Vis03 Workshop. DT-MRI Visualization

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

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Vis03 Workshop. DT-MRI Visualization

  1. 1. DT-MRI VisualizationFiber tractographyDiffusion tensor filtering and interpolation Leonid Zhukov
  2. 2. Fiber tractographyn  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. 3. Fiber tractographyn  Difficulties: •  voxelization / resolution •  noise •  ill-posedness of the problemn  Algorithms: •  Deterministic algorithms •  Probabilistic methods •  PDE based methodsn  Data: •  Discrete •  Continious 3
  4. 4. Deterministic algorithmsn  Mori et al. 1999, Jones et al. 1999, Conturo et al. 1999 •  Follow local main diffusion direction from voxel to voxel, heuristicsn  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 deflectionn  Basser et al. 2000 •  Continues spline approximation to tensor field and integral curvesn  Gossl et al. 2001 •  State space model , Kalman filteringn  Zhukov et al. 2002 •  Moving Least Squares filter , integral curves 4
  5. 5. Probabilistic & PDE based methodsProbabilistic methods:n  Poupon et al. 2000, 2001 •  regularization of tensor field, Markovian fieldsn  Hagmann et al. 2003 •  random walk , random direction distributed according to local diffusion properties, regularization terms, coliniarity with previous stepPDE based methods:n  Parker et al., 2002 •  Level set methods, diffusion front propagation 5
  6. 6. Fiber tractography 6
  7. 7. Data: anisotropy 7
  8. 8. Data: anisotropy 8
  9. 9. Fiber tracing 1) noise filtering 2) continues representation 3) local averaging filter “with memory” and look ahead (oriented anisotropic) 9
  10. 10. Streamline integration fibertrackingn  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. 11. MLS methodn  Continues tensor field by interpolationn  Evaluation of local vector field direction is delayed until tracking (eigen-computations)n  Local tensor filtering by polynomial approximationn  Look ahead / memory, local weighted averagen  Filtering is simultaneous with tracingn  Tuned up level of smoothingn  EU1, RK2,4 integrationn  Anisotropy controlled Zhukov and Barr, 2002 11
  12. 12. Interpolation Continues tensor field representation – component-wise interpolation 12
  13. 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. 14. MLS filter Local filter: moving oriented least squares (MLS) tensor filter 14
  15. 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. 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. 17. Tracing algorithm 17
  18. 18. Example: Gordon’s brain data Data: SCI Institute, University of Utah 18
  19. 19. Brain structure: corona radiata 19
  20. 20. MLS effect 20
  21. 21. Brain structure: singulum bundle 21
  22. 22. Example: canine heart data Data: Dr Edward Hsu, Dept. of Bioengineering, Duke University 22
  23. 23. Canine heart myofibers 23
  24. 24. New developmentsn  Fiber groupingn  Initial value problem, boundary value problemn  Fiber merging and splittingn  Additional constraints – model surface etcn  Fiber distribution analysis 24

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