Detecting Gray Matter Maturation via Tensor-based Surface Morphometry

Moo K. Chung, Keith J. Worsley1, S. Robbins1, Tomás Paus1, Jay N. Giedd2, Judith L. Rapoport2, Alan C. Evans1
Department of Statistics
Department of Biostatistis and Medical Informatics
W.M. Keck laboratory for functional brain imaging and behavior, University of Wisconsin-Madison
Department of Mathematics and Statistics, McGill University
1Montreal Neurological Institute
2Child Psychiatry Branch, National Institute of Mental Health

We present a unified computational approach to tensor-based surface morphometry in detecting the gray matter growth patterns for 28 children and young adults aged between 12 and 16. The gray matter has the topology of a 2D highly convoluted thin sheet. As the brain develops over time, the cortical surface area, thickness, curvatures and the total gray matter volume change. It is highly likely that such age-related surface deformations are not uniform. By measuring how such surface metrics change over time, the regions of the most rapid structural changes can be detected.


We used anatomic segmentation using proximities (ASP) method (McDonalds et al, 2001) to generate both outer and inner surface meshes from classified MRIs. Then the surface meshes were parameterized by local quadratic polynomials (Chung et al, 2003). The cortical surface deformation was modeled as the boundary of ulticomponent fluids (Drew, 1991). Using the same stochastic assumption on the deformation field used in Chung et al. (2001), the distributions of area dilatation rate, cortical thickness and curvature changes are derived (Chung et al, 2003). To increase the signal to noise ratio, diffusion smoothing (Andrade,2001; Chung et al. 2003) has been developed and applied to surface data. Afterwards, statistical inference on the cortical surface is performed via random fields theory (Worsley et al., 1994).


It is found that the total cortical surface area and gray matter volume shrinks, while the cortical thickness and curvature tends to increase between ages 12 and 16 with a highly localized area of cortical thickening and surface area shrinking found in the superior frontal sulcus at the same time. It seems that the increase in thickness and decrease in the superior frontal sulcus area are causing increased folding in the middle and superior frontal gyri (see Figure 1.). Because our technique is based on coordinate-invariant tensor geometry, artificial surface flattening (Angenent et al., 1999), which can destroy the inherent geometrical structures of the cortical surface, has been avoided.
Figure 1 Top: Bending energy computed on the inner cortical surface of a 14 year old subject. Bottom: t map showing the regions of curvature increase between ages 12 and 16. Most of curvature increase occurs on gyri.



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