Vis03 Workshop. DT-MRI Visualization
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This document discusses fiber tractography techniques for visualizing white matter tracts in the brain using diffusion tensor MRI (DT-MRI) data. It covers fiber tractography algorithms like deterministic and probabilistic methods. Specific algorithms discussed include moving least squares filtering for tensor field interpolation and streamline integration for fiber tracing. Examples of fiber tractography results are shown for the human brain and canine heart.
Vis03 Workshop. DT-MRI Visualization
- 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