An MCMC-based analysis of a multilevel model for functional MRI data

Functional neuroimaging technologies have inspired a revolution in the study of brain function and its correlation with behavior, disease, and environment. In these techniques, temporal three-dimensional images of the brain are analyzed to produce a quantitative description of brain function. Such techniques can, among other things, present evidence of localization of brain function within and between subjects. For example, when subjects perform motor tasks in a functional magnetic resonance imaging (fMRI) scanner, such as ﬁnger tapping, the analysis typically will present increased regional cerebral blood ﬂow (activation) in the motor cortex. Moreover, these techniques can also provide some information about how areas of the brain connect and communicate. In this chapter we further investigate a novel Markov chain Monte Carlo (MCMC) based analysis of a model from Bowman et al. (2008) that combines activation studies with the study of brain connectivity in a single uniﬁed approach. This idea of localization of brain function underlying fMRI activation studies has a longhistory,with early attempts fromthedebunkedscienceofphrenology in the earlynineteenth century and later breakthroughs by such luminaries as Broca, Wernicke, and Brodman (see Gazzaniga et al., 2002, for an accessible brief history). Prior to newmeasurement techniques, studies of brain function and localization were limited to animal studies, or post-mortem evaluation of patients with stroke damage or injuries. However, new measurement techniques, such as fMRI, positron emission tomography (PET), and electroencephalography, allow modern researchers noninvasively to study brain function in human subjects. In contrast with the study of functional localization, the companion idea of connectivityhas a shorter history. Functional connectivity is deﬁned as correlation between remote neurophysiological events (Friston et al., 2007). This idea is based on the principal of functional integration of geographically separated areas of the brain. Such integration is supported by the existence of anatomical connections between cortical areas aswell as oneswithin the cortical sheet (see the discussion in Friston et al., 2007). This neuroanatomical model suggests a hierarchical structure of connectivity that includes correlations within and between areas of functional specialization. Therefore, we use this hierarchical biological model of brain function to explore a multilevel statistical model that simultaneously considers potentially long-range correlations as well as shorter-range ones. We focus on analyzing fMRI data in particular, though the statistical and computationaltechniques apply more broadly to other functional neuroimaging modalities. Functionalpanied by a localized increase in blood ﬂow (Roy and Sherrington, 1890). More speciﬁcally, neuronal activity requires energy,which is supplied by chemical reactions fromoxygenated hemoglobin. Therefore, provided a cognitive task is localized, a temporal comparison of blood oxygenation levelswhen the task is being executed versuswhen it is notwould reveal areas of the brain where neurons are active. This is the principle of blood oxygenation level dependent (BOLD) fMRI (Ogawa et al., 1990). In this technique, a subject in anMRI scanner is asked to perform a task at speciﬁc timings while images targeting the BOLD signal are taken in rapid succession, usually one image every 2-3 seconds. Examples of tasks aremotor tasks, pressing a button after a visual stimulus, mentally rotating ﬁgures and so on. The development of a well-controlled task, or paradigm, that isolates the particular cognitive function of interest is not covered in this chapter. We focus on using Bayesian multilevel models via MCMC for the analysis of functionalneuroimaging studies. We emphasize the analysis of so-called group-level fMRI data. In such studies one is interested in the commonality of activation and connectivity within groups and differences between groups, such as comparing diseased and control subjects. In the following two subsections, we provide an overview of existing related fMRIresearch and introduce the data used to illustrate the methods. In Section 14.2, we give details on the processing and ﬁrst-stage analysis of the data. In Section 14.3, we introduce the multilevel model used for analysis and outline the details of the MCMC procedure. In Section 14.4, we propose novel methods for analyzing and visualizing the output from the Markov chain, including the analysis of voxel means, regional means, and intra-and inter-regional connectivity. We conclude with a discussion.