which formed a representative age group for which manual segmentations were also available. These subjects were aligned using a combination of automatic segmentation and the groupwise registration method presented in this paper. The computed transformations were used to map the manual segmentations into the resulting average space, thus providing an independent measure of tissue alignment. The resulting overlap of the manually segmented regions in the common space was evaluated with DSC coefficients of 0.84 ± 0.02 for the CP and 0.94 ± 0.01 for the NCP. This was comparable to the underlying differences between manual and automated tissue segmentation, indicating that the groupwise registration had resolved the majority of true differences in anatomy. In addition, we confirmed that all deformations remained diffeomorphic for these regularization parameters.

4.4. Directionality of growth from TBM

For each subject, the Jacobian matrix maps were computed, from the resulting deformation fields, to quantify the pattern of deformation required to spatially normalize individual anatomies. For each subject, we computed the DCM maps from which DDV maps were extracted. An illustration of the DDV maps for a representative subject is shown inFigure 7. Using the DDV maps, we performed multivariate, multiple linear regression on the population with age as the independent variable and the directional coefficients as the dependent variables. The regression coefficients were tested for statistical significance. The growth directions are specified in the initial orientation of the average anatomical target space (axial slices with respect to a fetal brain). Among the approaches that can be used to represent growth directions, the artificial Cartesian scanning coordinates allows us to model anisotropic brain growth within a framework that is easy to understand and interpret. Regions with significant age-related changes in growth direction are shown overlaid on the spatially normalized average MRI and displayed using RView software.

We also computed, using the DDV maps, a PGD map for the subject population.

4.5. Results and Discussion

In this paper, we have shown that the anisotropic growth that occurs during fetal brain development can be quantified using the proposed descriptors. By using these descriptors in conjunction with the TBM framework, we have detected significant changes in the direction of anisotropic growth in the age interval being studied. Significant changes in direction of growth occur primarily in the cortical plate at locations corresponding to the formation of primary sulci. When the direction of cortical growth at any sulcus changes rapidly, it occurs in conjunction with change in direction of growth in the underlying cerebral mantle.

Figure 8 shows a distinct spatial pattern in the PGD for the age range studied. The parietal and occipital regions of cerebral mantle, near the mid-line, show a strong growth along the anterior-posterior (A-P) axis during this period. Along the cortical plate, PGD alternates between superior-inferior (S-I) and right-left (R-L) axis corresponding to the formation of sulci and gyri respectively. Regions of the cerebral mantle underlying locations of sulcal formation show a predominant growth along the S-I axis to accommodate changes in tissue distribution at the sulci and gyri. The ventricles do not show a distinct direction of growth as during this period in fetal brain development, the ventricles do not change significantly in absolute size as the brain expands in volume around them [35,13].

Figures 9 –11 show the regions where directional growth has changed significantly with age. The regions showing significant changes correspond to regions of major cortical folding. The largest clusters of significant voxels occur at the Sylvian fissure (Fig. 9) where the significant acceleration of growth along the R-L axis and deceleration along the S-I axis indicate deepening of the fissure. As marked by the dotted circle, we see that the combination growth acceleration along the R-L axis and deceleration along S-I axis at the superior aspect of the temporal lobe results in closing of the Sylvian fissure [6,1,32]. To accommodate these changes in the cortical regions, we see that the cerebral mantle underlying the insular region is being “stretched” along the S-I axis, since growth along the R-L axis is restricted by neighboring structures. This combination of directional growth may be likened to the ultrasongraphy-based characterization of the temporal operculum “overriding the insula” by progressing from a 45° angle with the insula to a rounded gyrus that covers the posterior half of the insula in the axial plane [32].

InFigure 10, the white arrow indicates the location of the developing central sulcus. Similar to the Sylvian fissure, the R-L growth has significantly increased while S-I growth shows decrease at this sulcus. In contrast, the appearance of the inter-hemispheric fissure (shown by the dotted circle inFig. 10) is characterized by accelerated expansion of the cerebral mantle in the S-I direction paired with deceleration along the R-L axis.

At the choroidal fissure, inFig. 11, we notice a significant deceleration in growth along the R-L axis with no significant acceleration in either of the other two directions. This corresponds to the apparent shrinkage of the choroidal fissure with respect to surrounding tissues because by 19 weeks GA the fissure has reached its mature form [6].

In addition to regions of cortical folding, another region showing a large cluster of significant voxels occurs at the hippocampus. InFig. 12, we see that formation of the hippocampus is associated with accelerated growth along the R-L axis while growth along the S-I axis shows deceleration. Infolding and laminar organization of the hippocampus is established between 18 and 21 weeks GA [19,20]. Further growth of the hippocampus may be a result of lateral expansion of the subfields, which would result in R-L expansion, but this is yet to be shown by histological study.

Considering the PGD inFigure 8 together with directional changes in growth indicated byFigures 9 –12, we see that brain growth is characterized by spatially distinct variations in growth directions. In some regions this directionality does not change significantly as the fetus matures. For example, the cerebral mantle which showed a very pronounced growth along the A-P axis inFigure 8 does not exhibit significant accelerations and decelerations in any direction in the period of growth considered for this study. Major shape changes in the cortex occur due to significant changes in directional growth at sites of sulci and gyri. The effect of these changes in direction on underlying tissue is determined by the rate of those changes in the age range being studied. For example, the operculization of the Sylvian fissure and changes at the inter-hemispheric fissure occur at a rapid rate and thereby the change in directionality in both the CP and the underlying cerebral mantle are captured. During the same age range, the rate the choroidal and central sulci show a slower rate of growth in the same age range [16], therefore the changes in the underlying cerebral mantle are not significantly higher than the surrounding tissue.

4.6. Comparison to results from scalar TBM models

Figure 14 shows an overview of results from the proposed directional TBM method and scalar, volume based morphometric model that study fetal brain growth, at an identical age range [34]. Both the scalar and the proposed directional growth models examine the growth patterns associated with gyrogenesis along much of the developing cerebral mantle. The scalar model detects regions where statistically significant changes in local volume occur in the age range being studied. By including directional information, we were able to specify the axis along which brain dimensions change resulting in volume changes. Localizing the axis of dimension change allows us to characterize interconnected changes associated with gyrification across tissue types. For example, the findings from the current DDV model and the volume growth rate model of the same dataset [34] showed bilateral differential growth at the emerging cingulate sulcus in both the cortical plate and underlying subplate (Figure 9 andFigure 14 (b)). The tissues that would be associated with the crest of the adjacent gyri do not share the pattern of increased growth rate. Importantly, the DDV indicates a cle ar increase in growth rate along the right-left axis, which corresponds to increasing depth of the central sulcus that affects more than just the shape of the cortical surface. In conjunction with the growth rate model, the current directional TBM model allows an estimation of the rate of sulcal deepening to then be made over multiple tissues.

Using diectional information in conjunction with scalar TBM analysis also enhances our understanding of the appearance of structural lateralization. For example, both scalar [34] and directional analysis of the same dataset used here showed significant growth rate asymmetry in the peri-Sylvian region. Specifically, the right superior temporal gyrus and temporal operculum grew faster in the right hemisphere and the inferior frontal gyrus and frontal operculum expanded faster on the left. Similarly, local mean curvature analysis detected asymmetries in cortical folding that match the growth rate spatial pattern [16]. Together these findings suggested the Sylvian fissure hemispheric asymmetries (flat on left, posteriorly arched on right) observed in the mature brain [25,18] actively form during primary gyrogenesis and that the right hemisphere undergoes cortical folding earlier than the left. Results from the current directional analysis of asymmetry shows that this reliable hemispheric asymmetry is only significantly associated with greater right-left expansion in the posterior part of the temporal operculum (Figure 13). The directional information illustrates that the right Sylvian fissure is emerging sooner by expansion of the temporal operculum laterally, rather than by differences in growth direction along the insular region. The right-left acceleration in the temporal region, in contrast to the frontal or parietal, may also be a driving factor in the shape differences of the Sylvian fissure. Modeling the mechanisms by which the fissure reaches mature form would necessitate extending the directional TBM model to term, when the contributions of latter emerging gyri could be evaluated.

4.7. Limitations

When using structural MRI (T1W or T2W), regions of uniform tissue result in regions with uniform intensity and therefore lack contrasting features for registration. This limits the interpretation of results from any brain volume mapping technique in regions deep within uniform tissue. In the absence of dense features, such as those provided by diffusion tensor imaging for TBM [37], the resulting maps of volume differences between anatomies reflect an optimally smooth representation of deformations that must occur within the region to create the observed differences in the surrounding boundaries (e.g., thickening, elongation, folding). When using T2W MRI data for brain volume mapping, the final deformation maps are inevitably linked to the regularization method used during the registration process.

In both the current study and other studies that use similar methods, the significant regions detected in the cerebral mantle are in agreement with published literature (from histology and other methods). This provides a validation of the claim that even in regions where the regularization effects are most pronounced, characteristic patterns detected by this method are still useful in understanding the process of fetal brain growth. Most TBM studies (fetal brain or otherwise) include some level of regularization without it influencing the final outcome of the study. Therefore, the dependence of the deformations on the regularization does not however limit the usefulness and statistical significance of the characteristic volume change patterns extracted by the TBM approach.

Highlights.

• Mathematical framework to detect anisotropic volume changes associated with brain deformation

• Framework includes two novel descriptors that quantify directionality of volume change

• Used, with TBM, to model population-wide patterns in brain morphological changes

• Proposed method used to map local patterns of directional growth in fetal human brain

• Also used to map directional hemispheric asymmetry in growth

• 1.Afif A, Bouvier R, Buenerd A, Trouillas J, Mertens P. Development of the human fetal insular cortex: study of the gyration from 13 to 28 gestational weeks. Brain Struct Funct. 2007;212(3–4):335–346. doi: 10.1007/s00429-007-0161-1. [DOI] [PubMed] [Google Scholar]
• 2.Aljabar P, Bhatia KK, Murgasova M, Hajnal JV, Boardman JP, Srinivasan L, Rutherford MA, Dyet LE, Edwards AD, Rueck-ert D. Assessment of brain growth in early childhood using deformation-based morphometry. Neuroimage. 2008;39(1):348–358. doi: 10.1016/j.neuroimage.2007.07.067. [DOI] [PubMed] [Google Scholar]
• 3.Armstrong E, Schleicher A, Omran H, Curtis M, Zilles K. The ontogeny of human gyrification. Cerebral Cortex. 1995;5(1):56–63. doi: 10.1093/cercor/5.1.56. [DOI] [PubMed] [Google Scholar]
• 4.Ashburner J, Hutton C, Frackowiak R, Johnsrude I, Price C, Fris-ton K. Identifying global anatomical differences: Deformation-based mor-phometry. Human Brain Mapping. 1998;6(5–6):348–357. doi: 10.1002/(SICI)1097-0193(1998)6:5/6<348::AID-HBM4>3.0.CO;2-P. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 5.Batchelor P, Castellano Smith A, Hill D, Hawkes D, Cox T, Dean A. Measures of folding applied to the development of the human fetal brain. IEEE Transactions on Medical Imaging. 2002;21(8):953–965. doi: 10.1109/TMI.2002.803108. [DOI] [PubMed] [Google Scholar]
• 6.Chi J, Dooling E, Gilles F. Gyral development of human brain. Annals of Neurology. 1977;1(1):86–93. doi: 10.1002/ana.410010109. [DOI] [PubMed] [Google Scholar]
• 7.Davatzikos C, Vaillant M, Resnick S, Prince J, Letovsky S, Bryan R. A computerized approach for morphological analysis of the corpus callosum. Journal of Computer Assisted Tomography. 1996;20(1):88–97. doi: 10.1097/00004728-199601000-00017. [DOI] [PubMed] [Google Scholar]
• 8.De Souza Neto E, Peric D, Owen D. Computational methods for plasticity : theory and applications. Wiley; 2008. [Google Scholar]
• 9.Dubois J, Benders M, Cachia A, Lazeyras F, a Vinh Leuchter R, Sizonenko S, Borradori-Tolsa C, Mangin J, Huppi P. Mapping the early cortical folding process in the preterm newborn brain. Cerebral Cortex. 2008;18(6):1444–1454. doi: 10.1093/cercor/bhm180. [DOI] [PubMed] [Google Scholar]
• 10.Fisher R. Statistical Methods for Research Workers. Oliver and Boyd; 1932. [Google Scholar]
• 11.Gogtay N, Giedd J, Lusk L, Hayashi K, Greenstein D, Vaituzis A, Nugent T, Herman D, Clasen L, Toga A, Rapoport J, Thompson P. Dynamic mapping of human cortical development during childhood through early adulthood. Proceedings of the National Academy of Sciences USA. 2004;101(21):8174–8179. doi: 10.1073/pnas.0402680101. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 12.Golub G, Van Loan C. Matrix Computations (Johns Hopkins Studies in Mathematical Sciences) 3rd ed. The Johns Hopkins University Press; 1996. [Google Scholar]
• 13.Grossman R, Hoffman C, Mardor Y, Biegon A. Quantitative MRI measurements of human fetal brain development in utero. Neuroimage. 2006;33(2):463–470. doi: 10.1016/j.neuroimage.2006.07.005. [DOI] [PubMed] [Google Scholar]
• 14.Habas PA, Kim K, Corbett-Detig JM, Rousseau F, Glenn OA, Barkovich AJ, Studholme C. A spatiotemporal atlas of MR intensity, tissue probability and shape of the fetal brain with application to segmentation. Neuroimage. 2010;53(2):460–470. doi: 10.1016/j.neuroimage.2010.06.054. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 15.Habas PA, Kim K, Rousseau F, Glenn OA, Barkovich AJ, Studholme C. Atlas-based segmentation of developing tissues in the human brain with quantitative validation in young fetuses. Human Brain Mapping. 2010;31(9):1348–1358. doi: 10.1002/hbm.20935. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 16.Habas PA, Scott JA, Roosta A, Rajagopalan V, Kim K, Rousseau F, Barkovich AJ, Glenn OA, Studholme C. Early folding patterns and asymmetries of the normal human brain detected from in utero MRI. Cerebral Cortex. doi: 10.1093/cercor/bhr053. In Press. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 17.Hilgetag CC, Barbas H. Role of mechanical factors in the morphology of the primate cerebral cortex. PLoS Computational Biology. 2006;2(3):e22. doi: 10.1371/journal.pcbi.0020022. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 18.Hill J, Inder T, Neil J, Dierker D, Harwell J, Van Essen D. Similar patterns of cortical expansion during human development and evolution. Proceedings of the National Academy of Sciences USA. 2010;107(29):13135–13140. doi: 10.1073/pnas.1001229107. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 19.Humphrey T. The development of the human hippocampal fissure. J Anat. 1967;101:655–676. [PMC free article] [PubMed] [Google Scholar]
• 20.Kier E, Kim J, Fulbright R, Bronen R. Embryology of the human fetal hippocampus: MR imaging, anatomy and histology. American Journal of Neuroradiology. 1997;18:525–532. [PMC free article] [PubMed] [Google Scholar]
• 21.Kim K, Habas PA, Rousseau F, Glenn OA, Barkovich AJ, Studholme C. Intersection based motion correction of multislice MRI for 3-D in utero fetal brain image formation. IEEE Transactions on Medical Imaging. 2010;29(1):146–158. doi: 10.1109/TMI.2009.2030679. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 22.Kochunov P, Castro C, Davis D, Dudley D, Brewer J, Zhang Y, Kroenke C, Purdy D, Fox P, Simerly C. Mapping primary gyrogenesis during fetal development in primate brains: high-resolution in utero structural MRI of fetal brain development in pregnant baboons. Frontiers of Neuroscience. 2010;4(3):20. doi: 10.3389/fnins.2010.00020. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 23.Lancaster J, Kochunov P, Thompson P, Toga A, Fox P. Asymmetry of the brain surface from deformation field analysis. Human Brain Mapping. 2003;19(2):79–89. doi: 10.1002/hbm.10105. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 24.Lee J, Fonov V, Evans A. Mapping brain growth of early childhood using deformation based morphometry. Neuroimage. 2009;47(Supplement 1):S153–S153. doi: 10.1016/j.neuroimage.2007.07.067. [DOI] [PubMed] [Google Scholar]
• 25.LeMay M. Morphological cerebral asymmetries of modern man, fossil man, and nonhuman primate. Annals of the New York Academy of Sciences. 1976;280:349–366. doi: 10.1111/j.1749-6632.1976.tb25499.x. [DOI] [PubMed] [Google Scholar]
• 26.Lenroot RK, Gogtay N, Greenstein DK, Wells EM, Wallace GL, Clasen LS, Blumenthal JD, Lerch J, Zijdenbos AP, Evans AC, Thompson PM, Giedd JN. Sexual dimorphism of brain developmental trajectories during childhood and adolescence. Neuroimage. 2007;36(4):1065–1073. doi: 10.1016/j.neuroimage.2007.03.053. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 27.Lepore N, Brun CA, Chou Y-Y, Chiang M-C, Dutton RA, Hayashi KM, Luders E, Lopez OL, Aizenstein H, Toga AW, Becker JT, Thompson PM. Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors. IEEE Transactions on Medical Imaging. 2008;27(1):129–141. doi: 10.1109/TMI.2007.906091. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 28.Lund U. Least circular distance regression for directional data. Journal of Applied Statistics. 1999;26(6):723–733. [Google Scholar]
• 29.Modersitzki J. Numerical methods for image registration. Oxford University Press; 2004. [Google Scholar]
• 30.Nichols T, Holmes A. Nonparametric permutation tests for functional neuroimaging: A primer with examples. Human Brain Mapping. 2002;15:1–25. doi: 10.1002/hbm.1058. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 31.Noll W, Truesdell C. The Non-Linear Field Theories of Mechanics. Springer-Verlag; 1965. [Google Scholar]
• 32.Quarello E, Stirnemann J, Ville Y, Guibaud L. Assessment of fetal Sylvian fissure operculization between 22 and 32 weeks: A subjective approach. Ultrasound in Obstetrics and Gynecology. 2008;32(1):44–49. doi: 10.1002/uog.5353. [DOI] [PubMed] [Google Scholar]
• 33.Rajagopalan V, Scott J, Habas P, Kim K, Rousseau F, Glenn O, Barkovich A, Studholme C. Measures for characterizing directionality specific volume changes in TBM of brain growth. Medical Image Computing and Computer Assisted Intervention. 2010;6362(2):339–346. doi: 10.1007/978-3-642-15745-5_42. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 34.Rajagopalan V, Scott JA, Habas PA, Corbett-Detig JM, Kim K, Rousseau F, Barkovich AJ, Glenn OA, Studholme C. Local tissue growth patterns underlying normal fetal human brain gyrification quantified in utero. Journal of Neuroscience. 2011;31:2878–2887. doi: 10.1523/JNEUROSCI.5458-10.2011. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 35.Scott JA, Habas PA, Kim K, Rajagopalan V, Hamzelou KS, Corbett-Detig JM, Barkovich AJ, Glenn OA, Studholme C. Growth trajectories of the human fetal brain tissues estimated from 3d reconstructed in utero MRI. International Journal of Developmental Neuroscience. 2011;29(5):529–536. doi: 10.1016/j.ijdevneu.2011.04.001. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 36.Smart IH, McSherry GM. Gyrus formation in the cerebral cortex in the ferret. I. Description of the external changes. Journal of Anatomy. 1986;146:141–152. [PMC free article] [PubMed] [Google Scholar]
• 37.Studholme C. Dense feature deformation morphometry: Incorporating DTI data into conventional MRI morphometry. Medical Image Analysis. 2008;12(6):742–751. doi: 10.1016/j.media.2008.03.010. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 38.Studholme C. Mapping fetal brain development in utero using magnetic resonance imaging: The big bang of brain mapping. Annual Review of Biomedical Engineering. 2011;13:345–368. doi: 10.1146/annurev-bioeng-071910-124654. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 39.Studholme C, Cardenas V. Population based analysis of directional information in serial deformation tensor morphometry. Medical Image Computing and Computer Assisted Intervention. 2007:311–318. doi: 10.1007/978-3-540-75759-7_38. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 40.Studholme C, Cardenas V, Schuff N, Rosen H, Miller B, Weiner M. Detecting spatially consistent structural differences in Alzheimer’s and fronto temporal dementia using deformation morphometry. Medical Image Computing and Computer Assisted Intervention. 2001:41–48. [Google Scholar]
• 41.Studholme C, Hill DLG, Hawkes DJ. An overlap invariant entropy measure of 3D medical image alignment. Pattern Recognition. 1999;32(1):71–86. [Google Scholar]
• 42.Thirion J. Image matching as a diffusion process: An analogy with maxwell’s demons. Medical Image Analysis. 1998;2(3):243–260. doi: 10.1016/s1361-8415(98)80022-4. [DOI] [PubMed] [Google Scholar]
• 43.Thompson PM, Giedd JN, Woods RP, MacDonald D, Evans AC, Toga AW. Growth patterns in the developing brain detected by using continuum mechanical tensor maps. Nature. 2000;404(6774):190–193. doi: 10.1038/35004593. [DOI] [PubMed] [Google Scholar]
• 44.Thompson PM, Mega MS, Woods RP, Zoumalan CI, Lind-shield CJ, Blanton RE, Moussai J, Holmes CJ, Cummings JL, Toga AW. Cortical change in Alzheimer’s disease detected with a disease-specific population-based brain atlas. Cerebral Cortex. 2001;11(1):1–16. doi: 10.1093/cercor/11.1.1. [DOI] [PubMed] [Google Scholar]
• 45.Tzarouchi LC, Astrakas LG, Xydis V, Zikou A, Kosta P, Drougia A, Andronikou S, Argyropoulou MI. Age-related grey matter changes in preterm infants: An MRI study. Neuroimage. 2009;47(4):1148–1153. doi: 10.1016/j.neuroimage.2009.03.072. [DOI] [PubMed] [Google Scholar]
• 46.Viola P, Wells WM. Alignment by maximization of mutual information. International Journal of Computer Vision. 1997;24(2):137–154. [Google Scholar]
• 47.Wang W, Hoerder-Suabedissen A, Oeschger F, Bayatti N, Ip B, Lindsay S, Supramaniam V, Srinivasan L, Rutherford M, Moll-gard K, Clowry G, Molnar Z. Subplate in the developing cortex of mouse and human. Journal of Anatomy. 2010;217:368–380. doi: 10.1111/j.1469-7580.2010.01274.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
• 48.Zhang H, Awate S, Das S, Woo J, Melhem E, Gee J, Yushkevich P. A tract-specific framework for white matter morphometry combining macroscopic and microscopic tract features. Medical Image Computing and Computer Assisted Intervention. 2009:141–149. doi: 10.1007/978-3-642-04271-3_18. [DOI] [PMC free article] [PubMed] [Google Scholar]