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. 2010;13(Pt 2):363-70.
doi: 10.1007/978-3-642-15745-5_45.

Spatial regularization of functional connectivity using high-dimensional Markov random fields

Wei Liu  1 , Peihong Zhu, Jeffrey S Anderson, Deborah Yurgelun-Todd, P Thomas Fletcher
Affiliations

Spatial regularization of functional connectivity using high-dimensional Markov random fields

Wei Liu et al. Med Image Comput Comput Assist Interv. 2010.

Abstract

In this paper we present a new method for spatial regularization of functional connectivity maps based on Markov Random Field (MRF) priors. The high level of noise in fMRI leads to errors in functional connectivity detection algorithms. A common approach to mitigate the effects of noise is to apply spatial Gaussian smoothing, which can lead to blurring of regions beyond their actual boundaries and the loss of small connectivity regions. Recent work has suggested MRFs as an alternative spatial regularization in detection of fMRI activation in task-based paradigms. We propose to apply MRF priors to the computation of functional connectivity in resting-state fMRI. Our Markov priors are in the space of pairwise voxel connections, rather than in the original image space, resulting in a MRF whose dimension is twice that of the original image. The high dimensionality of the MRF estimation problem leads to computational challenges. We present an efficient, highly parallelized algorithm on the Graphics Processing Unit (GPU). We validate our approach on a synthetically generated example as well as real data from a resting state fMRI study.

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Figures

Fig. 1
Fig. 1
Test of synthetic data, showing the (a) ground-truth connectivity, (b) correlation of original, noisy data, (c) correlation of Gaussian-smoothed data, (d) connectivity based on noisy correlations, (e) connectivity based on smoothed data, (f) connectivity computed using proposed MRF model.
Fig. 2
Fig. 2
Correlation map and Posterior Connectivity map between seed voxel and slice containing the seed. First row is subject 1. (a) the correlation map computed from data without spatial smoothing. (b) correlation map of data after smoothing. (c) Posterior probability computed from MRF. Second row (d,e,f) is subject 2 with same test.
Fig. 3
Fig. 3
Thresholded correlation map and Posterior Connectivity map between seed voxel and slice, overlaid to T2 image. First row is subject 1. (a) the correlation map computed from data without spatial smoothing. (b) After smoothing. (c) Posterior probability by MRF. Second row (d,e,f) is subject 2 with same test.
See this image and copyright information in PMC

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