Transcript mbi2008 7414

Generalized Tensor-Based
Morphometry (TBM) for the
analysis of brain MRI and DTI
Natasha Leporé, Laboratory of
Neuro Imaging at UCLA
TBM o verview
Target
Source
TBM
TBM mathematical overview
Jacobian matrix (2D)
Outline of talk
MRI:
1. Statistical Analysis
2. Nonlinear Registration
3. Template selection
DTI:
4. Extension to DTI
TBM
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 !
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.
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.
Changes in the corpus callosum
TEMPLATE
DETERMINANT
ANGLE OF ROTATION
GEODESIC
ANISOTROPY
 = √ (JT J)
det  = 11 22 - 122
acos(u1.x)
√ Tr ( N – Tr ( N )* I/3 )2
TRACE
MAXIMUM
EIGENVALUE
EIGENVALUES
DEFORMATION
TENSORS
Trace () = 11 + 22
maximum (λ1 , λ2)
(λ1 , λ2)
( N11 , √ 2N12 , N22)
with N = log , I identity matrix, u1 eigenvector , (λ1 , λ2) eigenvalues
Volume and shape statistics for the
whole brain
Log p-values
Determinants
Log p-values
Deformation Tensors
TBM
Fluid vs elastic registration
But in fact …
u
vΔt1
vΔt2
vΔtn
At each voxel, u(x,y) and v(x,y) = du/dt
u analysis (elastic) and v analysis (fluid)
Riemannian fluid registration
(Brun et al., MICCAI 2007)
F : Driving force from the intensity difference between images
Similarity
term
Regularization
term
???
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.
Regularizer
Elastic Registration
(Pennec, 2005)
Fluid
Registration
where
∑ v : rate of strain
Riemannian fluid registration
(Brun et al., MICCAI 2007)
F : Driving force from the intensity difference between images
Similarity
term
Regularization
term
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
Statistics on twins
Intraclass correlation:
Twin 1
MSwithin
MSbetween - MSwithin
ICC =
MSbetween + MSwithin
MS: Mean square
We use the ICC to compute the
correlation of the deformation
tensors (well, their determinants …)
in twin pairs.
Twin 2
MSbetween
Accuracy of the Riemannian fluid
registration method
Image 1
Image 2
registered
to image 1
Image 2
Difference
btw warped
image and
initial image
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
Consistency of results: two fluid
methods - genetic studies
Significance of the Intraclass Correlation (ICC)
TBM
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
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!
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.
Anatomical correlations in twins
Identical twins
Fraternal twins
p-values
Significance of the Intraclass Correlation (ICC)
Distance
Template centering
Number of Templates
Distance to all the brains in the dataset
using 1 to 9 templates
TBM for DTI
(Lee et al., MICCAI 2008)
We can use almost the same procedure for DTI data!
MRI vs. DTI
Registration:
1. 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:
1. Perform statistics on the diffusion tensors
instead of the deformation tensors
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