Model-Driven Harmonic Parameterization of the Cortical Surface: HIP-HOP

In the context of inter subject brain surface matching, we present a parameterization of the cortical surface constrained by a model of cortical organization. The parameterization is defined via an harmonic mapping of each hemisphere surface to a rectangular planar domain that integrates a representation of the model. As opposed to previous landmark-based registration methods we do not match folds between individuals but instead optimize the fit between cortical sulci and specific iso-coordinate axis in the model. This strategy overcomes some limitation to sulcus-based registration techniques such as topological variability in sulcal landmarks across subjects. Experiments on 62 subjects with manually traced sulci are presented and compared with the result of the Freesurfer software. The evaluation involves a measure of dispersion of sulci with both angular and area distortions. We show that the model-based strategy can lead to a natural, efficient and very fast (less than 5 min per hemisphere) method for defining inter subjects correspondences. We discuss how this approach also reduces the problems inherent to anatomically defined landmarks and open the way to the investigation of cortical organization through the notion of orientation and alignment of structures across the cortex.

[1]  Arthur W. Toga,et al.  Diffeomorphic Sulcal Shape Analysis on the Cortex , 2012, IEEE Transactions on Medical Imaging.

[2]  Alain Trouvé,et al.  Diffeomorphisms Groups and Pattern Matching in Image Analysis , 1998, International Journal of Computer Vision.

[3]  B. Argall,et al.  Simplified intersubject averaging on the cortical surface using SUMA , 2006, Human brain mapping.

[4]  Y. Samson,et al.  "Sulcal root" generic model: a hypothesis to overcome the variability of the human cortex folding patterns. , 2005, Neurologia medico-chirurgica.

[5]  David C. Van Essen,et al.  Surface-based approaches to spatial localization and registration in primate cerebral cortex , 2004, NeuroImage.

[6]  Guillaume Auzias,et al.  Automatic sulcal line extraction on cortical surfaces using geodesic path density maps , 2012, NeuroImage.

[7]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[8]  Kenneth Stephenson,et al.  Cortical cartography using the discrete conformal approach of circle packings , 2004, NeuroImage.

[9]  Lok Ming Lui,et al.  Brain Surface Conformal Parameterization Using Riemann Surface Structure , 2007, IEEE Transactions on Medical Imaging.

[10]  Alan C. Evans,et al.  Spatial distribution of deep sulcal landmarks and hemispherical asymmetry on the cortical surface. , 2010, Cerebral cortex.

[11]  D. V. von Cramon,et al.  Deep sulcal landmarks provide an organizing framework for human cortical folding. , 2008, Cerebral cortex.

[12]  Jean-Francois Mangin,et al.  Sulcal pattern and morphology of the superior temporal sulcus , 2004, NeuroImage.

[13]  D. Louis Collins,et al.  Atlas-based clustering of sulcal patterns — Application to the left inferior frontal sulcus , 2012, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI).

[14]  Lok Ming Lui,et al.  Automatic Landmark Tracking and its Application to the Optimization of Brain Conformal Mapping , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[15]  Guillermo Sapiro,et al.  Conformal Surface Parameterization for Texture Mapping , 1999 .

[16]  Roberto Toro,et al.  Geometric atlas: modeling the cortex as an organized surface , 2003, NeuroImage.

[17]  T. Chan,et al.  Genus zero surface conformal mapping and its application to brain surface mapping. , 2004, IEEE transactions on medical imaging.

[18]  A. Dale,et al.  Cortical Surface-Based Analysis II: Inflation, Flattening, and a Surface-Based Coordinate System , 1999, NeuroImage.

[19]  Michael I. Miller,et al.  Large Deformation Diffeomorphic Metric Curve Mapping , 2008, International Journal of Computer Vision.

[20]  Arthur W. Toga,et al.  Sulcal set optimization for cortical surface registration , 2010, NeuroImage.

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

[22]  Colin Studholme,et al.  Early folding patterns and asymmetries of the normal human brain detected from in utero MRI. , 2012, Cerebral cortex.

[23]  E. Duchesnay,et al.  A framework to study the cortical folding patterns , 2004, NeuroImage.

[24]  Jerry L. Prince,et al.  Cortical Surface Alignment Using Geometry Driven Multispectral Optical Flow , 2005, IPMI.

[25]  Jerry L. Prince,et al.  Mapping techniques for aligning sulci across multiple brains. , 2004 .

[26]  W. T. Tutte.  How to Draw a Graph , 1963 .

[27]  Paul M. Thompson,et al.  Surface-Constrained Volumetric Brain Registration Using Harmonic Mappings , 2007, IEEE Transactions on Medical Imaging.

[28]  Monica K. Hurdal,et al.  Discrete conformal methods for cortical brain flattening , 2009, NeuroImage.

[29]  Michael S. Floater,et al.  One-to-one piecewise linear mappings over triangulations , 2003, Math. Comput..

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

[31]  Steven Robbins,et al.  An unbiased iterative group registration template for cortical surface analysis , 2007, NeuroImage.

[32]  Jean-Francois Mangin,et al.  Cortical sulci recognition and spatial normalization , 2011, Medical Image Anal..

[33]  Monica K. Hurdal,et al.  Chemically Based Mathematical Model for Development of Cerebral Cortical Folding Patterns , 2009, PLoS Comput. Biol..

[34]  Mathieu Desbrun,et al.  Unconstrained Spherical Parameterization , 2007, J. Graph. Tools.

[35]  Hyunjin Park,et al.  Cortical surface registration using spherical thin-plate spline with sulcal lines and mean curvature as features , 2012, Journal of Neuroscience Methods.

[36]  Nicholas Ayache,et al.  Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration , 2010, IEEE Transactions on Medical Imaging.

[37]  Jean-Francois Mangin,et al.  Model-driven parameterization of the cortical surface for localization and inter-subject matching , 2010, NeuroImage.

[38]  Katrin Amunts,et al.  Cortical Folding Patterns and Predicting Cytoarchitecture , 2007, Cerebral cortex.

[39]  Mark Meyer,et al.  Intrinsic Parameterizations of Surface Meshes , 2002, Comput. Graph. Forum.

[40]  Guilherme Carvalhal Ribas,et al.  Study of fetal and postnatal morphological development of the brain sulci. , 2013, Journal of neurosurgery. Pediatrics.

[41]  Ulrich Pinkall,et al.  Computing Discrete Minimal Surfaces and Their Conjugates , 1993, Exp. Math..

[42]  Paul M. Thompson,et al.  Inferring brain variability from diffeomorphic deformations of currents: An integrative approach , 2008, Medical Image Anal..

[43]  Richard M. Leahy,et al.  Comparison of landmark-based and automatic methods for cortical surface registration , 2010, NeuroImage.

[44]  Shing-Tung Yau,et al.  Slit Map: Conformal Parameterization for Multiply Connected Surfaces , 2008, GMP.

[45]  Paul M. Thompson,et al.  Conformal Slit Mapping and Its Applications to Brain Surface Parameterization , 2008, MICCAI.

[46]  Mert R. Sabuncu,et al.  Learning Task-Optimal Registration Cost Functions for Localizing Cytoarchitecture and Function in the Cerebral Cortex , 2010, IEEE Transactions on Medical Imaging.

[47]  Lok Ming Lui,et al.  Optimized Conformal Surface Registration with Shape-based Landmark Matching , 2010, SIAM J. Imaging Sci..

[48]  M. Miller.  Computational anatomy: shape, growth, and atrophy comparison via diffeomorphisms , 2004, NeuroImage.

[49]  Ron Kikinis,et al.  On the Laplace-Beltrami operator and brain surface flattening , 1999, IEEE Transactions on Medical Imaging.

[50]  Jean-Francois Mangin,et al.  A New Cortical Surface Parcellation Model and Its Automatic Implementation , 2006, MICCAI.

[51]  Alain Trouvé,et al.  Diffeomorphic Brain Registration Under Exhaustive Sulcal Constraints , 2011, IEEE Transactions on Medical Imaging.

[52]  D. V. van Essen,et al.  Functional and structural mapping of human cerebral cortex: solutions are in the surfaces. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[53]  Lok Ming Lui,et al.  Optimization of Brain Conformal Mapping with Landmarks , 2005, MICCAI.