MaxEnt 2007 Saratoga Springs, NY
Computing the ProbabilityOf Brain Connectivity with Diffusion Tensor MRI
JS ShimonyAA EpsteinGL Bretthorst
Neuroradiology SectionNIL and BMRL
Part 1: Diffusion Tensor (DT) MRI(Brain Connectivity later)
• Diffusion MR images can measure water proton displacements at the cellular level
• Probing motion at microscopic scale (m), orders of magnitude smaller than macroscopic MR resolution (mm)
• This has found numerous research and clinical applications
Diffusion Tensor Imaging Model
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Basser et al., JMR, 1994 (103) 247Uses 8 parameters (D ≠ data)
How Diffusion is Measured by MRI
Diffusion Sensitization (q)S
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Image courtesy: C. Kroenke
Mean Diffusivitiy
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• Mean Diffusivity is the average of the diffusion in the different directions
Diffusion Anisotropy• Anisotropy is normalized
standard deviation of diffusion measurements in different directions
• FA and RA most common• Range from 0 to 1
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Part 2: Brain Connectivity
•DT data provides a directional tensor field in the brain, used to map neuronal fibers
•Detailed WM anatomy used in:–Pre-surgical planning–Neuroscience interest in functional networks
•Previously could only be done using cadavers or invasive studies in primates
•Termed DT Tractography (DTT)
Streamline DTT
• Advantages:– Conceptually and computationally simple– Was the first to be developed
• Disadvantages:– Limited to high anisotropy, high signal areas– Can only produce one track – Can’t handle track splitting – Has the greatest difficulty with crossing fibers
DTT and Crossing Fibers
• Major limitation of current methods of DTT
• Difficult to resolve with current methods and SNR
• Volume averaging effects• Known areas in the brain• Decrease sensitivity and
specificity, distorts connection probabilities
Probabilistic DTT
• Behrens et al. MRM 2003 50:1077-1088• Advantages:
– Better accounts for experimental errors – More robust tracking results– Better deals with crossing fibers, low SNR
• Disadvantages:– Computationally intense – Probabilities will be modified by crossing
fibers
Probabilistic Tractography
• Since each pixel is independent in this model the probability for the DT parameters given the data D can be factored:
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• Express DT parameters for pixel i
Utilize Angular Error Estimations
Cone of angularuncertainty
Angularpdf
Low Anisotropy High Anisotropy
Part 3: Methods and Results
• Use prior information!!!• Assumption of pixel independence is
non_biological • Nerve fiber bundles can travel over long
distances in the brain and cross many pixels
• Incorporate this into the model via a: “Nearest Neighbor Connectivity Parameter”
Adding the Connectivity Parameter
• No independence between the pixels• Each pixel depends on its neighbors via
the prior of its connectivity
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• Add nearest neighbor connectivity parameter
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Adding Connectivity Parameter
• The preference for connectivity is indicated by the prior for ij
• Express this as the probability that a water molecule will diffuse from pixel i to j
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Parallel Processing Details• Connection between
neighboring pixels complicates the calculations
• When processing on a parallel computer, the values of the neighbors cannot change
• Example in 1D and 2D
Summary• DT imaging provides accurate estimation of
the tensor field of the WM in the brain• Accurate estimation of the connectivity
between different brain regions is of great clinical and research interest
• Prior work has assumed independent pixels• Prior information on local connectivity may
provide a more accurate representation of the underlying tissue structure
• Acknowledgements: NIH K23 HD053212, NMSS PP1262, and Chris Kroenke