Brain Mapping with the Ricci Flow Conformal Parameterization and Multivariate Statistics on Deformation Tensors
2nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA-2008)
Yalin Wang, Xiaotian Yin, Jie Zhang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, and Shing-Tung Yau
By solving the Yamabe equation with the discrete surface
Ricci flow method, we can conformally parameterize a multiple bound-
ary surface by a multi-hole disk. The resulting parameterizations do not
have any singularities and they are intrinsic and stable. For applications
in brain mapping research, first, we convert a cortical surface model
into a multiple boundary surface by cutting along selected anatomical
landmark curves. Secondly, we conformally parameterize each cortical
surface using a multi-hole disk. Inter-subject cortical surface matching
is performed by solving a constrained harmonic map in the canonical
parameter domain. To map group differences in cortical morphometry,
we then compute a manifold version of Hotelling’s T2 test on the Ja-
cobian matrices. Permutation testing was used to estimate statistical
significance. We studied brain morphology in 21 patients with Williams
Syndrome (WE) and 21 matched healthy control subjects with the pro-
posed method. The results demonstrate our algorithm’s potential power
to effectively detect group differences on cortical surfaces.