Physiological Gaussian Process Priors for the Hemodynamics in fMRI Analysis

Background: Inference from fMRI data faces the challenge that the hemodynamic system that relates neural activity to the observed BOLD fMRI signal is unknown. New Method: We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modeled nonparametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD response, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in a flexible way, and simultaneously gives us the nonparametric flexibility of the GP. Results: Results on simulated data show that the proposed model is able to discriminate between active and non-active voxels also when the GP prior deviates from the true hemodynamics. Our model finds time varying dynamics when applied to real fMRI data. Comparison with Existing Method(s): The proposed model is better at detecting activity in simulated data than standard models, without inflating the false positive rate. When applied to real fMRI data, our GP model in several cases finds brain activity where previously proposed LTI models does not. Conclusions: We have proposed a new non-linear model for the hemodynamics in task fMRI, that is able to detect active voxels, and gives the opportunity to ask new kinds of questions related to hemodynamics.Comment: 18 pages, 14 figure

Fast joint detection-estimation of evoked brain activity in event-related fMRI using a variational approach

In standard clinical within-subject analyses of event-related fMRI data, two steps are usually performed separately: detection of brain activity and estimation of the hemodynamic response. Because these two steps are inherently linked, we adopt the so-called region-based Joint Detection-Estimation (JDE) framework that addresses this joint issue using a multivariate inference for detection and estimation. JDE is built by making use of a regional bilinear generative model of the BOLD response and constraining the parameter estimation by physiological priors using temporal and spatial information in a Markovian modeling. In contrast to previous works that use Markov Chain Monte Carlo (MCMC) techniques to approximate the resulting intractable posterior distribution, we recast the JDE into a missing data framework and derive a Variational Expectation-Maximization (VEM) algorithm for its inference. A variational approximation is used to approximate the Markovian model in the unsupervised spatially adaptive JDE inference, which allows fine automatic tuning of spatial regularisation parameters. It follows a new algorithm that exhibits interesting properties compared to the previously used MCMC-based approach. Experiments on artificial and real data show that VEM-JDE is robust to model mis-specification and provides computational gain while maintaining good performance in terms of activation detection and hemodynamic shape recovery

Within-Subject Joint Independent Component Analysis of Simultaneous fMRI/ERP in an Auditory Oddball Paradigm

The integration of event-related potential (ERP) and functional magnetic resonance imaging (fMRI) can contribute to characterizing neural networks with high temporal and spatial resolution. This research aimed to determine the sensitivity and limitations of applying joint independent component analysis (jICA) within-subjects, for ERP and fMRI data collected simultaneously in a parametric auditory frequency oddball paradigm. In a group of 20 subjects, an increase in ERP peak amplitude ranging 1–8 μV in the time window of the P300 (350–700 ms), and a correlated increase in fMRI signal in a network of regions including the right superior temporal and supramarginal gyri, was observed with the increase in deviant frequency difference. JICA of the same ERP and fMRI group data revealed activity in a similar network, albeit with stronger amplitude and larger extent. In addition, activity in the left pre- and post-central gyri, likely associated with right hand somato-motor response, was observed only with the jICA approach. Within-subject, the jICA approach revealed significantly stronger and more extensive activity in the brain regions associated with the auditory P300 than the P300 linear regression analysis. The results suggest that with the incorporation of spatial and temporal information from both imaging modalities, jICA may be a more sensitive method for extracting common sources of activity between ERP and fMRI

Stability

Reproducibility is imperative for any scientific discovery. More often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical results relative to "reasonable" perturbations to data and to the model used. Jacknife, bootstrap, and cross-validation are based on perturbations to data, while robust statistics methods deal with perturbations to models. In this article, a case is made for the importance of stability in statistics. Firstly, we motivate the necessity of stability for interpretable and reliable encoding models from brain fMRI signals. Secondly, we find strong evidence in the literature to demonstrate the central role of stability in statistical inference, such as sensitivity analysis and effect detection. Thirdly, a smoothing parameter selector based on estimation stability (ES), ES-CV, is proposed for Lasso, in order to bring stability to bear on cross-validation (CV). ES-CV is then utilized in the encoding models to reduce the number of predictors by 60% with almost no loss (1.3%) of prediction performance across over 2,000 voxels. Last, a novel "stability" argument is seen to drive new results that shed light on the intriguing interactions between sample to sample variability and heavier tail error distribution (e.g., double-exponential) in high-dimensional regression models with $p$ predictors and $n$ independent samples. In particular, when $p/n\rightarrow\kappa\in(0.3,1)$ and the error distribution is double-exponential, the Ordinary Least Squares (OLS) is a better estimator than the Least Absolute Deviation (LAD) estimator.Comment: Published in at http://dx.doi.org/10.3150/13-BEJSP14 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Experimental Design Modulates Variance in BOLD Activation: The Variance Design General Linear Model

Typical fMRI studies have focused on either the mean trend in the blood-oxygen-level-dependent (BOLD) time course or functional connectivity (FC). However, other statistics of the neuroimaging data may contain important information. Despite studies showing links between the variance in the BOLD time series (BV) and age and cognitive performance, a formal framework for testing these effects has not yet been developed. We introduce the Variance Design General Linear Model (VDGLM), a novel framework that facilitates the detection of variance effects. We designed the framework for general use in any fMRI study by modeling both mean and variance in BOLD activation as a function of experimental design. The flexibility of this approach allows the VDGLM to i) simultaneously make inferences about a mean or variance effect while controlling for the other and ii) test for variance effects that could be associated with multiple conditions and/or noise regressors. We demonstrate the use of the VDGLM in a working memory application and show that engagement in a working memory task is associated with whole-brain decreases in BOLD variance.Comment: 18 pages, 7 figure

Flexible multivariate hemodynamics fMRI data analyses and simulations with PyHRF

International audienceAs part of fMRI data analysis, the pyhrf package provides a set of tools for addressing the two 3 main issues involved in intra-subject fMRI data analysis: (i) the localization of cerebral regions 4 that elicit evoked activity and (ii) the estimation of the activation dynamics also referenced to 5 as the recovery of the Hemodynamic Response Function (HRF). To tackle these two problems, 6 pyhrf implements the Joint Detection-Estimation framework (JDE) which recovers parcel-level 7 HRFs and embeds an adaptive spatio-temporal regularization scheme of activation maps. With 8 respect to the sole detection issue (i), the classical voxelwise GLM procedure is also available 9 through nipy, whereas Finite Impulse Response (FIR) and temporally regularized FIR models 10 are implemented to deal with HRF estimation concerns (ii). Several parcellation tools are also 11 integrated such as spatial and functional clustering. Parcellations may be used for spatial 12 averaging prior to FIR/RFIR analysis or to specify the spatial support of the HRF estimates 13 in the JDE approach. These analysis procedures can be applied either to volumic data sets or 14 to data projected onto the cortical surface. For validation purpose, this package is shipped with 15 artificial and real fMRI data sets, which are used in this paper to compare the outcome of the 16 different available approaches. The artificial fMRI data generator is also described to illustrate 17 how to simulate different activation configurations, HRF shapes or nuisance components. To 18 cope with the high computational needs for inference, pyhrf handles distributing computing 19 by exploiting cluster units as well as multiple cores computers. Finally, a dedicated viewer is 20 presented, which handles n-dimensional images and provides suitable features to explore whole 21 brain hemodynamics (time series, maps, ROI mask overlay)