Elsevier

NeuroImage

Volume 39, Issue 1, 1 January 2008, Pages 146-156
NeuroImage

A Bayesian hierarchical framework for spatial modeling of fMRI data

https://doi.org/10.1016/j.neuroimage.2007.08.012Get rights and content

Abstract

Applications of functional magnetic resonance imaging (fMRI) have provided novel insights into the neuropathophysiology of major psychiatric, neurological, and substance abuse disorders and their treatments. Modern activation studies often compare localized task-induced changes in brain activity between experimental groups. Complementary approaches consider the ensemble of voxels constituting an anatomically defined region of interest (ROI) or summary statistics, such as means or quantiles, of the ROI. In this work, we present a Bayesian extension of voxel-level analyses that offers several notable benefits. Among these, it combines whole-brain voxel-by-voxel modeling and ROI analyses within a unified framework. Secondly, an unstructured variance/covariance matrix for regional mean parameters allows for the study of inter-regional (long-range) correlations, and the model employs an exchangeable correlation structure to capture intra-regional (short-range) correlations. Estimation is performed using Markov Chain Monte Carlo (MCMC) techniques implemented via Gibbs sampling. We apply our Bayesian hierarchical model to two novel fMRI data sets: one considering inhibitory control in cocaine-dependent men and the second considering verbal memory in subjects at high risk for Alzheimer’s disease.

Introduction

Functional neuroimaging techniques enable in vivo investigations into the neural basis of human cognition, emotions, and behaviors. In practice, applications of functional magnetic resonance imaging (fMRI) have provided insights into the pathogenesis and pathophysiology of major psychiatric, neurologic, and substance abuse disorders, as well as the neural responses to their treatments. Depending on objectives, fMRI experiments are often employed to study activation or functional connectivity. Activation studies seek to characterize the magnitude and volume of neural responses to experimental tasks by detecting differences in patterns of brain activity between various experimental conditions, between different subgroups of subjects, or between two or more scanning sessions. In contrast, functional connectivity studies seek to identify areas of the brain that share similar temporal task-related neural responses. We consider a variant of this concept by targeting brain regions that exhibit spatial correlations between summary statistics of the blood oxygen level-dependent (BOLD) neural response profiles, such as task-specific mean effects. These spatial correlations are interpretable as task-related functional connections. We develop a common statistical framework that simultaneously considers activation and task-related functional connectivity. Of note, the model incorporates both long-range and short-range task-related connectivity.

We build on the conventional two-stage approach applied in activation studies for fMRI data. This approach considers individualized voxel-specific time series models in the first stage and voxel-specific population- or group-level models at the second stage (Worsley et al., 2002). In this study, we principally focus on the second stage modeling. The typical voxel-by-voxel second stage regression analyses address spatial correlations by a process of smoothing and Markovian assumptions on resulting statistical maps. We instead focus on both short-range and long-range correlations and formal estimation in a comprehensive statistical model.

Specifically, we develop a spatial Bayesian hierarchical model that is applicable for making inferences regarding task-related changes in brain activity and that identifies and accounts for prominent task-related connectivity. This multilevel model is estimated using Markov Chain Monte Carlo (MCMC) techniques. Our Bayesian method offers inferential advantages by providing samples from the joint posterior probability distribution for all of the model parameters, rather than p-values, providing greater flexibility in the inferences that may be drawn from a functional neuroimaging study. Furthermore, our proposed spatial model extends the assumptions underlying previously applied methods and establishes a novel unified framework for voxel-specific and regional (or region of interest (ROI)) inferences, which also uncovers prominent task-related functional connections between remote voxels.

Below, we discuss relevant literature before presenting the proposed Bayesian hierarchical model, estimation procedures, and applications of our model to experimental data from two fMRI studies.

Section snippets

Literature review

There is emerging recognition of the importance of modeling correlations between voxels both for estimation and inferences. Some investigators attempt to capture correlations between the measured brain activity in a given voxel with the activity in neighboring voxels. For example, Katanoda et al. (2002) address spatial correlations by incorporating the time series from neighboring (physically contiguous) voxels. Similarly, Gössl et al. (2001) and Woolrich et al. (2004a) consider correlations

Experimental fMRI data

In this paper, we highlight the analysis of two novel fMRI data sets that motivated the developed model and represent good examples of its utility. Below we briefly describe each in turn before introducing the model.

The first experiment considers inhibitory control in cocaine-dependent men. Impairments in inhibitory control over drug related behaviors are common characteristics of addicts (Kalivas and Volkow, 2005). We consider an fMRI study that evaluates the impact of cocaine addiction and

A hierarchical model for functional neuroimaging data

We formulate a model that builds on the conventional two-stage modeling approach for fMRI data that emulates a random effects analysis. Our model captures temporal correlations via the approximate random effects structure and also by addressing serial dependencies between each subject’s repeated measurements (Worsley et al., 2002). We then extend the conventional approach by fitting a spatial Bayesian hierarchical model at the second stage, where we capture correlations in BOLD effects between

Results

We apply our Bayesian hierarchical model to both the fMRI study of inhibitory control in cocaine-dependent men as well as to the auditory memory encoding and retrieval study of individuals who are at high risk for developing Alzheimer’s disease. We divide our investigations into two sections: mean comparisons (in Voxel level and regional mean comparisons) and variance components (in Regional variance components). We use the cocaine-dependence data to highlight relevant mean comparisons and the

Discussion

We propose a spatial Bayesian hierarchical model for analyzing functional neuroimaging data, which has several key advantages over alternative approaches. First, our model provides a unified framework to obtain neuroactivation inferences as well as task-related functional connectivity inferences, rather than treating these as distinct analytical objectives. Secondly, we may investigate neuroactivation both at the voxel level and at a regional level. It is important to note that the voxel-level

Acknowledgments

The work of Bowman was supported by the National Institute of Mental Health (NIH grants K25-MH65473 and R01-MH079251). The work of Bassett and Caffo was supported by NIH grants AG016324 and EB003491.

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