Data-driven haemodynamic response function extraction using Fourier-wavelet regularised deconvolution

Estimation of static and dynamic functional connectivity in resting-state fMRI using zero-frequency resonator

Resting-state functional magnetic resonance imaging (rs-fMRI) is increasingly being used to infer the functional organization of the brain. Blood oxygen level-dependent (BOLD) features related to spontaneous neuronal activity, are yet to be clearly understood. Prior studies have hypothesized that rs-fMRI is spontaneous event-related and these events convey crucial information about the neuronal activity in estimating resting state functional connectivity (FC). Attempts have been made to extract these temporal events using a predetermined threshold. However, the thresholding methods in addition to being very sensitive to noise, may consider redundant events or exclude the low-valued inflection points. Here, we extract the event-related temporal onsets from the rs-fMRI time courses using a zero-frequency resonator (ZFR). The ZFR reflects the transient behavior of the BOLD events at its output. The conditional rate (CR) of the BOLD events occurring in a time course with respect to a seed time course is used to derive static FC. The temporal activity around the estimated events called high signal-to-noise ratio (SNR) segments are also obtained in the rs-fMRI time course and are then used to compute static and dynamic FCs during rest. Coactivation pattern (CAP) is the dynamic FC obtained using the high SNR segments driven by the ZFR. The static FC demonstrates that the ZFR-based CR distinguishes the coactivation and non-coactivation scores well in the distribution. CAP analysis demonstrated the stable and longer dwell time dominant resting state functional networks with high SNR segments driven by the ZFR. Static and dynamic FC analysis underpins that the ZFR-driven temporal onsets of BOLD events derive reliable and consistent FCs in the resting brain using a subset of the time points.

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.

Preserved canonicality of the BOLD hemodynamic response reflects healthy cognition: Insights into the healthy brain through the window of Multiple Sclerosis

The hemodynamic response function (HRF), a model of brain blood-flow changes in response to neural activity, reflects communication between neurons and the vasculature that supplies these neurons in part by means of glial cell intermediaries (e.g., astrocytes). Intact neural-vascular communication might play a central role in optimal cognitive performance. This hypothesis can be tested by comparing healthy individuals to those with known white-matter damage and impaired performance, as seen in Multiple Sclerosis (MS). Glial cell intermediaries facilitate the ability of neurons to adequately convey metabolic needs to cerebral vasculature for sufficient oxygen and nutrient perfusion. In this study, we isolated measurements of the HRF that could quantify the extent to which white-matter affects neural-vascular coupling and cognitive performance. HRFs were modeled from multiple brain regions during multiple cognitive tasks using piecewise cubic spline functions, an approach that minimized assumptions regarding HRF shape that may not be valid for diseased populations, and were characterized using two shape metrics (peak amplitude and time-to-peak). Peak amplitude was reduced, and time-to-peak was longer, in MS patients relative to healthy controls. Faster time-to-peak was predicted by faster reaction time, suggesting an important role for vasodilatory speed in the physiology underlying processing speed. These results support the hypothesis that intact neural-glial-vascular communication underlies optimal neural and cognitive functioning.

Identification of neurovascular changes associated with cerebral amyloid angiopathy from subject-specific hemodynamic response functions

Cerebral amyloid angiopathy (CAA) is a small-vessel disease preferentially affecting posterior brain regions. Recent evidence has demonstrated the efficacy of functional MRI in detecting CAA-related neurovascular injury, however, it is unknown whether such perturbations are associated with changes in the hemodynamic response function (HRF). Here we estimated HRFs from two different brain regions from block design activation data, in light of recent findings demonstrating how block designs can accurately reflect HRF parameter estimates while maximizing signal detection. Patients with a diagnosis of probable CAA and healthy controls performed motor and visual stimulation tasks. Time-to-peak (TTP), full-width at half-maximum (FWHM), and area under the curve (AUC) of the estimated HRFs were compared between groups and to MRI features associated with CAA including cerebral microbleed (CMB) count. Motor HRFs in CAA patients showed significantly wider FWHM ( P = 0.006) and delayed TTP ( P = 0.03) compared to controls. In the patient group, visual HRF FWHM was positively associated with CMB count ( P = 0.03). These findings indicate that hemodynamic abnormalities in patients with CAA may be reflected in HRFs estimated from block designs across different brain regions. Moreover, visual FWHM may be linked to structural MR indications associated with CAA.

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.

A method to analyze low signal-to-noise ratio functional magnetic resonance imaging data

The current practice of using a single, representative hemodynamic response function (canonical HRF) to model functional magnetic resonance imaging (fMRI) data is questionable given the trial-to-trial variability of the brain's responses. In addition, the changes in blood-oxygenation level due to sensory stimulation may be small, especially when auditory stimuli are used. Here we introduce a correlation-based single trial analysis method for fMRI data analysis to deal with the low signal-to-noise (SNR) ratio and variability of the HRF in response to repeated, identical auditory stimuli. The correlation technique identifies the "active" trials, i.e., those showing a robust hemodynamic response among all single trials. Using data collected from 14 healthy subjects, it was found that the correlation method can find significant differences between brain areas and brain states in actual fMRI data. Also, the correlation-based method confirmed that the superior temporal gyrus (STG), inferior frontal gyrus (IFG), dorsolateral prefrontal cortex (DLPFC) and thalamus (THA) are involved in auditory information processing in general, and the involvement of the bilateral STG, right THA and left DLPFC in sensory gating. In contrast, conventional analysis failed to find any regions involved in sensory gating. The findings suggest that our single trial analysis method can increase the sensitivity of fMRI data analysis.

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.

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.

Fractional-order time series models for extracting the haemodynamic response from functional magnetic resonance imaging data

The postprocessing of functional magnetic resonance imaging (fMRI) data to study the brain functions deals mainly with two objectives: signal detection and extraction of the haemodynamic response. Signal detection consists of exploring and detecting those areas of the brain that are triggered due to an external stimulus. Extraction of the haemodynamic response deals with describing and measuring the physiological process of activated regions in the brain due to stimulus. The haemodynamic response represents the change in oxygen levels since the brain functions require more glucose and oxygen upon stimulus that implies a change in blood flow. In the literature, different approaches to estimate and model the haemodynamic response have been proposed. These approaches can be discriminated in model structures that either provide a proper representation of the obtained measurements but provide no or a limited amount of physiological information, or provide physiological insight but lacks a proper fit to the data. In this paper, a novel model structure is studied for describing the haemodynamics in fMRI measurements: fractional models. We show that these models are flexible enough to describe the gathered data with the additional merit of providing physiological information.

TWave: high-order analysis of functional MRI

The traditional approach to functional image analysis models images as matrices of raw voxel intensity values. Although such a representation is widely utilized and heavily entrenched both within neuroimaging and in the wider data mining community, the strong interactions among space, time, and categorical modes such as subject and experimental task inherent in functional imaging yield a dataset with "high-order" structure, which matrix models are incapable of exploiting. Reasoning across all of these modes of data concurrently requires a high-order model capable of representing relationships between all modes of the data in tandem. We thus propose to model functional MRI data using tensors, which are high-order generalizations of matrices equivalent to multidimensional arrays or data cubes. However, several unique challenges exist in the high-order analysis of functional medical data: naïve tensor models are incapable of exploiting spatiotemporal locality patterns, standard tensor analysis techniques exhibit poor efficiency, and mixtures of numeric and categorical modes of data are very often present in neuroimaging experiments. Formulating the problem of image clustering as a form of Latent Semantic Analysis and using the WaveCluster algorithm as a baseline, we propose a comprehensive hybrid tensor and wavelet framework for clustering, concept discovery, and compression of functional medical images which successfully addresses these challenges. Our approach reduced runtime and dataset size on a 9.3GB finger opposition motor task fMRI dataset by up to 98% while exhibiting improved spatiotemporal coherence relative to standard tensor, wavelet, and voxel-based approaches. Our clustering technique was capable of automatically differentiating between the frontal areas of the brain responsible for task-related habituation and the motor regions responsible for executing the motor task, in contrast to a widely used fMRI analysis program, SPM, which only detected the latter region. Furthermore, our approach discovered latent concepts suggestive of subject handedness nearly 100× faster than standard approaches. These results suggest that a high-order model is an integral component to accurate scalable functional neuroimaging.

Time series fMRI measures detect changes in pontine raphé following acute tryptophan depletion

Serotonin is synthesized from its precursor, tryptophan, by brainstem raphé neurons and their synaptic terminals in limbic regions. The omission of tryptophan from an Acute Tryptophan Depletion (ATD) diet transiently diminishes serotonin synthesis, alters raphé activity, and mimics symptoms of depression. Raphé functional magnetic resonance imaging (fMRI) poses challenges using signal-averaging analyses. Time-series properties of fMRI blood oxygenation level dependent (BOLD) signals may hold promise, so we analyzed raphé signals for changes with the ATD diet. Eleven remitted (previously depressed) patients were awake with eyes-closed during seven-minute resting scans with 0.5s(-1) sampling. BOLD signal time-series data were frequency-filtered using wavelet transforms, yielding three octave-width frequency bands from 0.25 to 0.03s(-1) and an unbounded band below 0.03s(-1). Spectral power, reflecting signal information, increased in pontine raphé at high frequencies (0.25 to 0.125s(-1)) during ATD (compared to control, balanced, diet, P<0.004) but was unchanged at other frequencies. Functional connectivity, the correlation between time-series data from pairs of regions, weakened between pontine raphé and anterior thalamus at low frequencies during ATD (P<0.05). This preliminarily supports using fMRI time-series features to assess pontine raphé function. Whether, and how, high frequency activity oscillations interfere with low frequency signaling requires further study.

Relating BOLD fMRI and neural oscillations through convolution and optimal linear weighting

The exact relationship between neural activity and BOLD fMRI is unknown. However, several recent findings, recorded invasively in both humans and monkeys, show a positive correlation of BOLD to high-frequency (30-150 Hz) oscillatory power changes and a negative correlation to low-frequency (8-30 Hz) power changes arising from cortical areas. In this study, we computed the time series correlation between BOLD GE-EPI fMRI at 7 T and neural activity measures from noninvasive MEG, using a time-frequency beam former for source localisation. A sinusoidal drifting grating was presented visually for 4 s followed by a 20 s rest period in both recording modalities. The MEG time series were convolved with either a measured or canonical haemodynamic response function (HRF) for comparison with the measured BOLD data, and the BOLD data were deconvolved with either a measured or a canonical HRF for comparison with the measured MEG. In the visual cortex, the higher frequencies (mid-gamma=52-75 Hz and high-gamma=75-98 Hz) were positively correlated with BOLD whilst the lower frequencies (alpha=8-12 Hz and beta=12-25 Hz) were negatively correlated with BOLD. Furthermore, regression including all frequency bands predicted BOLD better than stimulus timing alone, although no individual frequency band predicted BOLD as well as stimulus timing. For this paradigm, there was, in general, no difference between using the SPM canonical HRF compared to the subject-specific measured HRF. In conclusion, MEG replicates findings from invasive recordings with regard to time series correlations with BOLD data. Conversely, deconvolution of BOLD data provides a neural estimate which correlates well with measured neural effects as a function of neural oscillation frequency.