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Fiber tractoriented quantitative analysis of Diffusion Tensor MRI data

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Title: Fiber tractoriented quantitative analysis of Diffusion Tensor MRI data


1
Fiber tract-oriented quantitative analysis of
Diffusion Tensor MRI data
Isabelle Corouge
  • Postdoctoral fellow,
  • Dept of Computer Science and Psychiatry,
  • UNC-Chapel Hill

2
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
3
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

4
Fiber Extraction
  • Extraction by tractography Fillard03
  • 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

5
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

6
Fiber Clustering into Bundles
  • Examples
  • 3Tesla high resolution (2x2x2 mm3) DT MRI
  • Cortico-spinal tract of left and right hemisphere

Before
Neonate
After
7
Fiber Clustering into Bundles
  • Graph-theoretic approach

Fornix cluster
Longitudinal fasciculus
6 clusters
(2312 streamlines)
Images from Casey Goodlett
8
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

9
Local Shape Properties
a
c
b
Curvature
For each curve
a
c
a
c
c
a
b
b
b
Mean s
10
Diffusion Properties
FA
FA Mean s
Adult
Neonate
11
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

12
Geometric Modeling
  • Sets of aligned shapes and estimated mean shape

Right cortico spinal tract
Callosal tract
13
Geometric Modeling
  • First and second modes of deformation
  • Subject 1, callosal tract

Mode 1
Mode 2
14
The tensors come in
15
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 !

16
From Tom Fletcher
17
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 !

18
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

19
Geodesic distance
From Tom Fletcher
  • Algebraic computation

20
Tensor Statistics and Tensor Interpolation
  • Average of a set of tensors
  • Variance of a set of tensors
  • Interpolation of tensors weighted-average

21
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
22
Experiments and Results
  • Average of diffusion tensors in cross-sections
    along tracts

Genu
Splenium
2 weeks-old
One year-old
23
Experiments and Results
  • Diffusion properties along fiber tracts

Eigenvalues
Mean Diffusivity
Fractional Anistropy
Genu
Splenium
24
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

25
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)
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