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Analysis and processing of Diffusion Weighted MRI. Remco Duits Anna Vilanova Luc Florack. Tom Dela Haije Rutger Fick. Supervised by : Collaboration : with. Overview of presentation. Short introduction to DW-MRI Enhancement of DW-MRI data Fiber tracking. Diffusion of water. - PowerPoint PPT Presentation
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Analysis and processing of Diffusion Weighted MRI
Supervised by:
Collaboration:with
Remco DuitsAnna VilanovaLuc Florack
Tom Dela HaijeRutger Fick
Slide 1 of 31
Overview of presentation
1) Short introduction to DW-MRI2) Enhancement of DW-MRI data3) Fiber tracking
Slide 2 of 31
Diffusion of water
Diffusion is dependent on orientation
Slide 3 of 31
Visualization
4Slide 4 of 31
Goal
Slide 5 of 31
Overview
Raw Data
Water Diffusion Modelling
Tensor(s)Water PDF
Othermodels
Fiber PDF
Fiber Tracking
Clinical Information
Low signal for high diffusion
Slide 6 of 31
Constrained Spherical Deconvolution
Original data(single fiber)
Spherical Deconvolution
ConstrainedSpherical Deconvolution
Slide 7 of 31
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
Slide 8 of 31
Rotating coordinate systemz
yx
• diffusion
• diffusio
n
Slide 9 of 31
Evolutions in new frame• Contour Enhancement
Contour Enhancement
Slide 10 of 31
Evolutions in new frame• Contour Completion
Contour completion
Slide 11 of 31
Results
Slide 12 of 31
Results on simple fibertracking
Phantom dataset from the ISBI reconstruction challenge (2013)
• Fibertracking on CSD • Fibertracking on enhanced CSD
Slide 13 of 31
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
Slide 14 of 31
Local fiber trackingStreamline tracing:• Compute main
direction of diffusion (AKA: reduce to vectorfield: )
• Integrate along vectorfield from given seedpoint
Slide 15 of 31
Advantages/Disadvantages
• Advantages– Computationally cheap– Easy to implement
• Disadvantages– Error accumulation– Sensitive to noise
Slide 16 of 31
Local method: example
Slide 17 of 31
Global fibertracking• curve
Curvature• Corresponding energy functional
External cost (data) Geodesic energy• Find for given end points/directions
Solved for C(x)=1
Slide 18 of 31
Horizontal curves
Slide 19 of 31
Lifting the optimal curve problem to
The energy functional to minimize
subject to the constraints along the curve:
Slide 20 of 31
Solutions sub-Riemannian geodesics Ghosh&Dela Haije&Duits
Slide 21 of 31
Optimal control problem
Slide 22 of 31
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
Slide 24 of 31
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?
Slide 25 of 31
Intuition
Slide 26 of 31
Search areaSimulate convection Geodesics to endpoints
Slide 27 of 31
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
Slide 28 of 31
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)
Slide 30 of 31
Any questions, ideas or suggestions?
Slide 31 of 31