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

Estimation of neuronal task information in fMRI using zero frequency resonator

In functional magnetic resonance imaging (fMRI), temporal onsets of BOLD events contain crucial information on activity-inducing signals and make a significant impact in the analysis of functional connectivity (FC). In literature, the estimation of the onsets of the BOLD events from the acquired blood oxygen level-dependent (BOLD) signal using fMRI is mostly performed by choosing locations with a high value of the BOLD signal. This approach may give false onset points because it can incorporate redundant onsets which could be due to non-neuronal activity or can exclude true low-valued BOLD signals. In this study, we present a novel approach to estimating the temporal onsets of the BOLD events using a zero frequency resonator (ZFR) without necessitating information regarding the experimental paradigm (EP). The proposed approach exploits the impulse-like characteristic of activity-inducing signal to estimate the temporal onset points of BOLD events using ZFR which has been widely studied in the area of speech signal processing to estimate the glottal closure instances. The idea behind the approach is that an ideal neuronal impulse has, in principle, equal energy at all frequencies, including around the zero frequency, and will preserve the information of the temporal onsets of the BOLD events at its output. The ZFR-based approach estimates two important features, namely: 1) task-induced temporal onsets of the BOLD events in the fMRI time course and 2) high SNR (HSNR) regions around the estimated BOLD events. Both the estimated features are used to obtain the FC. Results are demonstrated using both the synthetic and experimental (event-related finger tapping and block design working memory) data. We show that a small number of plausible time points, estimated by ZFR, can convey sufficient information indicating the associated activation pattern. The method also illustrates its significance over the conventional correlation and threshold-based conditional rate analysis to estimate FC. The study demonstrates that ZFR-estimated BOLD events and HSNR regions can produce sufficient functionality of the brain in the task paradigm.

Deconvolution of the Functional Ultrasound Response in the Mouse Visual Pathway Using Block-Term Decomposition

Functional ultrasound (fUS) indirectly measures brain activity by detecting changes in cerebral blood volume following neural activation. Conventional approaches model such functional neuroimaging data as the convolution between an impulse response, known as the hemodynamic response function (HRF), and a binarized representation of the input signal based on the stimulus onsets, the so-called experimental paradigm (EP). However, the EP may not characterize the whole complexity of the activity-inducing signals that evoke the hemodynamic changes. Furthermore, the HRF is known to vary across brain areas and stimuli. To achieve an adaptable framework that can capture such dynamics of the brain function, we model the multivariate fUS time-series as convolutive mixtures and apply block-term decomposition on a set of lagged fUS autocorrelation matrices, revealing both the region-specific HRFs and the source signals that induce the hemodynamic responses. We test our approach on two mouse-based fUS experiments. In the first experiment, we present a single type of visual stimulus to the mouse, and deconvolve the fUS signal measured within the mouse brain's lateral geniculate nucleus, superior colliculus and visual cortex. We show that the proposed method is able to recover back the time instants at which the stimulus was displayed, and we validate the estimated region-specific HRFs based on prior studies. In the second experiment, we alter the location of the visual stimulus displayed to the mouse, and aim at differentiating the various stimulus locations over time by identifying them as separate sources.

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.

Sequential Dictionary Learning From Correlated Data: Application to fMRI Data Analysis

Sequential dictionary learning via the K-SVD algorithm has been revealed as a successful alternative to conventional data driven methods, such as independent component analysis for functional magnetic resonance imaging (fMRI) data analysis. fMRI data sets are however structured data matrices with notions of spatio-temporal correlation and temporal smoothness. This prior information has not been included in the K-SVD algorithm when applied to fMRI data analysis. In this paper, we propose three variants of the K-SVD algorithm dedicated to fMRI data analysis by accounting for this prior information. The proposed algorithms differ from the K-SVD in their sparse coding and dictionary update stages. The first two algorithms account for the known correlation structure in the fMRI data by using the squared Q, R-norm instead of the Frobenius norm for matrix approximation. The third and last algorithms account for both the known correlation structure in the fMRI data and the temporal smoothness. The temporal smoothness is incorporated in the dictionary update stage via regularization of the dictionary atoms obtained with penalization. The performance of the proposed dictionary learning algorithms is illustrated through simulations and applications on real fMRI data.

Recovering HRFs from overlapping ROIs in fMRI data using thresholding correlations for sparse dictionary learning

Recovering region-specific hemodynamic response function (HRF) in noisy fMRI data is essential to characterize the temporal dynamics of functionally coherent brain regions during activation. Data-driven techniques not based on sparsity fails to recover sub-region HRFs from overlapping regions of interest (ROIs) in task-related activations. This paper exploits spatial sparsity for recovering distinct HRFs from un-delineated overlapping ROIs in fMRI data. Spatial sparsity is realized using thresholding correlation for dictionary learning. The effectiveness of the proposed procedure is illustrated on both simulated and an experimental fMRI data obtained during a visual-task.

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.

Prewhitening High-Dimensional fMRI Data Sets Without Eigendecomposition

This letter proposes an algorithm for linear whitening that minimizes the mean squared error between the original and whitened data without using the truncated eigendecomposition (ED) of the covariance matrix of the original data. This algorithm uses Lanczos vectors to accurately approximate the major eigenvectors and eigenvalues of the covariance matrix of the original data. The major advantage of the proposed whitening approach is its low computational cost when compared with that of the truncated ED. This gain comes without sacrificing accuracy, as illustrated with an experiment of whitening a high-dimensional fMRI data set.

Functional brain connectivity as revealed by singular spectrum analysis

Correlation based measures have widely been used to characterize brain connectivity. In this paper, a new approach based on singular spectrum analysis is proposed to characterize brain connectivity. It is obtained by deriving the common basis vector of two or more trajectory matrices associated with functional brain responses. This approach has the advantage illustrating the existence of joint variations of the functional brain responses and to characterize the correlation structure. The performance of the method are illustrated on both simulated autoregressive data and real fMRI data.

Comparing causality measures of fMRI data using PCA, CCA and vector autoregressive modelling

Extracting the directional interaction between activated brain areas from functional magnetic resonance imaging (fMRI) time series measurements of their activity is a significant step in understanding the process of brain functions. In this paper, the directional interaction between fMRI time series characterizing the activity of two neuronal sites is quantified using two measures; one derived based on univariate autoregressive and autoregressive exogenous (AR/ARX) and other derived based on multivariate vector autoregressive and vector autoregressive exogenous (VAR/VARX) models. The significance and effectiveness of these measures is illustrated on both simulated and real fMRI data sets. It has been revealed that VAR modelling of the regions of interest is robust in inferring true causality compared to principal component analysis (PCA) and canonical correlation analysis (CCA) based causality methods.