Diffeomorphic metric surface mapping in subregion of the superior temporal gyrus

This paper describes the application of large deformation diffeomorphic metric mapping to cortical surfaces based on the shape and geometric properties of subregions of the superior temporal gyrus in the human brain. The anatomical surfaces of the cortex are represented as triangulated meshes. The diffeomorphic matching algorithm is implemented by defining a norm between the triangulated meshes, based on the algorithms of Vaillant and Glaunès. The diffeomorphic correspondence is defined as a flow of the extrinsic three dimensional coordinates containing the cortical surface that registers the initial and target geometry by minimizing the norm. The methods are demonstrated in 40 high-resolution MRI cortical surfaces of planum temporale (PT) constructed from subsets of the superior temporal gyrus (STG). The effectiveness of the algorithm is demonstrated via the Euclidean positional distance, distance of normal vectors, and curvature before and after the surface matching as well as the comparison with a landmark matching algorithm. The results demonstrate that both the positional and shape variability of the anatomical configurations are being represented by the diffeomorphic maps.

[1]  Godfrey D. Pearlson,et al.  Asymmetry of the planum temporale: methodological considerations and clinical associations , 1995, Psychiatry Research: Neuroimaging.

[2]  H. Seldon,et al.  Does brain white matter growth expand the cortex like a balloon? Hypothesis and consequences , 2005, Laterality.

[3]  Paul Dupuis,et al.  Variational problems on ows of di eomorphisms for image matching , 1998 .

[4]  Ron Kikinis,et al.  Progressive decrease of left Heschl gyrus and planum temporale gray matter volume in first-episode schizophrenia: a longitudinal magnetic resonance imaging study. , 2003, Archives of general psychiatry.

[5]  L. Younes,et al.  Diffeomorphic matching of distributions: a new approach for unlabelled point-sets and sub-manifolds matching , 2004, CVPR 2004.

[6]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[7]  Jerry L Prince,et al.  Cortical surface segmentation and mapping , 2004, NeuroImage.

[8]  R. Bajcsy,et al.  Elastic Matching: Continuum Mechanical and Probabilistic Analysis , 1999 .

[9]  J. T. Ratnanather,et al.  Validating Cortical Surface Analysis of Medial Prefrontal Cortex , 2001, NeuroImage.

[10]  L. Younes,et al.  Statistics on diffeomorphisms via tangent space representations , 2004, NeuroImage.

[11]  Michael I. Miller,et al.  Validation of semiautomated methods for quantifying cingulate cortical metrics in schizophrenia , 2004, Psychiatry Research: Neuroimaging.

[12]  David C. Van Essen,et al.  Application of Information Technology: An Integrated Software Suite for Surface-based Analyses of Cerebral Cortex , 2001, J. Am. Medical Informatics Assoc..

[13]  Michael I. Miller,et al.  Brain Segmentation and the Generation of Cortical Surfaces , 1999, NeuroImage.

[14]  Alain Trouvé,et al.  Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms , 2005, International Journal of Computer Vision.

[15]  Michael I. Miller,et al.  Large deformation diffeomorphic metric mapping of vector fields , 2005, IEEE Transactions on Medical Imaging.

[16]  H. Seldon,et al.  The left human speech-processing cortex is thinner but longer than the right , 2003, Laterality.

[17]  Jerry L. Prince,et al.  Topology correction in brain cortex segmentation using a multiscale, graph-based algorithm , 2002, IEEE Transactions on Medical Imaging.

[18]  Alain Trouvé,et al.  Geodesic Shooting for Computational Anatomy , 2006, Journal of Mathematical Imaging and Vision.

[19]  D. V. van Essen,et al.  Surface-based approaches to spatial localization and registration in primate cerebral cortex. , 2004, NeuroImage.

[20]  Bernd Hamann,et al.  Curvature Approximation for Triangulated Surfaces , 1993, Geometric Modelling.

[21]  Sabine Landau,et al.  Evidence for altered neuronal organisation within the planum temporale in major psychiatric disorders , 2005, Schizophrenia Research.

[22]  Stephen R. Marsland,et al.  Measuring Geodesic Distances on the Space of Bounded Diffeomorphisms , 2002, BMVC.

[23]  Joan Alexis Glaunès.  Transport par difféomorphismes de points, de mesures et de courants pour la comparaison de formes et l'anatomie numérique , 2005 .

[24]  M. Miller,et al.  Landmark Matching via Large Deformation , 2000 .

[25]  Xiao Han,et al.  Cortical surface reconstruction using a topology preserving geometric deformable model , 2001, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA 2001).

[26]  R. Kikinis,et al.  Planum temporale and Heschl gyrus volume reduction in schizophrenia: a magnetic resonance imaging study of first-episode patients. , 2000, Archives of general psychiatry.

[27]  Michael I. Miller,et al.  Dynamic programming generation of boundaries of local coordinatized submanifolds in the neocortex: application to the planum temporale , 2003, NeuroImage.

[28]  Robert A. Melter,et al.  Vision Geometry , 1992 .

[29]  U. Grenander,et al.  Computational anatomy: an emerging discipline , 1998 .

[30]  Guido Gerig,et al.  Unbiased diffeomorphic atlas construction for computational anatomy , 2004, NeuroImage.

[31]  L. Younes,et al.  Evidence of Structural Remodeling in the Dyssynchronous Failing Heart , 2005, Circulation research.

[32]  David C. Van Essen,et al.  A Population-Average, Landmark- and Surface-based (PALS) atlas of human cerebral cortex , 2005, NeuroImage.

[33]  Michael I. Miller,et al.  Differential geometry of the cortical surface , 1995, Optics & Photonics.

[34]  Michael I. Miller,et al.  Landmark matching via large deformation diffeomorphisms , 2000, IEEE Trans. Image Process..

[35]  J. Gee,et al.  Geodesic estimation for large deformation anatomical shape averaging and interpolation , 2004, NeuroImage.

[36]  Kiralee M. Hayashi,et al.  Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia , 2004, NeuroImage.

[37]  D. V. van Essen,et al.  Structural and Functional Analyses of Human Cerebral Cortex Using a Surface-Based Atlas , 1997, The Journal of Neuroscience.

[38]  Joan Alexis Glaunès,et al.  Surface Matching via Currents , 2005, IPMI.

[39]  Jerry L. Prince,et al.  Mapping Techniques for Aligning Sulci across Multiple Brains , 2003, MICCAI.

[40]  R A Robb,et al.  Analyze: a comprehensive, operator-interactive software package for multidimensional medical image display and analysis. , 1989, Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society.

[41]  L. Younes,et al.  On the metrics and euler-lagrange equations of computational anatomy. , 2002, Annual review of biomedical engineering.

[42]  T. Crow,et al.  The cytoarchitecture of sulcal folding in Heschl’s sulcus and the temporal cortex in the normal brain and schizophrenia: lamina thickness and cell density , 2004, Neuroscience Letters.

[43]  A. Dale,et al.  High‐resolution intersubject averaging and a coordinate system for the cortical surface , 1999, Human brain mapping.

[44]  Laurent Younes,et al.  Geodesic Interpolating Splines , 2001, EMMCVPR.

[45]  Michael I. Miller,et al.  Large deformation diffeomorphic metric mapping of fiber orientations , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.