Study of Connectivity in the Brain Using the Full Diffusion Tensor from MRI
IPMI '01 Proceedings of the 17th International Conference on Information Processing in Medical Imaging
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Probabilistic anatomical connectivity using completion fields
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
A hamilton-jacobi-bellman approach to high angular resolution diffusion tractography
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
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Partial differential equations have been successfully used for fibre tractography and for mapping connectivity indices in the brain. However, the current implementation of methods which require 3D orientation to be tracked can suffer from serious shortcomings when invariance to 3D rotation is desired. In this paper we focus on the 3D stochastic completion field and introduce a new methodology to solve the underlying PDE in a manner that achieves rotation invariance. The key idea is to use spherical harmonics to solve the Fokker-Planck equation representing the evolution of the probability density function of a 3D directional random walk. We validate the new approach by presenting improved connectivity indices on synthetic data, on the MICCAI 2009 Fibre Cup phantom and on a biological phantom comprised of two rat spinal chords in a crossing configuration.