Bayesian hierarchical multi-subject multiscale analysis of functional MRI data

Estimation of fMRI responses related to epileptic discharges using Bayesian hierarchical modeling

Simultaneous electroencephalography-functional MRI (EEG-fMRI) is a unique and noninvasive method for epilepsy presurgical evaluation. When selecting voxels by null-hypothesis tests, the conventional analysis may overestimate fMRI response amplitudes related to interictal epileptic discharges (IEDs), especially when IEDs are rare. We aimed to estimate fMRI response amplitudes represented by blood oxygen level dependent (BOLD) percentage changes related to IEDs using a hierarchical model. It involves the local and distributed hemodynamic response homogeneity to regularize estimations. Bayesian inference was applied to fit the model. Eighty-two epilepsy patients who underwent EEG-fMRI and subsequent surgery were included in this study. A conventional voxel-wise general linear model was compared to the hierarchical model on estimated fMRI response amplitudes and on the concordance between the highest response cluster and the surgical cavity. The voxel-wise model overestimated fMRI responses compared to the hierarchical model, evidenced by a practically and statistically significant difference between the estimated BOLD percentage changes. Only the hierarchical model differentiated brief and long-lasting IEDs with significantly different BOLD percentage changes. Overall, the hierarchical model outperformed the voxel-wise model on presurgical evaluation, measured by higher prediction performance. When compared with a previous study, the hierarchical model showed higher performance metric values, but the same or lower sensitivity. Our results demonstrated the capability of the hierarchical model of providing more physiologically reasonable and more accurate estimations of fMRI response amplitudes induced by IEDs. To enhance the sensitivity of EEG-fMRI for presurgical evaluation, it may be necessary to incorporate more appropriate spatial priors and bespoke decision strategies.

Joint Bayesian Estimation of Voxel Activation and Inter-regional Connectivity in fMRI Experiments

Brain activation and connectivity analyses in task-based functional magnetic resonance imaging (fMRI) experiments with multiple subjects are currently at the forefront of data-driven neuroscience. In such experiments, interest often lies in understanding activation of brain voxels due to external stimuli and strong association or connectivity between the measurements on a set of pre-specified groups of brain voxels, also known as regions of interest (ROI). This article proposes a joint Bayesian additive mixed modeling framework that simultaneously assesses brain activation and connectivity patterns from multiple subjects. In particular, fMRI measurements from each individual obtained in the form of a multi-dimensional array/tensor at each time are regressed on functions of the stimuli. We impose a low-rank parallel factorization decomposition on the tensor regression coefficients corresponding to the stimuli to achieve parsimony. Multiway stick-breaking shrinkage priors are employed to infer activation patterns and associated uncertainties in each voxel. Further, the model introduces region-specific random effects which are jointly modeled with a Bayesian Gaussian graphical prior to account for the connectivity among pairs of ROIs. Empirical investigations under various simulation studies demonstrate the effectiveness of the method as a tool to simultaneously assess brain activation and connectivity. The method is then applied to a multi-subject fMRI dataset from a balloon-analog risk-taking experiment, showing the effectiveness of the model in providing interpretable joint inference on voxel-level activations and inter-regional connectivity associated with how the brain processes risk. The proposed method is also validated through simulation studies and comparisons to other methods used within the neuroscience community.

Voxel Forecast for Precision Oncology: Predicting Spatially Variant and Multiscale Cancer Therapy Response on Longitudinal Quantitative Molecular Imaging

PURPOSE

Prediction of spatially variant response to cancer therapies can inform risk-adaptive management within precision oncology. We developed the "Voxel Forecast" multiscale regression framework for predicting spatially variant tumor response to chemoradiotherapy on fluorodeoxyglucose (FDG) positron emission tomography/computed tomography (PET/CT) imaging.

EXPERIMENTAL DESIGN

Twenty-five patients with locally advanced non-small cell lung cancer, enrolled on the FLARE-RT phase II trial (NCT02773238), underwent FDG PET/CT imaging prior to (PETpre) and during week 3 (PETmid) of concurrent chemoradiotherapy. Voxel Forecast was designed to predict tumor voxel standardized uptake value (SUV) on PETmid from baseline patient-level and voxel-level covariates using a custom generalized least squares (GLS) algorithm. Matérn covariance matrices were fit to patient- specific empirical variograms of distance-dependent intervoxel correlation. Regression coefficients from variogram-based weights and corresponding standard errors were estimated using the jackknife technique. The framework was validated using statistical simulations of known spatially variant tumor response. Mean absolute prediction errors (MAEs) of Voxel Forecast models were calculated under leave-one-patient-out cross-validation.

RESULTS

Patient-level forecasts resulted in tumor voxel SUV MAE on PETmid of 1.5 g/mL while combined patient- and voxel-level forecasts achieved lower MAE of 1.0 g/mL (P < 0.0001). PETpre voxel SUV was the most important predictor of PETmid voxel SUV. Patients with a greater percentage of under-responding tumor voxels were classified as PETmid nonresponders (P = 0.030) with worse overall survival prognosis (P < 0.001).

CONCLUSIONS

Voxel Forecast multiscale regression provides a statistical framework to predict voxel-wise response patterns during therapy. Voxel Forecast can be extended to predict spatially variant response on multimodal quantitative imaging and may eventually guide optimized spatial-temporal dose distributions for precision cancer therapy.

Bayesian inference for psychology, part IV: parameter estimation and Bayes factors

In the psychological literature, there are two seemingly different approaches to inference: that from estimation of posterior intervals and that from Bayes factors. We provide an overview of each method and show that a salient difference is the choice of models. The two approaches as commonly practiced can be unified with a certain model specification, now popular in the statistics literature, called spike-and-slab priors. A spike-and-slab prior is a mixture of a null model, the spike, with an effect model, the slab. The estimate of the effect size here is a function of the Bayes factor, showing that estimation and model comparison can be unified. The salient difference is that common Bayes factor approaches provide for privileged consideration of theoretically useful parameter values, such as the value corresponding to the null hypothesis, while estimation approaches do not. Both approaches, either privileging the null or not, are useful depending on the goals of the analyst.

Variational Bayesian inversion for hierarchical unsupervised generative embedding (HUGE)

A recently introduced hierarchical generative model unified the inference of effective connectivity in individual subjects and the unsupervised identification of subgroups defined by connectivity patterns. This hierarchical unsupervised generative embedding (HUGE) approach combined a hierarchical formulation of dynamic causal modelling (DCM) for fMRI with Gaussian mixture models and relied on Markov chain Monte Carlo (MCMC) sampling for inference. While well suited for the inversion of complex hierarchical models, MCMC-based sampling suffers from a computational burden that is prohibitive for many applications. To address this problem, this paper derives an efficient variational Bayesian (VB) inversion scheme for HUGE that simultaneously provides approximations to the posterior distribution over model parameters and to the log model evidence. The face validity of the VB scheme was tested using two synthetic fMRI datasets with known ground truth. Additionally, an empirical fMRI dataset of stroke patients and healthy controls was used to evaluate the practical utility of the method in application to real-world problems. Our analyses demonstrate good performance of our VB scheme, with a marked speed-up of model inversion by two orders of magnitude compared to MCMC, while maintaining a similar level of accuracy. Notably, additional acceleration would be possible if parallel computing techniques were applied. Generally, our VB implementation of HUGE is fast enough to support multi-start procedures for whole-group analyses, a useful strategy to ameliorate problems with local extrema. HUGE thus represents a potentially useful practical solution for an important problem in clinical neuromodeling and computational psychiatry, i.e., the unsupervised detection of subgroups in heterogeneous populations that are defined by effective connectivity.

Pitfalls in Organizational Neuroscience: A Critical Review and Suggestions for Future Research

The potential of neuroscience to be a viable framework for studying human behavior in organizations depends on scholars’ ability to evaluate, design, analyze, and accurately interpret neuroscientific research. Prior to the publishing of this special issue, relatively little guidance has been available in the management literature for scholars seeking to integrate neuroscience and organization science in a balanced, informative and methodologically rigorous manner. In response to this need, we address design logic and inferential issues involved in evaluating and conducting neuroscience research capable of informing organizational science. Specifically, neuroscience methods of functional magnetic resonance imaging, electroencephalography, lesion studies, transcranial magnetic stimulation, and transcranial direct current stimulation are reviewed, with attention to how these methods might be combined to achieve convergent evidence. We then discuss strengths and limitations of various designs, highlighting the issue of reverse inference as precarious yet necessary for organizational neuroscience. We offer solutions for addressing limitations related to reverse inference, and propose features that allow stronger inferences to be made. The article concludes with a review of selected empirical work in organizational neuroscience in light of these critical design features.

Fast Translation Invariant Multiscale Image Denoising

Translation invariant (TI) cycle spinning is an effective method for removing artifacts from images. However, for a method using O(n) time, the exact TI cycle spinning by averaging all possible circulant shifts requires O(n(2)) time where n is the number of pixels, and therefore is not feasible in practice. Existing literature has investigated efficient algorithms to calculate TI version of some denoising approaches such as Haar wavelet. Multiscale methods, especially those based on likelihood decomposition, such as penalized likelihood estimator and Bayesian methods, have become popular in image processing because of their effectiveness in denoising images. As far as we know, there is no systematic investigation of the TI calculation corresponding to general multiscale approaches. In this paper, we propose a fast TI (FTI) algorithm and a more general k-TI (k-TI) algorithm allowing TI for the last k scales of the image, which are applicable to general d-dimensional images (d = 2, 3, …) with either Gaussian or Poisson noise. The proposed FTI leads to the exact TI estimation but only requires O(n log2 n) time. The proposed k-TI can achieve almost the same performance as the exact TI estimation, but requires even less time. We achieve this by exploiting the regularity present in the multiscale structure, which is justified theoretically. The proposed FTI and k-TI are generic in that they are applicable on any smoothing techniques based on the multiscale structure. We demonstrate the FTI and k-TI algorithms on some recently proposed state-of-the-art methods for both Poisson and Gaussian noised images. Both simulations and real data application confirm the appealing performance of the proposed algorithms. MATLAB toolboxes are online accessible to reproduce the results and be implemented for general multiscale denoising approaches provided by the users.

Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping

A graph based framework for fMRI brain activation mapping is presented. The approach exploits the spectral graph wavelet transform (SGWT) for the purpose of defining an advanced multi-resolutional spatial transformation for fMRI data. The framework extends wavelet based SPM (WSPM), which is an alternative to the conventional approach of statistical parametric mapping (SPM), and is developed specifically for group-level analysis. We present a novel procedure for constructing brain graphs, with subgraphs that separately encode the structural connectivity of the cerebral and cerebellar gray matter (GM), and address the inter-subject GM variability by the use of template GM representations. Graph wavelets tailored to the convoluted boundaries of GM are then constructed as a means to implement a GM-based spatial transformation on fMRI data. The proposed approach is evaluated using real as well as semi-synthetic multi-subject data. Compared to SPM and WSPM using classical wavelets, the proposed approach shows superior type-I error control. The results on real data suggest a higher detection sensitivity as well as the capability to capture subtle, connected patterns of brain activity.

Bayesian Models for fMRI Data Analysis

Functional magnetic resonance imaging (fMRI), a noninvasive neuroimaging method that provides an indirect measure of neuronal activity by detecting blood flow changes, has experienced an explosive growth in the past years. Statistical methods play a crucial role in understanding and analyzing fMRI data. Bayesian approaches, in particular, have shown great promise in applications. A remarkable feature of fully Bayesian approaches is that they allow a flexible modeling of spatial and temporal correlations in the data. This paper provides a review of the most relevant models developed in recent years. We divide methods according to the objective of the analysis. We start from spatio-temporal models for fMRI data that detect task-related activation patterns. We then address the very important problem of estimating brain connectivity. We also touch upon methods that focus on making predictions of an individual's brain activity or a clinical or behavioral response. We conclude with a discussion of recent integrative models that aim at combining fMRI data with other imaging modalities, such as EEG/MEG and DTI data, measured on the same subjects. We also briefly discuss the emerging field of imaging genetics.

Toward a multisubject analysis of neural connectivity

Directed acyclic graphs (DAGs) and associated probability models are widely used to model neural connectivity and communication channels. In many experiments, data are collected from multiple subjects whose connectivities may differ but are likely to share many features. In such circumstances, it is natural to leverage similarity among subjects to improve statistical efficiency. The first exact algorithm for estimation of multiple related DAGs was recently proposed by Oates, Smith, Mukherjee, and Cussens ( 2014 ). In this letter we present examples and discuss implications of the methodology as applied to the analysis of fMRI data from a multisubject experiment. Elicitation of tuning parameters requires care, and we illustrate how this may proceed retrospectively based on technical replicate data. In addition to joint learning of subject-specific connectivity, we allow for heterogeneous collections of subjects and simultaneously estimate relationships between the subjects themselves. This letter aims to highlight the potential for exact estimation in the multisubject setting.

A hierarchical model for simultaneous detection and estimation in multi-subject fMRI studies

In this paper we introduce a new hierarchical model for the simultaneous detection of brain activation and estimation of the shape of the hemodynamic response in multi-subject fMRI studies. The proposed approach circumvents a major stumbling block in standard multi-subject fMRI data analysis, in that it both allows the shape of the hemodynamic response function to vary across region and subjects, while still providing a straightforward way to estimate population-level activation. An efficient estimation algorithm is presented, as is an inferential framework that allows for not only tests of activation, but also tests for deviations from some canonical shape. The model is validated through simulations and application to a multi-subject fMRI study of thermal pain.

A spatio-temporal nonparametric Bayesian variable selection model of fMRI data for clustering correlated time courses

In this paper we present a novel wavelet-based Bayesian nonparametric regression model for the analysis of functional magnetic resonance imaging (fMRI) data. Our goal is to provide a joint analytical framework that allows to detect regions of the brain which exhibit neuronal activity in response to a stimulus and, simultaneously, infer the association, or clustering, of spatially remote voxels that exhibit fMRI time series with similar characteristics. We start by modeling the data with a hemodynamic response function (HRF) with a voxel-dependent shape parameter. We detect regions of the brain activated in response to a given stimulus by using mixture priors with a spike at zero on the coefficients of the regression model. We account for the complex spatial correlation structure of the brain by using a Markov random field (MRF) prior on the parameters guiding the selection of the activated voxels, therefore capturing correlation among nearby voxels. In order to infer association of the voxel time courses, we assume correlated errors, in particular long memory, and exploit the whitening properties of discrete wavelet transforms. Furthermore, we achieve clustering of the voxels by imposing a Dirichlet process (DP) prior on the parameters of the long memory process. For inference, we use Markov Chain Monte Carlo (MCMC) sampling techniques that combine Metropolis-Hastings schemes employed in Bayesian variable selection with sampling algorithms for nonparametric DP models. We explore the performance of the proposed model on simulated data, with both block- and event-related design, and on real fMRI data.