USING ANISOTROPIC DIFFUSION TO TRACK NEURAL FIBERS

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

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

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

4. What is Diffusion Tensor Imaging? • New way to use Magnetic Resonance • Tracks H2O in the brain along fibers • Diseases it could diagnose • ADHD • Multiple Sclerosis

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

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

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

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

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

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

11. Fourth Step: Repeat Diffusion • HUGE first drop VS small first drop • Smaller is better, more precision • 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 • Why keep it? • It accounts for all points at once

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

15. Ahhh… An Observation • We put random data in and observed • After a long time we saw the structure of the fiber • 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 • 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 • An Eigenvalue, , is a number that scales a function with out changing its shape • Therefore a ZERO Eigenvalue gives the unchanged static solution

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

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

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

22. Acknowledgements 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

23. Questions?