NA-MIC National Alliance for Medical Image Computing http://na-mic.org DTI atlas building for population analysis: Application to PNL SZ study Casey Goodlett, Tom Fletcher, Sarang Joshi, Guido Gerig UNC Chapel Hill, Univ. of Utah
Dec 26, 2015
NA-MICNational Alliance for Medical Image Computing http://na-mic.org
DTI atlas building for population analysis: Application to PNL SZ study
Casey Goodlett, Tom Fletcher, Sarang Joshi, Guido Gerig
UNC Chapel Hill, Univ. of Utah
National Alliance for Medical Image Computing http://na-mic.org Slide 2
Building of Population Averages
Motivation:
•Map population into common coordinate space
•Learn about normal variability
•Describe difference from normal
•Use as normative atlas for segmentationSarang Joshi, Brad Davis, Matthieu Jomier, Guido Gerig, Unbiased Diffeomorphic
Atlas Construction for Computational Anatomy, vol. 23, NeuroImage 2004B. Avants and J.C. Gee, “Geodesic estimation for large deformation anatomical
shape averaging and interpolation,” Neuroimage, vol. 23, pp. 139–150, 2004.
National Alliance for Medical Image Computing http://na-mic.org Slide 3
Population-Based DTI Analysis
Casey Goodlett, MICCAI’06
National Alliance for Medical Image Computing http://na-mic.org Slide 5
Registration
DTI Images
(1:N)
Scalar Images
From Manifold
Detector on FA
Structural
Average
H-fields
(1:N)
Structural
Operator
Atlas
(Affine,
Fluid)
H-1-fields
(1:N)
National Alliance for Medical Image Computing http://na-mic.org Slide 6
Atlas formation
DTI Images
Tensor
AveragingDTI Atlas
Rotate Tensors
based on JH-1
H-fields
(1:N) Riemannian
Symmetric
Space
National Alliance for Medical Image Computing http://na-mic.org Slide 7
Structural Image
• Want images aligned by geometry of fiber tracts
• FA occurs in thin manifolds– sheets– tubes
• FA'' highlights fiber geometry (maximum eigenvalue)
• FA'' does not directly optimize correspondence of tensor derived property
National Alliance for Medical Image Computing http://na-mic.org Slide 8
FA image and Curvature Image
National Alliance for Medical Image Computing http://na-mic.org Slide 11
Mathematics of Spatial Transformation
h x = x Fx
h(x) is a mapping from R3 to R3. h(x) can be locally
approximated as a linear function.
F is the local Jacobian of the transformation and can be processed the same
as for a global transformation. SVD can be used to extract the rotation
component of F.
F=URD'=RDRT
National Alliance for Medical Image Computing http://na-mic.org Slide 12
Processing of DTI
• Diffusion tensors are symmetric positive-definite matrices
• Riemannian symmetric spaces (Fletcher, Pennec)
• Log-Euclidean Framework
National Alliance for Medical Image Computing http://na-mic.org Slide 15
Atlas: Average + Set of transformed tensor fields
ROIs and tracts in atlas space transferred to every image.
National Alliance for Medical Image Computing http://na-mic.org Slide 16
Atlas-Based Tractography
Atlas
Image BImage A
National Alliance for Medical Image Computing http://na-mic.org Slide 17
PNL Data: Colored FA and MD
Average of Control Group (N=13)
Average of SZ Group
(N=12)
FA MD
FA MD
National Alliance for Medical Image Computing http://na-mic.org Slide 18
Full Brain Tractography on Atlas
MedINRIA Tool (Pierre Fillard, INRIA)
NEW: NAMIC compatible: Reads NRRD format and writes NAMIC fiber format output, is promoted together with NAMIC FiberViewer tool.
National Alliance for Medical Image Computing http://na-mic.org Slide 19
Tractography in PNL Atlas
Corpus Callosum middle part
Cingulum full
Cingulum “spine”
National Alliance for Medical Image Computing http://na-mic.org Slide 20
more tracts…
Uncinate Fasciculus UF colored with FA
ant post
National Alliance for Medical Image Computing http://na-mic.org Slide 21
FA distributions in cross-sections
National Alliance for Medical Image Computing http://na-mic.org Slide 22
Tractography per Group
Cingulum SZ GroupCingulum Control Group
Tractography applied to tensor fields of the set of controls mapped to the atlas (left) ad the set of SZ mapped to the atlas (right).
National Alliance for Medical Image Computing http://na-mic.org Slide 23
Very, very preliminary tests …
FA along cingulum per group
0
0.1
0.2
0.3
0.4
0.5
0.6
-80 -60 -40 -20 0 20 40
arclength (mm)
FA
FA-NC
FA-SZ
Poly. (FA-SZ)
Poly. (FA-NC)
SZ seems to have lower FA in middle portion of cingulum.
What does it mean w.r.t. diffusion properties?
National Alliance for Medical Image Computing http://na-mic.org Slide 24
ctd.
SZ group seems to have lower lambda1 and slightly higher radial diffusion (average lambda2 + lambda3) in middle region.
L1 along cingulum per group
0
2
4
6
8
10
12
14
-80 -60 -40 -20 0 20 40
arclength (mm)
L1
L1-NC
L1-SZ
Poly. (L1-SZ)
Poly. (L1-NC)
L23 along cingulum per group
0
1
2
3
4
5
6
7
8
9
10
-80 -60 -40 -20 0 20 40
arclength (mm)
L23
L23-NC
L23-SZ
Poly. (L23-SZ)
Poly. (L23-NC)
National Alliance for Medical Image Computing http://na-mic.org Slide 25
ctd.
MD along cingulum per group
0
2
4
6
8
10
12
-80 -60 -40 -20 0 20 40
arclength (mm)
MD
MD-NC
MD-SZ
Poly. (MD-SZ)
Poly. (MD-NC)
GA along cingulum per group
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-80 -60 -40 -20 0 20 40
arclength (mm)
GA
GA-NC
GA-SZ
Poly. (GA-SZ)
Poly. (GA-NC)
MD seems very similar for both groups.
GA shows same pattern as FA but much higher values.
National Alliance for Medical Image Computing http://na-mic.org Slide 26
same game with cc …
Middle cc in central region shows decrease of FA and increase of MD for SZ group
National Alliance for Medical Image Computing http://na-mic.org Slide 27
and with uncinate fasciculus
Maybe no group difference.
National Alliance for Medical Image Computing http://na-mic.org Slide 28
Voxel-based Analysis: FA
Control Atlas SZ Atlas Difference
Can we trust these difference maps? Do we see residuum of deformation or FA difference?
axial low
axial high
National Alliance for Medical Image Computing http://na-mic.org Slide 29
Voxel-based Analysis: MD
Controls SZ Difference
Mismatch of two atlases illustrates a problem of our atlas building: Edges of structures not well-aligned.
axial low
axial high
National Alliance for Medical Image Computing http://na-mic.org Slide 30
Problem: What is a good image match feature?
Features from tensor field driving nonlinear registration?
National Alliance for Medical Image Computing http://na-mic.org Slide 31
Image match should consider boundaries and tract locations
Maxev FA MD
Maxev FA MD
National Alliance for Medical Image Computing http://na-mic.org Slide 32
Towards improved image match features
• MD does not show underlying wm structure
• FA shows strong wm features but not anatomical boundaries
• FA’’ (Hessian) emphasizes center lines
• → Would like measure derived from full tensor field
Thick and thin structures show similar center features
National Alliance for Medical Image Computing http://na-mic.org Slide 33
Hessian of tensor field?
zzzyzx
yzyyyx
xzxyxx
MMM
MMM
MMM • Each element is matrix
• Choice of Norm?
National Alliance for Medical Image Computing http://na-mic.org Slide 34
Hessian of Tensor Field
• max_ev: maximum eigenvalue of each element
• norm: norm of each element
• tensor_ev: SIAM*
evji
ji
kknnijlliill
H
3x3x(3x3) = 3*27elements*Lathauwer, SIAM J. MATRIX ANAL. APPL. Vol. 21, No. 4, pp. 1253–1278
National Alliance for Medical Image Computing http://na-mic.org Slide 36
Current Work: Towards better image match features
Collaboration with Fillard/Pennec, INRIA
Second derivative of tensor field (1st ev of Hessian)
tensor_ev max_ev norm
tensor_ev max_ev norm
National Alliance for Medical Image Computing http://na-mic.org Slide 37
Conclusions• Core methods: Nonlinear deformation (diffeomorphic) and
“good” feature maps• Atlas-building will require Slicer-3 “pipeline” (currently Linux
script)• After automatic construction of atlas with set of deformed
tensor fields:– Efficient, user-guided analysis (15’ per tract or region)– Full set of measurements (FA, GA, MD, lambda1..3, radial diffusion
etc.)
• Current research: Image match features• Set of tracts with associated tensors from aligned images:
Ready for tensor statistics (Fletcher, e.g.)
National Alliance for Medical Image Computing http://na-mic.org Slide 38
Conclusion PNL DTI study
• Low hanging fruits were not as low as expected …
• What was promised for Christmas is available now
• Encouraging results on multiple key structures (cc, UF, cingulum, fornix etc.)
• Plan for programmer’s week: To teach about tools and generate clinically relevant results (Goodlett, Kubicki, Bouix).