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

Cortical origin of theta error signals

A multi-scale approach elucidated the origin of the error-related-negativity (ERN), with its associated theta-rhythm, and the post-error-positivity (Pe) in macaque supplementary eye field (SEF). Using biophysical modeling, synaptic inputs to a subpopulation of layer-3 (L3) and layer-5 (L5) pyramidal cells (PCs) were optimized to reproduce error-related spiking modulation and inter-spike intervals. The intrinsic dynamics of dendrites in L5 but not L3 error PCs generate theta rhythmicity with random phases. Saccades synchronized the phases of the theta-rhythm, which was magnified on errors. Contributions from error PCs to the laminar current source density (CSD) observed in SEF were negligible and could not explain the observed association between error-related spiking modulation in L3 PCs and scalp-EEG. CSD from recorded laminar field potentials in SEF was comprised of multipolar components, with monopoles indicating strong electro-diffusion, dendritic/axonal electrotonic current leakage outside SEF, or violations of the model assumptions. Our results also demonstrate the involvement of secondary cortical regions, in addition to SEF, particularly for the later Pe component. The dipolar component from the observed CSD paralleled the ERN dynamics, while the quadrupolar component paralleled the Pe. These results provide the most advanced explanation to date of the cellular mechanisms generating the ERN.

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.

Inferring Macroscale Brain Dynamics via Fusion of Simultaneous EEG-fMRI

Advances in the instrumentation and signal processing for simultaneously acquired electroencephalography and functional magnetic resonance imaging (EEG-fMRI) have enabled new ways to observe the spatiotemporal neural dynamics of the human brain. Central to the utility of EEG-fMRI neuroimaging systems are the methods for fusing the two data streams, with machine learning playing a key role. These methods can be dichotomized into those that are symmetric and asymmetric in terms of how the two modalities inform the fusion. Studies using these methods have shown that fusion yields new insights into brain function that are not possible when each modality is acquired separately. As technology improves and methods for fusion become more sophisticated, the future of EEG-fMRI for noninvasive measurement of brain dynamics includes mesoscale mapping at ultrahigh magnetic resonance fields, targeted perturbation-based neuroimaging, and using deep learning to uncover nonlinear representations that link the electrophysiological and hemodynamic measurements.

Comparing dynamic causal models of neurovascular coupling with fMRI and EEG/MEG

This technical note presents a dynamic causal modelling (DCM) procedure for evaluating different models of neurovascular coupling in the human brain - using combined electromagnetic (M/EEG) and functional magnetic resonance imaging (fMRI) data. This procedure compares the evidence for biologically informed models of neurovascular coupling using Bayesian model comparison. First, fMRI data are used to localise regionally specific neuronal responses. The coordinates of these responses are then used as the location priors in a DCM of electrophysiological responses elicited by the same paradigm. The ensuing estimates of model parameters are then used to generate neuronal drive functions, which model pre- or post-synaptic activity for each experimental condition. These functions form the input to a model of neurovascular coupling, whose parameters are estimated from the fMRI data. Crucially, this enables one to evaluate different models of neurovascular coupling, using Bayesian model comparison - asking, for example, whether instantaneous or delayed, pre- or post-synaptic signals mediate haemodynamic responses. We provide an illustrative application of the procedure using a single-subject auditory fMRI and MEG dataset. The code and exemplar data accompanying this technical note are available through the statistical parametric mapping (SPM) software.

Investigating Human Neurovascular Coupling Using Functional Neuroimaging: A Critical Review of Dynamic Models

The mechanisms that link a transient neural activity to the corresponding increase of cerebral blood flow (CBF) are termed neurovascular coupling (NVC). They are possibly impaired at early stages of small vessel or neurodegenerative diseases. Investigation of NVC in humans has been made possible with the development of various neuroimaging techniques based on variations of local hemodynamics during neural activity. Specific dynamic models are currently used for interpreting these data that can include biophysical parameters related to NVC. After a brief review of the current knowledge about possible mechanisms acting in NVC we selected seven models with explicit integration of NVC found in the literature. All these models were described using the same procedure. We compared their physiological assumptions, mathematical formalism, and validation. In particular, we pointed out their strong differences in terms of complexity. Finally, we discussed their validity and their potential applications. These models may provide key information to investigate various aspects of NVC in human pathology.

The Role of Extracellular Conductivity Profiles in Compartmental Models for Neurons: Particulars for Layer 5 Pyramidal Cells

With the rapid increase in the number of technologies aimed at observing electric activity inside the brain, scientists have felt the urge to create proper links between intracellular- and extracellular-based experimental approaches. Biophysical models at both physical scales have been formalized under assumptions that impede the creation of such links. In this work, we address this issue by proposing a multicompartment model that allows the introduction of complex extracellular and intracellular resistivity profiles. This model accounts for the geometrical and electrotonic properties of any type of neuron through the combination of four devices: the integrator, the propagator, the 3D connector, and the collector. In particular, we applied this framework to model the tufted pyramidal cells of layer 5 (PCL5) in the neocortex. Our model was able to reproduce the decay and delay curves of backpropagating action potentials (APs) in this type of cell with better agreement with experimental data. We used the voltage drops of the extracellular resistances at each compartment to approximate the local field potentials generated by a PCL5 located in close proximity to linear microelectrode arrays. Based on the voltage drops produced by backpropagating APs, we were able to estimate the current multipolar moments generated by a PCL5. By adding external current sources in parallel to the extracellular resistances, we were able to create a sensitivity profile of PCL5 to electric current injections from nearby microelectrodes. In our model for PCL5, the kinetics and spatial profile of each ionic current were determined based on a literature survey, and the geometrical properties of these cells were evaluated experimentally. We concluded that the inclusion of the extracellular space in the compartmental models of neurons as an extra electrotonic medium is crucial for the accurate simulation of both the propagation of the electric potentials along the neuronal dendrites and the neuronal reactivity to an electrical stimulation using external microelectrodes.

EEG-fMRI integration for the study of human brain function

Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) have proved to be extremely valuable tools for the non-invasive study of human brain function. Moreover, due to a notable degree of complementarity between the two modalities, the combination of EEG and fMRI data has been actively sought in the last two decades. Although initially focused on epilepsy, EEG-fMRI applications were rapidly extended to the study of healthy brain function, yielding new insights into its underlying mechanisms and pathways. Nevertheless, EEG and fMRI have markedly different spatial and temporal resolutions, and probe neuronal activity through distinct biophysical processes, many aspects of which are still poorly understood. The remarkable conceptual and methodological challenges associated with EEG-fMRI integration have motivated the development of a wide range of analysis approaches over the years, each relying on more or less restrictive assumptions, and aiming to shed further light on the mechanisms of brain function along with those of the EEG-fMRI coupling itself. Here, we present a review of the most relevant EEG-fMRI integration approaches yet proposed for the study of brain function, supported by a general overview of our current understanding of the biophysical mechanisms coupling the signals obtained from the two modalities.

Transfer Function between EEG and BOLD Signals of Epileptic Activity

Simultaneous electroencephalogram (EEG)-functional Magnetic Resonance Imaging (fMRI) recordings have seen growing application in the evaluation of epilepsy, namely in the characterization of brain networks related to epileptic activity. In EEG-correlated fMRI studies, epileptic events are usually described as boxcar signals based on the timing information retrieved from the EEG, and subsequently convolved with a hemodynamic response function to model the associated Blood Oxygen Level Dependent (BOLD) changes. Although more flexible approaches may allow a higher degree of complexity for the hemodynamics, the issue of how to model these dynamics based on the EEG remains an open question. In this work, a new methodology for the integration of simultaneous EEG-fMRI data in epilepsy is proposed, which incorporates a transfer function from the EEG to the BOLD signal. Independent component analysis of the EEG is performed, and a number of metrics expressing different models of the EEG-BOLD transfer function are extracted from the resulting time courses. These metrics are then used to predict the fMRI data and to identify brain areas associated with the EEG epileptic activity. The methodology was tested on both ictal and interictal EEG-fMRI recordings from one patient with a hypothalamic hamartoma. When compared to the conventional analysis approach, plausible, consistent, and more significant activations were obtained. Importantly, frequency-weighted EEG metrics yielded superior results than those weighted solely on the EEG power, which comes in agreement with previous literature. Reproducibility, specificity, and sensitivity should be addressed in an extended group of patients in order to further validate the proposed methodology and generalize the presented proof of concept.

Dynamic causal modelling of lateral interactions in the visual cortex

This paper presents a dynamic causal model based upon neural field models of the Amari type. We consider the application of these models to non-invasive data, with a special focus on the mapping from source activity on the cortical surface to a single channel. We introduce a neural field model based upon the canonical microcircuit (CMC), in which neuronal populations are assigned to different cortical layers. We show that DCM can disambiguate between alternative (neural mass and field) models of cortical activity. However, unlike neural mass models, DCM with neural fields can address questions about neuronal microcircuitry and lateral interactions. This is because they are equipped with interlaminar connections and horizontal intra-laminar connections that are patchy in nature. These horizontal or lateral connections can be regarded as connecting macrocolumns with similar feature selectivity. Crucially, the spatial parameters governing horizontal connectivity determine the separation (width) of cortical macrocolumns. Thus we can estimate the width of macro columns, using non-invasive electromagnetic signals. We illustrate this estimation using dynamic causal models of steady-state or ongoing spectral activity measured using magnetoencephalography (MEG) in human visual cortex. Specifically, we revisit the hypothesis that the size of a macrocolumn is a key determinant of neuronal dynamics, particularly the peak gamma frequency. We are able to show a correlation, over subjects, between columnar size and peak gamma frequency — that fits comfortably with established correlations between peak gamma frequency and the size of visual cortex defined retinotopically. We also considered cortical excitability and assessed its relative influence on observed gamma activity. This example highlights the potential utility of dynamic causal modelling and neural fields in providing quantitative characterisations of spatially extended dynamics on the cortical surface — that are parameterised in terms of horizontal connections, implicit in the cortical micro-architecture and its synaptic parameters.

Pitfalls in the dipolar model for the neocortical EEG sources

For about six decades, primary current sources of the electroencephalogram (EEG) have been assumed dipolar in nature. In this study, we used electrophysiological recordings from anesthetized Wistar rats undergoing repeated whisker deflections to revise the biophysical foundations of the EEG dipolar model. In a first experiment, we performed three-dimensional recordings of extracellular potentials from a large portion of the barrel field to estimate intracortical multipolar moments generated either by single spiking neurons (i.e., pyramidal cells, PC; spiny stellate cells, SS) or by populations of them while experiencing synchronized postsynaptic potentials. As expected, backpropagating spikes along PC dendrites caused dipolar field components larger in the direction perpendicular to the cortical surface (49.7 ± 22.0 nA·mm). In agreement with the fact that SS cells have “close-field” configurations, their dipolar moment at any direction was negligible. Surprisingly, monopolar field components were detectable both at the level of single units (i.e., −11.7 ± 3.4 nA for PC) and at the mesoscopic level of mixed neuronal populations receiving extended synaptic inputs within either a cortical column (−0.44 ± 0.20 μA) or a 2.5-m3-voxel volume (−3.32 ± 1.20 μA). To evaluate the relationship between the macroscopically defined EEG equivalent dipole and the mesoscopic intracortical multipolar moments, we performed concurrent recordings of high-resolution skull EEG and laminar local field potentials. From this second experiment, we estimated the time-varying EEG equivalent dipole for the entire barrel field using either a multiple dipole fitting or a distributed type of EEG inverse solution. We demonstrated that mesoscopic multipolar components are altogether absorbed by any equivalent dipole in both types of inverse solutions. We conclude that the primary current sources of the EEG in the neocortex of rodents are not precisely represented by a single equivalent dipole and that the existence of monopolar components must be also considered at the mesoscopic level.

Parallel independent component analysis using an optimized neurovascular coupling for concurrent EEG-fMRI sources

The complexity of the human brain and the limitation of any one imaging approach motivates the need for multimodal measurements to better understand cerebral processing. A very natural goal is to integrate electrophysiological and hemodynamic activity. Among them, concurrent EEG-fMRI studies have shown great promise for understanding intrinsic brain properties yet analyzing such data presents a significant methodological challenge. Here, we propose a multivariate parallel ICA decomposition incorporating dynamic neurovascular coupling for concurrent EEG-fMRI recordings. The goal of our algorithm is to fuse multimodal EEG-fMRI information and detect/interpret the relationship between electrophysiological and hemodynamic sources via a temporal neurovascular connection enhancement. We analyze the performance of the algorithm on a valid simulation based on real EEG and fMRI components (sources) from our previous works and a neurovascular coupling built from an extended 'balloon model'. The results from our simulations yield an accurate source tracking and linkage for concurrent EEG-fMRI, and provide a novel and efficient way to combine EEG and hemodynamic responses.

Modeling the spontaneous Ca2+ oscillations in astrocytes: Inconsistencies and usefulness

Spontaneous calcium (Ca2+) oscillations (SCOs) in astrocytes might be a crucial signaling for the multipurpose role of this type of cell in several brain functions. To interpret experimental data of astrocytic SCOs, which has been largely observed in the last decade, several groups have attempted to accommodate biophysical models that were developed in the past for Ca2+ signaling in other cell types. In most of the cases, only predictive strategies were used to estimate specific parameters of these modified models from actual experiments. In this study, we discuss the most remarkable models used to describe Ca2+ signaling in astrocytes. At the same time, we aim to revise the particulars of applying these models to interpret epifluorescent time series obtained from large regions of interest. Specially, we developed a detailed model for global Ca2+ signaling in the somata of astrocytes. In order to estimate some of the parameters in our model, we propose a deductive reasoning strategy, i.e., a statistical inference method that results from combining a filtering technique and a maximum likelihood principle. By means of computer simulations, we evaluate the accuracy of this estimation's strategy. Finally, we use the new model, in combination with a recent experimental findings by our group, to estimate the degree of cluster coupling inside the soma during the genesis of global Ca2+ events.

A short history of causal modeling of fMRI data

Twenty years ago, the discovery of the blood oxygen level dependent (BOLD) contrast and invention of functional magnetic resonance imaging (MRI) not only allowed for enhanced analyses of regional brain activity, but also laid the foundation for novel approaches to studying effective connectivity, which is essential for mechanistically interpretable accounts of neuronal systems. Dynamic causal modeling (DCM) and Granger causality (G-causality) modeling have since become the most frequently used techniques for inferring effective connectivity from fMRI data. In this paper, we provide a short historical overview of these approaches, describing milestones of their development from our subjective perspectives.

Dynamic models of BOLD contrast

This personal recollection looks at the evolution of ideas about the dynamics of the blood oxygenation level dependent (BOLD) signal, with an emphasis on the balloon model. From the first detection of the BOLD response it has been clear that the signal exhibits interesting dynamics, such as a pronounced and long-lasting post-stimulus undershoot. The BOLD response, reflecting a change in local deoxyhemoglobin, is a combination of a hemodynamic response, related to changes in blood flow and venous blood volume, and a metabolic response related to oxygen metabolism. Modeling is potentially a way to understand the complex path from changes in neural activity to the BOLD signal. In the early days of fMRI it was hoped that the hemodynamic/metabolic response could be modeled in a unitary way, with blood flow, oxygen metabolism, and venous blood volume-the physiological factors that affect local deoxyhemoglobin-all tightly linked. The balloon model was an attempt to do this, based on the physiological ideas of limited oxygen delivery at baseline and a slow recovery of venous blood volume after the stimulus (the balloon effect), and this simple model of the physiology worked well to simulate the BOLD response. However, subsequent experiments suggest a more complicated picture of the underlying physiology, with blood flow and oxygen metabolism driven in parallel, possibly by different aspects of neural activity. In addition, it is still not clear whether the post-stimulus undershoot is a hemodynamic or a metabolic phenomenon, although the original venous balloon effect is unlikely to be the full explanation, and a flow undershoot is likely to be important. Although our understanding of the physics of the BOLD response is now reasonably solid, our understanding of the underlying physiological relationships is still relatively poor, and this is the primary hurdle for future models of BOLD dynamics.

Quantifying the uncertainty of spontaneous Ca2+ oscillations in astrocytes: particulars of Alzheimer's disease

The quantification of spontaneous calcium (Ca(2+)) oscillations (SCOs) in astrocytes presents a challenge because of the large irregularities in the amplitudes, durations, and initiation times of the underlying events. In this article, we use a stochastic context to account for such SCO variability, which is based on previous models for cellular Ca(2+) signaling. First, we found that passive Ca(2+) influx from the extracellular space determine the basal concentration of this ion in the cytosol. Second, we demonstrated the feasibility of estimating both the inositol 1,4,5-trisphosphate (IP(3)) production levels and the average number of IP(3) receptor channels in the somatic clusters from epifluorescent Ca(2+) imaging through the combination of a filtering strategy and a maximum-likelihood criterion. We estimated these two biophysical parameters using data from wild-type adult mice and age-matched transgenic mice overexpressing the 695-amino-acid isoform of human Alzheimer β-amyloid precursor protein. We found that, together with an increase in the passive Ca(2+) influx, a significant reduction in the sensitivity of G protein-coupled receptors might lie beneath the abnormalities in the astrocytic Ca(2+) signaling, as was observed in rodent models of Alzheimer's disease. This study provides new, to our knowledge, indices for a quantitative analysis of SCOs in normal and pathological astrocytes.

Modeling habituation in rat EEG-evoked responses via a neural mass model with feedback

Habituation is a generic property of the neural response to repeated stimuli. Its strength often increases as inter-stimuli relaxation periods decrease. We propose a simple, broadly applicable control structure that enables a neural mass model of the evoked EEG response to exhibit habituated behavior. A key motivation for this investigation is the ongoing effort to develop model-based reconstruction of multi-modal functional neuroimaging data. The control structure proposed here is illustrated and validated in the context of a biophysical neural mass model, developed by Riera et al. (Hum Brain Mapp 27(11):896-914, 2006; 28(4):335-354, 2007), and of simplifications thereof, using data from rat EEG response to medial nerve stimuli presented at frequencies from 1 to 8 Hz. Performance was tested by predictions of both the response to the next stimulus based on the current one, and also of continued stimuli trains over 4-s time intervals based on the first stimulus in the interval, with similar success statistics. These tests demonstrate the ability of simple generative models to capture key features of the evoked response, including habituation.

EEG-fMRI integration: a critical review of biophysical modeling and data analysis approaches

The diverse nature of cerebral activity, as measured using neuroimaging techniques, has been recognised long ago. It seems obvious that using single modality recordings can be limited when it comes to capturing its complex nature. Thus, it has been argued that moving to a multimodal approach will allow neuroscientists to better understand the dynamics and structure of this activity. This means that integrating information from different techniques, such as electroencephalography (EEG) and the blood oxygenated level dependent (BOLD) signal recorded with functional magnetic resonance imaging (fMRI), represents an important methodological challenge. In this work, we review the work that has been done thus far to derive EEG/fMRI integration approaches. This leads us to inspect the conditions under which such an integration approach could work or fail, and to disclose the types of scientific questions one could (and could not) hope to answer with it.

Effective connectivity: influence, causality and biophysical modeling

This is the final paper in a Comments and Controversies series dedicated to "The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution". We argue that discovering effective connectivity depends critically on state-space models with biophysically informed observation and state equations. These models have to be endowed with priors on unknown parameters and afford checks for model Identifiability. We consider the similarities and differences among Dynamic Causal Modeling, Granger Causal Modeling and other approaches. We establish links between past and current statistical causal modeling, in terms of Bayesian dependency graphs and Wiener-Akaike-Granger-Schweder influence measures. We show that some of the challenges faced in this field have promising solutions and speculate on future developments.

Dynamic causal modeling with neural fields

The aim of this paper is twofold: first, to introduce a neural field model motivated by a well-known neural mass model; second, to show how one can estimate model parameters pertaining to spatial (anatomical) properties of neuronal sources based on EEG or LFP spectra using Bayesian inference. Specifically, we consider neural field models of cortical activity as generative models in the context of dynamic causal modeling (DCM). This paper considers the simplest case of a single cortical source modeled by the spatiotemporal dynamics of hidden neuronal states on a bounded cortical surface or manifold. We build this model using multiple layers, corresponding to cortical lamina in the real cortical manifold. These layers correspond to the populations considered in classical (Jansen and Rit) neural mass models. This allows us to formulate a neural field model that can be reduced to a neural mass model using appropriate constraints on its spatial parameters. In turn, this enables one to compare and contrast the predicted responses from equivalent neural field and mass models respectively. We pursue this using empirical LFP data from a single electrode to show that the parameters controlling the spatial dynamics of cortical activity can be recovered, using DCM, even in the absence of explicit spatial information in observed data.

Bayesian comparison of neurovascular coupling models using EEG-fMRI

Functional magnetic resonance imaging (fMRI), with blood oxygenation level-dependent (BOLD) contrast, is a widely used technique for studying the human brain. However, it is an indirect measure of underlying neuronal activity and the processes that link this activity to BOLD signals are still a topic of much debate. In order to relate findings from fMRI research to other measures of neuronal activity it is vital to understand the underlying neurovascular coupling mechanism. Currently, there is no consensus on the relative roles of synaptic and spiking activity in the generation of the BOLD response. Here we designed a modelling framework to investigate different neurovascular coupling mechanisms. We use Electroencephalographic (EEG) and fMRI data from a visual stimulation task together with biophysically informed mathematical models describing how neuronal activity generates the BOLD signals. These models allow us to non-invasively infer the degree of local synaptic and spiking activity in the healthy human brain. In addition, we use Bayesian model comparison to decide between neurovascular coupling mechanisms. We show that the BOLD signal is dependent upon both the synaptic and spiking activity but that the relative contributions of these two inputs are dependent upon the underlying neuronal firing rate. When the underlying neuronal firing is low then the BOLD response is best explained by synaptic activity. However, when the neuronal firing rate is high then both synaptic and spiking activity are required to explain the BOLD signal.

Functional magnetic resonance imaging (fMRI), with blood oxygenation level-dependent (BOLD) contrast, is a widely used technique for studying the human brain. However, the relationship between neuronal activity and blood flow, the basis of fMRI, is still under much debate. A growing body of evidence from animal studies suggests that fMRI signals are more closely coupled to synaptic input activity than to the spiking output of a neuronal population. However, data from neurosurgical patients does not seem to support this view and this hypothesis hasn't yet been tested in the healthy human brain. Here we design a powerful and efficient modelling framework that can be used to non-invasively compare different biologically plausible hypotheses of neurovascular coupling. We use this framework to explore the contribution of these two aspects of neuronal activity (synaptic and spiking) to the generation of hemodynamic signals in human visual cortex, with Electroencephalographic (EEG)-fMRI data. Our results provide preliminary evidence that depending on the frequency of the visual stimulus and underlying firing rate, fMRI relates closer to synaptic activity (low-frequencies) or to both synaptic and spiking activities (high-frequencies).

Development of a variational scheme for model inversion of multi-area model of brain. Part I: simulation evaluation

We previously developed an integrated model of the brain within a single cortical area for functional Magnetic Resonance Imaging (fMRI), electroencephalography (EEG), and magnetoencephalography (MEG) using an extended neural mass model (ENMM). We then extended ENMM from a single-area to a multi-area model to develop a neural mass model of the entire brain. To this end, we derived a nonlinear state-space representation of the multi-area model. In Parts I and II of these two companion papers (henceforth called Part I and Part II), we develop and evaluate a variational Bayesian expectation maximization (VBEM) method to estimate parameters of multi-area ENMM (MEN) using E/MEG data. In Part I, we derive a state-space representation of MEN and use VBEM method for model inversion (parameter estimation). We evaluate and validate performance of VBEM method for model inversion of MEN using simulation studies in various signal-to-noise ratios. Details of VBEM method are presented in Part II. The proposed approach provides a useful technique for analyzing effective connectivity using non-invasive EEG and MEG methods.

MEG and fMRI Fusion for Non-Linear Estimation of Neural and BOLD Signal Changes

The combined analysis of magnetoencephalography (MEG)/electroencephalography and functional magnetic resonance imaging (fMRI) measurements can lead to improvement in the description of the dynamical and spatial properties of brain activity. In this paper we empirically demonstrate this improvement using simulated and recorded task related MEG and fMRI activity. Neural activity estimates were derived using a dynamic Bayesian network with continuous real valued parameters by means of a sequential Monte Carlo technique. In synthetic data, we show that MEG and fMRI fusion improves estimation of the indirectly observed neural activity and smooths tracking of the blood oxygenation level dependent (BOLD) response. In recordings of task related neural activity the combination of MEG and fMRI produces a result with greater signal-to-noise ratio, that confirms the expectation arising from the nature of the experiment. The highly non-linear model of the BOLD response poses a difficult inference problem for neural activity estimation; computational requirements are also high due to the time and space complexity. We show that joint analysis of the data improves the system's behavior by stabilizing the differential equations system and by requiring fewer computational resources.

A dynamic model of neurovascular coupling: implications for blood vessel dilation and constriction

Neurovascular coupling in response to stimulation of the rat barrel cortex was investigated using concurrent multichannel electrophysiology and laser Doppler flowmetry. The data were used to build a linear dynamic model relating neural activity to blood flow. Local field potential time series were subject to current source density analysis, and the time series of a layer IV sink of the barrel cortex was used as the input to the model. The model output was the time series of the changes in regional cerebral blood flow (CBF). We show that this model can provide excellent fit of the CBF responses for stimulus durations of up to 16 s. The structure of the model consisted of two coupled components representing vascular dilation and constriction. The complex temporal characteristics of the CBF time series were reproduced by the relatively simple balance of these two components. We show that the impulse response obtained under the 16-s duration stimulation condition generalised to provide a good prediction to the data from the shorter duration stimulation conditions. Furthermore, by optimising three out of the total of nine model parameters, the variability in the data can be well accounted for over a wide range of stimulus conditions. By establishing linearity, classic system analysis methods can be used to generate and explore a range of equivalent model structures (e.g., feed-forward or feedback) to guide the experimental investigation of the control of vascular dilation and constriction following stimulation.

A dynamic causal model study of neuronal population dynamics

In this paper, we compare mean-field and neural-mass models of electrophysiological responses using Bayesian model comparison. In previous work, we presented a mean-field model of neuronal dynamics as observed with magnetoencephalography and electroencephalography. Unlike neural-mass models, which consider only the mean activity of neuronal populations, mean-field models track the distribution (e.g., mean and dispersion) of population activity. This can be important if the mean affects the dispersion or vice versa. Here, we introduce a dynamical causal model based on mean-field (i.e., population density) models of neuronal activity, and use it to assess the evidence for a coupling between the mean and dispersion of hidden neuronal states using observed electromagnetic responses. We used Bayesian model comparison to compare homologous mean-field and neural-mass models, asking whether empirical responses support a role for population variance in shaping neuronal dynamics. We used the mismatch negativity (MMN) and somatosensory evoked potentials (SEP) as representative neuronal responses in physiological and non-physiological paradigms respectively. Our main conclusion was that although neural-mass models may be sufficient for cognitive paradigms, there is clear evidence for an effect of dispersion at the high levels of depolarization evoked in SEP paradigms. This suggests that (i) the dispersion of neuronal states within populations generating evoked brain signals can be manifest in observed brain signals and that (ii) the evidence for their effects can be accessed with dynamic causal model comparison.

Model driven EEG/fMRI fusion of brain oscillations

This article reviews progress and challenges in model driven EEG/fMRI fusion with a focus on brain oscillations. Fusion is the combination of both imaging modalities based on a cascade of forward models from ensemble of post-synaptic potentials (ePSP) to net primary current densities (nPCD) to EEG; and from ePSP to vasomotor feed forward signal (VFFSS) to BOLD. In absence of a model, data driven fusion creates maps of correlations between EEG and BOLD or between estimates of nPCD and VFFS. A consistent finding has been that of positive correlations between EEG alpha power and BOLD in both frontal cortices and thalamus and of negative ones for the occipital region. For model driven fusion we formulate a neural mass EEG/fMRI model coupled to a metabolic hemodynamic model. For exploratory simulations we show that the Local Linearization (LL) method for integrating stochastic differential equations is appropriate for highly nonlinear dynamics. It has been successfully applied to small and medium sized networks, reproducing the described EEG/BOLD correlations. A new LL-algebraic method allows simulations with hundreds of thousands of neural populations, with connectivities and conduction delays estimated from diffusion weighted MRI. For parameter and state estimation, Kalman filtering combined with the LL method estimates the innovations or prediction errors. From these the likelihood of models given data are obtained. The LL-innovation estimation method has been already applied to small and medium scale models. With improved Bayesian computations the practical estimation of very large scale EEG/fMRI models shall soon be possible.

Bootstrap generation and evaluation of an fMRI simulation database

Computer simulations have played a critical role in functional magnetic resonance imaging (fMRI) research, notably in the validation of new data analysis methods. Many approaches have been used to generate fMRI simulations, but there is currently no generic framework to assess how realistic each one of these approaches may be. In this article, a statistical technique called parametric bootstrap was used to generate a simulation database that mimicked the parameters found in a real database, which comprised 40 subjects and five tasks. The simulations were evaluated by comparing the distributions of a battery of statistical measures between the real and simulated databases. Two popular simulation models were evaluated for the first time by applying the bootstrap framework. The first model was an additive mixture of multiple components and the second one implemented a non-linear motion process. In both models, the simulated components included the following brain dynamics: a baseline, physiological noise, neural activation and random noise. These models were found to successfully reproduce the relative variance of the components and the temporal autocorrelation of the fMRI time series. By contrast, the level of spatial autocorrelation was found to be drastically low using the additive model. Interestingly, the motion process in the second model intrisically generated some slow time drifts and increased the level of spatial autocorrelations. These experiments demonstrated that the bootstrap framework is a powerful new tool that can pinpoint the respective strengths and limitations of simulation models.

Study of neurovascular coupling in humans via simultaneous magnetoencephalography and diffuse optical imaging acquisition

By combining diffuse optical imaging (DOI) and magnetoencephalography (MEG) we investigate neurovascular coupling non-invasively in human subjects using median-nerve stimulation. Previous fMRI studies have shown a habituation effect in the hemodynamic blood oxygen level-dependent (BOLD) response for stimulation periods longer than 2 s. With DOI and MEG we can test whether this effect in hemodynamic response can be accounted for by a habituation effect in the neural response. Our experimental results show that the habituation effect in the hemodynamic response is stronger than that in the earliest cortical neural response (N20). Using a linear convolution model to predict hemodynamic responses we found that including late neural components (> or = 30 ms) improves the prediction of the hemoglobin response. This finding suggests that in addition to the initial evoked-response deflections related to the talamic afferent input, later cortical activity is needed to predict the hemodynamic response.

Identification and comparison of stochastic metabolic/hemodynamic models (sMHM) for the generation of the BOLD signal

This paper extends a previously formulated deterministic metabolic/hemodynamic model for the generation of blood oxygenated level dependent (BOLD) responses to include both physiological and observation stochastic components (sMHM). This adds a degree of flexibility when fitting the model to actual data by accounting for un-modelled activity. We then show how the innovation method can be used to estimate unobserved metabolic/hemodynamic as well as vascular variables of the sMHM, from simulated and actual BOLD data. The proposed estimation method allowed for doing model comparison by calculating the model's AIC and BIC. This methodology was then used to select between different neurovascular coupling assumptions underlying sMHM. The proposed framework was first validated on simulations and then applied to BOLD data from a motor task experiment. The models under comparison in the analysis of the actual data considered that vascular response was coupled to: (I) inhibition, (II) excitation, (III) both excitation and inhibition. Data was best described by model II, although model III was also supported.

Dynamic causal models and autopoietic systems

Dynamic Causal Modelling (DCM) and the theory of autopoietic systems are two important conceptual frameworks. In this review, we suggest that they can be combined to answer important questions about self-organising systems like the brain. DCM has been developed recently by the neuroimaging community to explain, using biophysical models, the non-invasive brain imaging data are caused by neural processes. It allows one to ask mechanistic questions about the implementation of cerebral processes. In DCM the parameters of biophysical models are estimated from measured data and the evidence for each model is evaluated. This enables one to test different functional hypotheses (i.e., models) for a given data set. Autopoiesis and related formal theories of biological systems as autonomous machines represent a body of concepts with many successful applications. However, autopoiesis has remained largely theoretical and has not penetrated the empiricism of cognitive neuroscience. In this review, we try to show the connections that exist between DCM and autopoiesis. In particular, we propose a simple modification to standard formulations of DCM that includes autonomous processes. The idea is to exploit the machinery of the system identification of DCMs in neuroimaging to test the face validity of the autopoietic theory applied to neural subsystems. We illustrate the theoretical concepts and their implications for interpreting electroencephalographic signals acquired during amygdala stimulation in an epileptic patient. The results suggest that DCM represents a relevant biophysical approach to brain functional organisation, with a potential that is yet to be fully evaluated.

Integrated MEG/fMRI model validated using real auditory data

The main objective of this paper is to present methods and results for the estimation of parameters of our proposed integrated magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI) model. We use real auditory MEG and fMRI datasets from 7 normal subjects to estimate the parameters of the model. The MEG and fMRI data were acquired at different times, but the stimulus profile was the same for both techniques. We use independent component analysis (ICA) to extract activation-related signal from the MEG data. The stimulus-correlated ICA component is used to estimate MEG parameters of the model. The temporal and spatial information of the fMRI datasets are used to estimate fMRI parameters of the model. The estimated parameters have reasonable means and standard deviations for all subjects. Goodness of fit of the real data to our model shows the possibility of using the proposed model to simulate realistic datasets for evaluation of integrated MEG/fMRI analysis methods.

The Brain Connectivity Workshops: moving the frontiers of computational systems neuroscience

Understanding the link between neurobiology and cognition requires that neuroscience moves beyond mere structure-function correlations. An explicit systems perspective is needed in which putative mechanisms of how brain function is constrained by brain structure are mathematically formalized and made accessible for experimental investigation. Such a systems approach critically rests on a better understanding of brain connectivity in its various forms. Since 2002, frontier topics of connectivity and neural system analysis have been discussed in a multidisciplinary annual meeting, the Brain Connectivity Workshop (BCW), bringing together experimentalists and theorists from various fields. This article summarizes some of the main discussions at the two most recent workshops, 2006 at Sendai, Japan, and 2007 at Barcelona, Spain: (i) investigation of cortical micro- and macrocircuits, (ii) models of neural dynamics at multiple scales, (iii) analysis of "resting state" networks, and (iv) linking anatomical to functional connectivity. Finally, we outline some central challenges and research trajectories in computational systems neuroscience for the next years.

Neural correlates of tactile detection: a combined magnetoencephalography and biophysically based computational modeling study

Previous reports conflict as to the role of primary somatosensory neocortex (SI) in tactile detection. We addressed this question in normal human subjects using whole-head magnetoencephalography (MEG) recording. We found that the evoked signal (0-175 ms) showed a prominent equivalent current dipole that localized to the anterior bank of the postcentral gyrus, area 3b of SI. The magnitude and timing of peaks in the SI waveform were stimulus amplitude dependent and predicted perception beginning at approximately 70 ms after stimulus. To make a direct and principled connection between the SI waveform and underlying neural dynamics, we developed a biophysically realistic computational SI model that contained excitatory and inhibitory neurons in supragranular and infragranular layers. The SI evoked response was successfully reproduced from the intracellular currents in pyramidal neurons driven by a sequence of lamina-specific excitatory input, consisting of output from the granular layer (approximately 25 ms), exogenous input to the supragranular layers (approximately 70 ms), and a second wave of granular output (approximately 135 ms). The model also predicted that SI correlates of perception reflect stronger and shorter-latency supragranular and late granular drive during perceived trials. These findings strongly support the view that signatures of tactile detection are present in human SI and are mediated by local neural dynamics induced by lamina-specific synaptic drive. Furthermore, our model provides a biophysically realistic solution to the MEG signal and can predict the electrophysiological correlates of human perception.

Biophysical model for integrating neuronal activity, EEG, fMRI and metabolism

Our goal is to model the coupling between neuronal activity, cerebral metabolic rates of glucose and oxygen consumption, cerebral blood flow (CBF), electroencephalography (EEG) and blood oxygenation level-dependent (BOLD) responses. In order to accomplish this, two previous models are coupled: a metabolic/hemodynamic model (MHM) for a voxel, linking BOLD signals and neuronal activity, and a neural mass model describing the neuronal dynamics within a voxel and its interactions with voxels of the same area (short-range interactions) and other areas (long-range interactions). For coupling both models, we take as the input to the BOLD model, the number of active synapses within the voxel, that is, the average number of synapses that will receive an action potential within the time unit. This is obtained by considering the action potentials transmitted between neuronal populations within the voxel, as well as those arriving from other voxels. Simulations are carried out for testing the integrated model. Results show that realistic evoked potentials (EP) at electrodes on the scalp surface and the corresponding BOLD signals for each voxel are produced by the model. In another simulation, the alpha rhythm was reproduced and reasonable similarities with experimental data were obtained when calculating correlations between BOLD signals and the alpha power curve. The origin of negative BOLD responses and the characteristics of EEG, PET and BOLD signals in Alzheimer's disease were also studied.