Estimation of the hemodynamic response in event-related functional MRI: Bayesian networks as a framework for efficient Bayesian modeling and inference

Joint direct estimation of hemodynamic response function and activation level in brain functional high density diffuse optical tomography

High density diffuse optical tomography has become increasingly important to detect underlying neuronal activities. Conventional methods first estimate the time courses of the changes in the absorption coefficients for all the voxels, and then estimate the hemodynamic response function (HRF). Activation-level maps are extracted at last based on this HRF. However, the error propagation among the successive processes degrades and even misleads the final results. Besides, the computation burden is heavy. To address the above problems, a direct method is proposed in this paper to simultaneously estimate the HRF and the activation-level maps from the boundary fluxes. It is assumed that all the voxels in the same activated brain region share the same HRF but differ in the activation levels, and no prior information is imposed on the specific shape of the HRF. The dynamic simulation and phantom experiments demonstrate that the proposed method outperforms the conventional one in terms of the estimation accuracy and computation speed.

An integrated framework for joint HRF and drift estimation and HbO/HbR signal improvement in fNIRS data

Nonparametric hemodynamic response function (HRF) estimation in functional near-infrared spectroscopy (fNIRS) data plays an important role when investigating the temporal dynamics of a brain region response during activations. Assuming the drift arising from both physical and physiological effects in fNIRS data is Lipschitz continuous; a novel algorithm for joint HRF and drift estimation is derived in this paper. The proposed algorithm estimates the HRF by applying a first-order differencing to the fNIRS time series samples in order to remove the drift effect. An estimate of the drift is then obtained using a wavelet thresholding technique applied to the residuals generated by removing the estimated induced activation response from the fNIRS time-series. It is shown that the proposed HRF estimator is √N consistent whereas the estimator of the drift is asymptotically optimal. The de-drifted fNIRS oxygenated (HbO) and deoxygenated (HbR) hemoglobin responses are then obtained by removing the corresponding estimated drifts from the fNIRS time-series. Its performance is assessed using both simulated and real fNIRS data sets. The application results reveal that the proposed joint HRF and drift estimation method is efficient both computationally and in terms of accuracy. In comparison to traditional model based methods used for HRF estimation, the proposed novel method avoids the selection of a model to remove the drift component. As a result, the proposed method finds an optimal estimate of the fNIRS drift and offers a model-free approach to de-drift the HbO/HbR responses.

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.

HRF estimation in fMRI data with an unknown drift matrix by iterative minimization of the Kullback-Leibler divergence

Hemodynamic response function (HRF) estimation in noisy functional magnetic resonance imaging (fMRI) plays an important role when investigating the temporal dynamic of a brain region response during activations. Nonparametric methods which allow more flexibility in the estimation by inferring the HRF at each time sample have provided improved performance in comparison to the parametric methods. In this paper, the mixed-effects model is used to derive a new algorithm for nonparametric maximum likelihood HRF estimation. In this model, the random effect is used to better account for the variability of the drift. Contrary to the usual approaches, the proposed algorithm has the benefit of considering an unknown and therefore flexible drift matrix. This allows the effective representation of a broader class of drift signals and therefore the reduction of the error in approximating the drift component. Estimates of the HRF and the hyperparameters are derived by iterative minimization of the Kullback-Leibler divergence between a model family of probability distributions defined using the mixed-effects model and a desired family of probability distributions constrained to be concentrated on the observed data. The performance of proposed method is demonstrated on simulated and real fMRI data, the latter originating from both event-related and block design fMRI experiments.

Investigation of Linear Coupling Between Single-Event Blood Flow Responses and Interictal Discharges in a Model of Experimental Epilepsy

A successful outcome of epilepsy neurosurgery relies on an accurate delineation of the epileptogenic region to be resected. Functional magnetic resonance imaging (fMRI) would allow doing this noninvasively at high spatial resolution. However, a clear, quantitative description of the relationship between hemodynamic changes and the underlying epileptiform neuronal activity is still missing, thereby preventing the systematic use of fMRI for routine epilepsy surgery planning. To this aim, we used a local epilepsy model to record simultaneously cerebral blood flow (CBF) with laser Doppler (LD) and local field potentials (LFP) in rat frontal cortex. CBF responses to individual interictal-like spikes were large and robust. Their amplitude correlated linearly with spike amplitude. Moreover, the CBF response added linearly in time over a large range of spiking rates. CBF responses could thus be predicted by a linear model of the kind currently used for the interpretation of fMRI data, but including also the spikes’ amplitudes as additional information. Predicted and measured CBF responses matched accurately. For high spiking frequencies (above ∼0.2 Hz), the responses saturated but could eventually recover, indicating the presence of multiple neurovascular coupling mechanisms, which might act at different spatiotemporal scales. Spatially, CBF responses peaked at the center of epileptic activity and displayed a spatial specificity at least as good as the millimeter. These results suggest that simultaneous electroencephalographic and blood flow-based fMRI recordings should be suitable for the noninvasive precise localization of hyperexcitable regions in epileptic patients candidate for neurosurgery.

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.

Influence of heart rate on the BOLD signal: the cardiac response function

It has previously been shown that low-frequency fluctuations in both respiratory volume and cardiac rate can induce changes in the blood-oxygen level dependent (BOLD) signal. Such physiological noise can obscure the detection of neural activation using fMRI, and it is therefore important to model and remove the effects of this noise. While a hemodynamic response function relating respiratory variation (RV) and the BOLD signal has been described [Birn, R.M., Smith, M.A., Jones, T.B., Bandettini, P.A., 2008b. The respiration response function: The temporal dynamics of fMRI signal fluctuations related to changes in respiration. Neuroimage 40, 644-654.], no such mapping for heart rate (HR) has been proposed. In the current study, the effects of RV and HR are simultaneously deconvolved from resting state fMRI. It is demonstrated that a convolution model including RV and HR can explain significantly more variance in gray matter BOLD signal than a model that includes RV alone, and an average HR response function is proposed that well characterizes our subject population. It is observed that the voxel-wise morphology of the deconvolved RV responses is preserved when HR is included in the model, and that its form is adequately modeled by Birn et al.'s previously-described respiration response function. Furthermore, it is shown that modeling out RV and HR can significantly alter functional connectivity maps of the default-mode network.

Nonlinear estimation of the BOLD signal

Signal variations in functional Magnetic Resonance Imaging experiments essentially reflect the vascular system response to increased demand for oxygen caused by neuronal activity, termed the blood oxygenation level dependent (BOLD) effect. The most comprehensive model to date of the BOLD signal is formulated as a mixed continuous-discrete-time system of nonlinear stochastic differential equations. Previous approaches to the analysis of this system have been based on linearised approximations of the dynamics, which are limited in their ability to capture the inherent nonlinearities in the physiological system. In this paper we present a nonlinear filtering method for simultaneous estimation of the hidden physiological states and the system parameters, based on an iterative coordinate descent framework. State estimates of the cerebral blood flow, cerebral blood volume and deoxyhaemoglobin content are determined using a particle filter, demonstrated via simulation to be accurate, robust and efficient in comparison to linearisation-based techniques. The adaptive state and parameter estimation algorithm generates physiologically reasonable parameter estimates for experimental fMRI data. It is anticipated that signal processing techniques for modelling and estimation will become increasingly important in fMRI analyses as limitations of linear and linearised modelling are reached.

Activation detection in diffuse optical imaging by means of the general linear model

Due to its non-invasive nature and low cost, diffuse optical imaging (DOI) is becoming a commonly used technique to assess functional activation in the brain. When imaging with DOI, two major issues arise in the data analysis: (i) the separation of noise of physiological origin and the recovery of the functional response; (ii) the tomographic image reconstruction problem. This paper focuses on the first issue. Although the general linear model (GLM) has been extensively used in functional magnetic resonance imaging (fMRI), DOI has mostly relied on filtering and averaging of raw data to recover brain functional activation. This is mainly due to the high temporal resolution of DOI which implies a new design of the drift basis modelling physiology. In this paper, we provide (i) a filtering method based on cosine functions that is more adapted than standard averaging techniques for DOI specifically; (ii) a new mode-locking technique to recover small signals and locate them temporally with high precision (shift method). Results on real data show the capability of the shift method to retrieve HbR and HbO(2) peak locations.

Symmetrical event-related EEG/fMRI information fusion in a variational Bayesian framework

In this work, we propose a symmetrical multimodal EEG/fMRI information fusion approach dedicated to the identification of event-related bioelectric and hemodynamic responses. Unlike existing, asymmetrical EEG/fMRI data fusion algorithms, we build a joint EEG/fMRI generative model that explicitly accounts for local coupling/uncoupling of bioelectric and hemodynamic activities, which are supposed to share a common substrate. Under a dedicated assumption of spatio-temporal separability, the spatial profile of the common EEG/fMRI sources is introduced as an unknown hierarchical prior on both markers of cerebral activity. Thereby, a devoted Variational Bayesian (VB) learning scheme is derived to infer common EEG/fMRI sources from a joint EEG/fMRI dataset. This yields an estimate of the common spatial profile, which is built as a trade-off between information extracted from EEG and fMRI datasets. Furthermore, the spatial structure of the EEG/fMRI coupling/uncoupling is learned exclusively from the data. The proposed data generative model and devoted VBEM learning scheme thus provide an un-supervised well-balanced approach for the fusion of EEG/fMRI information. We first demonstrate our approach on synthetic data. Results show that, in contrast to classical EEG/fMRI fusion approach, the method proved efficient and robust regardless of the EEG/fMRI discordance level. We apply the method on EEG/fMRI recordings from a patient with epilepsy, in order to identify brain areas involved during the generation of epileptic spikes. The results are validated using intracranial EEG measurements.

Hidden Markov multiple event sequence models: A paradigm for the spatio-temporal analysis of fMRI data

This paper presents a novel, completely unsupervised fMRI brain mapping method that addresses the three problems of hemodynamic response function (HRF) variability, hemodynamic event timing, and fMRI response non-linearity. Spatial and temporal information are directly taken into account into the core of the activation detection process. In practice, activation detection at voxel v is formulated in terms of temporal alignment between sequences of hemodynamic response onsets (HROs) detected in the fMRI signal at v and in the spatial neighborhood of v, and the input sequence of stimuli or stimulus onsets. Event-related and epoch paradigms are considered. The multiple event sequence alignment problem is solved within the probabilistic framework of hidden Markov multiple event sequence models (HMMESMs), a new class of hidden Markov models. Results obtained on real and synthetic data significantly outperform those obtained with the popular statistical parametric mapping (SPM2) method without requiring any prior definition of the expected activation patterns, the HMMESM mapping approach being completely unsupervised.

Remapping in human visual cortex

With each eye movement, stationary objects in the world change position on the retina, yet we perceive the world as stable. Spatial updating, or remapping, is one neural mechanism by which the brain compensates for shifts in the retinal image caused by voluntary eye movements. Remapping of a visual representation is believed to arise from a widespread neural circuit including parietal and frontal cortex. The current experiment tests the hypothesis that extrastriate visual areas in human cortex have access to remapped spatial information. We tested this hypothesis using functional magnetic resonance imaging (fMRI). We first identified the borders of several occipital lobe visual areas using standard retinotopic techniques. We then tested subjects while they performed a single-step saccade task analogous to the task used in neurophysiological studies in monkeys, and two conditions that control for visual and motor effects. We analyzed the fMRI time series data with a nonlinear, fully Bayesian hierarchical statistical model. We identified remapping as activity in the single-step task that could not be attributed to purely visual or oculomotor effects. The strength of remapping was roughly monotonic with position in the visual hierarchy: remapped responses were largest in areas V3A and hV4 and smallest in V1 and V2. These results demonstrate that updated visual representations are present in cortical areas that are directly linked to visual perception.

A haemodynamic response function model in spatio-temporal diffuse optical tomography

Diffuse optical tomography (DOT) is a new and effective technique for functional brain imaging. It can detect local changes in both oxygenated and deoxygenated haemoglobin concentrations in tissue based on differential absorption at multiple wavelengths. Traditional methods in spatio-temporal analysis of haemoglobin concentrations in diffuse optical tomography first reconstruct the spatial distribution at different time instants independently, then look at the temporal dynamics on each pixel, without incorporating any temporal information as a prior in the image reconstruction. In this work, we present a temporal haemodynamic response function model described by a basis function expansion, in a joint spatio-temporal DOT reconstruction of haemoglobin concentration changes during simulated brain activation. In this joint framework, we simultaneously employ spatial regularization, spectral information and temporal assumptions. We also present an efficient algorithm for solving the associated large-scale systems. The expected improvements in spatial resolution and contrast-to-noise ratio are illustrated with simulations of human brain activation.