Semiparametric Bayesian models for human brain mapping

Functional magnetic resonance imaging (fMRI) has led to enormous progress in human brain mapping. Adequate analysis of the massive spatiotemporal data sets generated by this imaging technique, combining parametric and non-parametric components, imposes challenging problems in statistical modelling. Complex hierarchical Bayesian models in combination with computer-intensive Markov chain Monte Carlo inference are promising tools.The purpose of this paper is twofold. First, it provides a review of general semiparametric Bayesian models for the analysis of fMRI data. Most approaches focus on important but separate temporal or spatial aspects of the overall problem, or they proceed by stepwise procedures. Therefore, as a second aim, we suggest a complete spatiotemporal model for analysing fMRI data within a unified semiparametric Bayesian framework. An application to data from a visual stimulation experiment illustrates our approach and demonstrates its computational feasibility

Markov Chain Monte Carlo Random Effects Modeling in Magnetic Resonance Image Processing Using the BRugs Interface to WinBUGS

A common feature of many magnetic resonance image (MRI) data processing methods is the voxel-by-voxel (a voxel is a volume element) manner in which the processing is performed. In general, however, MRI data are expected to exhibit some level of spatial correlation, rendering an independent-voxels treatment inefficient in its use of the data. Bayesian random effect models are expected to be more efficient owing to their information-borrowing behaviour. To illustrate the Bayesian random effects approach, this paper outlines a Markov chain Monte Carlo (MCMC) analysis of a perfusion MRI dataset, implemented in R using the BRugs package. BRugs provides an interface to WinBUGS and its GeoBUGS add-on. WinBUGS is a widely used programme for performing MCMC analyses, with a focus on Bayesian random effect models. A simultaneous modeling of both voxels (restricted to a region of interest) and multiple subjects is demonstrated. Despite the low signal-to-noise ratio in the magnetic resonance signal intensity data, useful model signal intensity profiles are obtained. The merits of random effects modeling are discussed in comparison with the alternative approaches based on region-of-interest averaging and repeated independent voxels analysis. This paper focuses on perfusion MRI for the purpose of illustration, the main proposition being that random effects modeling is expected to be beneficial in many other MRI applications in which the signal-to-noise ratio is a limiting factor

Bayesian analysis of functional magnetic resonance imaging data with spatially varying auto‐regressive orders

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148250/1/rssc12320.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148250/2/rssc12320_am.pd

Application of Spatial Bayesian Hierarchical Models to fMRI Data

Bayesian modelling has attracted great interest in cognitive science and offered a flexible and interpretable way to study cognitive processes using functional magnetic resonance imaging data. In this chapter, a spatial Bayesian hierarchical model is applied to an event-related fMRI study of cognitive control using the Simon test. We consider a sparse spatial generalized linear mixed-effects model to capture the spatial dependence among activated voxels and temporal parameters and to benefit computationally by reducing dimensionality. We demonstrate that the proposed model has the capability of identification of the brain areas related to cognitive tasks. Moreover, the reduction in the false positive rate is observed in the simulation study, and the relevant brain regions involved in processing cognitive control are clearly detected in a real-life fMRI example

A spatiotemporal nonparametric Bayesian model of multi-subject fMRI data

In this paper we propose a unified, probabilistically coherent framework for the analysis of task-related brain activity in multi-subject fMRI experiments. This is distinct from two-stage “group analysis” approaches traditionally considered in the fMRI literature, which separate the inference on the individual fMRI time courses from the inference at the population level. In our modeling approach we consider a spatiotemporal linear regression model and specifically account for the between-subjects heterogeneity in neuronal activity via a spatially informed multi-subject nonparametric variable selection prior. For posterior inference, in addition to Markov chain Monte Carlo sampling algorithms, we develop suitable variational Bayes algorithms. We show on simulated data that variational Bayes inference achieves satisfactory results at more reduced computational costs than using MCMC, allowing scalability of our methods. In an application to data collected to assess brain responses to emotional stimuli our method correctly detects activation in visual areas when visual stimuli are presented

fMRI activation detection with EEG priors

The purpose of brain mapping techniques is to advance the understanding of the relationship between structure and function in the human brain in so-called activation studies. In this work, an advanced statistical model for combining functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) recordings is developed to fuse complementary information about the location of neuronal activity. More precisely, a new Bayesian method is proposed for enhancing fMRI activation detection by the use of EEG-based spatial prior information in stimulus based experimental paradigms. I.e., we model and analyse stimulus influence by a spatial Bayesian variable selection scheme, and extend existing high-dimensional regression methods by incorporating prior information on binary selection indicators via a latent probit regression with either a spatially-varying or constant EEG effect. Spatially-varying effects are regularized by intrinsic Markov random field priors. Inference is based on a full Bayesian Markov Chain Monte Carlo (MCMC) approach. Whether the proposed algorithm is able to increase the sensitivity of mere fMRI models is examined in both a real-world application and a simulation study. We observed, that carefully selected EEG--prior information additionally increases sensitivity in activation regions that have been distorted by a low signal-to-noise ratio

Improving the accuracy of brain activation maps in the group-level analysis of fMRI data utilizing spatiotemporal Gaussian process model

OBJECTIVE: Accuracy and precision of the statistical analysis methods used for brain activation maps are essential. Adjusting models to consider spatiotemporal correlation embedded in fMRI data may increase their accuracy, but it also introduces a high computational cost. The present study aimed to apply and assess the spatiotemporal Gaussian process (STGP) model to improve accuracy and reduce cost. METHODS: We applied the spatiotemporal Gaussian process (STGP) model for both simulated and experimental memory tfMRI data and compared the findings with fast, fully Bayesian, and General Linear Models (GLM). To assess their accuracy and precision, the models were fitted to the simulated data (1000 voxels,100 times point for 50 people), and an average of accuracy indexes of 100 repetitions was computed. Functional and activation maps for all models were calculated in experimental data analysis. RESULTS: STGP model resulted in a higher Z-score in the whole brain, in the 1000 most activated voxels, and in the frontal lobe as the approved memory area. Based on the simulated data, the STGP model showed more accuracy and precision than the other two models. However, its computational time was more than the GLM, as the price of model correction, but much less than that of the fast, fully Bayesian model. CONCLUSION: Spatiotemporal correlation further improved the accuracy of the STGP compared to the GLM and fast, fully Bayesian model. This can result in more accurate activation maps. Moreover, the STGP model’s computational speed appears to be reasonable for model application

State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing

Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a challenging problem in functional neuroimaging. The number of potential sources within the brain exceeds by an order of magnitude the number of recording sites. As a consequence, the estimates for the magnitude and location of the neural sources will be ill-conditioned because of the underdetermined nature of the problem. One well-known technique designed to address this imbalance is the minimum norm estimator (MNE). This approach imposes an $L^2$ regularization constraint that serves to stabilize and condition the source parameter estimates. However, these classes of regularizer are static in time and do not consider the temporal constraints inherent to the biophysics of the MEG experiment. In this paper we propose a dynamic state-space model that accounts for both spatial and temporal correlations within and across candidate intracortical sources. In our model, the observation model is derived from the steady-state solution to Maxwell's equations while the latent model representing neural dynamics is given by a random walk process.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS483 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org