A Stochastic Geometry Model for Functional Magnetic Resonance Images

Differential network knockoff filter with application to brain connectivity analysis

The brain functional connectivity can typically be represented as a brain functional network, where nodes represent regions of interest (ROIs) and edges symbolize their connections. Studying group differences in brain functional connectivity can help identify brain regions and recover the brain functional network linked to neurodegenerative diseases. This process, known as differential network analysis focuses on the differences between estimated precision matrices for two groups. Current methods struggle with individual heterogeneity in measuring the brain connectivity, false discovery rate (FDR) control, and accounting for confounding factors, resulting in biased estimates and diminished power. To address these issues, we present a two-stage FDR-controlled feature selection method for differential network analysis using functional magnetic resonance imaging (fMRI) data. First, we create individual brain connectivity measures using a high-dimensional precision matrix estimation technique. Next, we devise a penalized logistic regression model that employs individual brain connectivity data and integrates a new knockoff filter for FDR control when detecting significant differential edges. Through extensive simulations, we showcase the superiority of our approach compared to other methods. Additionally, we apply our technique to fMRI data to identify differential edges between Alzheimer's disease and control groups. Our results are consistent with prior experimental studies, emphasizing the practical applicability of our method.

Characterizing cross-subject spatial interaction patterns in functional magnetic resonance imaging studies: A two-stage point-process model

We develop a two-stage spatial point process model that introduces new characterizations of activation patterns in multisubject functional Magnetic Resonance Imaging (fMRI) studies. Conventionally multisubject fMRI methods rely on combining information across subjects one voxel at a time in order to identify locations of peak activation in the brain. The two-stage model that we develop here addresses shortcomings of standard methods by explicitly modeling the spatial structure of functional signals and recognizing that corresponding cross-subject functional signals can be spatially misaligned. In our first stage analysis, we introduce a marked spatial point process model that captures the spatial features of the functional response and identifies a configuration of activation units for each subject. The locations of these activation units are used as input for the second stage model. The point process model of the second stage analysis is developed to characterize multisubject activation patterns by estimating the strength of cross-subject interactions at different spatial ranges. The model uses spatial neighborhoods to account for the cross-subject spatial misalignment in corresponding functional units. We applied our methods to an fMRI study of 21 individuals who performed an attention test. We identified four brain regions that are involved in the test and found that our model results agree well with our understanding of how these regions engage with the tasks performed during the attention test. Our results highlighted that cross-subject interactions are stronger in brain areas that have a more specific function in performing the experimental tasks than in other areas.

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.

Combining spatial priors and anatomical information for fMRI detection

In this paper, we analyze Markov Random Field (MRF) as a spatial regularizer in fMRI detection. The low signal-to-noise ratio (SNR) in fMRI images presents a serious challenge for detection algorithms, making regularization necessary to achieve good detection accuracy. Gaussian smoothing, traditionally employed to boost SNR, often produces over-smoothed activation maps. Recently, the use of MRF priors has been suggested as an alternative regularization approach. However, solving for an optimal configuration of the MRF is NP-hard in general. In this work, we investigate fast inference algorithms based on the Mean Field approximation in application to MRF priors for fMRI detection. Furthermore, we propose a novel way to incorporate anatomical information into the MRF-based detection framework and into the traditional smoothing methods. Intuitively speaking, the anatomical evidence increases the likelihood of activation in the gray matter and improves spatial coherency of the resulting activation maps within each tissue type. Validation using the receiver operating characteristic (ROC) analysis and the confusion matrix analysis on simulated data illustrates substantial improvement in detection accuracy using the anatomically guided MRF spatial regularizer. We further demonstrate the potential benefits of the proposed method in real fMRI signals of reduced length. The anatomically guided MRF regularizer enables significant reduction of the scan length while maintaining the quality of the resulting activation maps.

Modeling inter-subject variability in FMRI activation location: a Bayesian hierarchical spatial model

The aim of this article is to develop a spatial model for multi-subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi-subject data, some work on spatial modeling of single-subject data, and some recent work on spatial modeling of multi-subject data. However, there has been no work on spatial models that explicitly account for inter-subject variability in activation locations. In this article, we use the idea of activation centers and model the inter-subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical framework which allows us to draw inferences at all levels: the population level, the individual level, and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question that is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass-univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data.

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.

Bayesian kernel methods for analysis of functional neuroimages

We propose an approach to analyzing functional neuroimages in which 1) regions of neuronal activation are described by a superposition of spatial kernel functions, the parameters of which are estimated from the data and 2) the presence of activation is detected by means of a generalized likelihood ratio test (GLRT). Kernel methods have become a staple of modern machine learning. Herein, we show that these techniques show promise for neuroimage analysis. In an on-off design, we model the spatial activation pattern as a sum of an unknown number of kernel functions of unknown location, amplitude, and/or size. We employ two Bayesian methods of estimating the kernel functions. The first is a maximum a posteriori (MAP) estimation method based on a Reversible-Jump Markov-chain Monte-Carlo (RJMCMC) algorithm that searches for both the appropriate model complexity and parameter values. The second is a relevance vector machine (RVM), a kernel machine that is known to be effective in controlling model complexity (and thus discouraging overfitting). In each method, after estimating the activation pattern, we test for local activation using a GLRT. We evaluate the results using receiver operating characteristic (ROC) curves for simulated neuroimaging data and example results for real fMRI data. We find that, while RVM and RJMCMC both produce good results, RVM requires far less computation time, and thus appears to be the more promising of the two approaches.

From Spatial Regularization to Anatomical Priors in fMRI Analysis

In this paper, we study Markov Random Fields as spatial smoothing priors in fMRI detection. Relatively high noise in fMRI images presents a serious challenge for the detection algorithms, creating a need for spatial regularization of the signal. Gaussian smoothing, traditionally employed to boost the signal-to-noise ratio, often removes small activation regions. Recently, the use of Markov priors has been suggested as an alternative regularization approach. In this work, we investigate fast approximate inference algorithms for using MRFs in fMRI detection, propose a novel way to incorporate anatomical information into the detection framework, validate the methods through ROC analysis on simulated data and demonstrate their application in a real fMRI study.