A fully Bayesian approach to the parcel-based detection-estimation of brain activity in fMRI

Conscious but not thinking-Mind-blanks during visuomotor tracking: An fMRI study of endogenous attention lapses

Attention lapses (ALs) are complete lapses of responsiveness in which performance is briefly but completely disrupted and during which, as opposed to microsleeps, the eyes remain open. Although the phenomenon of ALs has been investigated by behavioural and physiological means, the underlying cause of an AL has largely remained elusive. This study aimed to investigate the underlying physiological substrates of behaviourally identified endogenous ALs during a continuous visuomotor task, primarily to answer the question: Were the ALs during this task due to extreme mind-wandering or mind-blanks? The data from two studies were combined, resulting in data from 40 healthy non-sleep-deprived subjects (20M/20F; mean age 27.1 years, 20-45). Only 17 of the 40 subjects were used in the analysis due to a need for a minimum of two ALs per subject. Subjects performed a random 2-D continuous visuomotor tracking task for 50 and 20 min in Studies 1 and 2, respectively. Tracking performance, eye-video, and functional magnetic resonance imaging (fMRI) were recorded simultaneously. A human expert visually inspected the tracking performance and eye-video recordings to identify and categorise lapses of responsiveness as microsleeps or ALs. Changes in neural activity during 85 ALs (17 subjects) relative to responsive tracking were estimated by whole-brain voxel-wise fMRI and by haemodynamic response (HR) analysis in regions of interest (ROIs) from seven key networks to reveal the neural signature of ALs. Changes in functional connectivity (FC) within and between the key ROIs were also estimated. Networks explored were the default mode network, dorsal attention network, frontoparietal network, sensorimotor network, salience network, visual network, and working memory network. Voxel-wise analysis revealed a significant increase in blood-oxygen-level-dependent activity in the overlapping dorsal anterior cingulate cortex and supplementary motor area region but no significant decreases in activity; the increased activity is considered to represent a recovery-of-responsiveness process following an AL. This increased activity was also seen in the HR of the corresponding ROI. Importantly, HR analysis revealed no trend of increased activity in the posterior cingulate of the default mode network, which has been repeatedly demonstrated to be a strong biomarker of mind-wandering. FC analysis showed decoupling of external attention, which supports the involuntary nature of ALs, in addition to the neural recovery processes. Other findings were a decrease in HR in the frontoparietal network before the onset of ALs, and a decrease in FC between default mode network and working memory network. These findings converge to our conclusion that the ALs observed during our task were involuntary mind-blanks. This is further supported behaviourally by the short duration of the ALs (mean 1.7 s), which is considered too brief to be instances of extreme mind-wandering. This is the first study to demonstrate that at least the majority of complete losses of responsiveness on a continuous visuomotor task are, if not due to microsleeps, due to involuntary mind-blanks.

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.

Cortical thickness analysis in temporal lobe epilepsy using fully Bayesian spectral method in magnetic resonance imaging

BACKGROUND

Temporal lobe epilepsy (TLE) is the most common type of epilepsy associated with changes in the cerebral cortex throughout the brain. Magnetic resonance imaging (MRI) is widely used for detecting such anomalies; nevertheless, it produces spatially correlated data that cannot be considered by the usual statistical models. This study aimed to compare cortical thicknesses between patients with TLE and healthy controls by considering the spatial dependencies across different regions of the cerebral cortex in MRI.

METHODS

In this study, T1-weighted MRI was performed on 20 healthy controls and 33 TLE patients. Nineteen patients had a left TLE and 14 had a right TLE. Cortical thickness was measured for all individuals in 68 regions of the cerebral cortex based on images. Fully Bayesian spectral method was utilized to compare the cortical thickness of different brain regions between groups. Neural networks model was used to classify the patients using the identified regions.

RESULTS

For the left TLE patients, cortical thinning was observed in bilateral caudal anterior cingulate, lateral orbitofrontal (ipsilateral), the bilateral rostral anterior cingulate, frontal pole and temporal pole (ipsilateral), caudal middle frontal and rostral middle frontal (contralateral side). For the right TLE patients, cortical thinning was only observed in the entorhinal area (ipsilateral). The AUCs of the neural networks for classification of left and right TLE patients versus healthy controls were 0.939 and 1.000, respectively.

CONCLUSION

Alteration of cortical gray matter thickness was evidenced as common effect of epileptogenicity, as manifested by the patients in this study using the fully Bayesian spectral method by taking into account the complex structure of the data.

Predicting Verbal Learning and Memory Assessments of Older Adults Using Bayesian Hierarchical Models

Verbal learning and memory summaries of older adults have usually been used to describe neuropsychiatric complaints. Bayesian hierarchical models are modern and appropriate approaches for predicting repeated measures data where information exchangeability is considered and a violation of the independence assumption in classical statistics. Such models are complex models for clustered data that account for distributions of hyper-parameters for fixed-term parameters in Bayesian computations. Repeated measures are inherently clustered and typically occur in clinical trials, education, cognitive psychology, and treatment follow-up. The Hopkins Verbal Learning Test (HVLT) is a general verbal knowledge and memory assessment administered repeatedly as part of a neurophysiological experiment to examine an individual's performance outcomes at different time points. Multiple trial-based scores of verbal learning and memory tests were considered as an outcome measurement. In this article, we attempted to evaluate the predicting effect of individual characteristics in considering within and between-group variations by fitting various Bayesian hierarchical models via the hybrid Hamiltonian Monte Carlo (HMC) under the Bayesian Regression Models using 'Stan' (BRMS) package of R. Comparisons of the fitted models were done using leave-one-out information criteria (LOO-CV), Widely applicable information criterion (WAIC), and K-fold cross-validation methods. The full hierarchical model with varying intercepts and slopes had the best predictive performance for verbal learning tests [from the Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE) study dataset] using the hybrid Hamiltonian-Markov Chain Monte Carlo approach.

Identification of Negative BOLD Responses in Epilepsy Using Windkessel Models

Alongside positive blood oxygenation level–dependent (BOLD) responses associated with interictal epileptic discharges, a variety of negative BOLD responses (NBRs) are typically found in epileptic patients. Previous studies suggest that, in general, up to four mechanisms might underlie the genesis of NBRs in the brain: (i) neuronal disruption of network activity, (ii) altered balance of neurometabolic/vascular couplings, (iii) arterial blood stealing, and (iv) enhanced cortical inhibition. Detecting and classifying these mechanisms from BOLD signals are pivotal for the improvement of the specificity of the electroencephalography–functional magnetic resonance imaging (EEG-fMRI) image modality to identify the seizure-onset zones in refractory local epilepsy. This requires models with physiological interpretation that furnish the understanding of how these mechanisms are fingerprinted by their BOLD responses. Here, we used a Windkessel model with viscoelastic compliance/inductance in combination with dynamic models of both neuronal population activity and tissue/blood O₂ to classify the hemodynamic response functions (HRFs) linked to the above mechanisms in the irritative zones of epileptic patients. First, we evaluated the most relevant imprints on the BOLD response caused by variations of key model parameters. Second, we demonstrated that a general linear model is enough to accurately represent the four different types of NBRs. Third, we tested the ability of a machine learning classifier, built from a simulated ensemble of HRFs, to predict the mechanism underlying the BOLD signal from irritative zones. Cross-validation indicates that these four mechanisms can be classified from realistic fMRI BOLD signals. To demonstrate proof of concept, we applied our methodology to EEG-fMRI data from five epileptic patients undergoing neurosurgery, suggesting the presence of some of these mechanisms. We concluded that a proper identification and interpretation of NBR mechanisms in epilepsy can be performed by combining general linear models and biophysically inspired models.

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.

Regularized aggregation of statistical parametric maps

Combining statistical parametric maps (SPM) from individual subjects is the goal in some types of group-level analyses of functional magnetic resonance imaging data. Brain maps are usually combined using a simple average across subjects, making them susceptible to subjects with outlying values. Furthermore, t tests are prone to false positives and false negatives when outlying values are observed. We propose a regularized unsupervised aggregation method for SPMs to find an optimal weight for aggregation, which aids in detecting and mitigating the effect of outlying subjects. We also present a bootstrap-based weighted t test using the optimal weights to construct an activation map robust to outlying subjects. We validate the performance of the proposed aggregation method and test using simulated and real data examples. Results show that the regularized aggregation approach can effectively detect outlying subjects, lower their weights, and produce robust SPMs.

A Bayesian Approach for Estimating Dynamic Functional Network Connectivity in fMRI Data

Dynamic functional connectivity, i.e., the study of how interactions among brain regions change dynamically over the course of an fMRI experiment, has recently received wide interest in the neuroimaging literature. Current approaches for studying dynamic connectivity often rely on ad-hoc approaches for inference, with the fMRI time courses segmented by a sequence of sliding windows. We propose a principled Bayesian approach to dynamic functional connectivity, which is based on the estimation of time varying networks. Our method utilizes a hidden Markov model for classification of latent cognitive states, achieving estimation of the networks in an integrated framework that borrows strength over the entire time course of the experiment. Furthermore, we assume that the graph structures, which define the connectivity states at each time point, are related within a super-graph, to encourage the selection of the same edges among related graphs. We apply our method to simulated task-based fMRI data, where we show how our approach allows the decoupling of the task-related activations and the functional connectivity states. We also analyze data from an fMRI sensorimotor task experiment on an individual healthy subject and obtain results that support the role of particular anatomical regions in modulating interaction between executive control and attention networks.

Comparison of fMRI analysis methods for heterogeneous BOLD responses in block design studies

A large number of fMRI studies have shown that the temporal dynamics of evoked BOLD responses can be highly heterogeneous. Failing to model heterogeneous responses in statistical analysis can lead to significant errors in signal detection and characterization and alter the neurobiological interpretation. However, to date it is not clear that, out of a large number of options, which methods are robust against variability in the temporal dynamics of BOLD responses in block-design studies. Here, we used rodent optogenetic fMRI data with heterogeneous BOLD responses and simulations guided by experimental data as a means to investigate different analysis methods' performance against heterogeneous BOLD responses. Evaluations are carried out within the general linear model (GLM) framework and consist of standard basis sets as well as independent component analysis (ICA). Analyses show that, in the presence of heterogeneous BOLD responses, conventionally used GLM with a canonical basis set leads to considerable errors in the detection and characterization of BOLD responses. Our results suggest that the 3rd and 4th order gamma basis sets, the 7th to 9th order finite impulse response (FIR) basis sets, the 5th to 9th order B-spline basis sets, and the 2nd to 5th order Fourier basis sets are optimal for good balance between detection and characterization, while the 1st order Fourier basis set (coherence analysis) used in our earlier studies show good detection capability. ICA has mostly good detection and characterization capabilities, but detects a large volume of spurious activation with the control fMRI data.

Locally Estimated Hemodynamic Response Function and Activation Detection Sensitivity in Heroin-Cue Reactivity Study

Introduction:

A fixed hemodynamic response function (HRF) is commonly used for functional magnetic resonance imaging (fMRI) analysis. However, HRF may vary from region to region and subject to subject. We investigated the effect of locally estimated HRF (in functionally homogenous parcels) on activation detection sensitivity in a heroin cue reactivity study.

Methods:

We proposed a novel exploratory method for brain parcellation based on a probabilistic model to segregate the brain into spatially connected and functionally homogeneous components. Then, we estimated HRF and detected activated regions in response to an experimental task in each parcel using a joint detection estimation (JDE) method. We compared the proposed JDE method with the general linear model (GLM) that uses a fixed HRF and is implemented in FEAT (as a part of FMRIB Software Library, version 4.1).

Results:

1) Regions detected by JDE are larger than those detected by fixed HRF, 2) In group analysis, JDE found areas of activation not detected by fixed HRF. It detected drug craving a priori “regions-of-interest” in the limbic lobe (anterior cingulate cortex [ACC], posterior cingulate cortex [PCC] and cingulate gyrus), basal ganglia, especially striatum (putamen and head of caudate), and cerebellum in addition to the areas detected by the fixed HRF method, 3) JDE obtained higher Z-values of local maxima compared to those obtained by fixed HRF.

Conclusion:

In our study of heroin cue reactivity, our proposed method (that estimates HRF locally) outperformed the conventional GLM that uses a fixed HRF.

Statistical modeling of time-dependent fMRI activation effects

Functional magnetic resonance imaging (fMRI) activation detection within stimulus-based experimental paradigms is conventionally based on the assumption that activation effects remain constant over time. This assumption neglects the fact that the strength of activation may vary, for example, due to habituation processes or changing attention. Neither the functional form of time variation can be retrieved nor short-lasting effects can be detected by conventional methods. In this work, a new dynamic approach is proposed that allows to estimate time-varying effect profiles and hemodynamic response functions in event-related fMRI paradigms. To this end, we incorporate the time-varying coefficient methodology into the fMRI general regression framework. Inference is based on a voxelwise penalized least squares procedure. We assess the strength of activation and corresponding time variation on the basis of pointwise confidence intervals on a voxel level. Additionally, spatial clusters of effect curves are presented. Results of the analysis of an active oddball experiment show that activation effects deviating from a constant trend coexist with time-varying effects that exhibit different types of shapes, such as linear, (inversely) U-shaped or fluctuating forms. In a comparison to conventional approaches, like classical SPM, we observe that time-constant methods are rather insensitive to detect temporary effects, because these do not emerge when aggregated across the entire experiment. Hence, it is recommended to base activation detection analyses not merely on time-constant procedures but to include flexible time-varying effects that harbour valuable information on individual response patterns.

Optimizing affinity measures for parcellating brain structures based on resting state fMRI data: a validation on medial superior frontal cortex

BACKGROUND

Parcellating brain structures into functionally homogeneous subregions based on resting state fMRI data could be achieved by grouping image voxels using clustering algorithms, such as normalized cut. The affinity between brain voxels adopted in the clustering algorithms is typically characterized by a combination of the similarity of their functional signals and their spatial distance with parameters empirically specified. However, improper parameter setting of the affinity measure may result in parcellation results biased to spatial smoothness.

NEW METHOD

To obtain a functionally homogeneous and spatially contiguous brain parcellation result, we propose to optimize the affinity measure of image voxels using a constrained bi-level programming optimization method. Particularly, we first identify the space of all possible parameters that are able to generate spatially contiguous brain parcellation results. Then, within the constrained parameter space we search those leading to the brain parcellation results with optimal functional homogeneity and spatial smoothness.

RESULTS AND COMPARISON WITH EXISTING METHODS

The method has successfully parcellated medial superior frontal cortex into supplementary motor area (SMA) and pre-SMA for 106 subjects based on their resting state fMRI data. These results have been validated through functional connectivity analysis and meta-analysis of existing functional imaging studies and compared with those obtained by state-of-the-art brain parcellation methods.

CONCLUSIONS

The validation results have demonstrated that our method could obtain brain parcellation results consistent with the existing functional anatomy knowledge, and the comparison results have further demonstrated that optimizing affinity measure could improve the brain parcellation's robustness and functional homogeneity.

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.

Flexible multivariate hemodynamics fMRI data analyses and simulations with PyHRF

As part of fMRI data analysis, the pyhrf package provides a set of tools for addressing the two main issues involved in intra-subject fMRI data analysis: (1) the localization of cerebral regions that elicit evoked activity and (2) the estimation of activation dynamics also known as Hemodynamic Response Function (HRF) recovery. To tackle these two problems, pyhrf implements the Joint Detection-Estimation framework (JDE) which recovers parcel-level HRFs and embeds an adaptive spatio-temporal regularization scheme of activation maps. With respect to the sole detection issue (1), the classical voxelwise GLM procedure is also available through nipy, whereas Finite Impulse Response (FIR) and temporally regularized FIR models are concerned with HRF estimation (2) and are specifically implemented in pyhrf. Several parcellation tools are also integrated such as spatial and functional clustering. Parcellations may be used for spatial averaging prior to FIR/RFIR analysis or to specify the spatial support of the HRF estimates in the JDE approach. These analysis procedures can be applied either to volume-based data sets or to data projected onto the cortical surface. For validation purpose, this package is shipped with artificial and real fMRI data sets, which are used in this paper to compare the outcome of the different available approaches. The artificial fMRI data generator is also described to illustrate how to simulate different activation configurations, HRF shapes or nuisance components. To cope with the high computational needs for inference, pyhrf handles distributing computing by exploiting cluster units as well as multi-core machines. Finally, a dedicated viewer is presented, which handles n-dimensional images and provides suitable features to explore whole brain hemodynamics (time series, maps, ROI mask overlay).

Constructing fMRI connectivity networks: a whole brain functional parcellation method for node definition

BACKGROUND

Functional Magnetic Resonance Imaging (fMRI) is used for exploring brain functionality, and recently it was applied for mapping the brain connection patterns. To give a meaningful neurobiological interpretation to the connectivity network, it is fundamental to properly define the network framework. In particular, the choice of the network nodes may affect the final connectivity results and the consequent interpretation.

NEW METHOD

We introduce a novel method for the intra subject topological characterization of the nodes of fMRI brain networks, based on a whole brain parcellation scheme. The proposed whole brain parcellation algorithm divides the brain into clusters that are homogeneous from the anatomical and functional point of view, each of which constitutes a node. The functional parcellation described is based on the Tononi's cluster index, which measures instantaneous correlation in terms of intrinsic and extrinsic statistical dependencies.

RESULTS

The method performance and reliability were first tested on simulated data, then on a real fMRI dataset acquired on healthy subjects during visual stimulation. Finally, the proposed algorithm was applied to epileptic patients' fMRI data recorded during seizures, to verify its usefulness as preparatory step for effective connectivity analysis. For each patient, the nodes of the network involved in ictal activity were defined according to the proposed parcellation scheme and Granger Causality Analysis (GCA) was applied to infer effective connectivity.

CONCLUSIONS

We showed that the algorithm 1) performed well on simulated data, 2) was able to produce reliable inter subjects results and 3) led to a detailed definition of the effective connectivity pattern.

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.

Hemodynamic-informed parcellation of fMRI data in a joint detection estimation framework

Identifying brain hemodynamics in event-related functional MRI (fMRI) data is a crucial issue to disentangle the vascular response from the neuronal activity in the BOLD signal. This question is usually addressed by estimating the so-called hemodynamic response function (HRF). Voxelwise or region-/parcelwise inference schemes have been proposed to achieve this goal but so far all known contributions commit to pre-specified spatial supports for the hemodynamic territories by defining these supports either as individual voxels or a priori fixed brain parcels. In this paper, we introduce a joint parcellation-detection-estimation (JPDE) procedure that incorporates an adaptive parcel identification step based upon local hemodynamic properties. Efficient inference of both evoked activity, HRF shapes and supports is then achieved using variational approximations. Validation on synthetic and real fMRI data demonstrate the JPDE performance over standard detection estimation schemes and suggest it as a new brain exploration tool.

Bayesian hierarchical multi-subject multiscale analysis of functional MRI data

We develop a methodology for Bayesian hierarchical multi-subject multiscale analysis of functional Magnetic Resonance Imaging (fMRI) data. We begin by modeling the brain images temporally with a standard general linear model. After that, we transform the resulting estimated standardized regression coefficient maps through a discrete wavelet transformation to obtain a sparse representation in the wavelet space. Subsequently, we assign to the wavelet coefficients a prior that is a mixture of a point mass at zero and a Gaussian white noise. In this mixture prior for the wavelet coefficients, the mixture probabilities are related to the pattern of brain activity across different resolutions. To incorporate this information, we assume that the mixture probabilities for wavelet coefficients at the same location and level are common across subjects. Furthermore, we assign for the mixture probabilities a prior that depends on a few hyperparameters. We develop an empirical Bayes methodology to estimate the hyperparameters and, as these hyperparameters are shared by all subjects, we obtain precise estimated values. Then we carry out inference in the wavelet space and obtain smoothed images of the regression coefficients by applying the inverse wavelet transform to the posterior means of the wavelet coefficients. An application to computer simulated synthetic data has shown that, when compared to single-subject analysis, our multi-subject methodology performs better in terms of mean squared error. Finally, we illustrate the utility and flexibility of our multi-subject methodology with an application to an event-related fMRI dataset generated by Postle (2005) through a multi-subject fMRI study of working memory related brain activation.

Scale-Free and Multifractal Time Dynamics of fMRI Signals during Rest and Task

Scaling temporal dynamics in functional MRI (fMRI) signals have been evidenced for a decade as intrinsic characteristics of ongoing brain activity (Zarahn et al., 1997). Recently, scaling properties were shown to fluctuate across brain networks and to be modulated between rest and task (He, 2011): notably, Hurst exponent, quantifying long memory, decreases under task in activating and deactivating brain regions. In most cases, such results were obtained: First, from univariate (voxelwise or regionwise) analysis, hence focusing on specific cognitive systems such as Resting-State Networks (RSNs) and raising the issue of the specificity of this scale-free dynamics modulation in RSNs. Second, using analysis tools designed to measure a single scaling exponent related to the second order statistics of the data, thus relying on models that either implicitly or explicitly assume Gaussianity and (asymptotic) self-similarity, while fMRI signals may significantly depart from those either of those two assumptions (Ciuciu et al., 2008; Wink et al., 2008). To address these issues, the present contribution elaborates on the analysis of the scaling properties of fMRI temporal dynamics by proposing two significant variations. First, scaling properties are technically investigated using the recently introduced Wavelet Leader-based Multifractal formalism (WLMF; Wendt et al., 2007). This measures a collection of scaling exponents, thus enables a richer and more versatile description of scale invariance (beyond correlation and Gaussianity), referred to as multifractality. Also, it benefits from improved estimation performance compared to tools previously used in the literature. Second, scaling properties are investigated in both RSN and non-RSN structures (e.g., artifacts), at a broader spatial scale than the voxel one, using a multivariate approach, namely the Multi-Subject Dictionary Learning (MSDL) algorithm (Varoquaux et al., 2011) that produces a set of spatial components that appear more sparse than their Independent Component Analysis (ICA) counterpart. These tools are combined and applied to a fMRI dataset comprising 12 subjects with resting-state and activation runs (Sadaghiani et al., 2009). Results stemming from those analysis confirm the already reported task-related decrease of long memory in functional networks, but also show that it occurs in artifacts, thus making this feature not specific to functional networks. Further, results indicate that most fMRI signals appear multifractal at rest except in non-cortical regions. Task-related modulation of multifractality appears only significant in functional networks and thus can be considered as the key property disentangling functional networks from artifacts. These finding are discussed in the light of the recent literature reporting scaling dynamics of EEG microstate sequences at rest and addressing non-stationarity issues in temporally independent fMRI modes.

Concurrent bias correction in hemodynamic data assimilation

Low-frequency drift in fMRI datasets can be caused by various sources and are generally not of interest in a conventional task-based fMRI experiment. This feature complicates the assimilation approach that is always under specific assumption on statistics of system uncertainties. In this paper, we present a novel approach to the assimilation of nonlinear hemodynamic system with stochastic biased noise. By treating the drift variation as a random-walk process, the assimilation problem was translated into the identification of a nonlinear system in the presence of time-varying bias. We developed a bias aware unscented Kalman estimator to efficiently handle this problem. In this framework, the estimates of bias-free states and drift are separately carried out in two parallel filters, the optimal estimates of the system states then are corrected from bias-free states with drift estimates. The approach can simultaneously deal with the fMRI responses and drift in an assimilation cycle in an on-line fashion. It makes no assumptions of the structure and statistics of the drift, thereby is particularly suited for fMRI imaging where the formulation of real drift remains difficult to acquire. Experiments with synthetic data and real fMRI data are performed to demonstrate feasibility of our approach and to explore its potential advantages over classic polynomial approach. Moreover, we include the comparison of the variability of observables from the scanner and of normalized signal used in assimilation procedure in Appendix.

Detection of epileptic activity in fMRI without recording the EEG

EEG-fMRI localizes epileptic foci by detecting cerebral hemodynamic changes that are correlated to epileptic events visible in EEG. However, scalp EEG is insensitive to activity restricted to deep structures and recording the EEG in the scanner is complex and results in major artifacts that are difficult to remove. This study presents a new framework for identifying the BOLD manifestations of epileptic discharges without having to record the EEG. The first stage is based on the detection of epileptic events for each voxel by sparse representation in the wavelet domain. The second stage is to gather voxels according to proximity in time and space of detected activities. This technique was evaluated on data generated by superposing artificial responses at different locations and responses amplitude in the brain for 6 control subject runs. The method was able to detect effectively and consistently for responses amplitude of at least 1% above baseline. 46 runs from 15 patients with focal epilepsy were investigated. The results demonstrate that the method detected at least one concordant event in 37/41 runs. The maps of activation obtained from our method were more similar to those obtained by EEG-fMRI than to those obtained by the other method used in this context, 2D-Temporal Cluster Analysis. For 5 runs without event read on scalp EEG, 3 runs showed an activation concordant with the patient's diagnostic. It may therefore be possible, at least when spikes are infrequent, to detect their BOLD manifestations without having to record the EEG.

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.

Search for patterns of functional specificity in the brain: a nonparametric hierarchical Bayesian model for group fMRI data

Functional MRI studies have uncovered a number of brain areas that demonstrate highly specific functional patterns. In the case of visual object recognition, small, focal regions have been characterized with selectivity for visual categories such as human faces. In this paper, we develop an algorithm that automatically learns patterns of functional specificity from fMRI data in a group of subjects. The method does not require spatial alignment of functional images from different subjects. The algorithm is based on a generative model that comprises two main layers. At the lower level, we express the functional brain response to each stimulus as a binary activation variable. At the next level, we define a prior over sets of activation variables in all subjects. We use a Hierarchical Dirichlet Process as the prior in order to learn the patterns of functional specificity shared across the group, which we call functional systems, and estimate the number of these systems. Inference based on our model enables automatic discovery and characterization of dominant and consistent functional systems. We apply the method to data from a visual fMRI study comprised of 69 distinct stimulus images. The discovered system activation profiles correspond to selectivity for a number of image categories such as faces, bodies, and scenes. Among systems found by our method, we identify new areas that are deactivated by face stimuli. In empirical comparisons with previously proposed exploratory methods, our results appear superior in capturing the structure in the space of visual categories of stimuli.

Adaptively and spatially estimating the hemodynamic response functions in fMRI

In an event-related functional MRI data analysis, an accurate and robust extraction of the hemodynamic response function (HRF) and its associated statistics (e.g., magnitude, width, and time to peak) is critical to infer quantitative information about the relative timing of the neuronal events in different brain regions. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) to accurately estimate HRFs pertaining to each stimulus sequence across all voxels. MASM explicitly accounts for both spatial and temporal smoothness information, while incorporating such information to adaptively estimate HRFs in the frequency domain. One simulation study and a real data set are used to demonstrate the methodology and examine its finite sample performance in HRF estimation, which confirms that MASM significantly outperforms the existing methods including the smooth finite impulse response model, the inverse logit model and the canonical HRF.

Robust extrapolation scheme for fast estimation of 3D ising field partition functions: application to within-subject fMRI data analysis

In this paper, we present a fast numerical scheme to estimate Partition Functions (PF) of 3D Ising fields. Our strategy is applied to the context of the joint detection-estimation of brain activity from functional Magnetic Resonance Imaging (fMRI) data, where the goal is to automatically recover activated regions and estimate region-dependent hemodynamic filters. For any region, a specific binary Markov random field may embody spatial correlation over the hidden states of the voxels by modeling whether they are activated or not. To make this spatial regularization fully adaptive, our approach is first based upon a classical path-sampling method to approximate a small subset of reference PFs corresponding to prespecified regions. Then, the proposed extrapolation method allows us to approximate the PFs associated with the Ising fields defined over the remaining brain regions. In comparison with preexisting approaches, our method is robust to topological inhomogeneities in the definition of the reference regions. As a result, it strongly alleviates the computational burden and makes spatially adaptive regularization of whole brain fMRI datasets feasible.

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.

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.

Anatomically informed bayesian model selection for fMRI group data analysis

A new approach for fMRI group data analysis is introduced to overcome the limitations of standard voxel-based testing methods, such as Statistical Parametric Mapping (SPM). Using a Bayesian model selection framework, the functional network associated with a certain cognitive task is selected according to the posterior probabilities of mean region activations, given a pre-defined anatomical parcellation of the brain. This approach enables us to control a Bayesian risk that balances false positives and false negatives, unlike the SPM-like approach, which only controls false positives. On data from a mental calculation experiment, it detected the functional network known to be involved in number processing, whereas the SPM-like approach either swelled or missed the different activation regions.

Combined spatial and non-spatial prior for inference on MRI time-series

When modelling FMRI and other MRI time-series data, a Bayesian approach based on adaptive spatial smoothness priors is a compelling alternative to using a standard generalized linear model (GLM) on presmoothed data. Another benefit of the Bayesian approach is that biophysical prior information can be incorporated in a principled manner; however, this requirement for a fixed non-spatial prior on a parameter would normally preclude using spatial regularization on that same parameter. We have developed a Gaussian-process-based prior to apply adaptive spatial regularization while still ensuring that the fixed biophysical prior is correctly applied on each voxel. A parameterized covariance matrix provides separate control over the variance (the diagonal elements) and the between-voxel correlation (due to off-diagonal elements). Analysis proceeds using evidence optimization (EO), with variational Bayes (VB) updates used for some parameters. The method can also be applied to non-linear forward models by using a linear Taylor expansion centred on the latest parameter estimates. Applying the method to FMRI with a constrained haemodynamic response function (HRF) shape model shows improved fits in simulations, compared to using either the non-spatial or spatial-smoothness prior alone. We also analyse multi-inversion arterial spin labelling data using a non-linear perfusion model to estimate cerebral blood flow and bolus arrival time. By combining both types of prior information, this new prior performs consistently well across a wider range of situations than either prior alone, and provides better estimates when both types of prior information are relevant.