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Multi-valued Geodesic based Fiber Tracking for Diffusion Tensor Imaging

Multi-valued Geodesic based Fiber Tracking for Diffusion Tensor Imaging. Neda Sepasian. Supervised by Prof. Bart ter Haar Romeny, Dr. Anna Vilanova Bartoli Dr. J.H.M. ten Thije Boonkkamp. Overview. Diffusion tensor imaging(DTI) Fiber tracking Results Conclusion. Fiber Tracking.

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Multi-valued Geodesic based Fiber Tracking for Diffusion Tensor Imaging

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  1. Multi-valued Geodesic based Fiber Tracking for Diffusion Tensor Imaging Neda Sepasian Supervised by Prof. Bart ter Haar Romeny, Dr. Anna Vilanova Bartoli Dr. J.H.M. ten Thije Boonkkamp

  2. Overview • Diffusion tensor imaging(DTI) • Fiber tracking • Results • Conclusion

  3. Fiber Tracking Results Conclusion DTI MRI can be used to obtain local chemical and physical properties of water. Molecular diffusion Flow

  4. Fiber Tracking Results Conclusion DTI Diffusion Tensor Imaging Measuring the diffusion of water molecules gives us the shape and orientation of the diffusion ellipsoid.

  5. Fiber Tracking Results Conclusion DTI Low anisotropy Suitable for understanding the structure locally. Clutter in 3D Difficult to understand global structure High anisotropy

  6. Fiber Tracking Results Conclusion DTI Fiber Tracking: Provides a potential method for exploring a connectivity network of the brain.

  7. Fiber Tracking Results Conclusion DTI Streamline • Using only the dominant eigenvalue. • deviations in the eigenvectors caused the accumulate error. • In an isotropic region • We are locally maximizing the diffusion.

  8. Fiber Tracking Results Conclusion DTI Streamline

  9. Fiber Tracking Results Conclusion DTI Geodesics • The shortest path between points on the space. • Geodesics can be reconstructed using: • PDE based algorithms(eg. Eikonaleq.) • ODE based algorithms(Euler Lagrange eq.) Euler-Lagrange(EL) solution Correct solution Eikonal Solution

  10. Fiber Tracking Results Conclusion DTI Eikonal equation

  11. Fiber Tracking Results Conclusion DTI Eikonal equation • Solve the Eikonal equation using the numerical approximation: • Charpit’s system to reconstruct the fibers:

  12. Fiber Tracking Results Conclusion DTI Eikonal equation Fibers are selected using connectivity measure:

  13. Fiber Tracking Results Conclusion DTI Eikonal equation

  14. Fiber Tracking Results Conclusion DTI Eikonal equation • It is globally minimizing the geodesics using the inverse of the diffusion tensors. • Therefore it is more robust to noise but at the same time less sensitive to local orientations. • Only the first arrival time (unique solution) is computed at each grid point.

  15. Fiber Tracking Results Conclusion DTI Euler-Lagrange Equation

  16. Fiber Tracking Results Conclusion DTI Euler-Lagrange Equation • Solve the geodesic ODEs using well-known ODE solver like RK4.

  17. Fiber Tracking Results Conclusion DTI Euler-Lagrange Equation • Shoot rays in different initial direction with the same initial position. • Apply ray-tracing algorithm for finding the geodesic connecting two given points.

  18. Fiber Tracking Results Conclusion DTI Euler-Lagrange Equation

  19. Fiber Tracking Results Conclusion DTI Euler-Lagrange Equation

  20. Fiber Tracking Results Conclusion DTI Eikonal EL

  21. Fiber Tracking Results Conclusion DTI Classic fiber-tracking PDE based fiber-tracking

  22. Fiber Tracking Results Conclusion DTI EL based fiber-tracking

  23. Fiber Tracking Results Conclusion DTI HJ EL

  24. Fiber Tracking Results Conclusion DTI i iii Corpus Callosum (CC) trackts based on atlas Gray’s anatomy CC tracts using EL based algorithm ii

  25. Fiber Tracking Results Conclusion DTI EL based method

  26. Fiber Tracking Results Conclusion DTI (a) Arcuate fasciculus (ARC) ( f ) Uncinate fasciculus (UNC) EL based fiber-tracking

  27. Fiber Tracking Conclusion Results DTI Eikonal solution EL solution • Global minimization • Robust to noise • Accuracy for quantitative analysis • Algorithm efficiency • Only the first arrival time • Global minimization • Robust to noise • Accuracy for quantitative analysis • Algorithm efficiency • Multi-valued solution. • Less information is deduced from the computation

  28. Fiber Tracking Results Conclusion DTI What could be an ideal algorithm ???

  29. Fiber Tracking Conclusion Results DTI Other Challenges • Single tensor models are not sufficient • Fiber-tracking algorithms are still imperfect

  30. Fiber Tracking Conclusion Results DTI Work in progress!!! • Multi-valued HARDI fiber-tracking in single processor DTI HARDI • Multi-valued HARDI fiber-tracking in GPU (using CUDA)

  31. Acknowledgements • Dr. Olof Runborg (KTH, Stockholm, Sweden) • Luc Florack • Laura Astola • Evert Aart

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