[BIC-announce] CIM-SOCS PhD Oral Defense - Parya Momayyezsiahkal: Friday, June 29/12 at 10am in MC103

[Jennifer Campbell]

Hello everyone,

Parya Momayyezsiahkal, PhD candidate under the supervision of Professor 
Kaleem Siddiqi, Director of the Shape Analysis Group of the Centre for 
Intelligent Machines (CIM), is defending on:

DATE:	Friday, June 29, 2012
TIME: 	10:00 a.m.
PLACE: 	McConnell Eng. Bldg., Room 103

TITLE: 	3D stochastic completion fields for mapping brain connectivity
using diffusion magnetic resonance imaging

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ABSTRACT:

This thesis proposes a novel probabilistic method for measuring
anatomical connectivity in the brain based on measurements obtained from
diffusion magnetic resonance imaging. We approach the problem of fibre
tractography from the viewpoint that a computational theory should
relate to the underlying quantity that is being measured - the
anisotropic diffusion of water molecules in fibrous tissues. To
achieve this goal, the prior probability of completion between two
particular regions of interest is modelled by a 3D directional random
walk, which is representative of the ensemble anisotropic displacement
to which diffusion-MRI measurements have been sensitized. The 3D
directional random walk is controlled by a set of stochastic
differential equations whose solution provides the probability of
passing through every position and orientation in space, given initial
source and sink regions. Under such a model, particles tend to travel in
a straight line, with a slight perturbation in their 3D orientation  at
each step governed by two consecutive Brownian motions. The probability
density functions describing the likelihood of passing through a
particular position and orientation in 3D, given an initial
source region and a final sink region, are respectively called a
stochastic source field and a stochastic sink field. The final
stochastic completion field is estimated by the product of these two
densities and it represents the probability of passing through a
particular state in 3D, while bridging the gap between the two regions.
We show that the maximum likelihood curves obtained under the 3D
directional random walk are curves of least energy which minimize a
weighted sum of curvature squared, torsion squared and length. The 3D
directional random walk and the associated completion fields are an
extension of Williams and Jacobs' model for curve completion in the plane.

We then develop an efficient, local and parallelizable computational
method to obtain the stochastic completion fields by exploiting the
Fokker-Planck equation of the 3D directional random walk. This partial
differential equation describes the evolution of the probability
distribution of particles following such a random process.
Additionally, a rotation invariant solution is proposed using a
spherical harmonics basis to capture directions on the 2-sphere. In
analogy with the 2D completion model, we introduce additional diffusion
terms to make spatial advection errors isotropic. The 3D stochastic
completion field is further adapted to those problems where dense
orientation data is present, as is the case for diffusion MRI
measurements. The insertion  of angular drift terms into the overall
stochastic process provides a principled way  to compute completions,
while exploiting the local orientation information available  at each
voxel in the volume. Our algorithm provides a novel index of
connectivity between two regions of interest, which is based on the
overall probability for the computed completion curves between the two.
We then discuss an alternative model of the directional random walk,
where the 3D orientation change is drawn from a single distribution,
i.e., a 3D Brownian distribution.

The performance of the stochastic completion field algorithm is
validated qualitatively and quantitatively on diffusion-MRI data from
biological phantoms and on synthetic data. In vivo human data from 12
subjects is then used to investigate the algorithm's performance
qualitatively by comparing the output of our method with published
results based on another tractography method. Finally, we conclude
by discussing the advantages and limitations of the method developed in
this thesis and suggest directions for future work.

Committee:
Prof. X-W. Chang (Chair/Deputy)		Prof. K. Siddiqi (Supervisor)
Prof. J. Clark (External member)	Prof. M. Langer (Internal examiner)
TBA (Pro-Dean)				Prof. B. Pike (Committee member)

ALL ARE WELCOME

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