Bayesian deconvolution fMRI data using bilinear dynamical systems

Whole-brain multivariate hemodynamic deconvolution for functional MRI with stability selection

Conventionally, analysis of functional MRI (fMRI) data relies on available information about the experimental paradigm to establish hypothesized models of brain activity. However, this information can be inaccurate, incomplete or unavailable in multiple scenarios such as resting-state, naturalistic paradigms or clinical conditions. In these cases, blind estimates of neuronal-related activity can be obtained with paradigm-free analysis methods such as hemodynamic deconvolution. Yet, current formulations of the hemodynamic deconvolution problem have three important limitations: (1) their efficacy strongly depends on the appropriate selection of regularization parameters, (2) being univariate, they do not take advantage of the information present across the brain, and (3) they do not provide any measure of statistical certainty associated with each detected event. Here we propose a novel approach that addresses all these limitations. Specifically, we introduce multivariate sparse paradigm free mapping (Mv-SPFM), a novel hemodynamic deconvolution algorithm that operates at the whole brain level and adds spatial information via a mixed-norm regularization term over all voxels. Additionally, Mv-SPFM employs a stability selection procedure that removes the need to select regularization parameters and also lets us obtain an estimate of the true probability of having a neuronal-related BOLD event at each voxel and time-point based on the area under the curve (AUC) of the stability paths. Besides, we present a formulation tailored for multi-echo fMRI acquisitions (MvME-SPFM), which allows us to better isolate fluctuations of BOLD origin on the basis of their linear dependence with the echo time (TE) and to assign physiologically interpretable units (i.e., changes in the apparent transverse relaxation ΔR2∗) to the resulting deconvolved events. Remarkably, we demonstrate that Mv-SPFM achieves comparable performance even when using a single-echo formulation. We demonstrate that this algorithm outperforms existing state-of-the-art deconvolution approaches, and shows higher spatial and temporal agreement with the activation maps and BOLD signals obtained with a standard model-based linear regression approach, even at the level of individual neuronal events. Furthermore, we show that by employing stability selection, the performance of the algorithm depends less on the selection of temporal and spatial regularization parameters λ and ρ. Consequently, the proposed algorithm provides more reliable estimates of neuronal-related activity, here in terms of ΔR2∗, for the study of the dynamics of brain activity when no information about the timings of the BOLD events is available. This algorithm will be made publicly available as part of the splora Python package.

Global excitability and network structure in the human brain

We utilize a model of Wilson-Cowan oscillators to investigate structure-function relationships in the human brain by means of simulations of the spontaneous dynamics of brain networks generated through human connectome data. This allows us to establish relationships between the global excitability of such networks and global structural network quantities for connectomes of two different sizes for a number of individual subjects. We compare the qualitative behavior of such correlations between biological networks and shuffled networks, the latter generated by shuffling the pairwise connectivities of the former while preserving their distribution. Our results point towards a remarkable propensity of the brain to achieve a trade-off between low network wiring cost and strong functionality, and highlight the unique capacity of brain network topologies to exhibit a strong transition from an inactive state to a globally excited one.

Hemodynamic matrix factorization for functional magnetic resonance imaging

The General Linear Model (GLM) used in task-fMRI relates activated brain areas to extrinsic task conditions. The translation of resulting neural activation into a hemodynamic response is commonly approximated with a linear convolution model using a hemodynamic response function (HRF). There are two major limitations in GLM analysis. Firstly, the GLM assumes that neural activation is either on or off and matches the exact stimulus duration in the corresponding task timings. Secondly, brain networks observed in resting-state fMRI experiments present also during task experiments, but the GLM approach models these task-unrelated brain activity as noise. A novel kernel matrix factorization approach, called hemodynamic matrix factorization (HMF), is therefore proposed that addresses both limitations by assuming that task-related and task-unrelated brain activity can be modeled with the same convolution model as in GLM analysis. By contrast to the GLM, the proposed HMF is a blind source separation (BSS) technique, which decomposes fMRI data into modes. Each mode comprises of a neural activation time course and a spatial mapping. Two versions of HMF are proposed in which the neural activation time course of each mode is convolved with either the canonical HRF or predetermined subject-specific HRFs. Firstly, HMF with the canonical HRF is applied to two open-source cohorts. These cohorts comprise of several task experiments including motor, incidental memory, spatial coherence discrimination, verbal discrimination task and a very short localization task, engaging multiple parts of the eloquent cortex. HMF modes were obtained whose neural activation time course followed original task timings and whose corresponding spatial map matched cortical areas known to be involved in the respective task processing. Secondly, the alignment of these neural activation time courses to task timings were further improved by replacing the canonical HRF with subject-specific HRFs during HMF mode computation. In addition to task-related modes, HMF also produced seemingly task-unrelated modes whose spatial maps matched known resting-state networks. The validity of a fMRI task experiment relies on the assumption that the exposure to a stimulus for a given time causes an imminent increase in neural activation of equal duration. The proposed HMF is an attempt to falsify this assumption and allows to identify subject task participation that does not comply with the experiment instructions.

Augmenting interictal mapping with neurovascular coupling biomarkers by structured factorization of epileptic EEG and fMRI data

EEG-correlated fMRI analysis is widely used to detect regional BOLD fluctuations that are synchronized to interictal epileptic discharges, which can provide evidence for localizing the ictal onset zone. However, the typical, asymmetrical and mass-univariate approach cannot capture the inherent, higher order structure in the EEG data, nor multivariate relations in the fMRI data, and it is nontrivial to accurately handle varying neurovascular coupling over patients and brain regions. We aim to overcome these drawbacks in a data-driven manner by means of a novel structured matrix-tensor factorization: the single-subject EEG data (represented as a third-order spectrogram tensor) and fMRI data (represented as a spatiotemporal BOLD signal matrix) are jointly decomposed into a superposition of several sources, characterized by space-time-frequency profiles. In the shared temporal mode, Toeplitz-structured factors account for a spatially specific, neurovascular 'bridge' between the EEG and fMRI temporal fluctuations, capturing the hemodynamic response's variability over brain regions. By analyzing interictal data from twelve patients, we show that the extracted source signatures provide a sensitive localization of the ictal onset zone (10/12). Moreover, complementary parts of the IOZ can be uncovered by inspecting those regions with the most deviant neurovascular coupling, as quantified by two entropy-like metrics of the hemodynamic response function waveforms (9/12). Hence, this multivariate, multimodal factorization provides two useful sets of EEG-fMRI biomarkers, which can assist the presurgical evaluation of epilepsy. We make all code required to perform the computations available at https://github.com/svaneynd/structured-cmtf.

Psychophysiological Interactions in a Visual Checkerboard Task: Reproducibility, Reliability, and the Effects of Deconvolution

Psychophysiological interaction (PPI) is a regression based method to study task modulated brain connectivity. Despite its popularity in functional MRI (fMRI) studies, its reliability and reproducibility have not been evaluated. We investigated reproducibility and reliability of PPI effects during a simple visual task, and examined the effect of deconvolution on the PPI results. A large open-access dataset was analyzed (n = 138), where a visual task was scanned twice with repetition times (TRs) of 645 and 1,400 ms, respectively. We first replicated our previous results by using the left and right middle occipital gyrus as seeds. Then regions of interest (ROI)-wise analysis was performed among 20 visual-related thalamic and cortical regions, and negative PPI effects were found between many ROIs with the posterior fusiform gyrus as a hub region. Both the seed-based and ROI-wise results were similar between the two runs and between the two PPI methods with and without deconvolution. The non-deconvolution method and the short TR run in general had larger effect sizes and greater extents. However, the deconvolution method performed worse in the 645 ms TR run than the 1,400 ms TR run in the voxel-wise analysis. Given the general similar results between the two methods and the uncertainty of deconvolution, we suggest that deconvolution may be not necessary for PPI analysis on block-designed data. Lastly, intraclass correlations (ICC) between the two runs were much lower for the PPI effects than the activation main effects, which raise cautions on performing inter-subject correlations and group comparisons on PPI effects.

Nonparametric hemodynamic deconvolution of FMRI using homomorphic filtering

Functional magnetic resonance imaging (fMRI) is an indirect measure of neural activity which is modeled as a convolution of the latent neuronal response and the hemodynamic response function (HRF). Since the sources of HRF variability can be nonneural in nature, the measured fMRI signal does not faithfully represent underlying neural activity. Therefore, it is advantageous to deconvolve the HRF from the fMRI signal. However, since both latent neural activity and the voxel-specific HRF is unknown, the deconvolution must be blind. Existing blind deconvolution approaches employ highly parameterized models, and it is unclear whether these models have an over fitting problem. In order to address these issues, we 1) present a nonparametric deconvolution method based on homomorphic filtering to obtain the latent neuronal response from the fMRI signal and, 2) compare our approach to the best performing existing parametric model based on the estimation of the biophysical hemodynamic model using the Cubature Kalman Filter/Smoother. We hypothesized that if the results from nonparametric deconvolution closely resembled that obtained from parametric deconvolution, then the problem of over fitting during estimation in highly parameterized deconvolution models of fMRI could possibly be over stated. Both simulations and experimental results demonstrate support for our hypothesis since the estimated latent neural response from both parametric and nonparametric methods were highly correlated in the visual cortex. Further, simulations showed that both methods were effective in recovering the simulated ground truth of the latent neural response.

Variational Bayesian causal connectivity analysis for fMRI

The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience. We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data. The method uses a vector autoregressive model for the latent variables describing neuronal activity in combination with a linear observation model based on a convolution with a hemodynamic response function. Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm. The computational efficiency of the method enables us to apply it to large scale problems with high sampling rates and several hundred regions of interest. We use a comprehensive empirical evaluation with synthetic and real fMRI data to evaluate the performance of our method under various conditions.

Identifying effective connectivity parameters in simulated fMRI: a direct comparison of switching linear dynamic system, stochastic dynamic causal, and multivariate autoregressive models

The number and variety of connectivity estimation methods is likely to continue to grow over the coming decade. Comparisons between methods are necessary to prune this growth to only the most accurate and robust methods. However, the nature of connectivity is elusive with different methods potentially attempting to identify different aspects of connectivity. Commonalities of connectivity definitions across methods upon which base direct comparisons can be difficult to derive. Here, we explicitly define "effective connectivity" using a common set of observation and state equations that are appropriate for three connectivity methods: dynamic causal modeling (DCM), multivariate autoregressive modeling (MAR), and switching linear dynamic systems for fMRI (sLDSf). In addition while deriving this set, we show how many other popular functional and effective connectivity methods are actually simplifications of these equations. We discuss implications of these connections for the practice of using one method to simulate data for another method. After mathematically connecting the three effective connectivity methods, simulated fMRI data with varying numbers of regions and task conditions is generated from the common equation. This simulated data explicitly contains the type of the connectivity that the three models were intended to identify. Each method is applied to the simulated data sets and the accuracy of parameter identification is analyzed. All methods perform above chance levels at identifying correct connectivity parameters. The sLDSf method was superior in parameter estimation accuracy to both DCM and MAR for all types of comparisons.

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

In standard within-subject analyses of event-related functional magnetic resonance imaging (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 model. In contrast to previous works that use Markov Chain Monte Carlo (MCMC) techniques to sample 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 automatic fine-tuning of spatial regularization parameters. It provides a new algorithm that exhibits interesting properties in terms of estimation error and computational cost compared to the previously used MCMC-based approach. Experiments on artificial and real data show that VEM-JDE is robust to model misspecification and provides computational gain while maintaining good performance in terms of activation detection and hemodynamic shape recovery.

State-space analysis of working memory in schizophrenia: an fBIRN study

The neural correlates of working memory (WM) in schizophrenia (SZ) have been extensively studied using the multisite fMRI data acquired by the Functional Biomedical Informatics Research Network (fBIRN) consortium. Although univariate and multivariate analysis methods have been variously employed to localize brain responses under differing task conditions, important hypotheses regarding the representation of mental processes in the spatio-temporal patterns of neural recruitment and the differential organization of these mental processes in patients versus controls have not been addressed in this context. This paper uses a multivariate state-space model (SSM) to analyze the differential representation and organization of mental processes of controls and patients performing the Sternberg Item Recognition Paradigm (SIRP) WM task. The SSM is able to not only predict the mental state of the subject from the data, but also yield estimates of the spatial distribution and temporal ordering of neural activity, along with estimates of the hemodynamic response. The dynamical Bayesian modeling approach used in this study was able to find significant differences between the predictability and organization of the working memory processes of SZ patients versus healthy subjects. Prediction of some stimulus types from imaging data in the SZ group was significantly lower than controls, reflecting a greater level of disorganization/heterogeneity of their mental processes. Moreover, the changes in accuracy of predicting the mental state of the subject with respect to parametric modulations, such as memory load and task duration, may have important implications on the neurocognitive models for WM processes in both SZ and healthy adults. Additionally, the SSM was used to compare the spatio-temporal patterns of mental activity across subjects, in a holistic fashion and to derive a low-dimensional representation space for the SIRP task, in which subjects were found to cluster according to their diagnosis.

A functional MRI study of motor dysfunction in Friedreich's ataxia

Friedreich's ataxia (FRDA) is the most common form of hereditary ataxia. In addition to proximal spinal cord and brain stem atrophy, mild to moderate atrophy of the cerebellum has been reported in advanced FRDA. The aim of this study was to examine dysfunction in motor-related areas involved in the execution of finger tapping tasks in individuals with FRDA, and to investigate functional re-organization of cortico-cerebellar, cortico-striatal and parieto-frontal loops as a result of the cerebellar pathology. Thirteen right-handed individuals with FRDA and fourteen right-handed controls participated. Functional MRI images were acquired during four different finger tapping tasks consisting of visually cued regular and irregular single finger tapping tasks, a self-paced regular finger tapping task, and a visually cued multi-finger tapping task. Both groups showed significant activation of the motor-related network including the pre-central cortex and supplementary motor area bilaterally; the left primary motor cortex, somatosensory cortex and putamen; and the right cerebellum. During the visually cued regular finger tapping task, the right hemisphere of the cerebellar cortex, bilateral supplementary motor areas and right inferior parietal cortex showed higher activation in the healthy control group, while in individuals with FRDA the left premotor cortex, left somatosensory cortex and left inferior parietal cortex were more active. In addition, during the visually cued irregular finger tapping task, the right middle temporal gyrus in the control group and the right superior parietal lobule and left superior and middle temporal gyri in the individuals with FRDA showed higher activation. During visually cued multi-finger tapping task, the control group showed higher activation in the bilateral middle frontal gyri, bilateral somatosensory cortices, bilateral inferior parietal lobules, left premotor cortex, left supplementary area, right superior frontal gyrus and right cerebellum, while individuals with FRDA showed increased activity in the left inferior parietal lobule, left primary motor cortex, left middle occipital gyrus, right somatosensory cortex and the left cerebellum. Only the right crus I/II of the cerebellum showed higher activation in individuals with FRDA during the self-paced regular finger tapping task, whereas wide-spread regions including the left superior frontal gyrus, left central opercular cortex, left somatosensory cortex, left putamen, right cerebellum, bilateral primary motor cortices, bilateral inferior parietal lobules and the left insula were more active in the control group. Although the pattern of the BOLD signal from the putamen was different during the self-paced regular finger tapping task to the other tasks in controls, in individuals with FRDA there was no distinction of the signal between the tasks suggesting that primary cerebellar pathology may cause secondary basal ganglia dysregulation. While individuals with FRDA tapped at a slightly lower rate (0.59Hz) compared with controls (0.74Hz) they showed significantly decreased activity of the SMA and the inferior parietal lobule, which may suggest disruption to the fronto-parietal connections. These findings suggest that the motor impairments in individuals with FRDA result from dysfunction extending beyond the spinal cord and cerebellum to include sub-cortical and cortical brain regions.

Effective Connectivity Modeling for fMRI: Six Issues and Possible Solutions Using Linear Dynamic Systems

Analysis of directionally specific or causal interactions between regions in functional magnetic resonance imaging (fMRI) data has proliferated. Here we identify six issues with existing effective connectivity methods that need to be addressed. The issues are discussed within the framework of linear dynamic systems for fMRI (LDSf). The first concerns the use of deterministic models to identify inter-regional effective connectivity. We show that deterministic dynamics are incapable of identifying the trial-to-trial variability typically investigated as the marker of connectivity while stochastic models can capture this variability. The second concerns the simplistic (constant) connectivity modeled by most methods. Connectivity parameters of the LDSf model can vary at the same timescale as the input data. Further, extending LDSf to mixtures of multiple models provides more robust connectivity variation. The third concerns the correct identification of the network itself including the number and anatomical origin of the network nodes. Augmentation of the LDSf state space can identify additional nodes of a network. The fourth concerns the locus of the signal used as a "node" in a network. A novel extension LDSf incorporating sparse canonical correlations can select most relevant voxels from an anatomically defined region based on connectivity. The fifth concerns connection interpretation. Individual parameter differences have received most attention. We present alternative network descriptors of connectivity changes which consider the whole network. The sixth concerns the temporal resolution of fMRI data relative to the timescale of the inter-regional interactions in the brain. LDSf includes an "instantaneous" connection term to capture connectivity occurring at timescales faster than the data resolution. The LDS framework can also be extended to statistically combine fMRI and EEG data. The LDSf framework is a promising foundation for effective connectivity analysis.

Variational solution to the joint detection estimation of brain activity in fMRI

We address the issue of jointly detecting brain activity and estimating underlying brain hemodynamics from functional MRI data. We adopt the so-called Joint Detection Estimation (JDE) framework that takes spatial dependencies between voxels into account. We recast the JDE into a missing data framework and derive a Variational Expectation-Maximization (VEM) algorithm for its inference. It follows a new algorithm that has interesting advantages over the previously used intensive simulation methods (Markov Chain Monte Carlo, MCMC): tests on artificial data show that the VEM-JDE is more robust to model mis-specification while additional tests on real data confirm that it achieves similar performance in much less computation time.

A stochastic linear model for fMRI activation analyses

PURPOSE

The debate regarding how best to model variability of the hemodynamic response function in fMRI data has focussed on the linear vs. nonlinear nature of the optimal signal model, with few studies exploring the deterministic vs. stochastic nature of the dynamics. We propose a stochastic linear model (SLM) of the hemodynamic signal and noise dynamics to more robustly infer fMRI activation estimates.

METHODS

The SLM models the hemodynamic signal by an exogenous input autoregressive model driven by Gaussian state noise. Activation weights are inferred by a joint state-parameter iterative coordinate descent algorithm based on the Kalman smoother.

RESULTS

The SLM produced more accurate parameter estimates than the GLM for event-design simulated data. In application to block-design experimental visuo-motor task fMRI data, the SLM resulted in more punctate and well-defined motor cortex activation maps than the GLM, and was able to track variations in the hemodynamics, as expected from a stochastic model.

CONCLUSIONS

We demonstrate in application to both simulated and experimental fMRI data that in comparison to the GLM, the SLM produces more flexible, consistent and enhanced fMRI activation estimates.

Generalised filtering and stochastic DCM for fMRI

This paper is about the fitting or inversion of dynamic causal models (DCMs) of fMRI time series. It tries to establish the validity of stochastic DCMs that accommodate random fluctuations in hidden neuronal and physiological states. We compare and contrast deterministic and stochastic DCMs, which do and do not ignore random fluctuations or noise on hidden states. We then compare stochastic DCMs, which do and do not ignore conditional dependence between hidden states and model parameters (generalised filtering and dynamic expectation maximisation, respectively). We first characterise state-noise by comparing the log evidence of models with different a priori assumptions about its amplitude, form and smoothness. Face validity of the inversion scheme is then established using data simulated with and without state-noise to ensure that DCM can identify the parameters and model that generated the data. Finally, we address construct validity using real data from an fMRI study of internet addiction. Our analyses suggest the following. (i) The inversion of stochastic causal models is feasible, given typical fMRI data. (ii) State-noise has nontrivial amplitude and smoothness. (iii) Stochastic DCM has face validity, in the sense that Bayesian model comparison can distinguish between data that have been generated with high and low levels of physiological noise and model inversion provides veridical estimates of effective connectivity. (iv) Relaxing conditional independence assumptions can have greater construct validity, in terms of revealing group differences not disclosed by variational schemes. Finally, we note that the ability to model endogenous or random fluctuations on hidden neuronal (and physiological) states provides a new and possibly more plausible perspective on how regionally specific signals in fMRI are generated.

Multivariate dynamical systems models for estimating causal interactions in fMRI

Analysis of dynamical interactions between distributed brain areas is of fundamental importance for understanding cognitive information processing. However, estimating dynamic causal interactions between brain regions using functional magnetic resonance imaging (fMRI) poses several unique challenges. For one, fMRI measures Blood Oxygenation Level Dependent (BOLD) signals, rather than the underlying latent neuronal activity. Second, regional variations in the hemodynamic response function (HRF) can significantly influence estimation of causal interactions between them. Third, causal interactions between brain regions can change with experimental context over time. To overcome these problems, we developed a novel state-space Multivariate Dynamical Systems (MDS) model to estimate intrinsic and experimentally-induced modulatory causal interactions between multiple brain regions. A probabilistic graphical framework is then used to estimate the parameters of MDS as applied to fMRI data. We show that MDS accurately takes into account regional variations in the HRF and estimates dynamic causal interactions at the level of latent signals. We develop and compare two estimation procedures using maximum likelihood estimation (MLE) and variational Bayesian (VB) approaches for inferring model parameters. Using extensive computer simulations, we demonstrate that, compared to Granger causal analysis (GCA), MDS exhibits superior performance for a wide range of signal to noise ratios (SNRs), sample length and network size. Our simulations also suggest that GCA fails to uncover causal interactions when there is a conflict between the direction of intrinsic and modulatory influences. Furthermore, we show that MDS estimation using VB methods is more robust and performs significantly better at low SNRs and shorter time series than MDS with MLE. Our study suggests that VB estimation of MDS provides a robust method for estimating and interpreting causal network interactions in fMRI data.

On consciousness, resting state fMRI, and neurodynamics

BACKGROUND

During the last years, functional magnetic resonance imaging (fMRI) of the brain has been introduced as a new tool to measure consciousness, both in a clinical setting and in a basic neurocognitive research. Moreover, advanced mathematical methods and theories have arrived the field of fMRI (e.g. computational neuroimaging), and functional and structural brain connectivity can now be assessed non-invasively.

RESULTS

The present work deals with a pluralistic approach to "consciousness'', where we connect theory and tools from three quite different disciplines: (1) philosophy of mind (emergentism and global workspace theory), (2) functional neuroimaging acquisitions, and (3) theory of deterministic and statistical neurodynamics - in particular the Wilson-Cowan model and stochastic resonance.

CONCLUSIONS

Based on recent experimental and theoretical work, we believe that the study of large-scale neuronal processes (activity fluctuations, state transitions) that goes on in the living human brain while examined with functional MRI during "resting state", can deepen our understanding of graded consciousness in a clinical setting, and clarify the concept of "consiousness" in neurocognitive and neurophilosophy research.

Spatially adaptive mixture modeling for analysis of FMRI time series

Within-subject analysis in fMRI essentially addresses two problems, the detection of brain regions eliciting evoked activity and the estimation of the underlying dynamics. In Makni et aL, 2005 and Makni et aL, 2008, a detection-estimation framework has been proposed to tackle these problems jointly, since they are connected to one another. In the Bayesian formalism, detection is achieved by modeling activating and nonactivating voxels through independent mixture models (IMM) within each region while hemodynamic response estimation is performed at a regional scale in a nonparametric way. Instead of IMMs, in this paper we take advantage of spatial mixture models (SMM) for their nonlinear spatial regularizing properties. The proposed method is unsupervised and spatially adaptive in the sense that the amount of spatial correlation is automatically tuned from the data and this setting automatically varies across brain regions. In addition, the level of regularization is specific to each experimental condition since both the signal-to-noise ratio and the activation pattern may vary across stimulus types in a given brain region. These aspects require the precise estimation of multiple partition functions of underlying Ising fields. This is addressed efficiently using first path sampling for a small subset of fields and then using a recently developed fast extrapolation technique for the large remaining set. Simulation results emphasize that detection relying on supervised SMM outperforms its IMM counterpart and that unsupervised spatial mixture models achieve similar results without any hand-tuning of the correlation parameter. On real datasets, the gain is illustrated in a localizer fMRI experiment: brain activations appear more spatially resolved using SMM in comparison with classical general linear model (GLM)-based approaches, while estimating a specific parcel-based HRF shape. Our approach therefore validates the treatment of unsmoothed fMRI data without fixed GLM definition at the subject level and makes also the classical strategy of spatial Gaussian filtering deprecated.

Relating BOLD fMRI and neural oscillations through convolution and optimal linear weighting

The exact relationship between neural activity and BOLD fMRI is unknown. However, several recent findings, recorded invasively in both humans and monkeys, show a positive correlation of BOLD to high-frequency (30-150 Hz) oscillatory power changes and a negative correlation to low-frequency (8-30 Hz) power changes arising from cortical areas. In this study, we computed the time series correlation between BOLD GE-EPI fMRI at 7 T and neural activity measures from noninvasive MEG, using a time-frequency beam former for source localisation. A sinusoidal drifting grating was presented visually for 4 s followed by a 20 s rest period in both recording modalities. The MEG time series were convolved with either a measured or canonical haemodynamic response function (HRF) for comparison with the measured BOLD data, and the BOLD data were deconvolved with either a measured or a canonical HRF for comparison with the measured MEG. In the visual cortex, the higher frequencies (mid-gamma=52-75 Hz and high-gamma=75-98 Hz) were positively correlated with BOLD whilst the lower frequencies (alpha=8-12 Hz and beta=12-25 Hz) were negatively correlated with BOLD. Furthermore, regression including all frequency bands predicted BOLD better than stimulus timing alone, although no individual frequency band predicted BOLD as well as stimulus timing. For this paradigm, there was, in general, no difference between using the SPM canonical HRF compared to the subject-specific measured HRF. In conclusion, MEG replicates findings from invasive recordings with regard to time series correlations with BOLD data. Conversely, deconvolution of BOLD data provides a neural estimate which correlates well with measured neural effects as a function of neural oscillation frequency.

Bayesian analysis of neuroimaging data in FSL

Typically in neuroimaging we are looking to extract some pertinent information from imperfect, noisy images of the brain. This might be the inference of percent changes in blood flow in perfusion FMRI data, segmentation of subcortical structures from structural MRI, or inference of the probability of an anatomical connection between an area of cortex and a subthalamic nucleus using diffusion MRI. In this article we will describe how Bayesian techniques have made a significant impact in tackling problems such as these, particularly in regards to the analysis tools in the FMRIB Software Library (FSL). We shall see how Bayes provides a framework within which we can attempt to infer on models of neuroimaging data, while allowing us to incorporate our prior belief about the brain and the neuroimaging equipment in the form of biophysically informed or regularising priors. It allows us to extract probabilistic information from the data, and to probabilistically combine information from multiple modalities. Bayes can also be used to not only compare and select between models of different complexity, but also to infer on data using committees of models. Finally, we mention some analysis scenarios where Bayesian methods are impractical, and briefly discuss some practical approaches that we have taken in these cases.