title: Brain surface conformal parameterization with the Ricci flow.
abstract: In brain mapping research, parameterized 3-D surface models are of great interest for statistical comparisons of anatomy, surface-based registration, and signal processing. Here, we introduce the theories of continuous and discrete surface Ricci flow, which can create Riemannian metrics on surfaces with arbitrary topologies with user-defined Gaussian curvatures. The resulting conformal parameterizations have no singularities and they are intrinsic and stable. 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 to a parameter domain with a user-designed Gaussian curvature arrangement. In the parameter domain, a shape index based on conformal invariants is computed, and inter-subject cortical surface matching is performed by solving a constrained harmonic map. We illustrate various target curvature arrangements and demonstrate the stability of the method using longitudinal data. To map statistical differences in cortical morphometry, we studied brain asymmetry in 14 healthy control subjects. We used a manifold version of Hotelling's  T(2)  test, applied to the Jacobian matrices of the surface parameterizations. A permutation test, along with the cumulative distribution of   p-values, were used to estimate the overall statistical significance of differences. The results show our algorithm's power to detect subtle group differences in cortical surfaces.
authors.affiliation: Laboratory of Neuro Imaging, School of Medicine, University of California, Los Angeles, CA 90095 USA. ylwang@asu.edu
authors.forename: Yalin
authors.initials: Y
authors.lastname: Wang
authors.forename: Jie
authors.initials: J
authors.lastname: Shi
authors.forename: Xiaotian
authors.initials: X
authors.lastname: Yin
authors.forename: Xianfeng
authors.initials: X
authors.lastname: Gu
authors.forename: Tony F
authors.initials: TF
authors.lastname: Chan
authors.forename: Shing-Tung
authors.initials: ST
authors.lastname: Yau
authors.forename: Arthur W
authors.initials: AW
authors.lastname: Toga
authors.forename: Paul M
authors.initials: PM
authors.lastname: Thompson
mesh_terms: D000465:Algorithms; D002540:Cerebral Cortex / Q000033:anatomy & histology*; D003198:Computer Simulation; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008953:Models, Anatomic; D008959:Models, Neurological; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity