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MaxEnt 2007 Saratoga Springs, NY

Neuroradiology Section NIL and BMRL. MaxEnt 2007 Saratoga Springs, NY. Computing the Probability Of Brain Connectivity with Diffusion Tensor MRI JS Shimony AA Epstein GL Bretthorst. Part 1: Diffusion Tensor (DT) MRI (Brain Connectivity later).

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MaxEnt 2007 Saratoga Springs, NY

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  1. Neuroradiology Section NIL and BMRL MaxEnt 2007 Saratoga Springs, NY Computing the Probability Of Brain Connectivity with Diffusion Tensor MRI JS Shimony AA Epstein GL Bretthorst

  2. 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 (mm), orders of magnitude smaller than macroscopic MR resolution (mm) • This has found numerous research and clinical applications

  3. Diffusion: Left MCA stroke

  4. Standard Spin Echo Mz Mxy Mxy echo 180 90 RF/RO Gz

  5. Diffusion Spin Echo M=Mxyexp(-bD) Mz Mxy echo 180 90 RF/RO Gz D

  6. Diffusion: Pulse Sequence Echo Train 90 180 RF Gss EPI Readout Gro Gpe

  7. Anisotropic Diffusion in WM Fibers

  8. Diffusion: Single Direction

  9. Diffusion Tensor Imaging Model Basser et al., JMR, 1994 (103) 247 Uses 8 parameters (D≠ data) λ1 λ2 λ3

  10. How Diffusion is Measured by MRI Signal Amplitude Diffusion Sensitization (q) Image courtesy: C. Kroenke

  11. Diffusion Anisotropy Signal Amplitude Diffusion Sensitization (q) Image courtesy: C. Kroenke

  12. Mean Diffusivitiy λ1 λ2 λ3 • Mean Diffusivity is the average of the diffusion in the different directions

  13. Diffusion Anisotropy • Anisotropy is normalized standard deviation of diffusion measurements in different directions • FA and RA most common • Range from 0 to 1 RA=0 RA<1

  14. Baseline image / Anisotropy

  15. Color Diffusion

  16. 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)

  17. 3D Diffusion Tensor Field

  18. Example of Streamline Tracking

  19. 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

  20. Applications: Anatomy Jellison AJNR 25:356

  21. 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

  22. Crossing Fibers Locations

  23. 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

  24. Probabilistic Tractography • Express DT parameters for pixel i • Since each pixel is independent in this model the probability for the DT parameters given the data D can be factored:

  25. Utilize Angular Error Estimations Angular pdf Cone of angular uncertainty Low Anisotropy High Anisotropy

  26. Probabilistic Tracking End zone Start zone

  27. Example Probabilistic DTT

  28. 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”

  29. Adding the Connectivity Parameter • Add nearest neighbor connectivity parameter • No independence between the pixels • Each pixel depends on its neighbors via the prior of its connectivity

  30. Connectivity Parameter Prior

  31. Adding Connectivity Parameter • The preference for connectivity is indicated by the prior for Lij • Express this as the probability that a water molecule will diffuse from pixel i to j

  32. 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

  33. Method: 3x3x3 Simulation

  34. Results: Connectivity Parameter

  35. Coronal Section in Crossing Fiber area

  36. Anatomy Comparison

  37. Results: Connectivity Parameter

  38. 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

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