dti atlas building for population analysis: application to pnl sz study

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.


Population-Based DTI Analysis

Casey Goodlett, MICCAI’06


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)


Atlas formation

DTI Images

Tensor

AveragingDTI Atlas

Rotate Tensors

based on JH-1

H-fields

(1:N) Riemannian

Symmetric

Space


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


FA image and Curvature Image


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


Processing of DTI

• Diffusion tensors are symmetric positive-definite matrices

• Riemannian symmetric spaces (Fletcher, Pennec)

• Log-Euclidean Framework


Atlas: Average + Set of transformed tensor fields

ROIs and tracts in atlas space transferred to every image.


Atlas-Based Tractography

Atlas

Image BImage A


PNL Data: Colored FA and MD

Average of Control Group (N=13)

Average of SZ Group

(N=12)

FA MD

FA MD


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.


Tractography in PNL Atlas

Corpus Callosum middle part

Cingulum full

Cingulum “spine”


more tracts…

Uncinate Fasciculus UF colored with FA

ant post


FA distributions in cross-sections


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).


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?


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)


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.


same game with cc …

Middle cc in central region shows decrease of FA and increase of MD for SZ group


and with uncinate fasciculus

Maybe no group difference.


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


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


Problem: What is a good image match feature?

Features from tensor field driving nonlinear registration?


Image match should consider boundaries and tract locations

Maxev FA MD

Maxev FA MD


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


Hessian of tensor field?

zzzyzx

yzyyyx

xzxyxx

MMM

MMM

MMM • Each element is matrix

• Choice of Norm?


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


Hessian of Tensor Field


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


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.)


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).

dti atlas building for population analysis: application to pnl sz study

Documents