Trajectory Physics Based Fibertracking in Diffusion Tensor

Magnetic Resonance ImagingGarrett Jenkinson, Advisor: José Moura, Graduate Student: Hsun-Hsien Chang

Department of Electrical and Computer Engineering, Carnegie Mellon University Pittsburgh NMR Center, University of Pittsburgh

Motivation Advantages of Physics Based Algorithm Results

Discussion

• Intuitive• Underlying physics which created the data are used to reconstruct

• Momentum: • Like a memory of the system• More invariant to noise• Forces particle to follow a smooth trajectory

ρ = m v

•Clever creation of the force vector field•Takes in account the barycentric ratios as well as the principle vector from eigenanalysis

• Directionality (i.e. the problem of back-stepping)•Problem avoided altogether since only orthogonal forces effect particles trajectory

• Adjustable through the mass of the particle• Step size directly proportional to mass• Larger masses are less susceptible to noise• Smaller masses step faster, can make tighter turns

If molecule remains stationary the two gradient pulses negate each other, thus only regions of migrating water show signal loss

Image intensity in a diffusion tensor image is a function of the diffusion gradient applied:

I (g) = J e-b(g) ● D

Where: I (g) = image voxel intensity for each gradient g D = the diffusion tensor J = the baseline image intensity with no gradient applied b(g) = “b-matrix” calculated based on pulse sequence shown above

Solving for the diffusion tensor:

ln( J / I(g) ) = b(g) ● D

D= ln( J / I(g) ) b-1

This work involved the creation of a novel fibertracking routine which outperformed the existing algorithms in the presence of noise. By improving one of the most crucial steps in DT-MRI analysis, this work has lessened the SNR requirements for the raw data, allowing for more accurate 3D visualization of the heart in vivo. The ideal visualization (from a still heart) is below:

Problems in Fibertracking

Eigenanalysis decomposes the 3x3 diffusion tensor into an ellipsoid illustrating the probability of the self diffusion of water in a given direction:

( D – λ I ) v = 0

λ1 is the direction of highest diffusion probability, and many algorithms force their fibertracts to follow its corresponding vector

Problems:• NOISE• Great in linear case, what about others?• No guarantee of smooth paths• Directionality issues (back stepping)

The Trajectory Physics Solution

• Create a particle with a given mass, m, at the seeding point

• Use Diffusion Tensor data to create a force vector field• Direction of force given by λ1’s corresponding vector• Magnitude of force is given by Cl, the linear barycentric ratio

• Use trajectory physics to trace out the particle’s path• Only consider orthogonal forces, no change in speed

S = S0 + v0 t + ½ a t2

a = Ftan/mFtan = F – F ● v

cs

cl cp

m

vFtan

F

About the GUI

The algorithm has been implemented in the fully functional diffusion tensor toolbox with the following functionality:

• Easily load and view raw data and calculate Diffusion Tensors• Visualize Diffusion Tensor three ways

• Diffusion Weighted (grayscale based on mean diffusivity)• Barycentric Coloring (red, green, blue respectively correspond to linear, planar, and spherical)• Directional Coloring (red, green, blue corresponding to x,y and z components of principle eigenvector)

• Calculate and Visualize Force Vector Field for the tracking• Manually seed and visualize fibertracking using novel algorithm

Other Algorithms Physics Algorithm

Synthetic data was used at various SNR’s to test the algorithms’ performance, at higher SNR’s the physics algorithm outperforms the others using a mass of 1000

At the lowest SNR, a mass of 1000 results in average performance. Tuning the mass to 5000 results in improved performance to the point of beating out all others tested.

mass = 1000 mass = 5000

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Diffusion Tensor Magnetic Resonance Imaging

Diffusion Tensor magnetic resonance imaging (DT-MRI) is a recent advent in the field of medical imaging. Tissues with similar T1, T2 or proton densities, which appear homogeneous in conventional MRI, are given a new measure of contrast in DT-MRI based on the local diffusion of water.

Since coherently organized tissues such as muscle fibers or myelinated axon bundles create significantly anisotropic diffusion, fibertracking models can create high-detail three dimensional models to sub-voxel accuracies. Unfortunately, noise corrupts most DT-MRI data, especially in in vivo cardiac imaging. The goal of this research is to create a novel fibertracking model which have improved performance in the presence of noise.

References[1] Aherns, E. MRI in Neurosceince Lecture Slides. Carnegie Mellon University, Spring 2007.[2] Magnotta, V. and Cheng, P. Guided Diffusion Tensor Tractography with GTRACT: A Validation Study. Insight Journal, 2005.[3] Zhukov, L. and Barr, A. Heart-Muscle Fiber Reconstruction from Diffusion Tensor MRI. IEEE Visualization, 2003.

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