Double Diffeomorphism: Combining Morphometry and Structural Connectivity Analysis

The brain is composed of several neural circuits which may be seen as anatomical complexes composed of grey matter structures interconnected by white matter tracts. Grey and white matter components may be modeled as 3-D surfaces and curves, respectively. Neurodevelopmental disorders involve morphological and organizational alterations which cannot be jointly captured by usual shape analysis techniques based on single diffeomorphisms. We propose a new deformation scheme, called double diffeomorphism, which is a combination of two diffeomorphisms. The first one captures changes in structural connectivity, whereas the second one recovers the global morphological variations of both grey and white matter structures. This deformation model is integrated into a Bayesian framework for atlas construction. We evaluate it on a data-set of 3-D structures representing the neural circuits of patients with Gilles de la Tourette syndrome (GTS). We show that this approach makes it possible to localise, quantify, and easily visualise the pathological anomalies altering the morphology and organization of the neural circuits. Furthermore, results also indicate that the proposed deformation model better discriminates between controls and GTS patients than a single diffeomorphism.

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

[2]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..

[3]  N. Ayache,et al.  Computation of a probabilistic statistical shape model in a maximum-a-posteriori framework. , 2009, Methods of information in medicine.

[4]  Martha Elizabeth Shenton,et al.  Global Medical Shape Analysis Using the Laplace-Beltrami Spectrum , 2007, MICCAI.

[5]  Jerry L Prince,et al.  A computerized approach for morphological analysis of the corpus callosum. , 1996, Journal of computer assisted tomography.

[6]  F. Bookstein,et al.  Morphometric Tools for Landmark Data: Geometry and Biology , 1999 .

[7]  Stanley Durrleman,et al.  Statistical models of currents for measuring the variability of anatomical curves, surfaces and their evolution. (Modèles statistiques de courants pour mesurer la variabilité anatomique de courbes, de surfaces et de leur évolution) , 2010 .

[8]  Lea Fleischer,et al.  General Pattern Theory A Mathematical Study Of Regular Structures , 2016 .

[9]  Alain Trouvé,et al.  The Varifold Representation of Nonoriented Shapes for Diffeomorphic Registration , 2013, SIAM J. Imaging Sci..

[10]  Xavier Pennec,et al.  Sparse Multi-Scale Diffeomorphic Registration: The Kernel Bundle Framework , 2012, Journal of Mathematical Imaging and Vision.

[11]  Pietro Gori,et al.  Parsimonious Approximation of Streamline Trajectories in White Matter Fiber Bundles , 2016, IEEE Transactions on Medical Imaging.

[12]  Alain Trouvé,et al.  A Statistical Model of White Matter Fiber Bundles Based on Currents , 2009, IPMI.

[13]  Guido Gerig,et al.  Morphometry of anatomical shape complexes with dense deformations and sparse parameters , 2014, NeuroImage.

[14]  Alain Trouvé,et al.  Bayesian template estimation in computational anatomy , 2008, NeuroImage.

[15]  Oury Monchi,et al.  Cortico-basal ganglia and cortico-cerebellar circuits in Parkinson's disease: pathophysiology or compensation? , 2013, Behavioral neuroscience.

[16]  François-Xavier Vialard,et al.  Piecewise-diffeomorphic image registration: Application to the motion estimation between 3D CT lung images with sliding conditions , 2013, Medical Image Anal..

[17]  Keith Heberlein,et al.  Imaging human connectomes at the macroscale , 2013, Nature Methods.

[18]  Alain Trouvé,et al.  Registration of Multiple Shapes using Constrained Optimal Control , 2016, SIAM J. Imaging Sci..

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

[20]  Ulf Grenander,et al.  General Pattern Theory: A Mathematical Study of Regular Structures , 1993 .

[21]  Martin Styner,et al.  Framework for the Statistical Shape Analysis of Brain Structures using SPHARM-PDM. , 2006, The insight journal.

[22]  Dinggang Shen,et al.  A Hybrid Multishape Learning Framework for Longitudinal Prediction of Cortical Surfaces and Fiber Tracts Using Neonatal Data , 2016, MICCAI.

[23]  Danielle F. Pace,et al.  A Locally Adaptive Regularization Based on Anisotropic Diffusion for Deformable Image Registration of Sliding Organs , 2013, IEEE Transactions on Medical Imaging.

[24]  Jun Ma,et al.  Atlas Generation for Subcortical and Ventricular Structures With Its Applications in Shape Analysis , 2010, IEEE Transactions on Image Processing.

[25]  Anqi Qiu,et al.  Whole brain diffeomorphic metric mapping via integration of sulcal and gyral curves, cortical surfaces, and images , 2011, NeuroImage.

[26]  Bruce Fischl,et al.  Combined Volumetric and Surface Registration , 2009, IEEE Transactions on Medical Imaging.

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

[28]  Martin Styner,et al.  Multi-Object Analysis of Volume, Pose, and Shape Using Statistical Discrimination , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[29]  Martin Styner,et al.  Shape Modeling and Analysis with Entropy-Based Particle Systems , 2007, IPMI.

[30]  John H. Gilmore,et al.  Fiber Tract-Oriented Statistics for Quantitative Diffusion Tensor MRI Analysis , 2005, MICCAI.

[31]  A. Jacobson,et al.  Morphometric tools for landmark data , 1993 .

[32]  Pamela Guevara,et al.  Altered structural connectivity of cortico-striato-pallido-thalamic networks in Gilles de la Tourette syndrome , 2014, Brain : a journal of neurology.

[33]  Y. Amit,et al.  Towards a coherent statistical framework for dense deformable template estimation , 2007 .

[34]  Pietro Gori,et al.  Bayesian Atlas Estimation for the Variability Analysis of Shape Complexes , 2013, MICCAI.

[35]  Pietro Gori,et al.  Joint Morphometry of Fiber Tracts and Gray Matter Structures Using Double Diffeomorphisms , 2015, IPMI.

[36]  Guido Gerig,et al.  Optimal Data-Driven Sparse Parameterization of Diffeomorphisms for Population Analysis , 2011, IPMI.

[37]  Jean-Francois Mangin,et al.  Joint T1 and Brain Fiber Log-Demons Registration Using Currents to Model Geometry , 2012, MICCAI.

[38]  P. Thomas Fletcher,et al.  Principal geodesic analysis for the study of nonlinear statistics of shape , 2004, IEEE Transactions on Medical Imaging.

[39]  Paul A. Yushkevich,et al.  Structure-specific statistical mapping of white matter tracts , 2007, NeuroImage.

[40]  Anqi Qiu,et al.  Large Deformation Multiresolution Diffeomorphic Metric Mapping for Multiresolution Cortical Surfaces: A Coarse-to-Fine Approach , 2016, IEEE Transactions on Image Processing.

[41]  Stanley Durrleman,et al.  Bayesian Mixed Effect Atlas Estimation with a Diffeomorphic Deformation Model , 2015, SIAM J. Imaging Sci..

[42]  Pietro Gori,et al.  A Bayesian framework for joint morphometry of surface and curve meshes in multi‐object complexes , 2017, Medical Image Anal..

[43]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.