A Bayesian hierarchical framework for spatial modeling of fMRI data
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.
References (45)
- et al.
Hierarchical clustering to measure connectivity in fMRI resting state data
Magn. Reson. Imaging
(2002) - et al.
Whole brain segmentation: automated labeling of neuroanatomical structures in the human brain
Neuron
(2002) - et al.
Classical and Bayesian inference in neuroimaging: theory
NeuroImage
(2002) - et al.
Dissociable executive functions in the dynamic control of behavior: inhibition, error detection, and correction
NeuroImage
(2002) - et al.
Spatio-temporal regression model for the analysis of functional MRI data
NeuroImage
(2002) - et al.
Bayesian fMRI time series analysis with spatial priors
NeuroImage
(2005) - et al.
An exploration of aspects of Bayesian multiple testing
J. Stat. Plan. Inference
(2006) - et al.
Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain
NeuroImage
(2002) - et al.
Constrained linear basis sets for HRF modelling using variational Bayes
NeuroImage
(2004) - et al.
A general statistical analysis for fMRI data
NeuroImage
(2002)
A generalized estimating equations approach for spatially correlated binary data: applications to the analysis of neuroimaging data
Biometrics
Cortical and subcortical contributions to stop signal response inhibition: role of the subthalamic nucleus
J. Neurosci.
Familiar risk for Alzheimer’s disease alters fMRI activation patterns
Brain
Bayesian perspectives on multiple comparisons
J. Stat. Plan. Inference
Brain regions underlying response inhibition and interference monitoring and suppression
Eur. J. Neurosci.
Tutorial in biostatistics: likelihood methods for measuring statistical evidence
Stat. Med.
Patterns of brain activation in people at risk for Alzheimer’s disease
N. Engl. J. Med.
Spatiotemporal modeling of localized brain activity
Biostatistics
Spatio-temporal models for region of interest analyses of functional neuroimaging data
J. Am. Stat. Assoc.
Identifying spatial relationships in neural processing using a multiple classification approach
NeuroImage
Empirical Bayes methods and false discovery rates for microarrays
Genet. Epidemiol.
Automatically parcellating the human cerebral cortex
Cereb. Cortex
Cited by (103)
Context aware Markov chains models
2023, Knowledge-Based SystemsForecasting short-term defaults of firms in a commercial network via Bayesian spatial and spatio-temporal methods
2023, International Journal of ForecastingCitation Excerpt :Random effects are modelled as a multivariate normal distribution parametrised using the adjacency matrix. We acknowledge that these techniques are not novel, and have been widely used in medicine, mostly in functional magnetic resonance imaging (e.g., Bowman et al., 2008; Ge et al., 2014; Woolrich et al., 2004), or disease mapping (e.g., Adegboye & Kotze, 2012; Alegana et al., 2013; Watson et al., 2017), among other fields. However, to the best of our knowledge, they have not been fully exploited yet with a forecasting perspective in econometrics when dealing with thousands of data points interacting in a complex network.
Spectral Dependence
2022, Econometrics and StatisticsImproving the accuracy of brain activation maps in the group-level analysis of fMRI data utilizing spatiotemporal Gaussian process model
2021, Biomedical Signal Processing and ControlSpatial-Temporal Analysis of Multi-Subject Functional Magnetic Resonance Imaging Data
2021, Econometrics and Statistics