Empirical Markov Chain Monte Carlo Bayesian analysis of fMRI data

Fast joint detection-estimation of evoked brain activity in event-related FMRI using a variational approach

In standard within-subject analyses of event-related functional magnetic resonance imaging (fMRI) data, two steps are usually performed separately: detection of brain activity and estimation of the hemodynamic response. Because these two steps are inherently linked, we adopt the so-called region-based joint detection-estimation (JDE) framework that addresses this joint issue using a multivariate inference for detection and estimation. JDE is built by making use of a regional bilinear generative model of the BOLD response and constraining the parameter estimation by physiological priors using temporal and spatial information in a Markovian model. In contrast to previous works that use Markov Chain Monte Carlo (MCMC) techniques to sample the resulting intractable posterior distribution, we recast the JDE into a missing data framework and derive a variational expectation-maximization (VEM) algorithm for its inference. A variational approximation is used to approximate the Markovian model in the unsupervised spatially adaptive JDE inference, which allows automatic fine-tuning of spatial regularization parameters. It provides a new algorithm that exhibits interesting properties in terms of estimation error and computational cost compared to the previously used MCMC-based approach. Experiments on artificial and real data show that VEM-JDE is robust to model misspecification and provides computational gain while maintaining good performance in terms of activation detection and hemodynamic shape recovery.

Bayesian characterization of uncertainty in intra-subject non-rigid registration

In settings where high-level inferences are made based on registered image data, the registration uncertainty can contain important information. In this article, we propose a Bayesian non-rigid registration framework where conventional dissimilarity and regularization energies can be included in the likelihood and the prior distribution on deformations respectively through the use of Boltzmann's distribution. The posterior distribution is characterized using Markov Chain Monte Carlo (MCMC) methods with the effect of the Boltzmann temperature hyper-parameters marginalized under broad uninformative hyper-prior distributions. The MCMC chain permits estimation of the most likely deformation as well as the associated uncertainty. On synthetic examples, we demonstrate the ability of the method to identify the maximum a posteriori estimate and the associated posterior uncertainty, and demonstrate that the posterior distribution can be non-Gaussian. Additionally, results from registering clinical data acquired during neurosurgery for resection of brain tumor are provided; we compare the method to single transformation results from a deterministic optimizer and introduce methods that summarize the high-dimensional uncertainty. At the site of resection, the registration uncertainty increases and the marginal distribution on deformations is shown to be multi-modal.

A Bayesian multilevel model for fMRI data analysis

Bayesian approaches have been proposed by several functional magnetic resonance imaging (fMRI) researchers in order to overcome the fundamental limitations of the popular statistical parametric mapping method. However, the difficulties associated with subjective prior elicitation have prevented the widespread adoption of the Bayesian methodology by the neuroimaging community. In this paper, we present a Bayesian multilevel model for the analysis of brain fMRI data. The main idea is to consider that all the estimated group effects (fMRI activation patterns) are exchangeable. This means that all the collected voxel time series are considered manifestations of a few common underlying phenomena. In contradistinction to other Bayesian approaches, we think of the estimated activations as multivariate random draws from the same distribution without imposing specific prior spatial and/or temporal information for the interaction between voxels. Instead, a two-stage empirical Bayes prior approach is used to relate voxel regression equations through correlations between the regression coefficient vectors. The adaptive shrinkage properties of the Bayesian multilevel methodology are exploited to deal with spatial variations, and noise outliers. The characteristics of the proposed model are evaluated by considering its application to two real data sets.

A Bayesian hierarchical correlation model for fMRI cluster analysis

Data-driven cluster analysis is potentially suitable to search for, and discriminate between, distinct response signals in blood oxygenation level-dependent functional magnetic resonance imaging (BOLD fMRI), which appear during cerebrovascular disease. In contrast to model-driven methods, which test for a particular BOLD signal whose shape must be given beforehand, data-driven methods generate a set of BOLD signals directly from the fMRI data by clustering voxels into groups with correlated time signals. Here, we address the problem of selecting only the clusters that represent genuine responses to the experimental stimulus by modeling the correlation structure of the clustered data using a Bayesian hierarchical model. The model is empirically justified by demonstrating the hierarchical organization of the voxel correlations after cluster analysis. BOLD signal discrimination is demonstrated using: 1) simulations that contain multiple pathological BOLD response signals; and 2) fMRI data acquired during an event-related motor task. These demonstrations are compared with results from a model-driven method based on the general linear model. Our simulations show that the data-driven method can discriminate between the BOLD response signals, while the model-driven method only finds one signal. For fMRI, the data-driven method distinguishes between the BOLD signals appearing in the sensorimotor cortex and those in basal ganglia and putamen, while the model-driven method combines these signals into one activation map. We conclude that the proposed data-driven method provides an objective framework to identify and discriminate between distinct BOLD response signals.

Bayesian spatiotemporal model of fMRI data

This research describes a new Bayesian spatiotemporal model to analyse block-design BOLD fMRI studies. In the temporal dimension, we parameterise the hemodynamic response function's (HRF) shape with a potential increase of signal and a subsequent exponential decay. In the spatial dimension, we use Gaussian Markov random fields (GMRF) priors on activation characteristics parameters (location and magnitude) that embody our prior knowledge that evoked responses are spatially contiguous and locally homogeneous. The result is a spatiotemporal model with a small number of parameters, all of them interpretable. Simulations from the model are performed in order to ascertain the performance of the sampling scheme and the ability of the posterior to estimate model parameters, as well as to check the model sensitivity to signal to noise ratio. Results are shown on synthetic data and on real data from a block-design fMRI experiment.

A stimulus-locked vector autoregressive model for slow event-related fMRI designs

Neuroscientists have become increasingly interested in exploring dynamic relationships among brain regions. Such a relationship, when directed from one region toward another, is denoted by "effective connectivity." An fMRI experimental paradigm which is well-suited for examination of effective connectivity is the slow event-related design. This design presents stimuli at sufficient temporal spacing for determining within-trial trajectories of BOLD activation, allowing for the analysis of stimulus-locked temporal covariation of brain responses in multiple regions. This may be especially important for emotional stimuli processing, which can evolve over the course of several seconds, if not longer. However, while several methods have been devised for determining fMRI effective connectivity, few are adapted to event-related designs, which include nonstationary BOLD responses and multiple levels of nesting. We propose a model tailored for exploring effective connectivity of multiple brain regions in event-related fMRI designs--a semi-parametric adaptation of vector autoregressive (VAR) models, termed "stimulus-locked VAR" (SloVAR). Connectivity coefficients vary as a function of time relative to stimulus onset, are regularized via basis expansions, and vary randomly across subjects. SloVAR obtains flexible, data-driven estimates of effective connectivity and hence is useful for building connectivity models when prior information on dynamic regional relationships is sparse. Indices derived from the coefficient estimates can also be used to relate effective connectivity estimates to behavioral or clinical measures. We demonstrate the SloVAR model on a sample of clinically depressed and normal controls, showing that early but not late cortico-amygdala connectivity appears crucial to emotional control and early but not late cortico-cortico connectivity predicts depression severity in the depressed group, relationships that would have been missed in a more traditional VAR analysis.