Generalized%20Tensor-Based%20Morphometry%20(TBM)%20for%20the%20analysis%20of%20brain%20MRI%20and%20DTI

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Generalized Tensor-Based Morphometry (TBM) for
the analysis of brain MRI and DTI

• Natasha Leporé, Laboratory of Neuro Imaging at
  UCLA

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TBM overview
Target
Source
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TBM
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TBM mathematical overview
Jacobian matrix (2D)
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Outline of talk

• MRI
• 1. Statistical Analysis
• Nonlinear Registration
• Template selection
• DTI
• 4. Extension to DTI

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TBM
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Volume vs shape changes
(Lepore et al., TMI 2007)
Usual TBM (Volume changes)
But this does not take into account the direction
of the changes
J 0.5 0 0 2
So directional shrinkage and growth, but det(J)
1 !
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Shape and volume statistics
Multivariate statistics are computed on the 6
components of the deformation tensors
? (JTJ)1/2
Or more precisely, on their logarithm.
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Application to HIV/AIDS

• We are going to demonstrate our method using
• ?26 HIV/AIDS patients 14 controls
• ?Various kinds of statistics for
• 1. Volume changes
• 2. Volume and shape changes
• Permutation based statistics to avoid assuming a
  normal distribution.

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Changes in the corpus callosum
TEMPLATE DETERMINANT ANGLE OF ROTATION GEODESIC ANISOTROPY
v Tr ( N Tr ( N ) I/3 )2
? v (JT J)
det ? ?11 ?22 - ?122
acos(u1.x)
TRACE MAXIMUM EIGENVALUE EIGENVALUES DEFORMATION TENSORS
Trace (?) ?11 ?22
maximum (?1 , ?2)
(?1 , ?2)
( N11 , v 2N12 , N22)
with N log ?, I identity matrix, u1
eigenvector , (?1 , ?2) eigenvalues
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Volume and shape statistics for the whole brain
Log p-values
Log p-values
Deformation Tensors
Determinants
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TBM
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Fluid vs elastic registration
But in fact
At each voxel, u(x,y) and v(x,y) du/dt u
analysis (elastic) and v analysis (fluid)
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Riemannian fluid registration (Brun et al.,
MICCAI 2007)
F Driving force from the intensity difference
between images
Similarity term
Regularization term
???
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Building a Regularizer

• The natural way to do the regularization in
• TBM is to use the deformation tensors, since they
  
• characterize the distortion of the local volume.
• Since we are in the log-Euclidean framework,
• we want to use the matrix logarithms.
• We want to use a fluid regularizer so we can
• have large deformations.

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Regularizer
Elastic Registration (Pennec, 2005)
Fluid Registration
where
? v rate of strain
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Riemannian fluid registration
(Brun et al., MICCAI 2007)
F Driving force from the intensity difference
between images
Similarity term
Regularization term
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Implementation data

• 23 pairs of identical twins
• 23 pairs of fraternal twins
• 4T MRI scans, DTI 30 directions
• Data bank 1150 healthy twins (21-27 years old)
• MRI, HARDI and neuropsychological measures

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Statistics on twins
Twin 1
Twin 2
Intraclass correlation
MSwithin
MSbetween - MSwithin
MSbetween MSwithin
ICC
MS Mean square
We use the ICC to compute the correlation of the
deformation tensors (well, their determinants )
in twin pairs.
MSbetween
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Accuracy of the Riemannian fluid registration
method
Image 1
Image 2
Difference btw warped image and initial image
Image 2 registered to image 1
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Application of the Riemannian fluid method to
genetic studies
Percent mean absolute difference in regional
volume
Determinant of the Jacobian
Tangent of the Geodesic Anisotropy
Identical twins
Fraternal twins
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Consistency of results two fluid methods -
genetic studies
Significance of the Intraclass Correlation (ICC)
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TBM
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Template averaging
(Lepore et al., MICCAI 2008)

• Features are typically sharper in individual
  brain images than in mean anatomical templates
• But, we want to eliminate bias from registration
• to one individual
• Statistics are performed on deformation tensors
  

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Template averaging
(Lepore et al., MICCAI 2008)

• Features are typically sharper in individual
  brain images than in mean anatomical templates
• But, we want to eliminate bias from registration
• to one individual
• Statistics are performed on deformation tensors
  

So... compute the average (using deformation
tensors) after the registration!
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Averaging procedure
. . .
data
templates
common space
The new deformation tensors are the
(Log-Euclidean) average of the deformation
tensors at each voxel in the common space. Sum
over voxels to get a distance between brains.
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Anatomical correlations in twins
p-values
Identical twins
Fraternal twins
Significance of the Intraclass Correlation (ICC)
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Template centering
Distance
Number of Templates
Distance to all the brains in the dataset using 1
to 9 templates
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TBM for DTI
(Lee et al., MICCAI 2008)
We can use almost the same procedure for DTI data!
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MRI vs. DTI
Registration

• DTI data is harder to register, so register the
• MRI and apply the deformation to the DTI

2. The DTI tensors will be misaligned by the
registration, so tensors need to be rotated
Statistics

• Perform statistics on the diffusion tensors
• instead of the deformation tensors

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NYCAP algorithm team
Principal Investigator Paul Thompson
Graduate students Agatha Lee Caroline Brun
External Collaborator Xavier Pennec, INRIA
Research Assistants Yi-Yu Chou Marina
Barysheva