ÿþ<HTML> <HEAD> <TITLE>Riemann Surface :Publications :Abstract : Brain Mapping with the Ricci Flow Conformal Parameterization and Multivariate Statistics on Deformation Tensors</TITLE> </HEAD> <BODY> <H3> Brain Mapping with the Ricci Flow Conformal Parameterization and Multivariate Statistics on Deformation Tensors</H3> <BR> 2nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA-2008) <BR> Yalin Wang, Xiaotian Yin, Jie Zhang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, and Shing-Tung Yau <HR> 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. <HR> </BODY> </HTML>