Fiber tractography and Diffusion tensor filtering and interpolation. Talk at Vis 2003

1. DT-MRI Visualization
Fiber tractography
Diffusion tensor filtering and interpolation
Leonid Zhukov

2. Fiber tractography
n Fiber tractography – computing and following directions
of fiber bundles within the tissue based on DT-MRI data
• functional connectivity studies
• function to structure
???
2

3. Fiber tractography
n Difficulties:
• voxelization / resolution
• noise
• ill-posedness of the problem
n Algorithms:
• Deterministic algorithms
• Probabilistic methods
• PDE based methods
n Data:
• Discrete
• Continious
3

4. Deterministic algorithms
n Mori et al. 1999, Jones et al. 1999, Conturo et al. 1999
• Follow local main diffusion direction from voxel to voxel, heuristics
n Westin et al. 1999, 2002
• Diffusion tensors are projection operators rotating and scaling tracing “velocity”
n Weinstein et al. 1999, Lasar et al, 2000,2003
• Tensor deflection
n Basser et al. 2000
• Continues spline approximation to tensor field and integral curves
n Gossl et al. 2001
• State space model , Kalman filtering
n Zhukov et al. 2002
• Moving Least Squares filter , integral curves
4

5. Probabilistic & PDE based methods
Probabilistic methods:
n Poupon et al. 2000, 2001
• regularization of tensor field, Markovian fields
n Hagmann et al. 2003
• random walk , random direction distributed according to local diffusion properties,
regularization terms, coliniarity with previous step
PDE based methods:
n Parker et al., 2002
• Level set methods, diffusion front propagation
5

6. Fiber tractography
6

7. Data: anisotropy
7

8. Data: anisotropy
8

9. Fiber tracing
1) noise filtering
2) continues representation 3) local averaging filter “with memory”
and look ahead (oriented anisotropic)
9

10. Streamline integration fibertracking
n Main steps:
• Interpolate (approximate) the data, make it continuous
• Smooth and filter the data
• Tensor filed –> vector field
• Streamline integration (integral curve)
n Typical algorithm:
• Select starting points (region)
• Integrate forward from every point
• Stop if outside of domain
• Controlled by anisotropy
• Prevent sharp turns
10

11. MLS method
n Continues tensor field by interpolation
n Evaluation of local vector field direction is delayed until tracking
(eigen-computations)
n Local tensor filtering by polynomial approximation
n Look ahead / memory, local weighted average
n Filtering is simultaneous with tracing
n Tuned up level of smoothing
n EU1, RK2,4 integration
n Anisotropy controlled
Zhukov and Barr, 2002
11

12. Interpolation
Continues tensor field representation – component-wise interpolation
12

13. MLS filter
• smooth varying variable, corrupted by noise
• low–pass filter
• window: replace data point by local average
• preserves area under the curve
• higher order polynomial
• least squares fit
13

14. MLS filter
Local filter: moving oriented least squares (MLS) tensor filter
14

15. Integration
Streamline integration
(vector field):
vector vector
Forward Euler (RG-2,4) type integration (diverging field) :
vector vector vector
Inverse Euler –implicit scheme integration (converging field):
vector vector vector
15

16. Tracing algorithm
Tracing Procedure:
trace = fiber_trace(P,e) {
trace->add(P);
for (every starting point P) {
do {
Tp = filter(T,P,sphere); Pn = integrate_forward(P,e1,dt);
cl = anisotropy(Tp); Tp = filter(T,Pn,ellipsoid,e1);
if (cl > eps) { cl = anisotropy(Tp)
e1 = direction(Tp); if ( c1 > eps ) {
trace->add(Pn);
trace1 = fiber_trace(P, e1);
P = Pn;
trace2 = fiber_trace(P,-e1); e1 = direction(Tp);
trace = trace1 + trace2; }
} } while (cl >eps)
} return(trace);
}
16

17. Tracing algorithm
17

18. Example: Gordon’s brain data
Data: SCI Institute, University of Utah
18

19. Brain structure: corona radiata
19

20. MLS effect
20

21. Brain structure: singulum bundle
21

22. Example: canine heart data
Data: Dr Edward Hsu, Dept. of
Bioengineering, Duke University
22

23. Canine heart myofibers
23

24. New developments
n Fiber grouping
n Initial value problem, boundary value problem
n Fiber merging and splitting
n Additional constraints – model surface etc
n Fiber distribution analysis
24