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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
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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
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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
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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
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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?
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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
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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
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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
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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
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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
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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
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What the Fiber looks like!What the Fiber looks like!
A 3D view of straight fiberA 3D view of straight fiber
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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
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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
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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
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Static Solution?Static Solution?
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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
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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
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Here’s what happenedHere’s what happened
Same output!Same output!
Time to create Time to create decreases!decreases!
Circular fiber
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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
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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
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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
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Questions?Questions?