NAMIC: UNC – PNL collaboration- 1 - October 7, 2005 Fiber tract-oriented quantitative analysis of Diffusion Tensor MRI data Postdoctoral fellow, Dept of Computer Science and Psychiatry, UNC-Chapel Hill Isabelle Corouge

NAMIC: UNC – PNL collaboration- 2 - October 7, 2005 Motivations Diffusion Tensor MRI –Study white matter structural properties –Explore relationships between diffusion properties and brain connectivity Motivations –Inter-individual comparison –Characterization of normal variability –Atlas building –Pathology (e.g., tumor, fiber tract disruption) –Early brain development –Connectivity ? FA image

NAMIC: UNC – PNL collaboration- 3 - October 7, 2005 Quantitative DTI Analysis Spirit of our work –Alternative to voxel-based analysis –Fiber tract-based measurements: Diffusion properties within cross-sections and along bundles T Geometric modeling of fiber bundles T Fiber tract-oriented statistics of DTI Methodology outline DT images Fiber Extraction Clustering into bundles Fiber tract properties analysis Fiber tract shape modeling Modeling - Shape Statistics - Diffusion Tensors Statistics

NAMIC: UNC – PNL collaboration- 4 - October 7, 2005 Fiber Extraction Extraction by tractography [Fillard’03] –High resolution DTI data (baseline + 6 directional images, 2mm 3 ) –Principal diffusion direction tracking algorithm Source and target regions of interest Local continuity constraint, backward tracking, subvoxel precision “ Fibers”: streamlines through the vector field

NAMIC: UNC – PNL collaboration- 5 - October 7, 2005 Fiber Clustering into Bundles Motivation –Set of 3D curves, : 3D points –Presence of outliers (noise and ambiguities in the tensor field) –Reconstructed fibers might be part of different anatomical bundles Clustering: based on position and shape similarity Alternative implementation –Graph formalism & Normalized Cuts concept [C. Goodlett, PhD student] T Hierarchical, agglomerative algorithm A cluster C:  F i in C,  at least one F j in C, j  i such that: d(F i, F j ) < t Fiber space

NAMIC: UNC – PNL collaboration- 6 - October 7, 2005 Fiber Clustering into Bundles Examples: –3Tesla high resolution ( 2 x 2 x 2 mm 3 ) DT MRI –Cortico-spinal tract of left and right hemisphere …After Before…Neonate

NAMIC: UNC – PNL collaboration- 7 - October 7, 2005 Fiber Clustering into Bundles Graph-theoretic approach * Images from Casey Goodlett Fornix cluster Longitudinal fasciculus (2312 streamlines) 6 clusters

NAMIC: UNC – PNL collaboration- 8 - October 7, 2005 Fiber Tract Properties Analysis Analysis across fibers –Local shape properties: curvature/torsion –Diffusion properties: FA, MD, … Matching scheme –Definition of a common origin for each bundle –Parameterization of the fibers: cubic B-splines –Explicit point to point matching according to arclength Computation of pointwise mean and standard deviation of these features

NAMIC: UNC – PNL collaboration- 9 - October 7, 2005 Local Shape Properties Curvature For each curve Adult 1 NeonateAdult 2 Mean ± σ a b c a a a b b c c c b

NAMIC: UNC – PNL collaboration October 7, 2005 Diffusion Properties Adult Neonate FA FA: Mean ± σ

NAMIC: UNC – PNL collaboration October 7, 2005 Geometric Modeling of Individual Fiber Tracts Statistical modeling based on variability learning Construction of a training set –Parametric data representation –Matching: Dense point to point correspondence Pose parameter estimation: Procrustes analysis Estimation of a template curve: mean shape Characterization of statistical shape variability –Multidimensional statistical analysis: PCA

NAMIC: UNC – PNL collaboration October 7, 2005 Sets of aligned shapes and estimated mean shape Geometric Modeling Callosal tract Right cortico spinal tract

NAMIC: UNC – PNL collaboration October 7, 2005 Geometric Modeling First and second modes of deformation –Subject 1, callosal tract Mode 1 Mode 2 rotated view

NAMIC: UNC – PNL collaboration October 7, 2005 The tensors come in…

NAMIC: UNC – PNL collaboration October 7, 2005 Tensor Statistics and Tensor Interpolation Tensor: 3x3 symmetric definite-positive matrix PD(3): space of all 3D tensors –PD(3) is NOT a vector space  Linear statistics are not appropriate !

NAMIC: UNC – PNL collaboration October 7, 2005 * From Tom Fletcher

NAMIC: UNC – PNL collaboration October 7, 2005 Tensor Statistics and Tensor Interpolation Tensor: 3x3 symmetric definite-positive matrix PD(3): space of all 3D tensors –PD(3) is NOT a vector space  Linear statistics are not appropriate ! Positive-definiteness Determinant Linear Sym. Space NO YES Properties

NAMIC: UNC – PNL collaboration October 7, 2005 Tensor Statistics and Tensor Interpolation Tensor: 3x3 symmetric definite-positive matrix PD(3): space of all 3D tensors –PD(3) is NOT a vector space  Linear operations are not appropriate ! PD(3) is a Riemannian symmetric space Positive-definiteness Determinant Linear Sym. Space NO YES Properties

NAMIC: UNC – PNL collaboration October 7, 2005 Geodesic distance Algebraic computation * From Tom Fletcher

NAMIC: UNC – PNL collaboration October 7, 2005 Tensor Statistics and Tensor Interpolation Average of a set of tensors Variance of a set of tensors Interpolation of tensors: weighted-average

NAMIC: UNC – PNL collaboration October 7, 2005 Experiments and Results Data –3Tesla high resolution (2x2x2 mm 3 ) DT MRI database –8 subjects: 4 neonates at 2 weeks-old, 4 one year-old –Fiber tracts: genu and splenium Neonate at 2 weeks-oldOne year-old

NAMIC: UNC – PNL collaboration October 7, 2005 Experiments and Results Average of diffusion tensors in cross-sections along tracts 2 weeks-oldOne year-old Splenium Genu

NAMIC: UNC – PNL collaboration October 7, 2005 Experiments and Results Diffusion properties along fiber tracts Splenium Genu Eigenvalues Mean Diffusivity Fractional Anistropy

NAMIC: UNC – PNL collaboration October 7, 2005 Future Work Inter-individual comparison –Fiber-tract based coordinate system Representation of a fiber tract –Prototype curve + space trajectory Definition of the space trajectory –Representation by cables/ribbon-bundles/manifold Geodesic anisotropy Hpothesis testing

NAMIC: UNC – PNL collaboration October 7, 2005 Acknowledgements The team –Guido Gerig (UNC) –Casey Goodlett (UNC) –Weili Lin (UNC) –Sampath Vetsa (UNC) –Tom Fletcher (Utah) –Rémi Jean –Matthieu Jomier (France) –Sylvain Gouttard (France) –Clément Vachet (France) Software development –ITK, VTK, Qt –Julien Jomier (UNC)