fMRI activation maps based on the NN-ARx model

Arterial blood stealing as a mechanism of negative BOLD response: From the steady-flow with nonlinear phase separation to a windkessel-based model

Blood Oxygen Level Dependent (BOLD) signal indirectly characterizes neuronal activity by measuring hemodynamic and metabolic changes in the nearby microvasculature. A deeper understanding of how localized changes in electrical, metabolic and hemodynamic factors translate into a BOLD signal is crucial for the interpretation of functional brain imaging techniques. While positive BOLD responses (PBR) are widely considered to be linked with neuronal activation, the origins of negative BOLD responses (NBR) have remained largely unknown. As NBRs are sometimes observed in close proximity of regions with PBR, a blood "stealing" effect, i.e., redirection of blood from a passive periphery to the area with high neuronal activity, has been postulated. In this study, we used the Hagen-Poiseuille equation to model hemodynamics in an idealized microvascular network that account for the particulate nature of blood and nonlinearities arising from the red blood cell (RBC) distribution (i.e., the Fåhraeus, Fåhraeus-Lindqvist and the phase separation effects). Using this detailed model, we evaluate determinants driving this "stealing" effect in a microvascular network with geometric parameters within physiological ranges. Model simulations predict that during localized cerebral blood flow (CBF) increases due to neuronal activation-hyperemic response, blood from surrounding vessels is reallocated towards the activated region. This stealing effect depended on the resistance of the microvasculature and the uneven distribution of RBCs at vessel bifurcations. A parsimonious model consisting of two-connected windkessel regions sharing a supplying artery was proposed to simulate the stealing effect with a minimum number of parameters. Comparison with the detailed model showed that the parsimonious model can reproduce the observed response for hematocrit values within the physiological range for different species. Our novel parsimonious model promise to be of use for statistical inference (top-down analysis) from direct blood flow measurements (e.g., arterial spin labeling and laser Doppler/Speckle flowmetry), and when combined with theoretical models for oxygen extraction/diffusion will help account for some types of NBRs.

Identification of Negative BOLD Responses in Epilepsy Using Windkessel Models

Alongside positive blood oxygenation level–dependent (BOLD) responses associated with interictal epileptic discharges, a variety of negative BOLD responses (NBRs) are typically found in epileptic patients. Previous studies suggest that, in general, up to four mechanisms might underlie the genesis of NBRs in the brain: (i) neuronal disruption of network activity, (ii) altered balance of neurometabolic/vascular couplings, (iii) arterial blood stealing, and (iv) enhanced cortical inhibition. Detecting and classifying these mechanisms from BOLD signals are pivotal for the improvement of the specificity of the electroencephalography–functional magnetic resonance imaging (EEG-fMRI) image modality to identify the seizure-onset zones in refractory local epilepsy. This requires models with physiological interpretation that furnish the understanding of how these mechanisms are fingerprinted by their BOLD responses. Here, we used a Windkessel model with viscoelastic compliance/inductance in combination with dynamic models of both neuronal population activity and tissue/blood O₂ to classify the hemodynamic response functions (HRFs) linked to the above mechanisms in the irritative zones of epileptic patients. First, we evaluated the most relevant imprints on the BOLD response caused by variations of key model parameters. Second, we demonstrated that a general linear model is enough to accurately represent the four different types of NBRs. Third, we tested the ability of a machine learning classifier, built from a simulated ensemble of HRFs, to predict the mechanism underlying the BOLD signal from irritative zones. Cross-validation indicates that these four mechanisms can be classified from realistic fMRI BOLD signals. To demonstrate proof of concept, we applied our methodology to EEG-fMRI data from five epileptic patients undergoing neurosurgery, suggesting the presence of some of these mechanisms. We concluded that a proper identification and interpretation of NBR mechanisms in epilepsy can be performed by combining general linear models and biophysically inspired models.

Time-domain analysis for extracting fast-paced pupil responses

The eye pupil reacts to cognitive processes, but its analysis is challenging when luminance varies or when stimulation is fast-paced. Current approaches relying on deconvolution techniques do not account for the strong low-frequency spontaneous changes in pupil size or the large interindividual variability in the shape of the responses. Here a system identification framework is proposed in which the pupil responses to different parameters are extracted by means of an autoregressive model with exogenous inputs. In an example application of this technique, pupil size was shown to respond to the luminance and arousal scores of affective pictures presented in rapid succession. This result was significant in each subject (N = 5), but the pupil response varied between individuals both in amplitude and latency, highlighting the need for determining impulse responses subjectwise. The same method was also used to account for pupil size variations caused by respiration, illustrating the possibility to model the relation between pupil size and other continuous signals. In conclusion, this new framework for the analysis of pupil size data allows us to dissociate the response of the eye pupil from intermingled sources of influence and can be used to study the relation between pupil size and other physiological signals.

Identifying the default mode network structure using dynamic causal modeling on resting-state functional magnetic resonance imaging

The default mode network is part of the brain structure that shows higher neural activity and energy consumption when one is at rest. The key regions in the default mode network are highly interconnected as conveyed by both the white matter fiber tracing and the synchrony of resting-state functional magnetic resonance imaging signals. However, the causal information flow within the default mode network is still poorly understood. The current study used the dynamic causal modeling on a resting-state fMRI data set to identify the network structure underlying the default mode network. The endogenous brain fluctuations were explicitly modeled by Fourier series at the low frequency band of 0.01-0.08Hz, and those Fourier series were set as driving inputs of the DCM models. Model comparison procedures favored a model wherein the MPFC sends information to the PCC and the bilateral inferior parietal lobule sends information to both the PCC and MPFC. Further analyses provide evidence that the endogenous connectivity might be higher in the right hemisphere than in the left hemisphere. These data provided insight into the functions of each node in the DMN, and also validate the usage of DCM on resting-state fMRI data.

From gaze cueing to dual eye-tracking: novel approaches to investigate the neural correlates of gaze in social interaction

Tracking eye-movements provides easy access to cognitive processes involved in visual and sensorimotor processing. More recently, the underlying neural mechanisms have been examined by combining eye-tracking and functional neuroimaging methods. Apart from extracting visual information, gaze also serves important functions in social interactions. As a deictic cue, gaze can be used to direct the attention of another person to an object. Conversely, by following other persons' gaze we gain access to their attentional focus, which is essential for understanding their mental states. Social gaze has therefore been studied extensively to understand the social brain. In this endeavor, gaze has mostly been investigated from an observational perspective using static displays of faces and eyes. However, there is growing consent that observational paradigms are insufficient for an understanding of the neural mechanisms of social gaze behavior, which typically involve active engagement in social interactions. Recent methodological advances have allowed increasing ecological validity by studying gaze in face-to-face encounters in real-time. Such improvements include interactions using virtual agents in gaze-contingent eye-tracking paradigms, live interactions via video feeds, and dual eye-tracking in two-person setups. These novel approaches can be used to analyze brain activity related to social gaze behavior. This review introduces these methodologies and discusses recent findings on the behavioral functions and neural mechanisms of gaze processing in social interaction.

Spatio-temporal correlations from fMRI time series based on the NN-ARx model

For the purpose of statistical characterization of the spatio-temporal correlation structure of brain functioning from high-dimensional fMRI time series, we introduce an innovation approach. This is based on whitening the data by the Nearest-Neighbors AutoRegressive model with external inputs (NN-ARx). Correlations between the resulting innovations are an extension of the usual correlations, in which mean-correction is carried out by the dynamic NN-ARx model instead of the static, standard linear model for fMRI time series. Measures of dependencies between regions are defined by summarizing correlations among innovations at several time lags over pairs of voxels. Such summarization does not involve averaging the data over each region, which prevents loss of information in case of non-homogeneous regions. Statistical tests based on these measures are elaborated, which allow for assessing the correlation structure in search of connectivity. Results of application of the NN-ARx approach to fMRI data recorded in visual stimuli experiments are shown. Finally, a number of issues related with its potential and limitations are commented.

"Stay tuned": inter-individual neural synchronization during mutual gaze and joint attention

Eye contact provides a communicative link between humans, prompting joint attention. As spontaneous brain activity might have an important role in the coordination of neuronal processing within the brain, their inter-subject synchronization might occur during eye contact. To test this, we conducted simultaneous functional MRI in pairs of adults. Eye contact was maintained at baseline while the subjects engaged in real-time gaze exchange in a joint attention task. Averted gaze activated the bilateral occipital pole extending to the right posterior superior temporal sulcus, the dorso-medial prefrontal cortex, and the bilateral inferior frontal gyrus. Following a partner's gaze toward an object activated the left intraparietal sulcus. After all the task-related effects were modeled out, inter-individual correlation analysis of residual time-courses was performed. Paired subjects showed more prominent correlations than non-paired subjects in the right inferior frontal gyrus, suggesting that this region is involved in sharing intention during eye contact that provides the context for joint attention.

Identification and validation of effective connectivity networks in functional magnetic resonance imaging using switching linear dynamic systems

Dynamic connectivity networks identify directed interregional interactions between modeled brain regions in neuroimaging. However, problems arise when the regions involved in a task and their interconnections are not fully known a priori. Objective measures of model adequacy are necessary to validate such models. We present a connectivity formalism, the Switching Linear Dynamic System (SLDS), that is capable of identifying both Granger-Geweke and instantaneous connectivity that vary according to experimental conditions. SLDS explicitly models the task condition as a Markov random variable. The series of task conditions can be estimated from new data given an identified model providing a means to validate connectivity patterns. We use SLDS to model functional magnetic resonance imaging data from five regions during a finger alternation task. Using interregional connectivity alone, the identified model predicted the task condition vector from a different subject with a different task ordering with high accuracy. In addition, important regions excluded from a model can be identified by augmenting the model state space. A motor task model excluding primary motor cortices was augmented with a new neural state constrained by its connectivity with the included regions. The augmented variable time series, convolved with a hemodynamic kernel, was compared to all brain voxels. The right primary motor cortex was identified as the best region to add to the model. Our results suggest that the SLDS model framework is an effective means to address several problems with modeling connectivity including measuring overall model adequacy and identifying important regions missing from models.

Spatially adaptive mixture modeling for analysis of FMRI time series

Within-subject analysis in fMRI essentially addresses two problems, the detection of brain regions eliciting evoked activity and the estimation of the underlying dynamics. In Makni et aL, 2005 and Makni et aL, 2008, a detection-estimation framework has been proposed to tackle these problems jointly, since they are connected to one another. In the Bayesian formalism, detection is achieved by modeling activating and nonactivating voxels through independent mixture models (IMM) within each region while hemodynamic response estimation is performed at a regional scale in a nonparametric way. Instead of IMMs, in this paper we take advantage of spatial mixture models (SMM) for their nonlinear spatial regularizing properties. The proposed method is unsupervised and spatially adaptive in the sense that the amount of spatial correlation is automatically tuned from the data and this setting automatically varies across brain regions. In addition, the level of regularization is specific to each experimental condition since both the signal-to-noise ratio and the activation pattern may vary across stimulus types in a given brain region. These aspects require the precise estimation of multiple partition functions of underlying Ising fields. This is addressed efficiently using first path sampling for a small subset of fields and then using a recently developed fast extrapolation technique for the large remaining set. Simulation results emphasize that detection relying on supervised SMM outperforms its IMM counterpart and that unsupervised spatial mixture models achieve similar results without any hand-tuning of the correlation parameter. On real datasets, the gain is illustrated in a localizer fMRI experiment: brain activations appear more spatially resolved using SMM in comparison with classical general linear model (GLM)-based approaches, while estimating a specific parcel-based HRF shape. Our approach therefore validates the treatment of unsmoothed fMRI data without fixed GLM definition at the subject level and makes also the classical strategy of spatial Gaussian filtering deprecated.

Model estimation of cerebral hemodynamics between blood flow and volume changes: a data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV.

Nonlinear estimation of the BOLD signal

Signal variations in functional Magnetic Resonance Imaging experiments essentially reflect the vascular system response to increased demand for oxygen caused by neuronal activity, termed the blood oxygenation level dependent (BOLD) effect. The most comprehensive model to date of the BOLD signal is formulated as a mixed continuous-discrete-time system of nonlinear stochastic differential equations. Previous approaches to the analysis of this system have been based on linearised approximations of the dynamics, which are limited in their ability to capture the inherent nonlinearities in the physiological system. In this paper we present a nonlinear filtering method for simultaneous estimation of the hidden physiological states and the system parameters, based on an iterative coordinate descent framework. State estimates of the cerebral blood flow, cerebral blood volume and deoxyhaemoglobin content are determined using a particle filter, demonstrated via simulation to be accurate, robust and efficient in comparison to linearisation-based techniques. The adaptive state and parameter estimation algorithm generates physiologically reasonable parameter estimates for experimental fMRI data. It is anticipated that signal processing techniques for modelling and estimation will become increasingly important in fMRI analyses as limitations of linear and linearised modelling are reached.

An ARX model-based approach to trial by trial identification of fMRI-BOLD responses

Being able to estimate the fMRI-BOLD response following a single task or stimulus is certainly of value, since it allows to characterize its relationship to different aspects either of the stimulus, or of the subject's performance. In order to detect and characterize BOLD responses in single trials, we developed and validated a procedure based on an AutoRegressive model with eXogenous Input (ARX). The use of an individual exogenous input for each voxel makes the modeling sensitive enough to reveal differences across regions, avoiding any a priori assumption about the reference signal. The detection of variability across trials is ensured by a suitable choice, for each voxel, of the order of the moving average, which in our implementation determines the relative delay between the recorded and the reference signal. This is a quality useful in finding different time profiles of activation from high temporal resolution fMRI data. The results obtained from simulated fMRI data resulting from synthetic activations in actual noise indicate that such approach allows to evaluate important features of the response, such as the time to onset, and time to peak. Moreover, the results obtained from real high temporal resolution fMRI data acquired at l.5 T during a motor task are consistent with previous knowledge about the responses of different cortical areas in motor programming and execution. The proposed procedure should also prove useful as a pre-processing step in different approaches to the analysis of fMRI data.

Nonlinear local electrovascular coupling. II: From data to neuronal masses

In the companion article a local electrovascular coupling (LEVC) model was proposed to explain the continuous dynamics of electrical and vascular states within a cortical unit. These states produce certain mesoscopic reflections whose discrete time series can be reconstructed from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). In this article we develop a recursive optimization algorithm based on the local linearization (LL) filter and an innovation method to make statistical inferences about the LEVC model from both EEG and fMRI data, i.e., to estimate the unobserved states and the unknown parameters of the model. For a better understanding, the LL filter is described from a Bayesian point of view, providing the particulars for the case of hybrid data (e.g., EEG and fMRI), which could be sampled at different rates. The dynamics of the exogenous synaptic inputs going into the cortical unit are also estimated by introducing a set of Gaussian radial basis functions. In order to study the dynamics of the electrical and vascular states in the striate cortex of humans as well as their local interrelationships, we applied this algorithm to EEG and fMRI recordings obtained concurrently from two subjects while passively observing a radial checkerboard with a white/black pattern reversal. The EEG and fMRI data from the first subject was used to estimate the electrical/vascular states and parameters of the LEVC model in V1 for a 4.0 Hz reversion frequency. We used the EEG data from the second subject to investigate the changes in the dynamics of the electrical states when the frequency of reversion is varied from 0.5-4.0 Hz. Then we made use of the estimated electrical states to predict the effects on the vasculature that such variations produce.

Nonlinear local electrovascular coupling. I: A theoretical model

Here we present a detailed biophysical model of how brain electrical and vascular dynamics are generated within a basic cortical unit. The model was obtained from coupling a canonical neuronal mass and an expandable vasculature. In this proposal, we address several aspects related to electroencephalographic and functional magnetic resonance imaging data fusion: (1) the impact of the cerebral architecture (at different physical levels) on the observations; (2) the physiology involved in electrovascular coupling; and (3) energetic considerations to gain a better understanding of how the glucose budget is used during neuronal activity. The model has three components. The first is the canonical neural mass model of three subpopulations of neurons that respond to incoming excitatory synaptic inputs. The generation of the membrane potentials in the somas of these neurons and the electric currents flowing in the neuropil are modeled by this component. The second and third components model the electrovascular coupling and the dynamics of vascular states in an extended balloon approach, respectively. In the first part we describe, in some detail, the biophysical model and establish its face validity using simulations of visually evoked responses under different flickering frequencies and luminous contrasts. In a second part, a recursive optimization algorithm is developed and used to make statistical inferences about this forward/generative model from actual data.

Integrated MEG/EEG and fMRI model based on neural masses

We introduce a bottom-up model for integrating electroencephalography (EEG) or magnetoencephalography (MEG) with functional magnetic resonance imaging (fMRI). An extended neural mass model is proposed based on the physiological principles of cortical minicolumns and their connections. The fMRI signal is extracted from the proposed neural mass model by introducing a relationship between the stimulus and the neural activity and using the resultant neural activity as input of the extended Balloon model. The proposed model, validated using simulations, is instrumental in evaluating the upcoming combined methods for simultaneous analysis of MEG/EEG and fMRI.

fMRI MODELS OF DENDRITIC AND ASTROCYTIC NETWORKS

In order to elucidate the relationships between hierarchical structures within the neocortical neuropil and the information carried by an ensemble of neurons encompassing a single voxel, it is essential to predict through volume conductor modeling LFPs representing average extracellular potentials, which are expressed in terms of interstitial potentials of individual cells in networks of gap-junctionally connected astrocytes and synaptically connected neurons. These relationships have been provided and can then be used to investigate how the underlying neuronal population activity can be inferred from the measurement of the BOLD signal through electrovascular coupling mechanisms across the blood-brain barrier. The importance of both synaptic and extrasynaptic transmission as the basis of electrophysiological indices triggering vascular responses between dendritic and astrocytic networks, and sequential configurations of firing patterns in composite neural networks is emphasized. The purpose of this review is to show how fMRI data may be used to draw conclusions about the information transmitted by individual neurons in populations generating the BOLD signal.

Artifact reduction for simultaneous EEG/fMRI recording: Adaptive FIR reduction of imaging artifacts

OBJECTIVE

We present a new method of effectively removing imaging artifacts of electroencephalography (EEG) and extensively conserving the time-frequency features of EEG signals during simultaneous functional magnetic resonance imaging (fMRI) scanning under conventional conditions.

METHODS

Under the conventional conditions of a 5000 Hz EEG sampling rate, but in the absence of the MRI slice-timing signals, the imaging artifact during each slice scanning is theoretically inferred to be a linear combination of the average artifact waveform and its derivatives, deduced by band-limited Taylor's expansion. Technically, the imaging artifact reduction algorithm is equivalent to an adaptive finite impulse response (FIR) filter.

RESULTS

The capability of this novel method removing the imaging artifacts of EEG recording during fMRI scanning has been demonstrated by a phantom experiment. Moreover, the effectiveness of this method in conserving the time-frequency features of EEG activity has been evaluated by both visually evoked experiments and alpha waves.

CONCLUSIONS

The adaptive FIR method is an effective method of removing the imaging artifacts under conventional conditions, and also conserving the time-frequency EEG signals.

SIGNIFICANCE

The proposed adaptive FIR method, removing the imaging artifacts, combined with the wavelet-based non-linear noise reduction (WNNR) method [Wan X, Iwata K, Riera J, Ozaki T, Kitamura M, Kawashima R. Artifact reduction for EEG/fMRI recording: Nonlinear reduction of ballistocardiogram artifacts. Clin Neurophysiol 2006;117:668-80], reducing the ballistocardiogram artifacts (BAs), makes it feasible to obtain accurate EEG signals from the simultaneous EEG recordings during fMRI scanning.

Integrated MEG and fMRI model: synthesis and analysis

An integrated model for magnetoencephalography (MEG) and functional Magnetic Resonance Imaging (fMRI) is proposed. In the model, the neural activity is related to the Post Synaptic Potentials (PSPs) which is common link between MEG and fMRI. Each PSP is modeled by the direction and strength of its current flow which are treated as random variables. The overall neural activity in each voxel is used for equivalent current dipole in MEG and as input of extended Balloon model in fMRI. The proposed model shows the possibility of detecting activation by fMRI in a voxel while the voxel is silent for MEG and vice versa. Parameters of the model can illustrate situations like closed field due to non-pyramidal cells, canceling effect of inhibitory PSP on excitatory PSP, and effect of synchronicity. In addition, the model shows that the crosstalk from neural activities of the adjacent voxels in fMRI may result in the detection of activations in these voxels that contain no neural activities. The proposed model is instrumental in evaluating and comparing different analysis methods of MEG and fMRI. It is also useful in characterizing the upcoming combined methods for simultaneous analysis of MEG and fMRI.

Fusing EEG and fMRI based on a bottom-up model: inferring activation and effective connectivity in neural masses

The elucidation of the complex machinery used by the human brain to segregate and integrate information while performing high cognitive functions is a subject of imminent future consequences. The most significant contributions to date in this field, known as cognitive neuroscience, have been achieved by using innovative neuroimaging techniques, such as electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI), which measure variations in both the time and the space of some interpretable physical magnitudes. Extraordinary maps of cerebral activation involving function-restricted brain areas, as well as graphs of the functional connectivity between them, have been obtained from EEG and fMRI data by solving some spatio-temporal inverse problems, which constitutes a top-down approach. However, in many cases, a natural bridge between these maps/graphs and the causal physiological processes is lacking, leading to some misunderstandings in their interpretation. Recent advances in the comprehension of the underlying physiological mechanisms associated with different cerebral scales have provided researchers with an excellent scenario to develop sophisticated biophysical models that permit an integration of these neuroimage modalities, which must share a common aetiology. This paper proposes a bottom-up approach, involving physiological parameters in a specific mesoscopic dynamic equations system. Further observation equations encapsulating the relationship between the mesostates and the EEG/fMRI data are obtained on the basis of the physical foundations of these techniques. A methodology for the estimation of parameters from fused EEG/fMRI data is also presented. In this context, the concepts of activation and effective connectivity are carefully revised. This new approach permits us to examine and discuss some future prospects for the integration of multimodal neuroimages.