USING ANISOTROPIC USING ANISOTROPIC DIFFUSION TO TRACK NEURAL DIFFUSION TO TRACK NEURAL

FIBERS FIBERS

Sarah NeyerSarah NeyerNASA/JPL CSUN PAIRNASA/JPL CSUN PAIRAdvisor Dr. A. AlekseenkoAdvisor Dr. A. Alekseenko

FocusFocus

1.1. This talk focuses on the brain scanning This talk focuses on the brain scanning technique Diffusion Tensor Imagingtechnique Diffusion Tensor Imaging

2.2. The problems they are facing with itThe problems they are facing with it

3.3. Our proposal of a solutionOur proposal of a solution

4.4. The two milestones of the projectThe two milestones of the project

What is the Problem?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 Cannot assess the important data

gathered about intricate fibers in braingathered about intricate fibers in brain

Proposal: Proposal: New method to map these fibersNew method to map these fibers

What is Diffusion Tensor Imaging?What is Diffusion Tensor Imaging?

New way to use New way to use Magnetic ResonanceMagnetic Resonance

Tracks HTracks H22O in the O in the brain along fibersbrain along fibers

Diseases it could Diseases it could diagnosediagnose ADHDADHD Multiple SclerosisMultiple Sclerosis

Tracking FibersTracking Fibers Direction of fiber is known at every pointDirection of fiber is known at every point

Connecting the directions is the problemConnecting the directions is the problem

Where would this fiber go?Where would this fiber go?

Current MethodCurrent Method Chooses between Chooses between

directions when it directions when it comes to themcomes to them

Tracks one directionTracks one direction

It CANNOT track It CANNOT track branching fibersbranching fibers

Proposed MethodProposed Method Anisotropic Diffusion EquationAnisotropic Diffusion Equation

Looks at every direction at once!Looks at every direction at once!

It CAN account for branching fibersIt CAN account for branching fibers

First Step: Mimic diffusionFirst Step: Mimic diffusion

Ink drop on a piece of Ink drop on a piece of paperpaper

Where it will diffuse Where it will diffuse comes from the brain comes from the brain scanning datascanning data

Second Step: PropagationSecond Step: Propagation

1.1. Anisotropic diffusion: Anisotropic diffusion: Let it go anywhereLet it go anywhere

2.2. Isotropic diffusion:Isotropic diffusion:Sharpen the imageSharpen the image

Third Step: Track the ridgeThird Step: Track the ridge Ridge shows the fiberRidge shows the fiber

Collect points based Collect points based on highest curve on highest curve

Eliminate the shape Eliminate the shape

Fourth Step: Repeat DiffusionFourth Step: Repeat Diffusion HUGE first drop VS HUGE first drop VS

small first dropsmall first drop

Smaller is better, Smaller is better, more precisionmore precision

We start a new drop We start a new drop where old one where old one finishesfinishes

What the Fiber looks like!What the Fiber looks like!

A 3D view of straight fiberA 3D view of straight fiber

DisadvantagesDisadvantages The algorithm takes The algorithm takes

too much time to too much time to completecomplete

Why keep it?Why keep it?

It accounts for all It accounts for all points at oncepoints at once

What did we do?What did we do?Looked at the MATH behind diffusionLooked at the MATH behind diffusion

We made observations about behavior of We made observations about behavior of diffusiondiffusion

We came up with a faster algorithmWe came up with a faster algorithm

Ahhh… An Observation 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 After a long time we saw the structure of the

fiberfiber We realized that all we need is this solution, We realized that all we need is this solution,

called the STATIC SOLUTIONcalled the STATIC SOLUTION

Static Solution?Static Solution?

First step: Discretize the EquationFirst step: Discretize the Equation

Discretizing means that we put in the Discretizing means that we put in the data about how it acts in space and we data about how it acts in space and we can find how it acts in timecan find how it acts in time

We studied the resulting ODEs in matrix We studied the resulting ODEs in matrix formform

The discretized diffusion equation

Second Step: Analyze the Matrix Second Step: Analyze the Matrix

Look at the Eigenvector corresponding to Look at the Eigenvector corresponding to a zero Eigenvaluea zero Eigenvalue

An Eigenvalue, An Eigenvalue, is a number that scales is a number that scales a function with out changing its shapea function with out changing its shape

Therefore a ZERO Eigenvalue gives the Therefore a ZERO Eigenvalue gives the unchanged static solutionunchanged static solution

Here’s what happenedHere’s what happened

Same output!Same output!

Time to create Time to create decreases!decreases!

Circular fiber

SummarySummary We created an algorithm to find branching fibersWe created an algorithm to find branching fibers

using ANISOTROPIC DIFFUSION EQUATIONusing ANISOTROPIC DIFFUSION EQUATION

We looked at the Mathematics behind our We looked at the Mathematics behind our equationequation

We found that we need the STATIC SOLUTIONWe found that we need the STATIC SOLUTION

Future Research Future Research

Use complicated brain data in researchUse complicated brain data in research

Work on static solution to track ridgeWork on static solution to track ridge

I would like to thank my advisor I would like to thank my advisor Dr. Alekseenko for working with me on this Dr. Alekseenko for working with me on this ProjectProject

I would also like to thank the NASA/JPLI would also like to thank the NASA/JPLPAIR Program for giving me this research PAIR Program for giving me this research

opportunityopportunity

AcknowledgementsAcknowledgements

Questions?Questions?