Spatially Adaptive Mixture Modeling for Analysis of fMRI Time Series

Abstract

Within-subject analysis in fMRI essentially addresses two problems, the detection of brain regions eliciting evoked activity and the estimation of the underlying dynamics. In Makni et aL, 2005 and Makni et aL, 2008, a detection-estimation framework has been proposed to tackle these problems jointly, since they are connected to one another. In the Bayesian formalism, detection is achieved by modeling activating and nonactivating voxels through independent mixture models (IMM) within each region while hemodynamic response estimation is performed at a regional scale in a nonparametric way. Instead of IMMs, in this paper we take advantage of spatial mixture models (SMM) for their nonlinear spatial regularizing properties. The proposed method is unsupervised and spatially adaptive in the sense that the amount of spatial correlation is automatically tuned from the data and this setting automatically varies across brain regions. In addition, the level of regularization is specific to each experimental condition since both the signal-to-noise ratio and the activation pattern may vary across stimulus types in a given brain region. These aspects require the precise estimation of multiple partition functions of underlying Ising fields. This is addressed efficiently using first path sampling for a small subset of fields and then using a recently developed fast extrapolation technique for the large remaining set. Simulation results emphasize that detection relying on supervised SMM outperforms its IMM counterpart and that unsupervised spatial mixture models achieve similar results without any hand-tuning of the correlation parameter. On real datasets, the gain is illustrated in a localizer fMRI experiment: brain activations appear more spatially resolved using SMM in comparison with classical general linear model (GLM)-based approaches, while estimating a specific parcel-based HRF shape. Our approach therefore validates the treatment of unsmoothed fMRI data without fixed GLM definition at the subject level and makes also the classical strategy of spatial Gaussian filtering deprecated.

A spatio-temporal nonparametric Bayesian variable selection model of fMRI data for clustering correlated time courses

“…However, the use of a 3D Ising model presents itself with further modeling and computational challenges, in terms of hyper-parameter selection and posterior computation. See, for example, Risser et al (2009) and Vincent et al (2010). Future work may consider extending our framework to the 3D analysis of a few specific brain regions.…”

Adaptively and Spatially Estimating the Hemodynamic Response Functions in fMRI

“…In real fMRI studies, it is common that multiple stimuli are present [11]. Under the assumption of the LTI system, the BOLD signal is the individual response to the sum of all stimuli convoluted with their associated HRFs.…”

“…These smoothing methods can blur the information near the edges of the effect regions and thus dramatically increase the number of false positives and false negatives. An alternative approach is to model spatial dependence among spatially connected voxels by using conditional autoregressive (CAR), Markov random field (MRF) or other spatial correlation priors [9,11]. However, calculating the normalizing factor of MRF and estimating spatial correlation for a large number of voxels in the 3D volume are computationally intensive [2].…”

Spatial–temporal modelling of fMRI data through spatially regularized mixture of hidden process models

“…In this contribution we propose a new method for spatio-temporal modelling of fMRI data that advances the latter approach in four crucial aspects:

Previously, the localized temporal prototypes have mostly been General Linear Models (GLMs) (Friston et al, 1995) (see e.g. Penny and Friston, 2003; Kim et al, 2010; Vincent et al, 2010), which could be relatively simple (the onset and shape of HRF are assumed to be known and remain the same across all prototypes/voxels). Instead, we use as prototypes Hidden Process Model (HPM) (Hutchinson et al, 2009), which enables us to infer the contribution of individual cognitive processes to the observed fMRI data.

…”

“…Penny and Friston, 2003; Kim et al, 2010; Vincent et al, 2010), which could be relatively simple (the onset and shape of HRF are assumed to be known and remain the same across all prototypes/voxels). Instead, we use as prototypes Hidden Process Model (HPM) (Hutchinson et al, 2009), which enables us to infer the contribution of individual cognitive processes to the observed fMRI data.…”