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Fiber tract-oriented quantitative analysis of Diffusion Tensor MRI data. Isabelle Corouge. Postdoctoral fellow, Dept of Computer Science and Psychiatry, UNC-Chapel Hill. Motivations. Diffusion Tensor MRI Study white matter structural properties - PowerPoint PPT Presentation
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NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 1 - October 7, 2005
Fiber tract-oriented quantitative Fiber tract-oriented quantitative analysis of Diffusion Tensor analysis of Diffusion Tensor MRI dataMRI data
Postdoctoral fellow,Postdoctoral fellow,Dept of Computer Science Dept of Computer Science and Psychiatry,and Psychiatry,UNC-Chapel HillUNC-Chapel Hill
Isabelle CorougeIsabelle Corouge
NAMIC: UNC – PNL collaborationNAMIC: 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 collaborationNAMIC: 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
Geometric modeling of fiber bundles 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 collaborationNAMIC: UNC – PNL collaboration - 4 - October 7, 2005
Fiber Extraction
• Extraction by tractography [Fillard’03]
– High resolution DTI data (baseline + 6 directional images, 2mm3)– 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 collaborationNAMIC: 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]
Hierarchical, agglomerative algorithm
A cluster C: Fi in C, at least one Fj in C, j i such that: d(Fi, Fj) < t
Fiber space
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 6 - October 7, 2005
Fiber Clustering into Bundles
• Examples:– 3Tesla high resolution (2x2x2 mm3) DT MRI– Cortico-spinal tract of left and right hemisphere
…AfterBefore… Neonate
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 7 - October 7, 2005
Fiber Clustering into Bundles
• Graph-theoretic approach
* Images from Casey Goodlett
Fornix clusterLongitudinal fasciculus(2312 streamlines)
6 clusters
NAMIC: UNC – PNL collaborationNAMIC: 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 andstandard deviation of these features
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 9 - October 7, 2005
Local Shape Properties
Curvature
For
each
cu
rve
Adult 1 NeonateAdult 2
Mean
± σ
ab
c
a a
a
b b ccc
b
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 10 - October 7, 2005
Diffusion PropertiesA
du
ltN
eon
ate
FA FA: Mean ± σ
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 11 - 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 collaborationNAMIC: UNC – PNL collaboration - 12 - October 7, 2005
• Sets of aligned shapes and estimated mean shape
Geometric Modeling
Callosal tract
Right corticospinal tract
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 13 - October 7, 2005
Geometric Modeling
• First and second modes of deformation– Subject 1, callosal tract
Mode 1 Mode 2
rotated view
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 14 - October 7, 2005
The tensors come in…
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 15 - 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 collaborationNAMIC: UNC – PNL collaboration - 16 - October 7, 2005
* From Tom Fletcher
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 17 - 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
NO YES
YES
Properties
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 18 - 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
NO YES
YES
Properties
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 19 - October 7, 2005
Geodesic distance
• Algebraic computation
* From Tom Fletcher
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 20 - 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 collaborationNAMIC: UNC – PNL collaboration - 21 - October 7, 2005
Experiments and Results
• Data – 3Tesla high resolution (2x2x2 mm3) DT MRI database– 8 subjects: 4 neonates at 2 weeks-old, 4 one year-old– Fiber tracts: genu and splenium
Neonate at 2 weeks-old One year-old
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 22 - October 7, 2005
Experiments and Results
• Average of diffusion tensors in cross-sections along tracts
2 weeks-old One year-old
Sp
len
ium
Gen
u
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 23 - October 7, 2005
Experiments and Results
• Diffusion properties along fiber tracts
Sp
len
ium
Gen
u
Eigenvalues Mean Diffusivity Fractional Anistropy
NAMIC: UNC – PNL collaborationNAMIC: UNC – PNL collaboration - 24 - 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 collaborationNAMIC: UNC – PNL collaboration - 25 - 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)