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

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

Fiber Tracking DTI Results 3 MRI can be used to obtain local chemical and physical properties of water. 1.Molecular diffusion 2.Flow Conclusion

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

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

6 Fiber Tracking: Provides a potential method for exploring a connectivity network of the brain. Fiber tracking localStream-line Euler- Lagrange equation global Hamilton Jacobi PDEs Euler- Lagrange equation Fiber Tracking DTI Results Conclusion

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

Streamline 8 Fiber Tracking DTI Results Conclusion

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

Fiber Tracking DTI Results Eikonal equation Conclusion

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

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

Eikonal equation Fiber Tracking DTI Results Conclusion

 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. Fiber Tracking DTI Results Eikonal equation Conclusion

Euler-Lagrange Equation Fiber Tracking DTI Results Conclusion

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

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

18 Fiber Tracking DTI Results Conclusion Euler-Lagrange Equation

Fiber Tracking DTI Results Conclusion

20 DTI Results Fiber Tracking EikonalEL Conclusion

21 Classic fiber-trackingPDE based fiber-tracking DTI Results Fiber Tracking Conclusion

22 EL based fiber-tracking DTI Results Fiber Tracking Conclusion

23 DTI Results Fiber Tracking HJ EL Conclusion

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

25 DTI Results Fiber Tracking Conclusion EL based method

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

 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 Eikonal solutionEL solution DTI Fiber Tracking Conclusion Results

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

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

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

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