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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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1

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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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ii

i

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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