Analysis and processing of Diffusion Weighted MRI

Supervised by:

Collaboration:with

Remco DuitsAnna VilanovaLuc Florack

Tom Dela HaijeRutger Fick

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Overview of presentation

1) Short introduction to DW-MRI2) Enhancement of DW-MRI data3) Fiber tracking

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Diffusion of water

Diffusion is dependent on orientation

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Visualization

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Goal

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Overview

Raw Data

Water Diffusion Modelling

Tensor(s)Water PDF

Othermodels

Fiber PDF

Fiber Tracking

Clinical Information

Low signal for high diffusion

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Constrained Spherical Deconvolution

Original data(single fiber)

Spherical Deconvolution

ConstrainedSpherical Deconvolution

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Enhancement of PDFs

• PDFs contain information on the direction of water diffusion (water PDF) or fiber distribution (fiber PDF)

• Many models can be converted to a PDF- Often noisy and incoherent

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Rotating coordinate systemz

yx

• diffusion

• diffusio

n

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Evolutions in new frame• Contour Enhancement

Contour Enhancement

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Evolutions in new frame• Contour Completion

Contour completion

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Results

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Results on simple fibertracking

Phantom dataset from the ISBI reconstruction challenge (2013)

• Fibertracking on CSD • Fibertracking on enhanced CSD

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Fiber Tracking

• Problem: find anatomical fibers based on DW-MRI scan– Variants

• Find brain fiber between two areas• Find all fibers that pass through an area

• Mathematical problem? – Multiple options

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Local fiber trackingStreamline tracing:• Compute main

direction of diffusion (AKA: reduce to vectorfield: )

• Integrate along vectorfield from given seedpoint

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Advantages/Disadvantages

• Advantages– Computationally cheap– Easy to implement

• Disadvantages– Error accumulation– Sensitive to noise

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Local method: example

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Global fibertracking• curve

Curvature• Corresponding energy functional

External cost (data) Geodesic energy• Find for given end points/directions

Solved for C(x)=1

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Horizontal curves

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Lifting the optimal curve problem to

The energy functional to minimize

subject to the constraints along the curve:

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Solutions sub-Riemannian geodesics Ghosh&Dela Haije&Duits

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Optimal control problem

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Benefits and disadvantages

• Advantages– Robust to noise– No error accumulation

• Disadvantages– Computationally expensive– Needs more boundary conditions– Can sacrifice local error for global

optimizationSlide 23 of 31

Global method:example

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New idea: combine local and global

• Not global energy minimizers, but limit search to smaller search areas and combine solutions

• Add additional constraints to limit search space– Limit curvature to be below threshold– Do extra constraints change optimal curve

problem?

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Intuition

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Search areaSimulate convection Geodesics to endpoints

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Theoretical benefits• Advantages

– Robust to noise– Computational intermediate– Balance between local and global error– Limits to local or global method for

search area small or large• Disadvantages

– Extra parameters that need to be tuned

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How to find optimum curve?• Minimizer may not exist• Minimizer may not be unique• Different options

– Use Dijkstra to find cheapest path along tree-graph (restricts energy function)

– Try discrete subset of curves– Get an approximate minimizer and

iteratively refine itSlide 29 of 31

Past and Plans• Article published in NM-TMA (feb ‘13)• Enhancement Article published in JIMV• Refine ideas and publish proof-of-concept

to MICCAI conference (June)• Expand for journal article• Visit Berlin to work on new non-linear

enhancement technique (August)

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Any questions, ideas or suggestions?

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