Neuronal event detection in fMRI time series using iterative deconvolution techniques

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.

Comparison of hemodynamic response functions obtained from resting-state functional MRI and invasive electrophysiological recordings in rats

Resting-state functional MRI (rs-fMRI) is a popular technology that has enriched our understanding of brain and spinal cord functioning, including how different regions communicate (connectivity). But fMRI is an indirect measure of neural activity capturing blood hemodynamics. The hemodynamic response function (HRF) interfaces between the unmeasured neural activity and measured fMRI time series. The HRF is variable across brain regions and individuals, and is modulated by non-neural factors. Ignoring this HRF variability causes errors in FC estimates. Hence, it is crucial to reliably estimate the HRF from rs-fMRI data. Robust techniques have emerged to estimate the HRF from fMRI time series. Although such techniques have been validated non-invasively using simulated and empirical fMRI data, thorough invasive validation using simultaneous electrophysiological recordings, the gold standard, has been elusive. This report addresses this gap in the literature by comparing HRFs derived from invasive intracranial electroencephalogram recordings with HRFs estimated from simultaneously acquired fMRI data in six epileptic rats. We found that the HRF shape parameters (HRF amplitude, latency and width) were not significantly different (p>0.05) between ground truth and estimated HRFs. In the single pathological region, the HRF width was marginally significantly different (p=0.03). Our study provides preliminary invasive validation for the efficacy of the HRF estimation technique in reliably estimating the HRF non-invasively from rs-fMRI data directly. This has a notable impact on rs-fMRI connectivity studies, and we recommend that HRF deconvolution be performed to minimize HRF variability and improve connectivity estimates.

The confound of hemodynamic response function variability in human resting-state functional MRI studies

Functional magnetic resonance imaging (fMRI) is an indirect measure of neural activity with the hemodynamic response function (HRF) coupling it with unmeasured neural activity. The HRF, modulated by several non-neural factors, is variable across brain regions, individuals and populations. Yet, a majority of human resting-state fMRI connectivity studies continue to assume a non-variable HRF. In this article, with supportive prior evidence, we argue that HRF variability cannot be ignored as it substantially confounds within-subject connectivity estimates and between-subjects connectivity group differences. We also discuss its clinical relevance with connectivity impairments confounded by HRF aberrations in several disorders. We present limited data on HRF differences between women and men, which resulted in a 15.4% median error in functional connectivity estimates in a group-level comparison. We also discuss the implications of HRF variability for fMRI studies in the spinal cord. There is a need for more dialogue within the community on the HRF confound, and we hope that our article is a catalyst in the process.

An Anisotropic 4D Filtering Approach to Recover Brain Activation From Paradigm-Free Functional MRI Data

CONTEXT

Functional Magnetic Resonance Imaging (fMRI) is a non-invasive imaging technique that provides an indirect view into brain activity via the blood oxygen level dependent (BOLD) response. In particular, resting-state fMRI poses challenges to the recovery of brain activity without prior knowledge on the experimental paradigm, as it is the case for task fMRI. Conventional methods to infer brain activity from the fMRI signals, for example, the general linear model (GLM), require the knowledge of the experimental paradigm to define regressors and estimate the contribution of each voxel's time course to the task. To overcome this limitation, approaches to deconvolve the BOLD response and recover the underlying neural activations without a priori information on the task have been proposed. State-of-the-art techniques, and in particular the total activation (TA), formulate the deconvolution as an optimization problem with decoupled spatial and temporal regularization and an optimization strategy that alternates between the constraints.

APPROACH

In this work, we propose a paradigm-free regularization algorithm named Anisotropic 4D-fMRI (A4D-fMRI) that is applied on the 4D fMRI image, acting simultaneously in the 3D space and 1D time dimensions. Based on the idea that large image variations should be preserved as they occur during brain activations, whereas small variations considered as noise should be removed, the A4D-fMRI applies an anisotropic regularization, thus recovering the location and the duration of brain activations.

RESULTS

Using the experimental paradigm as ground truth, the A4D-fMRI is validated on synthetic and real task-fMRI data from 51 subjects, and its performance is compared to the TA. Results show higher correlations of the recovered time courses with the ground truth compared to the TA and lower computational times. In addition, we show that the A4D-fMRI recovers activity that agrees with the GLM, without requiring or using any knowledge of the experimental paradigm.

Multivariate semi-blind deconvolution of fMRI time series

Whole brain estimation of the haemodynamic response function (HRF) in functional magnetic resonance imaging (fMRI) is critical to get insight on the global status of the neurovascular coupling of an individual in healthy or pathological condition. Most of existing approaches in the literature works on task-fMRI data and relies on the experimental paradigm as a surrogate of neural activity, hence remaining inoperative on resting-stage fMRI (rs-fMRI) data. To cope with this issue, recent works have performed either a two-step analysis to detect large neural events and then characterize the HRF shape or a joint estimation of both the neural and haemodynamic components in an univariate fashion. In this work, we express the neural activity signals as a combination of piece-wise constant temporal atoms associated with sparse spatial maps and introduce an haemodynamic parcellation of the brain featuring a temporally dilated version of a given HRF model in each parcel with unknown dilation parameters. We formulate the joint estimation of the HRF shapes and spatio-temporal neural representations as a multivariate semi-blind deconvolution problem in a paradigm-free setting and introduce constraints inspired from the dictionary learning literature to ease its identifiability. A fast alternating minimization algorithm, along with its efficient implementation, is proposed and validated on both synthetic and real rs-fMRI data at the subject level. To demonstrate its significance at the population level, we apply this new framework to the UK Biobank data set, first for the discrimination of haemodynamic territories between balanced groups (n=24 individuals in each) patients with an history of stroke and healthy controls and second, for the analysis of normal aging on the neurovascular coupling. Overall, we statistically demonstrate that a pathology like stroke or a condition like normal brain aging induce longer haemodynamic delays in certain brain areas (e.g. Willis polygon, occipital, temporal and frontal cortices) and that this haemodynamic feature may be predictive with an accuracy of 74 % of the individual's age in a supervised classification task performed on n=459 subjects.

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.

Stability-Based Sparse Paradigm Free Mapping Algorithm for Deconvolution of Functional MRI Data

Neuronal-related activity can be estimated from functional magnetic resonance imaging (fMRI) data with no knowledge of the timings of blood oxygenation level-dependent (BOLD) events by means of deconvolution with regularized least-squares. This work proposes two improvements on the deconvolution algorithm of sparse paradigm free mapping (SPFM): a new formulation that enables the estimation of neuronal events with long, sustained activity; and the implementation of a subsampling approach based on stability selection that avoids the choice of any regularization parameter. The proposed method is evaluated on real fMRI data and compared with both the original SPFM algorithm and conventional analysis with a general linear model (GLM) that is aware of the temporal model of the neuronal-related activity. We demonstrate that the novel stability-based SPFM algorithm yields activation maps with higher resemblance to the maps obtained with GLM analyses and offers improved detection of neuronal-related events over SPFM, particularly in scenarios with low contrast-to-noise ratio.

Ant Colony Clustering for ROI Identification in Functional Magnetic Resonance Imaging

Brain network analysis using functional magnetic resonance imaging (fMRI) is a widely used technique. The first step of brain network analysis in fMRI is to detect regions of interest (ROIs). The signals from these ROIs are then used to evaluate neural networks and quantify neuronal dynamics. The two main methods to identify ROIs are based on brain atlas registration and clustering. This work proposes a bioinspired method that combines both paradigms. The method, dubbed HAnt, consists of an anatomical clustering of the signal followed by an ant clustering step. The method is evaluated empirically in both in silico and in vivo experiments. The results show a significantly better performance of the proposed approach compared to other brain parcellations obtained using purely clustering-based strategies or atlas-based parcellations.

A deconvolution algorithm for multi-echo functional MRI: Multi-echo Sparse Paradigm Free Mapping

This work introduces a novel algorithm for deconvolution of the BOLD signal in multi-echo fMRI data: Multi-echo Sparse Paradigm Free Mapping (ME-SPFM). Assuming a linear dependence of the BOLD percent signal change on the echo time (TE) and using sparsity-promoting regularized least squares estimation, ME-SPFM yields voxelwise time-varying estimates of the changes in the apparent transverse relaxation (ΔR₂^⁎) without prior knowledge of the timings of individual BOLD events. Our results in multi-echo fMRI data collected during a multi-task event-related paradigm at 3 Tesla demonstrate that the maps of R₂^⁎ changes obtained with ME-SPFM at the times of the stimulus trials show high spatial and temporal concordance with the activation maps and BOLD signals obtained with standard model-based analysis. This method yields estimates of ΔR₂^⁎ having physiologically plausible values. Owing to its ability to blindly detect events, ME-SPFM also enables us to map ΔR₂^⁎ associated with spontaneous, transient BOLD responses occurring between trials. This framework is a step towards deciphering the dynamic nature of brain activity in naturalistic paradigms, resting-state or experimental paradigms with unknown timing of the BOLD events.

Decoding fMRI events in sensorimotor motor network using sparse paradigm free mapping and activation likelihood estimates

Most functional MRI (fMRI) studies map task-driven brain activity using a block or event-related paradigm. Sparse paradigm free mapping (SPFM) can detect the onset and spatial distribution of BOLD events in the brain without prior timing information, but relating the detected events to brain function remains a challenge. In this study, we developed a decoding method for SPFM using a coordinate-based meta-analysis method of activation likelihood estimation (ALE). We defined meta-maps of statistically significant ALE values that correspond to types of events and calculated a summation overlap between the normalized meta-maps and SPFM maps. As a proof of concept, this framework was applied to relate SPFM-detected events in the sensorimotor network (SMN) to six motor functions (left/right fingers, left/right toes, swallowing, and eye blinks). We validated the framework using simultaneous electromyography (EMG)-fMRI experiments and motor tasks with short and long duration, and random interstimulus interval. The decoding scores were considerably lower for eye movements relative to other movement types tested. The average successful rate for short and long motor events were 77 ± 13% and 74 ± 16%, respectively, excluding eye movements. We found good agreement between the decoding results and EMG for most events and subjects, with a range in sensitivity between 55% and 100%, excluding eye movements. The proposed method was then used to classify the movement types of spontaneous single-trial events in the SMN during resting state, which produced an average successful rate of 22 ± 12%. Finally, this article discusses methodological implications and improvements to increase the decoding performance. Hum Brain Mapp 38:5778-5794, 2017. © 2017 Wiley Periodicals, Inc.

Effects of ageing and Alzheimer disease on haemodynamic response function: a challenge for event-related fMRI

Functional magnetic resonance imaging (fMRI) can generate brain images that show neuronal activity due to sensory, cognitive or motor tasks. Haemodynamic response function (HRF) may be considered as a biomarker to discriminate the Alzheimer disease (AD) from healthy ageing. As blood-oxygenation-level-dependent fMRI signal is much weak and noisy, particularly for the elderly subjects, a robust method is necessary for HRF estimation to efficiently differentiate the AD. After applying minimum description length wavelet as an extra denoising step, deconvolution algorithm is here employed for HRF estimation, substituting the averaging method used in the previous works. The HRF amplitude peaks are compared for three groups HRF of young, non-demented and demented elderly groups for both vision and motor regions. Prior works often reported significant differences in the HRF peak amplitude between the young and the elderly. The authors’ experimentations show that the HRF peaks are not significantly different comparing the young adults with the elderly (either demented or non-demented). It is here demonstrated that the contradictory findings of the previous studies on the HRF peaks for the elderly compared with the young are originated from the noise contribution in fMRI data.

Improving the precision of fMRI BOLD signal deconvolution with implications for connectivity analysis

An important, open problem in neuroimaging analyses is developing analytical methods that ensure precise inferences about neural activity underlying fMRI BOLD signal despite the known presence of confounds. Here, we develop and test a new meta-algorithm for conducting semi-blind (i.e., no knowledge of stimulus timings) deconvolution of the BOLD signal that estimates, via bootstrapping, both the underlying neural events driving BOLD as well as the confidence of these estimates. Our approach includes two improvements over the current best performing deconvolution approach; 1) we optimize the parametric form of the deconvolution feature space; and, 2) we pre-classify neural event estimates into two subgroups, either known or unknown, based on the confidence of the estimates prior to conducting neural event classification. This knows-what-it-knows approach significantly improves neural event classification over the current best performing algorithm, as tested in a detailed computer simulation of highly-confounded fMRI BOLD signal. We then implemented a massively parallelized version of the bootstrapping-based deconvolution algorithm and executed it on a high-performance computer to conduct large scale (i.e., voxelwise) estimation of the neural events for a group of 17 human subjects. We show that by restricting the computation of inter-regional correlation to include only those neural events estimated with high-confidence the method appeared to have higher sensitivity for identifying the default mode network compared to a standard BOLD signal correlation analysis when compared across subjects.

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.

Deconvolution filtering: temporal smoothing revisited

Inferences made from analysis of BOLD data regarding neural processes are potentially confounded by multiple competing sources: cardiac and respiratory signals, thermal effects, scanner drift, and motion-induced signal intensity changes. To address this problem, we propose deconvolution filtering, a process of systematically deconvolving and reconvolving the BOLD signal via the hemodynamic response function such that the resultant signal is composed of maximally likely neural and neurovascular signals. To test the validity of this approach, we compared the accuracy of BOLD signal variants (i.e., unfiltered, deconvolution filtered, band-pass filtered, and optimized band-pass filtered BOLD signals) in identifying useful properties of highly confounded, simulated BOLD data: (1) reconstructing the true, unconfounded BOLD signal, (2) correlation with the true, unconfounded BOLD signal, and (3) reconstructing the true functional connectivity of a three-node neural system. We also tested this approach by detecting task activation in BOLD data recorded from healthy adolescent girls (control) during an emotion processing task. Results for the estimation of functional connectivity of simulated BOLD data demonstrated that analysis (via standard estimation methods) using deconvolution filtered BOLD data achieved superior performance to analysis performed using unfiltered BOLD data and was statistically similar to well-tuned band-pass filtered BOLD data. Contrary to band-pass filtering, however, deconvolution filtering is built upon physiological arguments and has the potential, at low TR, to match the performance of an optimal band-pass filter. The results from task estimation on real BOLD data suggest that deconvolution filtering provides superior or equivalent detection of task activations relative to comparable analyses on unfiltered signals and also provides decreased variance over the estimate. In turn, these results suggest that standard preprocessing of the BOLD signal ignores significant sources of noise that can be effectively removed without damaging the underlying signal.

Decoding neural events from fMRI BOLD signal: a comparison of existing approaches and development of a new algorithm

Neuroimaging methodology predominantly relies on the blood oxygenation level dependent (BOLD) signal. While the BOLD signal is a valid measure of neuronal activity, variances in fluctuations of the BOLD signal are not only due to fluctuations in neural activity. Thus, a remaining problem in neuroimaging analyses is developing methods that ensure specific inferences about neural activity that are not confounded by unrelated sources of noise in the BOLD signal. Here, we develop and test a new algorithm for performing semiblind (i.e., no knowledge of stimulus timings) deconvolution of the BOLD signal that treats the neural event as an observable, but intermediate, probabilistic representation of the system's state. We test and compare this new algorithm against three other recent deconvolution algorithms under varied levels of autocorrelated and Gaussian noise, hemodynamic response function (HRF) misspecification and observation sampling rate. Further, we compare the algorithms' performance using two models to simulate BOLD data: a convolution of neural events with a known (or misspecified) HRF versus a biophysically accurate balloon model of hemodynamics. We also examine the algorithms' performance on real task data. The results demonstrated good performance of all algorithms, though the new algorithm generally outperformed the others (3.0% improvement) under simulated resting-state experimental conditions exhibiting multiple, realistic confounding factors (as well as 10.3% improvement on a real Stroop task). The simulations also demonstrate that the greatest negative influence on deconvolution accuracy is observation sampling rate. Practical and theoretical implications of these results for improving inferences about neural activity from fMRI BOLD signal are discussed.

Neurovascular deconvolution of optical signals as a proxy for the true neuronal inputs

Since the Kalman filter and Monte Carlo techniques, much theoretical work has been put into the development of signal deconvolution tools. Among recent developments taking place in neuroscience are Dynamic Expectation Maximization, Generalized Filtering and the Cubature Kalman Filter. While there are exciting prospects to use these tools for Dynamic Causal Modeling and other analyses of networks, there has been comparatively little work to validate the algorithms on controlled experimental data. In this work, the latest evolution of these tools, the square-root cubature Kalman smoother (SCKS), is tested for its effectiveness on multimodal neurovascular data. Multispectral intrinsic optical imaging and electrophysiological measurements of Wistar rats are used in combination with somatosensory stimulation. The Buxton-Friston (B-F) balloon model is then deconvolved with the SCKS algorithm to obtain the estimated neuronal inputs u(t) from the hemodynamic measurements (flow, oxy- and deoxygenated hemoglobin).

RESULTS

The estimated neuronal inputs are compared to the stimulation protocol and a sensitivity and specificity analysis is carried out. SCKS succeeds in recovering most of the stimulations. Next, the estimated inputs are compared to actual measures of neuronal activity: local field potentials (LFPs) and multiunit activity (MUA). Good sensitivity of the technique is obtained with both LFPs and MUA over the whole recordings, with the area of the ROC curves favoring LFPs. A weak correlation between SCKS estimated inputs and LFPs is found outside stimulation periods, significant at one standard deviation. Finally, the accuracy of state reconstructions is studied and SCKS reconstructed states are highly concordant with measured states.