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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.

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analysis and processing of diffusion weighted mri
Analysis and processing of DiffusionWeighted MRI

Remco Duits

Anna Vilanova

Luc Florack

Tom Dela Haije

Rutger Fick

Supervisedby:

Collaboration:

with

overview of presentation
Overview of presentation

Short introduction to DW-MRI

Enhancement of DW-MRI data

Fiber tracking

diffusion of water
Diffusion of water

Diffusion is dependentonorientation

overview
Overview

Water

Diffusion

Modelling

Fiber PDF

Tensor(s)

Raw Data

Water PDF

Fiber

Tracking

Low signal for high diffusion

Other

models

Clinical

Information

constrained spherical deconvolution
ConstrainedSphericalDeconvolution

Constrained

SphericalDeconvolution

Original data

(single fiber)

SphericalDeconvolution

enhancement of p dfs
Enhancement of PDFs
  • PDFs contain information on the direction of water diffusion (water PDF) or fiber distribution (fiber PDF)
  • Many models canbeconverted to a PDF

- Oftennoisy and incoherent

slide9

Rotatingcoordinate system

z

y

x

diffusion

diffusion

evolutions in new frame
Evolutions in new frame

Contour Enhancement

Contour Enhancement

evolutions in new frame1
Evolutions in new frame

Contour completion

Contour Completion

results on simple fibertracking
Resultsonsimplefibertracking

Fibertrackingon CSD

Fibertracking on enhanced CSD

Phantom dataset from the ISBI reconstructionchallenge (2013)

fiber tracking
Fiber Tracking
  • Problem: findanatomical fibers basedon DW-MRI scan
    • Variants
      • Findbrain fiber betweentwo areas
      • Find all fibers that pass throughanarea
  • Mathematicalproblem?
    • Multiple options
local fiber tracking
Local fiber tracking

Streamlinetracing:

  • Compute main direction of diffusion (AKA: reduce to vectorfield: )
  • Integratealongvectorfieldfromgivenseedpoint
advantages disadvantages
Advantages/Disadvantages
  • Advantages
    • Computationallycheap
    • Easy to implement
  • Disadvantages
    • Erroraccumulation
    • Sensitive to noise
global fibertracking
Global fibertracking
  • curve

Curvature

  • Corresponding energy functional

Solvedfor C(x)=1

Externalcost (data) Geodesicenergy

  • Find for given end points/directions
lifting the optimal curve problem to
Lifting the optimal curve problem to

The energy functional to minimize

subject to the constraints along the curve:

benefits and disadvantages
Benefits and disadvantages
  • Advantages
    • Robust to noise
    • No erroraccumulation
  • Disadvantages
    • Computationallyexpensive
    • Needs more boundaryconditions
    • Cansacrificelocalerrorforglobaloptimization
new idea combine local and global
New idea: combine local and global
  • Not global energy minimizers, but limit search to smaller search areas and combine solutions
  • Addadditionalconstraints to limit search space
    • Limit curvature to bebelowthreshold
    • Do extra constraintschangeoptimal curve problem?
search area
Search area

Simulateconvection

Geodesics to endpoints

theoretical benefits
Theoreticalbenefits
  • Advantages
    • Robust to noise
    • Computationalintermediate
    • Balance between local and global error
    • Limits to localorglobalmethodfor search areasmallorlarge
  • Disadvantages
    • Extra parameters thatneed to betuned
how to find optimum curve
How to find optimum curve?
  • Minimizermaynotexist
  • Minimizermaynotbeunique
  • Different options
    • UseDijkstra to findcheapestpathalongtree-graph (restrictsenergyfunction)
    • Try discrete subset of curves
    • Getanapproximateminimizer and iterativelyrefineit
past and plans
Past and Plans

Article published in NM-TMA (feb ‘13)

Enhancement Article published in JIMV

Refineideas and publishproof-of-concept to MICCAI conference (June)

Expandforjournalarticle

Visit Berlin to workonnewnon-linearenhancementtechnique (August)