Estimation Of Hemodynamic Response Function Research Articles

BOLD Response is more than just magnitude: Improving detection sensitivity through capturing hemodynamic profiles

Typical fMRI analyses often assume a canonical hemodynamic response function (HRF) that primarily focuses on the peak height of the overshoot, neglecting other morphological aspects. Consequently, reported analyses often reduce the overall response curve to a single scalar value. In this study, we take a data-driven approach to HRF estimation at the whole-brain voxel level, without assuming a response profile at the individual level. We then employ a roughness penalty at the population level to estimate the response curve, aiming to enhance predictive accuracy, inferential efficiency, and cross-study reproducibility. By examining a fast event-related FMRI dataset, we demonstrate the shortcomings and information loss associated with adopting the canonical approach. Furthermore, we address the following key questions: 1) To what extent does the HRF shape vary across different regions, conditions, and participant groups? 2) Does the data-driven approach improve detection sensitivity compared to the canonical approach? 3) Can analyzing the HRF shape help validate the presence of an effect in conjunction with statistical evidence? 4) Does analyzing the HRF shape offer evidence for whole-brain response during a simple task?

Modeling the Hemodynamic Response Function Using EEG-fMRI Data During Eyes-Open Resting-State Conditions and Motor Task Execution

Being able to accurately quantify the hemodynamic response function (HRF) that links the blood oxygen level dependent functional magnetic resonance imaging (BOLD-fMRI) signal to the underlying neural activity is important both for elucidating neurovascular coupling mechanisms and improving the accuracy of fMRI-based functional connectivity analyses. In particular, HRF estimation using BOLD-fMRI is challenging particularly in the case of resting-state data, due to the absence of information about the underlying neuronal dynamics. To this end, using simultaneously recorded electroencephalography (EEG) and fMRI data is a promising approach, as EEG provides a more direct measure of neural activations. In the present work, we employ simultaneous EEG-fMRI to investigate the regional characteristics of the HRF using measurements acquired during resting conditions. We propose a novel methodological approach based on combining distributed EEG source space reconstruction, which improves the spatial resolution of HRF estimation and using block-structured linear and nonlinear models, which enables us to simultaneously obtain HRF estimates and the contribution of different EEG frequency bands. Our results suggest that the dynamics of the resting-state BOLD signal can be sufficiently described using linear models and that the contribution of each band is region specific. Specifically, it was found that sensory-motor cortices exhibit positive HRF shapes, whereas the lateral occipital cortex and areas in the parietal cortex, such as the inferior and superior parietal lobule exhibit negative HRF shapes. To validate the proposed method, we repeated the analysis using simultaneous EEG-fMRI measurements acquired during execution of a unimanual hand-grip task. Our results reveal significant associations between BOLD signal variations and electrophysiological power fluctuations in the ipsilateral primary motor cortex, particularly for the EEG beta band, in agreement with previous studies in the literature.

A deep convolutional neural network for estimating hemodynamic response function with reduction of motion artifacts in fNIRS

Objective. Functional near-infrared spectroscopy (fNIRS) is a neuroimaging technique for monitoring hemoglobin concentration changes in a non-invasive manner. However, subject movements are often significant sources of artifacts. While several methods have been developed for suppressing this confounding noise, the conventional techniques have limitations on optimal selections of model parameters across participants or brain regions. To address this shortcoming, we aim to propose a method based on a deep convolutional neural network (CNN). Approach. The U-net is employed as a CNN architecture. Specifically, large-scale training and testing data are generated by combining variants of hemodynamic response function (HRF) with experimental measurements of motion noises. The neural network is then trained to reconstruct hemodynamic response coupled to neuronal activity with a reduction of motion artifacts. Main results. Using extensive analysis, we show that the proposed method estimates the task-related HRF more accurately than the existing methods of wavelet decomposition and autoregressive models. Specifically, the mean squared error and variance of HRF estimates, based on the CNN, are the smallest among all methods considered in this study. These results are more prominent when the semi-simulated data contain variants of shapes and amplitudes of HRF. Significance. The proposed CNN method allows for accurately estimating amplitude and shape of HRF with significant reduction of motion artifacts. This method may have a great potential for monitoring HRF changes in real-life settings that involve excessive motion artifacts.

RsHRF: A toolbox for resting-state HRF estimation and deconvolution

The hemodynamic response function (HRF) greatly influences the intra- and inter-subject variability of brain activation and connectivity, and might confound the estimation of temporal precedence in connectivity analyses, making its estimation necessary for a correct interpretation of neuroimaging studies. Additionally, the HRF shape itself is a useful local measure. However, most algorithms for HRF estimation are specific for task-related fMRI data, and only a few can be directly applied to resting-state protocols. Here we introduce rsHRF, a Matlab and Python toolbox that implements HRF estimation and deconvolution from the resting-state BOLD signal. We first provide an overview of the main algorithm, practical implementations, and then demonstrate the feasibility and usefulness of rsHRF by validation experiments with a publicly available resting-state fMRI dataset. We also provide tools for statistical analyses and visualization. We believe that this toolbox may significantly contribute to a better analysis and understanding of the components and variability of BOLD signals.

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.

Robust Hemodynamic Response Function Estimation From fNIRS Signals

Hemodynamic response function (HRF) estimation in functional near-infrared spectroscopy (fNIRS) plays an important role in characterizing the temporal dynamics of the brain response. Estimation based on semiparametric modeling is very useful for fNIRS signals. However, the Gaussian noise assumption may be too simplistic since the sources of noise and their nature are various in fNIRS. In this paper, the problem of HRF estimation using a semiparametric model whose nonparametric part is viewed as a nuisance component used to represent the drift is considered. A new robust HRF estimation procedure to minimize the impact of unexpected noise in fNIRS signals is developed. Within the proposed estimation method, the drift effect is removed by applying a first order difference to the fNIRS signal samples. Consistency and asymptotic normality of the proposed estimator are established and its effectiveness is illustrated on both simulated and real fNIRS data.

Hemodynamic Response Function Modeling to Determine the Areas with High Blood Supply in Block-Design fMRI Experiments

Background: Determining the activated brain areas due to different activities is one of the most common targets in functional magnetic resonance imaging (fMRI) data analysis, which could be carried out by hemodynamic response function (HRF) evaluation. The HR functions reflect changes of cerebral blood flow (CBF) in response to neural activity. Objectives: In this study, five models of HRF estimation were evaluated based on a simulated dataset. Models with higher accuracy were used to determine HRF parameters of the block-design fMRI data. Methods: The fMRI data were acquired in a 3 Tesla scanner. For block-design fMR imaging, CO2 gas was administered using a face-mask under physiological monitoring. Three patients with brain tumors were scanned. The fMRI data analysis was performed using the SPM 12 MATLAB toolbox. Akaike’s information criterion (AIC), Schwarz’ Bayesian (SBC), and mean square error (MSE) criteria were used to select the best HRF estimation model. Results: In simulation studies, the estimated HRFs by the canonical HRF plus its temporal derivative (TD), finite impulse response (FIR), and inverse logistic (IL) models were almost equal to the standard HRF. Mean square error, AIC, and SBC indices were ignorable for TD, FIR, and IL models (MSE/AIC/SBC magnitudes for TD, FIR, and IL models were 0.052/-1235.1/-1223.9, 0.055/-1206.4/-1194.9, and 0.068/-1091.5/-1049.2, respectively), which indicates that these models could accurately estimate HRF in block design fMRI studies. Conclusions: The HRF models could non-invasively evaluate the change of MR signal intensity under cerebrovascular reactivity (CVR) conditions and they might be helpful to investigate changes in human cerebral blood flow.

Estimation of Hemodynamic Response Function in the Brain and Brain Tumors: Comparison of Inverse Logistic and Canonical Hemodynamic Response Function Models

Estimation of Hemodynamic Response Function in the Brain and Brain Tumors: Comparison of Inverse Logistic and Canonical Hemodynamic Response Function Models

Motion artifact detection and correction in functional near-infrared spectroscopy: a new hybrid method based on spline interpolation method and Savitzky-Golay filtering.

Motion artifact contamination in near-infrared spectroscopy (NIRS) data has become an important challenge in realizing the full potential of NIRS for real-life applications. Various motion correction algorithms have been used to alleviate the effect of motion artifacts on the estimation of the hemodynamic response function. While smoothing methods, such as wavelet filtering, are excellent in removing motion-induced sharp spikes, the baseline shifts in the signal remain after this type of filtering. Methods, such as spline interpolation, on the other hand, can properly correct baseline shifts; however, they leave residual high-frequency spikes. We propose a hybrid method that takes advantage of different correction algorithms. This method first identifies the baseline shifts and corrects them using a spline interpolation method or targeted principal component analysis. The remaining spikes, on the other hand, are corrected by smoothing methods: Savitzky-Golay (SG) filtering or robust locally weighted regression and smoothing. We have compared our new approach with the existing correction algorithms in terms of hemodynamic response function estimation using the following metrics: mean-squared error, peak-to-peak error ([Formula: see text]), Pearson's correlation ([Formula: see text]), and the area under the receiver operator characteristic curve. We found that spline-SG hybrid method provides reasonable improvements in all these metrics with a relatively short computational time. The dataset and the code used in this study are made available online for the use of all interested researchers.

Effect of confounding variables on hemodynamic response function estimation using averaging and deconvolution analysis: An event-related NIRS study

Slow and rapid event-related designs are used in fMRI and functional near-infrared spectroscopy (fNIRS) experiments to temporally characterize the brain hemodynamic response to discrete events. Conventional averaging (CA) and the deconvolution method (DM) are the two techniques commonly used to estimate the Hemodynamic Response Function (HRF) profile in event-related designs. In this study, we conducted a series of simulations using synthetic and real NIRS data to examine the effect of the main confounding factors, including event sequence timing parameters, different types of noise, signal-to-noise ratio (SNR), temporal autocorrelation and temporal filtering on the performance of these techniques in slow and rapid event-related designs. We also compared systematic errors in the estimates of the fitted HRF amplitude, latency and duration for both techniques. We further compared the performance of deconvolution methods based on Finite Impulse Response (FIR) basis functions and gamma basis sets.Our results demonstrate that DM was much less sensitive to confounding factors than CA. Event timing was the main parameter largely affecting the accuracy of CA. In slow event-related designs, deconvolution methods provided similar results to those obtained by CA. In rapid event-related designs, our results showed that DM outperformed CA for all SNR, especially above -5 dB regardless of the event sequence timing and the dynamics of background NIRS activity. Our results also show that periodic low-frequency systemic hemodynamic fluctuations as well as phase-locked noise can markedly obscure hemodynamic evoked responses. Temporal autocorrelation also affected the performance of both techniques by inducing distortions in the time profile of the estimated hemodynamic response with inflated t-statistics, especially at low SNRs. We also found that high-pass temporal filtering could substantially affect the performance of both techniques by removing the low-frequency components of HRF profiles.Our results emphasize the importance of characterization of event timing, background noise and SNR when estimating HRF profiles using CA and DM in event-related designs.

FMRI hemodynamic response function estimation in autoregressive noise by avoiding the drift

The measured functional magnetic resonance imaging (fMRI) time series is typically corrupted by instrumental drift and physiological noise due to respiration and heartbeat giving rise to temporal correlation in the signals. Most methods proposed so far for nonparametric hemodynamic response function (HRF) estimation in fMRI data do not account for these confounding effects, and thus produce biased and inefficient estimates. The aim of this paper is to address this issue by modeling the noise in fMRI time series using an autoregressive model of order p (AR(p)). Making use of a semiparametric model to characterize the fMRI time series and the AR(p) to model the temporally correlated noise, a generalized least squares (GLS) estimator for voxelwise consistent nonparametric HRF estimation is derived. The proposed estimation method is a three-stage procedure that relies on first-order differencing to remove drift and a novel structured covariance estimator for the AR noise based on Cholesky decomposition to derive the best linear unbiased estimator (BLUE) of the HRF. We also establish the asymptotic consistency of the proposed estimator. Simulation results show that the proposed method generates more accurate HRF estimates compared to existing methods. When applied to real fMRI data, it demonstrates the effectiveness in uncovering the brain response temporal dynamics for both event-related and block-design paradigms. Our approach removes the two types of noise in fMRI data simultaneously, thus providing efficient estimation of brain hemodynamic responses, while allowing for flexible characterization of the shape and timing of the voxelwise HRF.

Data-driven HRF estimation for encoding and decoding models

Despite the common usage of a canonical, data-independent, hemodynamic response function (HRF), it is known that the shape of the HRF varies across brain regions and subjects. This suggests that a data-driven estimation of this function could lead to more statistical power when modeling BOLD fMRI data. However, unconstrained estimation of the HRF can yield highly unstable results when the number of free parameters is large. We develop a method for the joint estimation of activation and HRF by means of a rank constraint, forcing the estimated HRF to be equal across events or experimental conditions, yet permitting it to differ across voxels. Model estimation leads to an optimization problem that we propose to solve with an efficient quasi-Newton method, exploiting fast gradient computations. This model, called GLM with Rank-1 constraint (R1-GLM), can be extended to the setting of GLM with separate designs which has been shown to improve decoding accuracy in brain activity decoding experiments. We compare 10 different HRF modeling methods in terms of encoding and decoding scores on two different datasets. Our results show that the R1-GLM model outperforms competing methods in both encoding and decoding settings, positioning it as an attractive method both from the points of view of accuracy and computational efficiency.

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.

Joint maximum likelihood estimation of activation and Hemodynamic Response Function for fMRI.

Blood Oxygen Level Dependent (BOLD) functional magnetic resonance imaging (fMRI) maps the brain activity by measuring blood oxygenation level, which is related to brain activity via a temporal impulse response function known as the Hemodynamic Response Function (HRF). The HRF varies from subject to subject and within areas of the brain, therefore a knowledge of HRF is necessary for accurately computing voxel activations. Conversely a knowledge of active voxels is highly beneficial for estimating the HRF. This work presents a joint maximum likelihood estimation of HRF and activation based on low-rank matrix approximations operating on regions of interest (ROI). Since each ROI has limited data, a smoothing constraint on the HRF is employed via Tikhonov regularization. The method is analyzed under both white noise and colored noise. Experiments with synthetic data show that accurate estimation of the HRF is possible with this method without prior assumptions on the exact shape of the HRF. Further experiments involving real fMRI experiments with auditory stimuli are used to validate the proposed method.

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).

Effects of perceptual load on population receptive fields

Perceptual load at fixation reduces detection performance for peripheral stimuli and the neural responses they evoke. Here we used functional MRI and population receptive field (pRF) mapping (Dumoulin, 2008, NeuroImage, 39(2), 647-60) to test whether foveal load changes the spatial tuning functions of voxels in human V1-3. Participants (n=28) performed a fixation task at the centre of the screen (Schwartz, 2005, Cereb Cortex, 15(6), 770-786) while dynamic, high-contrast bar stimuli traversed the visual field. Each participant completed 4-8 mapping scan runs. High and low load fixation tasks alternated between runs (n=14) or once per run (n=14). Additionally, each participant completed two scan runs to estimate their individual hemodynamic response function (HRF) under either condition. We used the resulting HRF estimates for high and low perceptual load to generate predictions for the time series of respective mapping runs. Predictions were based on the assumption of two-dimensional Gaussian pRFs. We estimated pRF centre position and size according to the best fit between predictions and actual data. High perceptual load at fixation increased pRF sizes in para-foveal V1-3 (~3-6 degrees eccentricity). Additionally, the eccentricity of foveal pRFs in V1-3 (up to ~1 degree eccentricity) was pulled outwards. Thus, high attentional demand at central fixation yielded a blurring effect on representations outside the central visual field and a centrifugal effect for the representation of mapping stimuli very close to the task stimuli. These effects may reflect the competition between the representation of central target and task-irrelevant mapping stimuli. They indicate that attention changes the spatial tuning properties of pRFs. This could be a physiological mechanism for early attentional selection under high perceptual load, as suggested by Lavie’s load theory (Lavie, 2005, TiCS, 9(2), 75-82). Meeting abstract presented at VSS 2013

A Mixed L2 Norm Regularized HRF Estimation Method for Rapid Event-Related fMRI Experiments

Brain state decoding or “mind reading” via multivoxel pattern analysis (MVPA) has become a popular focus of functional magnetic resonance imaging (fMRI) studies. In brain decoding, stimulus presentation rate is increased as fast as possible to collect many training samples and obtain an effective and reliable classifier or computational model. However, for extremely rapid event-related experiments, the blood-oxygen-level-dependent (BOLD) signals evoked by adjacent trials are heavily overlapped in the time domain. Thus, identifying trial-specific BOLD responses is difficult. In addition, voxel-specific hemodynamic response function (HRF), which is useful in MVPA, should be used in estimation to decrease the loss of weak information across voxels and obtain fine-grained spatial information. Regularization methods have been widely used to increase the efficiency of HRF estimates. In this study, we propose a regularization framework called mixed L2 norm regularization. This framework involves Tikhonov regularization and an additional L2 norm regularization term to calculate reliable HRF estimates. This technique improves the accuracy of HRF estimates and significantly increases the classification accuracy of the brain decoding task when applied to a rapid event-related four-category object classification experiment. At last, some essential issues such as the impact of low-frequency fluctuation (LFF) and the influence of smoothing are discussed for rapid event-related experiments.

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.

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.

Regularized estimation of hemodynamic response function for fMRI data

One of the primary goals in analyzing fMRI data is to estimate the Hemodynamic Response Function (HRF), which is a large-dimensional parameter vector possessing some form of sparsity. This paper introduces a varyingdimensional model for the HRF, and develops novel regularization methods for estimating the HRF from fMRI time series via incorporating the sparsity feature. Particularly, we present three types of penalty choice methods: the Lasso, the adaptive Lasso and the SCAD. Simulation studies demonstrate the advantages of regularization methods, in terms of sparsity recovery, over conventional non-regularized approaches which restrict the HRF to be fixed low dimensional without capturing the sparsity structure. We illustrate the regularized methods for estimating the HRF using a real fMRI data set and compare with results offered by a popular imaging analysis tool AFNI.