1. USING ANISOTROPIC DIFFUSION TO TRACK NEURAL FIBERS Sarah Neyer NASA/JPL CSUN PAIR Advisor Dr. A. Alekseenko

2. Focus 1. This talk focuses on the brain scanning technique Diffusion Tensor Imaging 2. The problems they are facing with it 3. Our proposal of a solution 4. The two milestones of the project

3. What is the Problem? Problem: Problem: New imaging technique and we can’t use it! New imaging technique and we can’t use it! Meaning: Meaning: Cannot assess the important data gathered about intricate fibers in brain Cannot assess the important data gathered about intricate fibers in brain Proposal: Proposal: New method to map these fibers New method to map these fibers

4. What is Diffusion Tensor Imaging? New way to use Magnetic Resonance New way to use Magnetic Resonance Tracks H 2 O in the brain along fibers Tracks H 2 O in the brain along fibers Diseases it could diagnose Diseases it could diagnose ADHD Multiple Sclerosis

5. Tracking Fibers Direction of fiber is known at every point Direction of fiber is known at every point Connecting the directions is the problem Connecting the directions is the problem Where would this fiber go? Where would this fiber go?

6. Current Method Chooses between directions when it comes to them Chooses between directions when it comes to them Tracks one direction Tracks one direction It CANNOT track branching fibers It CANNOT track branching fibers

7. Proposed Method Anisotropic Diffusion Equation Anisotropic Diffusion Equation Looks at every direction at once! Looks at every direction at once! It CAN account for branching fibers It CAN account for branching fibers

8. First Step: Mimic diffusion Ink drop on a piece of paper Ink drop on a piece of paper Where it will diffuse comes from the brain scanning data Where it will diffuse comes from the brain scanning data

9. Second Step: Propagation 1. Anisotropic diffusion: Let it go anywhere 2. Isotropic diffusion: Sharpen the image

10. Third Step: Track the ridge Ridge shows the fiber Ridge shows the fiber Collect points based on highest curve Collect points based on highest curve Eliminate the shape Eliminate the shape

11. Fourth Step: Repeat Diffusion HUGE first drop VS small first drop HUGE first drop VS small first drop Smaller is better, more precision Smaller is better, more precision We start a new drop where old one finishes We start a new drop where old one finishes

12. What the Fiber looks like! A 3D view of straight fiber

13. Disadvantages The algorithm takes too much time to complete The algorithm takes too much time to complete Why keep it? Why keep it? It accounts for all points at once It accounts for all points at once

14. What did we do? Looked at the MATH behind diffusion Looked at the MATH behind diffusion We made observations about behavior of diffusion We made observations about behavior of diffusion We came up with a faster algorithm We came up with a faster algorithm

15. Ahhh… An Observation We put random data in and observed We put random data in and observed After a long time we saw the structure of the fiber After a long time we saw the structure of the fiber We realized that all we need is this solution, called the STATIC SOLUTION We realized that all we need is this solution, called the STATIC SOLUTION

16. Static Solution?

17. First step: Discretize the Equation Discretizing means that we put in the data about how it acts in space and we can find how it acts in time Discretizing means that we put in the data about how it acts in space and we can find how it acts in time We studied the resulting ODEs in matrix form We studied the resulting ODEs in matrix form The discretized diffusion equation

18. Second Step: Analyze the Matrix Look at the Eigenvector corresponding to a zero Eigenvalue Look at the Eigenvector corresponding to a zero Eigenvalue An Eigenvalue,  is a number that scales a function with out changing its shape An Eigenvalue,  is a number that scales a function with out changing its shape Therefore a ZERO Eigenvalue gives the unchanged static solution Therefore a ZERO Eigenvalue gives the unchanged static solution

19. Here’s what happened Same output! Same output! Time to create decreases! Time to create decreases! Circular fiber

20. Summary We created an algorithm to find branching fibers We created an algorithm to find branching fibers using ANISOTROPIC DIFFUSION EQUATION We looked at the Mathematics behind our equation We looked at the Mathematics behind our equation We found that we need the STATIC SOLUTION We found that we need the STATIC SOLUTION

21. Future Research Use complicated brain data in research Use complicated brain data in research Work on static solution to track ridge Work on static solution to track ridge

22. I would like to thank my advisor Dr. Alekseenko for working with me on this Project I would also like to thank the NASA/JPL PAIR Program for giving me this research opportunity Acknowledgements

23. Questions?