Trajectory Physics Based Fibertracking in Diffusion Tensor
Magnetic Resonance Imaging
Garrett Jenkinson, Advisor: José Moura, Graduate Student: Hsun-Hsien Chang
Department of Electrical and Computer Engineering, Carnegie Mellon University
Pittsburgh NMR Center, University of Pittsburgh
Problems in Fibertracking
Motivation
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.
Diffusion Tensor Magnetic Resonance Imaging
Results
Advantages of Physics Based Algorithm
Eigenanalysis decomposes the 3x3 diffusion tensor into an
ellipsoid illustrating the probability of the self diffusion of water in
a given direction:
(D–λI)v=0
λ1 is the direction of highest diffusion probability, and many
algorithms force their fibertracts to follow its corresponding vector
• 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=mv
Problems:
• NOISE
• Great in linear case,
what about others?
• No guarantee of
smooth paths
• Directionality issues
(back stepping)
•Clever creation of the force vector field
•Takes in account the barycentric ratios as well as the
principle vector from eigenanalysis
[1]
• 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
cs
[2]
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
The Trajectory Physics Solution
If molecule remains stationary the two gradient pulses negate
each other, thus only regions of migrating water show signal loss
Physics Algorithm
Other Algorithms
• 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
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.
[2]
5
10
15
mass = 1000
20
25
Discussion
30
35
[1]
40
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
cp
cl
• Use trajectory physics to trace out the particle’s path
• Only consider orthogonal forces, no change in speed
S = S0 + v0 t + ½ a
a = Ftan/m
Ftan = F – F ● v
v
Solving for the diffusion tensor:
ln( J / I(g) ) = b(g) ● D
D= ln( J / I(g) ) b-1
t2
Ftan
m
F
mass = 5000
45
20
40
60
80
100
120
About the GUI
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:
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
[3]
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.