Spatio-temporal modeling of localized brain activity

Identifying covariate-related subnetworks for whole-brain connectome analysis

Whole-brain connectome data characterize the connections among distributed neural populations as a set of edges in a large network, and neuroscience research aims to systematically investigate associations between brain connectome and clinical or experimental conditions as covariates. A covariate is often related to a number of edges connecting multiple brain areas in an organized structure. However, in practice, neither the covariate-related edges nor the structure is known. Therefore, the understanding of underlying neural mechanisms relies on statistical methods that are capable of simultaneously identifying covariate-related connections and recognizing their network topological structures. The task can be challenging because of false-positive noise and almost infinite possibilities of edges combining into subnetworks. To address these challenges, we propose a new statistical approach to handle multivariate edge variables as outcomes and output covariate-related subnetworks. We first study the graph properties of covariate-related subnetworks from a graph and combinatorics perspective and accordingly bridge the inference for individual connectome edges and covariate-related subnetworks. Next, we develop efficient algorithms to exact covariate-related subnetworks from the whole-brain connectome data with an $\ell_0$ norm penalty. We validate the proposed methods based on an extensive simulation study, and we benchmark our performance against existing methods. Using our proposed method, we analyze two separate resting-state functional magnetic resonance imaging data sets for schizophrenia research and obtain highly replicable disease-related subnetworks.

Modeling multivariate age-related imaging variables with dependencies

Neuroimaging techniques have been increasingly used to understand the neural biology of aging brains. The neuroimaging variables from distinct brain locations and modalities can exhibit age-related patterns that reflect localized neural decline. However, it is a challenge to identify the impacts of risk factors (eg, mental disorders) on multivariate imaging variables while simultaneously accounting for the dependence structure and nonlinear age trajectories using existing tools. We propose a mixed-effects model to address this challenge by building random effects based on the latent brain aging status. We develop computationally efficient algorithms to estimate the parameters of new random effects. The simulations show that our approach provides accurate parameter estimates, improves the inference efficiency, and reduces the root mean square error compared to existing methods. We further apply this method to the UK Biobank data to investigate the effects of tobacco smoking on the white matter integrity of the entire brain during aging and identify the adverse effects on white matter integrity with multiple fiber tracts.

A Spatio-temporal Model for Detecting the Effect of Cocaine Use Disorder on Functional Connectivity

Drug addiction can lead to many health-related problems and social concerns. Researchers are interested in the association between long-term drug usage and abnormal functional connectivity. Functional connectivity obtained from functional magnetic resonance imaging data promotes a variety of fundamental understandings in such association. Due to the complex correlation structure and large dimensionality, the modeling and analysis of the functional connectivity from neuroimage are challenging. By proposing a spatio-temporal model for multi-subject neuroimage data, we incorporate voxel-level spatio-temporal dependencies of whole-brain measurements to improve the accuracy of statistical inference. To tackle large-scale spatio-temporal neuroimage data, we develop a computational efficient algorithm to estimate the parameters. Our method is used to first identify functional connectivity, and then detect the effect of cocaine use disorder (CUD) on functional connectivity between different brain regions. The functional connectivity identified by our spatio-temporal model matches existing studies on brain networks, and further indicates that CUD may alter the functional connectivity in the medial orbitofrontal cortex subregions and the supplementary motor areas.

Bayes estimate of primary threshold in clusterwise functional magnetic resonance imaging inferences

Clusterwise statistical inference is the most widely used technique for functional magnetic resonance imaging (fMRI) data analyses. Clusterwise statistical inference consists of two steps: (i) primary thresholding that excludes less significant voxels by a prespecified cut-off (eg, p < . 001 ); and (ii) clusterwise thresholding that controls the familywise error rate caused by clusters consisting of false positive suprathreshold voxels. The selection of the primary threshold is critical because it determines both statistical power and false discovery rate (FDR). However, in most existing statistical packages, the primary threshold is selected based on prior knowledge (eg, p < . 001 ) without taking into account the information in the data. In this article, we propose a data-driven approach to algorithmically select the optimal primary threshold based on an empirical Bayes framework. We evaluate the proposed model using extensive simulation studies and real fMRI data. In the simulation, we show that our method can effectively increase statistical power by 20% to over 100% while effectively controlling the FDR. We then investigate the brain response to the dose-effect of chlorpromazine in patients with schizophrenia by analyzing fMRI scans and generate consistent results.

A Cortical Surface-Based Meta-Analysis of Human Reasoning

Recent advances in neuroimaging have augmented numerous findings in the human reasoning process but have yielded varying results. One possibility for this inconsistency is that reasoning is such an intricate cognitive process, involving attention, memory, executive functions, symbolic processing, and fluid intelligence, whereby various brain regions are inevitably implicated in orchestrating the process. Therefore, researchers have used meta-analyses for a better understanding of neural mechanisms of reasoning. However, previous meta-analysis techniques include weaknesses such as an inadequate representation of the cortical surface’s highly folded geometry. Accordingly, we developed a new meta-analysis method called Bayesian meta-analysis of the cortical surface (BMACS). BMACS offers a fast, accurate, and accessible inference of the spatial patterns of cognitive processes from peak brain activations across studies by applying spatial point processes to the cortical surface. Using BMACS, we found that the common pattern of activations from inductive and deductive reasoning was colocalized with the multiple-demand system, indicating that reasoning is a high-level convergence of complex cognitive processes. We hope surface-based meta-analysis will be facilitated by BMACS, bringing more profound knowledge of various cognitive processes.

A Bayesian spatial model for imaging genetics

We develop a Bayesian bivariate spatial model for multivariate regression analysis applicable to studies examining the influence of genetic variation on brain structure. Our model is motivated by an imaging genetics study of the Alzheimer's Disease Neuroimaging Initiative (ADNI), where the objective is to examine the association between images of volumetric and cortical thickness values summarizing the structure of the brain as measured by magnetic resonance imaging (MRI) and a set of 486 single nucleotide polymorphism (SNPs) from 33 Alzheimer's disease (AD) candidate genes obtained from 632 subjects. A bivariate spatial process model is developed to accommodate the correlation structures typically seen in structural brain imaging data. First, we allow for spatial correlation on a graph structure in the imaging phenotypes obtained from a neighborhood matrix for measures on the same hemisphere of the brain. Second, we allow for correlation in the same measures obtained from different hemispheres (left/right) of the brain. We develop a mean-field variational Bayes algorithm and a Gibbs sampling algorithm to fit the model. We also incorporate Bayesian false discovery rate (FDR) procedures to select SNPs. We implement the methodology in a new release of the R package bgsmtr. We show that the new spatial model demonstrates superior performance over a standard model in our application. Data used in the preparation of this article were obtained from the ADNI database (https://adni.loni.usc.edu).

Bayesian modeling of dependence in brain connectivity data

Brain connectivity studies often refer to brain areas as graph nodes and connections between nodes as edges, and aim to identify neuropsychiatric phenotype-related connectivity patterns. When performing group-level brain connectivity alternation analyses, it is critical to model the dependence structure between multivariate connectivity edges to achieve accurate and efficient estimates of model parameters. However, specifying and estimating dependencies between connectivity edges presents formidable challenges because (i) the dimensionality of parameters in the covariance matrix is high (of the order of the fourth power of the number of nodes); (ii) the covariance between a pair of edges involves four nodes with spatial location information; and (iii) the dependence structure between edges can be related to unknown network topological structures. Existing methods for large covariance/precision matrix regularization and spatial closeness-based dependence structure specification/estimation models may not fully address the complexity and challenges. We develop a new Bayesian nonparametric model that unifies information from brain network areas (nodes), connectivity (edges), and covariance between edges by constructing the function of covariance matrix based on the underlying network topological structure. We perform parameter estimation using an efficient Markov chain Monte Carlo algorithm. We apply our method to resting-state functional magnetic resonance imaging data from 60 subjects of a schizophrenia study and simulated data to demonstrate the performance of our method.

Mixed Spectrum Analysis on fMRI Time-Series

Temporal autocorrelation present in functional magnetic resonance image (fMRI) data poses challenges to its analysis. The existing approaches handling autocorrelation in fMRI time-series often presume a specific model of autocorrelation such as an auto-regressive model. The main limitation here is that the correlation structure of voxels is generally unknown and varies in different brain regions because of different levels of neurogenic noises and pulsatile effects. Enforcing a universal model on all brain regions leads to bias and loss of efficiency in the analysis. In this paper, we propose the mixed spectrum analysis of the voxel time-series to separate the discrete component corresponding to input stimuli and the continuous component carrying temporal autocorrelation. A mixed spectral analysis technique based on M-spectral estimator is proposed, which effectively removes autocorrelation effects from voxel time-series and identify significant peaks of the spectrum. As the proposed method does not assume any prior model for the autocorrelation effect in voxel time-series, varying correlation structure among the brain regions does not affect its performance. We have modified the standard M-spectral method for an application on a spatial set of time-series by incorporating the contextual information related to the continuous spectrum of neighborhood voxels, thus reducing considerably the computation cost. Likelihood of the activation is predicted by comparing the amplitude of discrete component at stimulus frequency of voxels across the brain by using normal distribution and modeling spatial correlations among the likelihood with a conditional random field. We also demonstrate the application of the proposed method in detecting other desired frequencies.

Quantification of the statistical effects of spatiotemporal processing of nontask FMRI data

Nontask functional magnetic resonance imaging (fMRI) has become one of the most popular noninvasive areas of brain mapping research for neuroscientists. In nontask fMRI, various sources of "noise" corrupt the measured blood oxygenation level-dependent signal. Many studies have aimed to attenuate the noise in reconstructed voxel measurements through spatial and temporal processing operations. While these solutions make the data more "appealing," many commonly used processing operations induce artificial correlations in the acquired data. As such, it becomes increasingly more difficult to derive the true underlying covariance structure once the data have been processed. As the goal of nontask fMRI studies is to determine, utilize, and analyze the true covariance structure of acquired data, such processing can lead to inaccurate and misleading conclusions drawn from the data if they are unaccounted for in the final connectivity analysis. In this article, we develop a framework that represents the spatiotemporal processing and reconstruction operations as linear operators, providing a means of precisely quantifying the correlations induced or modified by such processing rather than by performing lengthy Monte Carlo simulations. A framework of this kind allows one to appropriately model the statistical properties of the processed data, optimize the data processing pipeline, characterize excessive processing, and draw more accurate functional connectivity conclusions.

Brain Imaging Analysis

The increasing availability of brain imaging technologies has led to intense neuroscientific inquiry into the human brain. Studies often investigate brain function related to emotion, cognition, language, memory, and numerous other externally induced stimuli as well as resting-state brain function. Studies also use brain imaging in an attempt to determine the functional or structural basis for psychiatric or neurological disorders and, with respect to brain function, to further examine the responses of these disorders to treatment. Neuroimaging is a highly interdisciplinary field, and statistics plays a critical role in establishing rigorous methods to extract information and to quantify evidence for formal inferences. Neuroimaging data present numerous challenges for statistical analysis, including the vast amounts of data collected from each individual and the complex temporal and spatial dependence present. We briefly provide background on various types of neuroimaging data and analysis objectives that are commonly targeted in the field. We present a survey of existing methods targeting these objectives and identify particular areas offering opportunities for future statistical contribution.

Hierarchical vector auto-regressive models and their applications to multi-subject effective connectivity

Vector auto-regressive (VAR) models typically form the basis for constructing directed graphical models for investigating connectivity in a brain network with brain regions of interest (ROIs) as nodes. There are limitations in the standard VAR models. The number of parameters in the VAR model increases quadratically with the number of ROIs and linearly with the order of the model and thus due to the large number of parameters, the model could pose serious estimation problems. Moreover, when applied to imaging data, the standard VAR model does not account for variability in the connectivity structure across all subjects. In this paper, we develop a novel generalization of the VAR model that overcomes these limitations. To deal with the high dimensionality of the parameter space, we propose a Bayesian hierarchical framework for the VAR model that will account for both temporal correlation within a subject and between subject variation. Our approach uses prior distributions that give rise to estimates that correspond to penalized least squares criterion with the elastic net penalty. We apply the proposed model to investigate differences in effective connectivity during a hand grasp experiment between healthy controls and patients with residual motor deficit following a stroke.

Voxelwise multivariate analysis of multimodality magnetic resonance imaging

Most brain magnetic resonance imaging (MRI) studies concentrate on a single MRI contrast or modality, frequently structural MRI. By performing an integrated analysis of several modalities, such as structural, perfusion-weighted, and diffusion-weighted MRI, new insights may be attained to better understand the underlying processes of brain diseases. We compare two voxelwise approaches: (1) fitting multiple univariate models, one for each outcome and then adjusting for multiple comparisons among the outcomes and (2) fitting a multivariate model. In both cases, adjustment for multiple comparisons is performed over all voxels jointly to account for the search over the brain. The multivariate model is able to account for the multiple comparisons over outcomes without assuming independence because the covariance structure between modalities is estimated. Simulations show that the multivariate approach is more powerful when the outcomes are correlated and, even when the outcomes are independent, the multivariate approach is just as powerful or more powerful when at least two outcomes are dependent on predictors in the model. However, multiple univariate regressions with Bonferroni correction remain a desirable alternative in some circumstances. To illustrate the power of each approach, we analyze a case control study of Alzheimer's disease, in which data from three MRI modalities are available.

Spatio-Spectral Mixed Effects Model for Functional Magnetic Resonance Imaging Data

The goal of this paper is to model cognitive control related activation among predefined regions of interest (ROIs) of the human brain while properly adjusting for the underlying spatio-temporal correlations. Standard approaches to fMRI analysis do not simultaneously take into account both the spatial and temporal correlations that are prevalent in fMRI data. This is primarily due to the computational complexity of estimating the spatio-temporal covariance matrix. More specifically, they do not take into account multi-scale spatial correlation (between-ROIs and within-ROI). To address these limitations, we propose a spatio-spectral mixed effects model. Working in the spectral domain simplifies the temporal covariance structure because the Fourier coefficients are approximately uncorrelated across frequencies. Additionally, by incorporating voxel-specific and ROI-specific random effects, the model is able to capture the multi-scale spatial covariance structure: distance-dependent local correlation (within an ROI), and distance-independent global correlation (between-ROIs). Building on existing theory on linear mixed effects models to conduct estimation and inference, we applied our model to fMRI data to study activation in pre-specified ROIs in the prefontal cortex and estimate the correlation structure in the network. Simulation studies demonstrate that ignoring the multi-scale correlation leads to higher false positives.

BSMac: a MATLAB toolbox implementing a Bayesian spatial model for brain activation and connectivity

We present a statistical and graphical visualization MATLAB toolbox for the analysis of functional magnetic resonance imaging (fMRI) data, called the Bayesian Spatial Model for activation and connectivity (BSMac). BSMac simultaneously performs whole-brain activation analyses at the voxel and region of interest (ROI) levels as well as task-related functional connectivity (FC) analyses using a flexible Bayesian modeling framework (Bowman et al., 2008). BSMac allows for inputting data in either Analyze or Nifti file formats. The user provides information pertaining to subgroup memberships, scanning sessions, and experimental tasks (stimuli), from which the design matrix is constructed. BSMac then performs parameter estimation based on Markov Chain Monte Carlo (MCMC) methods and generates plots for activation and FC, such as interactive 2D maps of voxel and region-level task-related changes in neural activity and animated 3D graphics of the FC results. The toolbox can be downloaded from http://www.sph.emory.edu/bios/CBIS/. We illustrate the BSMac toolbox through an application to an fMRI study of working memory in patients with schizophrenia.

Modeling the spatial and temporal dependence in FMRI data

Functional magnetic resonance imaging (fMRI) data sets are large and characterized by complex dependence structures driven by highly sophisticated neurophysiology and aspects of the experimental designs. Typical analyses investigating task-related changes in measured brain activity use a two-stage procedure in which the first stage involves subject-specific models and the second-stage specifies group (or population) level parameters. Customarily, the first-level accounts for temporal correlations between the serial scans acquired during one scanning session. Despite accounting for these correlations, fMRI studies often include multiple sessions and temporal dependencies may persist between the corresponding estimates of mean neural activity. Further, spatial correlations between brain activity measurements in different locations are often unaccounted for in statistical modeling and estimation. We propose a two-stage, spatio-temporal, autoregressive model that simultaneously accounts for spatial dependencies between voxels within the same anatomical region and for temporal dependencies between a subject's estimates from multiple sessions. We develop an algorithm that leverages the special structure of our covariance model, enabling relatively fast and efficient estimation. Using our proposed method, we analyze fMRI data from a study of inhibitory control in cocaine addicts.

Skin cancer incidence is highly associated with ultraviolet-B radiation history

Recently, the increased amount of ultraviolet-B (UV-B) exposure due to ozone depletion has been found to be associated with increased incidence of skin cancer across the world. The quantification of individual, regional, and historical UV exposure directly affects establishment of the association between skin cancer and UV exposure, but accurate assessment and measurement have been challenging for decades. As a sequence, cumulative studies using different metrics reported conflicting results on whether UV radiation, including sunburns, early childhood sun exposure, and chronic exposure, increases melanoma risk. This paper aims to establish the relationship between UV-B and melanoma incidence across the continental U.S. using an ecological approach that incorporate more accurate UV-B exposure measured by the National Aeronautical and Space Administration Nimbus-7 total ozone mapping spectrometer, and the United State Department of Agriculture ground-based network. Using statistical linear mixed models, we found strong positive associations between the skin cancer and the past UV exposure or the past cumulative 3-year UV exposure 3 or 4 years ago. UV has regional distributions and its regional effects on the skin cancer incidence are still significant after adjusting the effect of UV exposure. Research findings yield deepened understanding of spatiotemporal distribution of melanoma incidence rates and a greater appreciation for the complexity and heterogeneity of melanoma risk factors especially the UV-B exposure at different temporal and spatial scales.

Activated region fitting: a robust high-power method for fMRI analysis using parameterized regions of activation

An important issue in the analysis of fMRI is how to account for the spatial smoothness of activated regions. In this article a method is proposed to accomplish this by modeling activated regions with Gaussian shapes. Hypothesis tests on the location, spatial extent, and amplitude of these regions are performed instead of hypothesis tests of individual voxels. This increases power and eases interpretation. Simulation studies show robust hypothesis tests under misspecification of the shape model, and increased power over standard techniques especially at low signal-to-noise ratios. An application to real single-subject data also indicates that the method has increased power over standard methods.

Predicting the brain response to treatment using a Bayesian hierarchical model with application to a study of schizophrenia

In vivo functional neuroimaging, including functional magnetic resonance imaging (fMRI) and positron emission tomography (PET), is becoming increasingly important in defining the pathophysiology of psychiatric disorders such as schizophrenia, major depression, and Alzheimer's disease. Furthermore, recent studies have begun to investigate the possibility of using functional neuroimaging to guide treatment selection for individual patients. By studying the changes between a patient's pre- and post-treatment brain activity, investigators are gaining insights into the impact of treatment on behavior-related neural processing traits associated with particular psychiatric disorders. Furthermore, these studies may shed light on the neural basis of response and nonresponse to specific treatments. The practical limitation of such studies is that the post-treatment scans offer little guidance to treatment selection in clinical settings, since treatment decisions precede the availability of post-treatment brain scans. This shortcoming represents the impetus for developing statistical methodology that would provide clinicians with predictive information concerning the effect of treatment on brain activity and, ultimately, symptom-related behaviors. We present a prediction algorithm that uses a patient's pretreatment scans, coupled with relevant patient characteristics, to forecast the patient's brain activity following a specified treatment regimen. We derive our predictive method from a Bayesian hierarchical model constructed on the pre- and post-treatment scans of designated training data. We perform estimation using the expectation-maximization algorithm. We evaluate the accuracy of our proposed prediction method using K-fold cross-validation, quantifying the error using two new measures that we propose for neuroimaging data. The proposed method is applicable to both PET and fMRI studies. We illustrate its use with a PET study of working memory in patients with schizophrenia and an fMRI data example is also provided.

Statistical approaches to functional neuroimaging data

The field of statistics makes valuable contributions to functional neuroimaging research by establishing procedures for the design and conduct of neuroimaging experiments and providing tools for objectively quantifying and measuring the strength of scientific evidence provided by the data. Two common functional neuroimaging research objectives include detecting brain regions that reveal task-related alterations in measured brain activity (activations) and identifying highly correlated brain regions that exhibit similar patterns of activity over time (functional connectivity). This article highlights various statistical procedures for analyzing data from activation studies and functional connectivity studies, focusing on functional magnetic resonance imaging (fMRI) and positron emission tomography (PET) data. Also discussed are emerging statistical methods for prediction using fMRI and PET data, which stand to increase the translational significance of functional neuroimaging data to clinical practice.

A Bayesian hierarchical framework for spatial modeling of fMRI data

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.