Transcript DTI
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 MRI can be used to obtain local chemical and physical properties of water. 1. 2. Molecular diffusion Flow DTI Fiber Tracking Results Conclusion Diffusion Tensor Imaging Measuring the diffusion of water molecules gives us the shape and orientation of the diffusion ellipsoid. Dxx D Dyx Dzx Dxz Dyz Dzz Dxy Dyy Dzy 1 1 v3 2 3 DTI v2 Results Fiber Tracking 4 Conclusion Low anisotropy Suitable for understanding the structure locally. Clutter in 3D Difficult to understand global structure DTI Results Fiber Tracking 5 Conclusion High anisotropy Fiber Tracking: Provides a potential method for exploring a connectivity network of the brain. Stream-line local Fiber tracking Hamilton Jacobi PDEs global DTI EulerLagrange equation Results Fiber Tracking 6 EulerLagrange equation Conclusion Streamline DTI Using only the dominant eigenvalue. deviations in the eigenvectors caused the accumulate error. In an isotropic region We are locally maximizing the diffusion. Results Fiber Tracking 7 Conclusion Streamline DTI Results Fiber Tracking 8 Conclusion 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 solution DTI Fiber Tracking Eikonal Solution Results EulerLagrange(EL) solution Conclusion Eikonal equation DTI Fiber Tracking Results Conclusion Eikonal equation Solve the Eikonal equation using the numerical approximation: Charpit’s system to reconstruct the fibers: DTI Fiber Tracking Results Conclusion Eikonal equation Fibers are selected using connectivity measure: DTI Fiber Tracking Results Conclusion Eikonal equation DTI Fiber Tracking Results Conclusion 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. DTI Fiber Tracking Results Conclusion Euler-Lagrange Equation DTI Fiber Tracking Results Conclusion Euler-Lagrange Equation Solve the geodesic ODEs using well-known ODE solver like RK4. DTI Fiber Tracking Results Conclusion 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. DTI Fiber Tracking Results Conclusion 18 Euler-Lagrange Equation DTI Fiber Tracking Results Conclusion Euler-Lagrange Equation DTI Fiber Tracking Results Conclusion 20 Eikonal DTI Fiber Tracking EL Results Conclusion 21 Classic fiber-tracking DTI Fiber Tracking PDE based fiber-tracking Results Conclusion 22 EL based fiber-tracking DTI Fiber Tracking Results Conclusion 23 HJ EL DTI Fiber Tracking Results Conclusion 24 i iii i. Corpus Callosum (CC) trackts based on atlas ii. Gray’s anatomy iii. CC tracts using EL based algorithm DTI Fiber Tracking Results Conclusion ii 25 EL based method DTI Fiber Tracking Results Conclusion 26 (a) Arcuate fasciculus (ARC) ( f ) Uncinate fasciculus (UNC) EL based fiber-tracking DTI Fiber Tracking Results Conclusion Eikonal solution EL solution Global minimization Robust to noise Accuracy for quantitative analysis Algorithm efficiency Only the first arrival time DTI Fiber Tracking Global minimization Robust to noise Accuracy for quantitative analysis Algorithm efficiency Multi-valued solution. Less information is deduced from the computation Results Conclusion 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 Results Conclusion Work in progress!!! Multi-valued HARDI fiber-tracking in single processor DTI HARDI Multi-valued HARDI fiber-tracking in GPU (using CUDA) DTI Fiber Tracking Results Conclusion 31