Fiber tract-oriented quantitative analysis of Diffusion Tensor MRI data

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

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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

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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

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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

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Fiber Clustering into Bundles

• Examples:– 3Tesla high resolution (2x2x2 mm3) DT MRI– Cortico-spinal tract of left and right hemisphere

…AfterBefore… Neonate

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Fiber Clustering into Bundles

• Graph-theoretic approach

* Images from Casey Goodlett

Fornix clusterLongitudinal fasciculus(2312 streamlines)

6 clusters

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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

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Local Shape Properties

Curvature

For

each

cu

rve

Adult 1 NeonateAdult 2

Mean

± σ

ab

c

a a

a

b b ccc

b

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Diffusion PropertiesA

du

ltN

eon

ate

FA FA: Mean ± σ

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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

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• Sets of aligned shapes and estimated mean shape

Geometric Modeling

Callosal tract

Right corticospinal tract

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Geometric Modeling

• First and second modes of deformation– Subject 1, callosal tract

Mode 1 Mode 2

rotated view

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The tensors come in…

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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 !

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* From Tom Fletcher

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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

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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

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Geodesic distance

• Algebraic computation

* From Tom Fletcher

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Tensor Statistics and Tensor Interpolation

• Average of a set of tensors

• Variance of a set of tensors

• Interpolation of tensors: weighted-average

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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

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Experiments and Results

• Average of diffusion tensors in cross-sections along tracts

2 weeks-old One year-old

Sp

len

ium

Gen

u

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Experiments and Results

• Diffusion properties along fiber tracts

Sp

len

ium

Gen

u

Eigenvalues Mean Diffusivity Fractional Anistropy

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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

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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)