Nonlinearities in rapid event-related fMRI explained by stimulus scaling

Fast Event-Related Mapping of Population Fingertip Tuning Properties in Human Sensorimotor Cortex at 7T

fMRI studies that investigate somatotopic tactile representations in the human cortex typically use either block or phase-encoded stimulation designs. Event-related (ER) designs allow for more flexible and unpredictable stimulation sequences than the other methods, but they are less efficient. Here, we compared an efficiency-optimized fast ER design (2.8-s average intertrial interval; ITI) to a conventional slow ER design (8-s average ITI) for mapping voxelwise fingertip tactile tuning properties in the sensorimotor cortex of six participants at 7 Tesla. The fast ER design yielded more reliable responses compared with the slow ER design, but with otherwise similar tuning properties. Concatenating the fast and slow ER data, we demonstrate in each individual brain the existence of two separate somatotopically-organized tactile representations of the fingertips, one in the primary somatosensory cortex (S1) on the postcentral gyrus, and the other shared across the motor and premotor cortices on the precentral gyrus. In both S1 and motor representations, fingertip selectivity decreased progressively, from narrowly-tuned Brodmann area (BA) 3b and BA4a, respectively, toward associative parietal and frontal regions that responded equally to all fingertips, suggesting increasing information integration along these two pathways. In addition, fingertip selectivity in S1 decreased from the cortical representation of the thumb to that of the pinky.

Imaging faster neural dynamics with fast fMRI: A need for updated models of the hemodynamic response

Fast fMRI enables the detection of neural dynamics over timescales of hundreds of milliseconds, suggesting it may provide a new avenue for studying subsecond neural processes in the human brain. The magnitudes of these fast fMRI dynamics are far greater than predicted by canonical models of the hemodynamic response. Several studies have established nonlinear properties of the hemodynamic response that have significant implications for fast fMRI. We first review nonlinear properties of the hemodynamic response function that may underlie fast fMRI signals. We then illustrate the breakdown of canonical hemodynamic response models in the context of fast neural dynamics. We will then argue that the canonical hemodynamic response function is not likely to reflect the BOLD response to neuronal activity driven by sparse or naturalistic stimuli or perhaps to spontaneous neuronal fluctuations in the resting state. These properties suggest that fast fMRI is capable of tracking surprisingly fast neuronal dynamics, and we discuss the neuroscientific questions that could be addressed using this approach.

Compressive Temporal Summation in Human Visual Cortex

Combining sensory inputs over space and time is fundamental to vision. Population receptive field models have been successful in characterizing spatial encoding throughout the human visual pathways. A parallel question, how visual areas in the human brain process information distributed over time, has received less attention. One challenge is that the most widely used neuroimaging method, fMRI, has coarse temporal resolution compared with the time-scale of neural dynamics. Here, via carefully controlled temporally modulated stimuli, we show that information about temporal processing can be readily derived from fMRI signal amplitudes in male and female subjects. We find that all visual areas exhibit subadditive summation, whereby responses to longer stimuli are less than the linear prediction from briefer stimuli. We also find fMRI evidence that the neural response to two stimuli is reduced for brief interstimulus intervals (indicating adaptation). These effects are more pronounced in visual areas anterior to V1-V3. Finally, we develop a general model that shows how these effects can be captured with two simple operations: temporal summation followed by a compressive nonlinearity. This model operates for arbitrary temporal stimulation patterns and provides a simple and interpretable set of computations that can be used to characterize neural response properties across the visual hierarchy. Importantly, compressive temporal summation directly parallels earlier findings of compressive spatial summation in visual cortex describing responses to stimuli distributed across space. This indicates that, for space and time, cortex uses a similar processing strategy to achieve higher-level and increasingly invariant representations of the visual world.SIGNIFICANCE STATEMENT Combining sensory inputs over time is fundamental to seeing. Two important temporal phenomena are summation, the accumulation of sensory inputs over time, and adaptation, a response reduction for repeated or sustained stimuli. We investigated these phenomena in the human visual system using fMRI. We built predictive models that operate on arbitrary temporal patterns of stimulation using two simple computations: temporal summation followed by a compressive nonlinearity. Our new temporal compressive summation model captures (1) subadditive temporal summation, and (2) adaptation. We show that the model accounts for systematic differences in these phenomena across visual areas. Finally, we show that for space and time, the visual system uses a similar strategy to achieve increasingly invariant representations of the visual world.

Using an achiasmic human visual system to quantify the relationship between the fMRI BOLD signal and neural response

Achiasma in humans causes gross mis-wiring of the retinal-fugal projection, resulting in overlapped cortical representations of left and right visual hemifields. We show that in areas V1-V3 this overlap is due to two co-located but non-interacting populations of neurons, each with a receptive field serving only one hemifield. Importantly, the two populations share the same local vascular control, resulting in a unique organization useful for quantifying the relationship between neural and fMRI BOLD responses without direct measurement of neural activity. Specifically, we can non-invasively double local neural responses by stimulating both neuronal populations with identical stimuli presented symmetrically across the vertical meridian to both visual hemifields, versus one population by stimulating in one hemifield. Measurements from a series of such doubling experiments show that the amplitude of BOLD response is proportional to approximately 0.5 power of the underlying neural response. Reanalyzing published data shows that this inferred relationship is general.

Using patient-specific hemodynamic response function in epileptic spike analysis of human epilepsy: a study based on EEG-fNIRS

Functional near-infrared spectroscopy (fNIRS) can be combined with electroencephalography (EEG) to continuously monitor the hemodynamic signal evoked by epileptic events such as seizures or interictal epileptiform discharges (IEDs, aka spikes). As estimation methods assuming a canonical shape of the hemodynamic response function (HRF) might not be optimal, we sought to model patient-specific HRF (sHRF) with a simple deconvolution approach for IED-related analysis with EEG-fNIRS data. Furthermore, a quadratic term was added to the model to account for the nonlinearity in the response when IEDs are frequent. Prior to analyzing clinical data, simulations were carried out to show that the HRF was estimable by the proposed deconvolution methods under proper conditions. EEG-fNIRS data of five patients with refractory focal epilepsy were selected due to the presence of frequent clear IEDs and their unambiguous focus localization. For each patient, both the linear sHRF and the nonlinear sHRF were estimated at each channel. Variability of the estimated sHRFs was seen across brain regions and different patients. Compared with the SPM8 canonical HRF (cHRF), including these sHRFs in the general linear model (GLM) analysis led to hemoglobin activations with higher statistical scores as well as larger spatial extents on all five patients. In particular, for patients with frequent IEDs, nonlinear sHRFs were seen to provide higher sensitivity in activation detection than linear sHRFs. These observations support using sHRFs in the analysis of IEDs with EEG-fNIRS data.

Assessing parameter identifiability for dynamic causal modeling of fMRI data

Deterministic dynamic causal modeling (DCM) for fMRI data is a sophisticated approach to analyse effective connectivity in terms of directed interactions between brain regions of interest. To date it is difficult to know if acquired fMRI data will yield precise estimation of DCM parameters. Focusing on parameter identifiability, an important prerequisite for research questions on directed connectivity, we present an approach inferring if parameters of an envisaged DCM are identifiable based on information from fMRI data. With the freely available “attention to motion” dataset, we investigate identifiability of two DCMs and show how different imaging specifications impact on identifiability. We used the profile likelihood, which has successfully been applied in systems biology, to assess the identifiability of parameters in a DCM with specified scanning parameters. Parameters are identifiable when minima of the profile likelihood as well as finite confidence intervals for the parameters exist. Intermediate epoch duration, shorter TR and longer session duration generally increased the information content in the data and thus improved identifiability. Irrespective of biological factors such as size and location of a region, attention should be paid to densely interconnected regions in a DCM, as those seem to be prone to non-identifiability. Our approach, available in the DCMident toolbox, enables to judge if the parameters of an envisaged DCM are sufficiently determined by underlying data without priors as opposed to primarily reflecting the Bayesian priors in a SPM–DCM. Assessments with the DCMident toolbox prior to a study will lead to improved identifiability of the parameters and thus might prevent suboptimal data acquisition. Thus, the toolbox can be used as a preprocessing step to provide immediate statements on parameter identifiability.

Larger neural responses produce BOLD signals that begin earlier in time

Functional MRI analyses commonly rely on the assumption that the temporal dynamics of hemodynamic response functions (HRFs) are independent of the amplitude of the neural signals that give rise to them. The validity of this assumption is particularly important for techniques that use fMRI to resolve sub-second timing distinctions between responses, in order to make inferences about the ordering of neural processes. Whether or not the detailed shape of the HRF is independent of neural response amplitude remains an open question, however. We performed experiments in which we measured responses in primary visual cortex (V1) to large, contrast-reversing checkerboards at a range of contrast levels, which should produce varying amounts of neural activity. Ten subjects (ages 22-52) were studied in each of two experiments using 3 Tesla scanners. We used rapid, 250 ms, temporal sampling (repetition time, or TR) and both short and long inter-stimulus interval (ISI) stimulus presentations. We tested for a systematic relationship between the onset of the HRF and its amplitude across conditions, and found a strong negative correlation between the two measures when stimuli were separated in time (long- and medium-ISI experiments, but not the short-ISI experiment). Thus, stimuli that produce larger neural responses, as indexed by HRF amplitude, also produced HRFs with shorter onsets. The relationship between amplitude and latency was strongest in voxels with lowest mean-normalized variance (i.e., parenchymal voxels). The onset differences observed in the longer-ISI experiments are likely attributable to mechanisms of neurovascular coupling, since they are substantially larger than reported differences in the onset of action potentials in V1 as a function of response amplitude.

Estimating neural response functions from fMRI

This paper proposes a methodology for estimating Neural Response Functions (NRFs) from fMRI data. These NRFs describe non-linear relationships between experimental stimuli and neuronal population responses. The method is based on a two-stage model comprising an NRF and a Hemodynamic Response Function (HRF) that are simultaneously fitted to fMRI data using a Bayesian optimization algorithm. This algorithm also produces a model evidence score, providing a formal model comparison method for evaluating alternative NRFs. The HRF is characterized using previously established "Balloon" and BOLD signal models. We illustrate the method with two example applications based on fMRI studies of the auditory system. In the first, we estimate the time constants of repetition suppression and facilitation, and in the second we estimate the parameters of population receptive fields in a tonotopic mapping study.

Sensitivity of BOLD response to increasing visual contrast: spin echo versus gradient echo EPI

Previous evidence showed that spin-echo (SE) BOLD signals offer an increased linearity and promptness with respect to gradient-echo (GE) acquisition, possibly providing a more accurate estimate of the amplitude of neuronal activity. However there is no evidence that the two sequences differ in representing different activation levels due to changes in stimulus intensity. In this study at 3T we compared GE and SE BOLD responses to visual stimuli at increasing contrast levels (5%, 20%, 60%, and 100%). Both sequences showed a monotonic increase of the BOLD response with stimulus contrast. While the larger sensitivity of GE yielded overall larger signal changes, step-wise increase in activation for GE was significant only when comparing 20% with 5% contrast, whereas for SE a significant increase was observed also when comparing 60% with 20% contrast. Moreover, BOLD responses normalized to the lowest contrast showed that relative increases of SE fMRI signal with increasing stimulus strength are larger with respect to the corresponding values of GE signal. This difference was observed also when excluding voxels attributed to large vessels, suggesting a non negligible role of the extravascular contribution to the modulation of SE fMRI signal with stimulus intensity. These results are shown to be in agreement with theoretical predictions that we derived from a recently proposed model of GE and SE functional signals. The present findings suggest that, despite the limited increase in functional localization accuracy at low field, SE fMRI might offer a potential advantage in distinguishing different levels of stimulus-evoked brain activity.

Mapping interictal epileptic discharges using mutual information between concurrent EEG and fMRI

OBJECTIVE

The mapping of haemodynamic changes related to interictal epileptic discharges (IED) in simultaneous electroencephalography (EEG) and functional MRI (fMRI) studies is usually carried out by means of EEG-correlated fMRI analyses where the EEG information specifies the model to test on the fMRI signal. The sensitivity and specificity critically depend on the accuracy of EEG detection and the validity of the haemodynamic model. In this study we investigated whether an information theoretic analysis based on the mutual information (MI) between the presence of epileptic activity on EEG and the fMRI data can provide further insights into the haemodynamic changes related to interictal epileptic activity. The important features of MI are that: 1) both recording modalities are treated symmetrically; 2) no requirement for a-priori models for the haemodynamic response function, or assumption of a linear relationship between the spiking activity and BOLD responses, and 3) no parametric model for the type of noise or its probability distribution is necessary for the computation of MI.

METHODS

Fourteen patients with pharmaco-resistant focal epilepsy underwent EEG-fMRI and intracranial EEG and/or surgical resection with positive postoperative outcome (seizure freedom or considerable reduction in seizure frequency) was available in 7/14 patients. We used nonparametric statistical assessment of the MI maps based on a four-dimensional wavelet packet resampling method. The results of MI were compared to the statistical parametric maps obtained with two conventional General Linear Model (GLM) analyses based on the informed basis set (canonical HRF and its temporal and dispersion derivatives) and the Finite Impulse Response (FIR) models.

RESULTS

The MI results were concordant with the electro-clinically or surgically defined epileptogenic area in 8/14 patients and showed the same degree of concordance as the results obtained with the GLM-based methods in 12 patients (7 concordant and 5 discordant). In one patient, the information theoretic analysis improved the delineation of the irritative zone compared with the GLM-based methods.

DISCUSSION

Our findings suggest that an information theoretic analysis can provide clinically relevant information about the BOLD signal changes associated with the generation and propagation of interictal epileptic discharges. The concordance between the MI, GLM and FIR maps support the validity of the assumptions adopted in GLM-based analyses of interictal epileptic activity with EEG-fMRI in such a manner that they do not significantly constrain the localization of the epileptogenic zone.

Transient and sustained components of the sensorimotor BOLD response in fMRI

Blood oxygenation level-dependent (BOLD) signal time courses in functional magnetic resonance imaging are estimated within the framework of general linear modeling by convolving an input function, that represents neural activity, with a canonical hemodynamic response function (HRF). Here we investigate the performance of different neural input functions and latency-optimized HRFs for modeling BOLD signals in response to vibrotactile somatosensory stimuli of variable durations (0.5, 1, 4, 7 s) in 14 young, healthy adults who were required to make button press responses at each stimulus cessation. Informed by electrophysiology and the behavioral task, three nested models with an increasing number of parameters were considered: a boxcar; boxcar and offset transient; and onset transient, boxcar and offset transient (TBT). The TBT model provided the best fit of the group-averaged BOLD time courses based on χ(2) and F statistics. Only the TBT model was capable of fitting the bimodal shape of the BOLD response to the 7-s stimulus and the relative peak amplitudes for all stimulus lengths in key somatosensory and motor areas. This suggests that the TBT model provides a more comprehensive description of brain sensorimotor responses in this experiment than provided by the simple boxcar model. Work comparing the activation maps obtained with the TBT model with magnetoencephalography data is under way.

Linear systems analysis of the fMRI signal

In 1995 when we began our investigations of the human visual system using fMRI, little was known about the temporal properties of the fMRI signal. Before we felt comfortable making quantitative estimates of neuronal responses with this new technique, we decided to first conduct a basic study of how the time-course of the fMRI response varied with stimulus timing and strength. The results ended up showing strong evidence that to a first approximation the hemodynamic transformation was linear in time. This was both important and remarkable: important because nearly all fMRI data analysis techniques assume or require linearity, and remarkable because the physiological basis of the hemodynamic transformation is so complex that we still have a far from complete understanding of it. In this paper, we provide highlights of the results of our original paper supporting the linear transform hypothesis. A reanalysis of the original data provides some interesting new insights into the published results. We also provide a detailed appendix describing of the properties and predictions of a linear system in time in the context of the transformation between neuronal responses and the BOLD signal.

Assessment of temporal state-dependent interactions between auditory fMRI responses to desired and undesired acoustic sources

A confounding factor in auditory functional magnetic resonance imaging (fMRI) experiments is the presence of the acoustic noise inherently associated with the echo planar imaging acquisition technique. Previous studies have demonstrated that this noise can induce unwanted neuronal responses that can mask stimulus-induced responses. Similarly, activation accumulated over multiple stimuli has been demonstrated to elevate the baseline, thus reducing the dynamic range available for subsequent responses. To best evaluate responses to auditory stimuli, it is necessary to account for the presence of all recent acoustic stimulation, beginning with an understanding of the attenuating effects brought about by interaction between and among induced unwanted neuronal responses, and responses to desired auditory stimuli. This study focuses on the characterization of the duration of this temporal memory and qualitative assessment of the associated response attenuation. Two experimental parameters--inter-stimulus interval (ISI) and repetition time (TR)--were varied during an fMRI experiment in which participants were asked to passively attend to an auditory stimulus. Results present evidence of a state-dependent interaction between induced responses. As expected, attenuating effects of these interactions become less significant as TR and ISI increase and in contrast to previous work, persist up to 18s after a stimulus presentation.

Linear coupling of undershoot with BOLD response in ER-fMRI and nonlinear BOLD response in rapid-presentation ER-fMRI

In event-related (ER) BOLD-fMRI brain activation studies, understanding the relationship between the elicited BOLD signal and its underlying neuronal activity is essential for any quantitative interpretation of the neural events from the BOLD measurements. This requires a better understanding of the dynamic BOLD response. Besides the neuronal activity-induced positive BOLD response, the dynamic response is also characterized by a profound post-stimulus undershoot. The relationship between the positive response and the post-stimulus undershoot, however, remains poorly understood. Earlier studies using block-design paradigms with long stimulation durations (>10s) do not suggest a quantitative relationship. Using an ER paradigm, this study revealed a linear coupling between the positive BOLD response and the post-stimulus undershoot across the human visual cortex. The voxelwise linear coupling across the visual cortex strongly supports a homogeneous hemodynamic response in ER paradigms, though the BOLD response magnitude varies substantially over a wide range across the visual cortex. Although underlying neuronal activity is responsible for a BOLD response, the blood volume fraction affects the magnitude of the BOLD response; the larger the blood volume fraction, the larger the magnitude. This effect needs to be accounted for in any quantitative interpretation of the BOLD measurements. In the absence of nonlinear neuronal activities, the nonlinear vascular response renders the estimated BOLD responses smaller in rapid presentation (RP) ER paradigms compared to that in ER paradigms, and this reduction effect also needs to be considered when interpreting the estimated BOLD responses in RP-ER paradigms. Interestingly, this nonlinear effect might be simply accounted for by a scaling factor across the visual cortex.

Contrast Response Functions for Single Gabor Patches: ROI-Based Analysis Over-Represents Low-Contrast Patches for GE BOLD

IMPORTANT FOR THE INTERPRETATION OF BOLD FMRI DATA IS A LINEAR RELATIONSHIP BETWEEN THE BOLD RESPONSE AND THE UNDERLYING NEURAL ACTIVITY: increased BOLD responses should reflect proportionate increases in the underlying neural activity. While previous studies have demonstrated a linear relationship between the peak amplitude of the BOLD response and neural activity in primary visual cortex (V1), these studies have used stimuli that excite large areas of cortex, and the linearity of the BOLD response has not been demonstrated when only a small patch of cortex is stimulated. The BOLD response to isolated Gabor patches of increasing contrast was measured with gradient echo (GE) BOLD and spin echo (SE) BOLD at 7 T. Our primary finding is notable spatial heterogeneity of the BOLD contrast response, particularly for the GE BOLD data, resulting in a more reliably linear relationship between BOLD data and estimated neural responses in the center of the cortical representations of the individual Gabor patches than near the edges. A control experiment with larger sinusoidal grating patches confirms that the observed sensitivity to voxel selection in the regions of interest-based analysis is unique to the small stimuli.

Statistical Analysis of fMRI Time-Series: A Critical Review of the GLM Approach

Functional magnetic resonance imaging (fMRI) is one of the most widely used tools to study the neural underpinnings of human cognition. Standard analysis of fMRI data relies on a general linear model (GLM) approach to separate stimulus induced signals from noise. Crucially, this approach relies on a number of assumptions about the data which, for inferences to be valid, must be met. The current paper reviews the GLM approach to analysis of fMRI time-series, focusing in particular on the degree to which such data abides by the assumptions of the GLM framework, and on the methods that have been developed to correct for any violation of those assumptions. Rather than biasing estimates of effect size, the major consequence of non-conformity to the assumptions is to introduce bias into estimates of the variance, thus affecting test statistics, power, and false positive rates. Furthermore, this bias can have pervasive effects on both individual subject and group-level statistics, potentially yielding qualitatively different results across replications, especially after the thresholding procedures commonly used for inference-making.

Functional magnetic resonance adaptation in visual neuroscience

Functional magnetic resonance imaging (fMRI) is a powerful non-invasive tool to investigate neuronal processing. In the last ten years a new methodological approach in the field of fMRI has been developed: fMRI adaptation. It has been found that the repetition of a stimulus leads to a decrease of the fMRI signal in the brain region that processes this stimulus. The phenomenon has been related to neuronal adaptation effects found in single-cell recordings. Since the first experiments that observed fMRI-adaptation effects, the method has been applied extensively to study various visual phenomena, such as the perception of motion, shape, objects, and orientation. The great advantage of fMRI adaptation is that it allows assessing the functional response profile of a brain region at a subvoxel level. The purpose of the current review is to evaluate the different experimental approaches used to elicit fMRI-adaptation effects. We discuss papers published in the domain of visual neuroscience that made use of fMRI-adaptation paradigms. In doing so, we focus on methodological considerations concerning experimental design, stimulus presentation and influencing factors such as awareness and attention. In the course of this review, we show that different fMRI-adaptation designs capture heterogeneous neuronal adaptation effects. As the picture of the mechanisms underlying neuronal adaptation changes from simple synaptic fatigue to complex network interactions, the concept of fMRI adaptation has to be redefined.

Modeling adaptation effects in fMRI analysis

The standard general linear model (GLM) for rapid event-related fMRI design protocols typically ignores reduction in hemodynamic responses in successive stimuli in a train due to incomplete recovery from the preceding stimuli. To capture this adaptation effect, we incorporate a region-specific adaptation model into GLM. The model quantifies the rate of adaptation across brain regions, which is of interest in neuroscience. Empirical evaluation of the proposed model demonstrates its potential to improve detection sensitivity. In the fMRI experiments using visual and auditory stimuli, we observed that the adaptation effect is significantly stronger in the visual area than in the auditory area, suggesting that we must account for this effect to avoid bias in fMRI detection.

Polarographic Electrode Measures of Cerebral Tissue Oxygenation: Implications for Functional Brain Imaging

The changes in blood flow, blood volume and oxygenation that accompany focal increases in neural activity are collectively referred to as the hemodynamic response and form the basis of non-invasive neuroimaging techniques such as blood oxygen level dependent (BOLD) functional magnetic resonance imaging. A principle factor influencing blood oxygenation, the cerebral metabolic rate of oxygen consumption is poorly understood and as such, data from imaging techniques are difficult to interpret in terms of the underlying neural activity. In particular how neurometabolic changes vary temporally, spatially and in magnitude remains uncertain. Furthermore knowledge of which aspects of neural activity are closely reflected by metabolic changes is essential for the correct interpretation of cognitive neuroscience studies in terms of information processing. Polarographic electrode measurements of cerebral tissue oxygenation in animal models following presentation of sensory stimuli have started to address these issues. Early studies demonstrated both increases and decreases in tissue oxygenation following neural activation. However a recent series of elegant studies in the cat visual system demonstrated a tight spatial and temporal coupling between evoked peri-synaptic activity and oxygen consumption following presentation of visual stimuli.