Tensor-Based Surface Morphometry applied to Gray Matter Maturation

Moo K. Chung, Keith J. Worsley, Tomas Paus, Steve Robbins, Jonathan Taylor1, Jay N. Giedd2, Judith L. Rapoport2, Alan C. Evans
Department of Statistics
W.M. Keck laboratory for functional brain imaging and behavior, University of Wisconsin-Madison
Department of Mathematics and Statistics
Montreal Neurological Institue, McGill University
1Department of Statistics, Stanford University
2Child Psychiatry Branch, National Institute of Mental Health
Abstract
We present tensor-based surface morthometry that does not require the regions of interest (ROI) and apply it to the problem of quantifying 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, curvature and 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.

Methods

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, 2002). The cortical surface deformaion 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 can be derived. To increase the signal to noise ratio, diffusion smoothing (Andrade ,2001; Chung et al., 2002) has been developed and applied to surface data. surfaceThe diffusion smoothing algorithm written in Matlab is freely available at http://www.stat.wisc.edu/~mchung.
Afterwards, statistical inference on the cortical surface is performed via random fields theory (Worsley et al., 1994).

Results and discussion

It is found that the 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 incresed foldings in the middle and superior frontal gyri (see the figure).

Because our technique is based on cordinate-invariant tensor geometry, artificial surface flattening (Andrade et al.,B 2001; Angenent et al., 1999), which can destroy the inherent geometrical structures of the cortical surface, has been avoided.
 
Top: Bending energy computed on the inner cortical surface of a 14 year old subject. Bottom: t map showing the regions of curvature increase. Most of curvature increase occurs on gyri.

References

Andrade, A., Kherif, F., Mangin, J., Worsley, K.J., Paradis, A., Simons, O., Dehaene, S., Le Bihan, D., Poline J-B. (2001) Detection of fMRI activation using cortical surface mapping, Human Brain Mapping, 12:79-93.

Chung, M.K., Worsley, K.J., Paus, T., Cherif, D.L., Collins, C., Giedd J., Rapoport, J.L., Evans, A.C. (2001) A unified statistical approach to deformation-based morphometry, NeuroImage, 14:595-606.

Chung, M.K., Worsley, K.J., Paus, T., Robbins, S., Taylor, J. Giedd, J.N., Rapoport, J.L., Evans, A.C. (2002) Tensor-based surface morphometry, Department TR 1049. http://www.stat.wisc.edu/~mchung.

Drew, D.A. (1991) Theory of multicomponent fluids, Springer-Verlag, New York.

MacDonalds, J.D., Kabani, N., Avis, D., Evans, A.C. (2001) Automated 3-D extraction of inner and outer surfaces of cerebral cortex from MRI, NeuroImage, 12:340-356.

Worsley, K.J., Marrett, S., Neelin, P., Vandal, A.C., Friston, K.J., Evans, A.C. (1996) A unified statistical approach for determining significant signals in images of cerebral activation, Human Brain Mapping, 4:58-73.