Post on 18-Jan-2016
description
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Multi-valued Geodesic based Fiber Tracking for Diffusion Tensor Imaging
Neda SepasianNeda Sepasian
Supervised byProf. Bart ter Haar Romeny,
Dr. Anna Vilanova Bartoli Dr. J.H.M. ten Thije Boonkkamp
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OverviewOverview
Diffusion tensor imaging(DTI) Fiber tracking Results Conclusion
Fiber TrackingDTI Results
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MRI can be used to obtain local chemical and physical properties of water.
1. Molecular diffusion2. Flow
Conclusion
Diffusion Tensor ImagingMeasuring the diffusion of water molecules gives us the shape and
orientation of the diffusion ellipsoid.
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v2
v3
DDxx Dxy DxzDyx Dyy DyzDzx Dzy Dzz
Fiber TrackingDTI Results Conclusion
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Suitable for understanding the structure locally. Clutter in 3D
Difficult to understand global structure
Fiber TrackingDTI ResultsHigh anisotropy
Low anisotropy
Conclusion
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Fiber Tracking: Provides a potential method for exploring a connectivity network of the brain.
Fiber TrackingDTI 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.
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Fiber TrackingDTI Results Conclusion
Streamline
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Fiber TrackingDTI Results Conclusion
Fiber TrackingDTI 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 solution Eikonal SolutionEuler-Lagrange(EL) solution
Conclusion
Fiber TrackingDTI Results
Eikonal equation
Conclusion
Solve the Eikonal equation using the numerical approximation:
Charpit’s system to reconstruct the fibers:
Eikonal equation
Fiber TrackingDTI Results Conclusion
Fiber TrackingDTI Results
Fibers are selected using connectivity measure:
Eikonal equation
Conclusion
Eikonal equation
Fiber TrackingDTI 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 TrackingDTI Results
Eikonal equation
Conclusion
Euler-Lagrange Equation
Fiber TrackingDTI Results Conclusion
Solve the geodesic ODEs using well-known ODE solver like RK4.
Fiber TrackingDTI 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 TrackingDTI Results Conclusion
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Fiber TrackingDTI Results Conclusion
Euler-Lagrange Equation
Euler-Lagrange Equation
Fiber TrackingDTI Results Conclusion
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DTI ResultsFiber Tracking
Eikonal EL
Conclusion
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Classic fiber-tracking PDE based fiber-tracking
DTI ResultsFiber Tracking Conclusion
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EL based fiber-tracking
DTI ResultsFiber Tracking Conclusion
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DTI ResultsFiber Tracking
HJ
EL
Conclusion
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i. Corpus Callosum (CC) trackts based on atlasii. Gray’s anatomy iii. CC tracts using EL based algorithm
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DTI ResultsFiber Tracking Conclusion
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DTI ResultsFiber Tracking Conclusion
EL based method
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(a) Arcuate fasciculus (ARC)( f ) Uncinate fasciculus (UNC)
EL based fiber-tracking
DTI ResultsFiber 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 solution EL solution
DTI Fiber Tracking ConclusionResults
What could be an ideal algorithm ???
DTI Fiber Tracking Results Conclusion
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Other Challenges
Single tensor models are not sufficient
Fiber-tracking algorithms are still imperfect
DTI Fiber Tracking ConclusionResults
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 ConclusionResults
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