A dynamic causal model study of neuronal population dynamics

Neurochemistry-enriched dynamic causal models of magnetoencephalography, using magnetic resonance spectroscopy

We present a hierarchical empirical Bayesian framework for testing hypotheses about neurotransmitters' concertation as empirical prior for synaptic physiology using ultra-high field magnetic resonance spectroscopy (7T-MRS) and magnetoencephalography data (MEG). A first level dynamic causal modelling of cortical microcircuits is used to infer the connectivity parameters of a generative model of individuals' neurophysiological observations. At the second level, individuals' 7T-MRS estimates of regional neurotransmitter concentration supply empirical priors on synaptic connectivity. We compare the group-wise evidence for alternative empirical priors, defined by monotonic functions of spectroscopic estimates, on subsets of synaptic connections. For efficiency and reproducibility, we used Bayesian model reduction (BMR), parametric empirical Bayes and variational Bayesian inversion. In particular, we used Bayesian model reduction to compare alternative model evidence of how spectroscopic neurotransmitter measures inform estimates of synaptic connectivity. This identifies the subset of synaptic connections that are influenced by individual differences in neurotransmitter levels, as measured by 7T-MRS. We demonstrate the method using resting-state MEG (i.e., task-free recording) and 7T-MRS data from healthy adults. Our results confirm the hypotheses that GABA concentration influences local recurrent inhibitory intrinsic connectivity in deep and superficial cortical layers, while glutamate influences the excitatory connections between superficial and deep layers and connections from superficial to inhibitory interneurons. Using within-subject split-sampling of the MEG dataset (i.e., validation by means of a held-out dataset), we show that model comparison for hypothesis testing can be highly reliable. The method is suitable for applications with magnetoencephalography or electroencephalography, and is well-suited to reveal the mechanisms of neurological and psychiatric disorders, including responses to psychopharmacological interventions.

Functional Connectivity of the Chemosenses: A Review

Functional connectivity approaches have long been used in cognitive neuroscience to establish pathways of communication between and among brain regions. However, the use of these analyses to better understand how the brain processes chemosensory information remains nascent. In this review, we conduct a literature search of all functional connectivity papers of olfaction, gustation, and chemesthesis, with 103 articles discovered in total. These publications largely use approaches of seed-based functional connectivity and psychophysiological interactions, as well as effective connectivity approaches such as Granger Causality, Dynamic Causal Modeling, and Structural Equation Modeling. Regardless of modality, studies largely focus on elucidating neural correlates of stimulus qualities such as identity, pleasantness, and intensity, with task-based paradigms most frequently implemented. We call for further "model free" or data-driven approaches in predictive modeling to craft brain-behavior relationships that are free from a priori hypotheses and not solely based on potentially irreproducible literature. Moreover, we note a relative dearth of resting-state literature, which could be used to better understand chemosensory networks with less influence from motion artifacts induced via gustatory or olfactory paradigms. Finally, we note a lack of genomics data, which could clarify individual and heritable differences in chemosensory perception.

Statistical Perspective on Functional and Causal Neural Connectomics: A Comparative Study

Representation of brain network interactions is fundamental to the translation of neural structure to brain function. As such, methodologies for mapping neural interactions into structural models, i.e., inference of functional connectome from neural recordings, are key for the study of brain networks. While multiple approaches have been proposed for functional connectomics based on statistical associations between neural activity, association does not necessarily incorporate causation. Additional approaches have been proposed to incorporate aspects of causality to turn functional connectomes into causal functional connectomes, however, these methodologies typically focus on specific aspects of causality. This warrants a systematic statistical framework for causal functional connectomics that defines the foundations of common aspects of causality. Such a framework can assist in contrasting existing approaches and to guide development of further causal methodologies. In this work, we develop such a statistical guide. In particular, we consolidate the notions of associations and representations of neural interaction, i.e., types of neural connectomics, and then describe causal modeling in the statistics literature. We particularly focus on the introduction of directed Markov graphical models as a framework through which we define the Directed Markov Property—an essential criterion for examining the causality of proposed functional connectomes. We demonstrate how based on these notions, a comparative study of several existing approaches for finding causal functional connectivity from neural activity can be conducted. We proceed by providing an outlook ahead regarding the additional properties that future approaches could include to thoroughly address causality.

Conductance-based dynamic causal modeling: A mathematical review of its application to cross-power spectral densities

Dynamic Causal Modeling (DCM) is a Bayesian framework for inferring on hidden (latent) neuronal states, based on measurements of brain activity. Since its introduction in 2003 for functional magnetic resonance imaging data, DCM has been extended to electrophysiological data, and several variants have been developed. Their biophysically motivated formulations make these models promising candidates for providing a mechanistic understanding of human brain dynamics, both in health and disease. However, due to their complexity and reliance on concepts from several fields, fully understanding the mathematical and conceptual basis behind certain variants of DCM can be challenging. At the same time, a solid theoretical knowledge of the models is crucial to avoid pitfalls in the application of these models and interpretation of their results. In this paper, we focus on one of the most advanced formulations of DCM, i.e. conductance-based DCM for cross-spectral densities, whose components are described across multiple technical papers. The aim of the present article is to provide an accessible exposition of the mathematical background, together with an illustration of the model's behavior. To this end, we include step-by-step derivations of the model equations, point to important aspects in the software implementation of those models, and use simulations to provide an intuitive understanding of the type of responses that can be generated and the role that specific parameters play in the model. Furthermore, all code utilized for our simulations is made publicly available alongside the manuscript to allow readers an easy hands-on experience with conductance-based DCM.

'Dark matter', second waves and epidemiological modelling

Recent reports using conventional Susceptible, Exposed, Infected and Removed models suggest that the next wave of the COVID-19 pandemic in the UK could overwhelm health services, with fatalities exceeding the first wave. We used Bayesian model comparison to revisit these conclusions, allowing for heterogeneity of exposure, susceptibility and transmission. We used dynamic causal modelling to estimate the evidence for alternative models of daily cases and deaths from the USA, the UK, Brazil, Italy, France, Spain, Mexico, Belgium, Germany and Canada over the period 25 January 2020 to 15 June 2020. These data were used to estimate the proportions of people (i) not exposed to the virus, (ii) not susceptible to infection when exposed and (iii) not infectious when susceptible to infection. Bayesian model comparison furnished overwhelming evidence for heterogeneity of exposure, susceptibility and transmission. Furthermore, both lockdown and the build-up of population immunity contributed to viral transmission in all but one country. Small variations in heterogeneity were sufficient to explain large differences in mortality rates. The best model of UK data predicts a second surge of fatalities will be much less than the first peak. The size of the second wave depends sensitively on the loss of immunity and the efficacy of Find-Test-Trace-Isolate-Support programmes. In summary, accounting for heterogeneity of exposure, susceptibility and transmission suggests that the next wave of the SARS-CoV-2 pandemic will be much smaller than conventional models predict, with less economic and health disruption. This heterogeneity means that seroprevalence underestimates effective herd immunity and, crucially, the potential of public health programmes.

Decreased effective connection from the parahippocampal gyrus to the prefrontal cortex in Internet gaming disorder: A MVPA and spDCM study

OBJECTIVES

Understanding the neural mechanisms underlying Internet gaming disorder (IGD) is essential for the condition's diagnosis and treatment. Nevertheless, the pathological mechanisms of IGD remain elusive at present. Hence, we employed multi-voxel pattern analysis (MVPA) and spectral dynamic causal modeling (spDCM) to explore this issue.

METHODS

Resting-state fMRI data were collected from 103 IGD subjects (male = 57) and 99 well-matched recreational game users (RGUs, male = 51). Regional homogeneity was calculated as the feature for MVPA based on the support vector machine (SVM) with leave-one- out cross-validation. Mean time series data extracted from the brain regions in accordance with the MVPA results were used for further spDCM analysis.

RESULTS

Results display a high accuracy of 82.67% (sensitivity of 83.50% and specificity of 81.82%) in the classification of the two groups. The most discriminative brain regions that contributed to the classification were the bilateral parahippocampal gyrus (PG), right anterior cingulate cortex (ACC), and middle frontal gyrus (MFG). Significant correlations were found between addiction severity (IAT and DSM scores) and the ReHo values of the brain regions that contributed to the classification. Moreover, the results of spDCM showed that compared with RGU, IGD showed decreased effective connectivity from the left PG to the right MFG and from the right PG to the ACC and decreased self-connection in the right PG.

CONCLUSIONS

These results show that the weakening of the PG and its connection with the prefrontal cortex, including the ACC and MFG, may be an underlying mechanism of IGD.

Modeling functional resting-state brain networks through neural message passing on the human connectome

In this work, we propose a natural model for information flow in the brain through a neural message-passing dynamics on a structural network of macroscopic regions, such as the human connectome (HC). In our model, each brain region is assumed to have a binary behavior (active or not), the strengths of interactions among them are encoded in the anatomical connectivity matrix defined by the HC, and the dynamics of the system is defined by the Belief Propagation (BP) algorithm, working near the critical point of the network. We show that in the absence of direct external stimuli the BP algorithm converges to a spatial map of activations that is similar to the Default Mode Network (DMN) of the brain, which has been defined from the analysis of functional MRI data. Moreover, we use Susceptibility Propagation (SP) to compute the matrix of long-range correlations between the different regions and show that the modules defined by a clustering of this matrix resemble several Resting State Networks (RSN) determined experimentally. Both results suggest that the functional DMN and RSNs can be seen as simple consequences of the anatomical structure of the brain and a neural message-passing dynamics between macroscopic regions. With the new model, we explore predictions on how functional maps change when the anatomical brain network suffers structural alterations, like in Alzheimer's disease and in lesions of the Corpus Callosum. The implications and novel interpretations suggested by the model, as well as the role of criticality, are discussed.

Bayesian Modelling of Induced Responses and Neuronal Rhythms

Neural rhythms or oscillations are ubiquitous in neuroimaging data. These spectral responses have been linked to several cognitive processes; including working memory, attention, perceptual binding and neuronal coordination. In this paper, we show how Bayesian methods can be used to finesse the ill-posed problem of reconstructing-and explaining-oscillatory responses. We offer an overview of recent developments in this field, focusing on (i) the use of MEG data and Empirical Bayes to build hierarchical models for group analyses-and the identification of important sources of inter-subject variability and (ii) the construction of novel dynamic causal models of intralaminar recordings to explain layer-specific activity. We hope to show that electrophysiological measurements contain much more spatial information than is often thought: on the one hand, the dynamic causal modelling of non-invasive (low spatial resolution) electrophysiology can afford sub-millimetre (hyper-acute) resolution that is limited only by the (spatial) complexity of the underlying (dynamic causal) forward model. On the other hand, invasive microelectrode recordings (that penetrate different cortical layers) can reveal laminar-specific responses and elucidate hierarchical message passing and information processing within and between cortical regions at a macroscopic scale. In short, the careful and biophysically grounded modelling of sparse data enables one to characterise the neuronal architectures generating oscillations in a remarkable detail.

Mapping Internet gaming disorder using effective connectivity: A spectral dynamic causal modeling study

OBJECTS

Understanding the neural basis underlying Internet gaming disorder (IGD) is essential for the diagnosis and treatment of this type of behavioural addiction. Aberrant resting-state functional connectivity (rsFC) of the default mode network (DMN) has been reported in individuals with IGD. Since rsFC is not a directional analysis, the effective connectivity within the DMN in IGD remains unclear. Here, we employed spectral dynamic causal modeling (spDCM) to explore this issue.

METHODS

Resting state fMRI data were collected from 64 IGD (age: 22.6 ± 2.2) and 63 well-matched recreational Internet game users (RGU, age: 23.1 ± 2.5). Voxel-based mean time series data extracted from the 4 brain regions within the DMN (medial prefrontal cortex, mPFC; posterior cingulate cortex, PCC; bilateral inferior parietal lobule, left IPL/right IPL) of two groups during the resting state were used for the spDCM analysis.

RESULTS

Compared with RGU, IGD showed reduced effective connectivity from the mPFC to the PCC and from the left IPL to the mPFC, with reduced self-connection in the PCC and the left IPL.

CONCLUSIONS

The spDCM could distinguish the changes in the functional architecture between two groups more precisely than rsFC. Our findings suggest that the decreased excitatory connectivity from the mPFC to the PCC may be a crucial biomarker for IGD. Future brain-based intervention should pay attention to dysregulation in the IPL-mPFC-PCC circuits.

Generic dynamic causal modelling: An illustrative application to Parkinson's disease

We present a technical development in the dynamic causal modelling of electrophysiological responses that combines qualitatively different neural mass models within a single network. This affords the option to couple various cortical and subcortical nodes that differ in their form and dynamics. Moreover, it enables users to implement new neural mass models in a straightforward and standardized way. This generic framework hence supports flexibility and facilitates the exploration of increasingly plausible models. We illustrate this by coupling a basal ganglia-thalamus model to a (previously validated) cortical model developed specifically for motor cortex. The ensuing DCM is used to infer pathways that contribute to the suppression of beta oscillations induced by dopaminergic medication in patients with Parkinson's disease. Experimental recordings were obtained from deep brain stimulation electrodes (implanted in the subthalamic nucleus) and simultaneous magnetoencephalography. In line with previous studies, our results indicate a reduction of synaptic efficacy within the circuit between the subthalamic nucleus and external pallidum, as well as reduced efficacy in connections of the hyperdirect and indirect pathway leading to this circuit. This work forms the foundation for a range of modelling studies of the synaptic mechanisms (and pathophysiology) underlying event-related potentials and cross-spectral densities.

A biophysical model of dynamic balancing of excitation and inhibition in fast oscillatory large-scale networks

Over long timescales, neuronal dynamics can be robust to quite large perturbations, such as changes in white matter connectivity and grey matter structure through processes including learning, aging, development and certain disease processes. One possible explanation is that robust dynamics are facilitated by homeostatic mechanisms that can dynamically rebalance brain networks. In this study, we simulate a cortical brain network using the Wilson-Cowan neural mass model with conduction delays and noise, and use inhibitory synaptic plasticity (ISP) to dynamically achieve a spatially local balance between excitation and inhibition. Using MEG data from 55 subjects we find that ISP enables us to simultaneously achieve high correlation with multiple measures of functional connectivity, including amplitude envelope correlation and phase locking. Further, we find that ISP successfully achieves local E/I balance, and can consistently predict the functional connectivity computed from real MEG data, for a much wider range of model parameters than is possible with a model without ISP.

Intersubject variability and induced gamma in the visual cortex: DCM with empirical Bayes and neural fields

This article describes the first application of a generic (empirical) Bayesian analysis of between‐subject effects in the dynamic causal modeling (DCM) of electrophysiological (MEG) data. It shows that (i) non‐invasive (MEG) data can be used to characterize subject‐specific differences in cortical microcircuitry and (ii) presents a validation of DCM with neural fields that exploits intersubject variability in gamma oscillations. We find that intersubject variability in visually induced gamma responses reflects changes in the excitation‐inhibition balance in a canonical cortical circuit. Crucially, this variability can be explained by subject‐specific differences in intrinsic connections to and from inhibitory interneurons that form a pyramidal‐interneuron gamma network. Our approach uses Bayesian model reduction to evaluate the evidence for (large sets of) nested models—and optimize the corresponding connectivity estimates at the within and between‐subject level. We also consider Bayesian cross‐validation to obtain predictive estimates for gamma‐response phenotypes, using a leave‐one‐out procedure. Hum Brain Mapp 37:4597–4614, 2016. © The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Optimally controlling the human connectome: the role of network topology

To meet ongoing cognitive demands, the human brain must seamlessly transition from one brain state to another, in the process drawing on different cognitive systems. How does the brain's network of anatomical connections help facilitate such transitions? Which features of this network contribute to making one transition easy and another transition difficult? Here, we address these questions using network control theory. We calculate the optimal input signals to drive the brain to and from states dominated by different cognitive systems. The input signals allow us to assess the contributions made by different brain regions. We show that such contributions, which we measure as energy, are correlated with regions' weighted degrees. We also show that the network communicability, a measure of direct and indirect connectedness between brain regions, predicts the extent to which brain regions compensate when input to another region is suppressed. Finally, we identify optimal states in which the brain should start (and finish) in order to minimize transition energy. We show that the optimal target states display high activity in hub regions, implicating the brain's rich club. Furthermore, when rich club organization is destroyed, the energy cost associated with state transitions increases significantly, demonstrating that it is the richness of brain regions that makes them ideal targets.

Bayesian model reduction and empirical Bayes for group (DCM) studies

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.

Effective connectivity of visual word recognition and homophone orthographic errors

The study of orthographic errors in a transparent language like Spanish is an important topic in relation to writing acquisition. The development of neuroimaging techniques, particularly functional magnetic resonance imaging (fMRI), has enabled the study of such relationships between brain areas. The main objective of the present study was to explore the patterns of effective connectivity by processing pseudohomophone orthographic errors among subjects with high and low spelling skills. Two groups of 12 Mexican subjects each, matched by age, were formed based on their results in a series of ad hoc spelling-related out-scanner tests: a high spelling skills (HSSs) group and a low spelling skills (LSSs) group. During the f MRI session, two experimental tasks were applied (spelling recognition task and visuoperceptual recognition task). Regions of Interest and their signal values were obtained for both tasks. Based on these values, structural equation models (SEMs) were obtained for each group of spelling competence (HSS and LSS) and task through maximum likelihood estimation, and the model with the best fit was chosen in each case. Likewise, dynamic causal models (DCMs) were estimated for all the conditions across tasks and groups. The HSS group's SEM results suggest that, in the spelling recognition task, the right middle temporal gyrus, and, to a lesser extent, the left parahippocampal gyrus receive most of the significant effects, whereas the DCM results in the visuoperceptual recognition task show less complex effects, but still congruent with the previous results, with an important role in several areas. In general, these results are consistent with the major findings in partial studies about linguistic activities but they are the first analyses of statistical effective brain connectivity in transparent languages.

Reliability of Dynamic Causal Modeling using the Statistical Parametric Mapping Toolbox

Dynamic causal modeling (DCM) is a recently developed approach for effective connectivity measurement in the brain. It has attracted considerable attention in recent years and quite widespread used to investigate brain connectivity in response to different tasks as well as auditory, visual, and somatosensory stimulation. This method uses complex algorithms, and currently the only implementation available is the Statistical Parametric Mapping (SPM8) toolbox with functionality for use on EEG and fMRI. The objective of the current work is to test the robustness of the toolbox when applied to EEG, by comparing results obtained from various versions of the software and operating systems when using identical datasets. Contrary to expectations, it was found that estimated connectivities were not consistent between different operating systems, the version of SPM8, or the version of MATLAB being used. The exact cause of this problem is not clear, but may relate to the high number of parameters in the model. Caution is thus recommended when interpreting the results of DCM estimated with the SPM8 software.

Bidirectional control of absence seizures by the basal ganglia: a computational evidence

Absence epilepsy is believed to be associated with the abnormal interactions between the cerebral cortex and thalamus. Besides the direct coupling, anatomical evidence indicates that the cerebral cortex and thalamus also communicate indirectly through an important intermediate bridge–basal ganglia. It has been thus postulated that the basal ganglia might play key roles in the modulation of absence seizures, but the relevant biophysical mechanisms are still not completely established. Using a biophysically based model, we demonstrate here that the typical absence seizure activities can be controlled and modulated by the direct GABAergic projections from the substantia nigra pars reticulata (SNr) to either the thalamic reticular nucleus (TRN) or the specific relay nuclei (SRN) of thalamus, through different biophysical mechanisms. Under certain conditions, these two types of seizure control are observed to coexist in the same network. More importantly, due to the competition between the inhibitory SNr-TRN and SNr-SRN pathways, we find that both decreasing and increasing the activation of SNr neurons from the normal level may considerably suppress the generation of spike-and-slow wave discharges in the coexistence region. Overall, these results highlight the bidirectional functional roles of basal ganglia in controlling and modulating absence seizures, and might provide novel insights into the therapeutic treatments of this brain disorder.

Epilepsy is a general term for conditions with recurring seizures. Absence seizures are one of several kinds of seizures, which are characterized by typical 2–4 Hz spike-and-slow wave discharges (SWDs). There is accumulating evidence that absence seizures are due to abnormal interactions between cerebral cortex and thalamus, and the basal ganglia may take part in controlling such brain disease via the indirect basal ganglia-thalamic pathway relaying at superior colliculus. Actually, the basal ganglia not only send indirect signals to thalamus, but also communicate with several key nuclei of thalamus through multiple direct GABAergic projections. Nevertheless, whether and how these direct pathways regulate absence seizure activities are still remain unknown. By computational modelling, we predicted that two direct inhibitory basal ganglia-thalamic pathways emitting from the substantia nigra pars reticulata may also participate in the control of absence seizures. Furthermore, we showed that these two types of seizure control can coexist in the same network, and depending on the instant network state, both lowing and increasing the activation of SNr neurons may inhibit the SWDs due to the existence of competition. Our findings emphasize the bidirectional modulation effects of basal ganglia on absence seizures, and might have physiological implications on the treatment of absence epilepsy.

Contrast gain control and horizontal interactions in V1: a DCM study

Using high-density electrocorticographic recordings – from awake-behaving monkeys – and dynamic causal modelling, we characterised contrast dependent gain control in visual cortex, in terms of synaptic rate constants and intrinsic connectivity. Specifically, we used neural field models to quantify the balance of excitatory and inhibitory influences; both in terms of the strength and spatial dispersion of horizontal intrinsic connections. Our results allow us to infer that increasing contrast increases the sensitivity or gain of superficial pyramidal cells to inputs from spiny stellate populations. Furthermore, changes in the effective spatial extent of horizontal coupling nuance the spatiotemporal filtering properties of cortical laminae in V1 — effectively preserving higher spatial frequencies. These results are consistent with recent non-invasive human studies of contrast dependent changes in the gain of pyramidal cells elaborating forward connections — studies designed to test specific hypotheses about precision and gain control based on predictive coding. Furthermore, they are consistent with established results showing that the receptive fields of V1 units shrink with increasing visual contrast.

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A new observation model suitable for ECoG recordings.

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An canonical microcircuit field model.

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A DCM treatment of multiple experimental conditions and trial-specific effects.

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Excitation-inhibition balance in terms of strength and dispersion.

Modeling ketamine effects on synaptic plasticity during the mismatch negativity

This paper presents a model-based investigation of mechanisms underlying the reduction of mismatch negativity (MMN) amplitudes under the NMDA-receptor antagonist ketamine. We applied dynamic causal modeling and Bayesian model selection to data from a recent ketamine study of the roving MMN paradigm, using a cross-over, double-blind, placebo-controlled design. Our modeling was guided by a predictive coding framework that unifies contemporary "adaptation" and "model adjustment" MMN theories. Comparing a series of dynamic causal models that allowed for different expressions of neuronal adaptation and synaptic plasticity, we obtained 3 major results: 1) We replicated previous results that both adaptation and short-term plasticity are necessary to explain MMN generation per se; 2) we found significant ketamine effects on synaptic plasticity, but not adaptation, and a selective ketamine effect on the forward connection from left primary auditory cortex to superior temporal gyrus; 3) this model-based estimate of ketamine effects on synaptic plasticity correlated significantly with ratings of ketamine-induced impairments in cognition and control. Our modeling approach thus suggests a concrete mechanism for ketamine effects on MMN that correlates with drug-induced psychopathology. More generally, this demonstrates the potential of modeling for inferring on synaptic physiology, and its pharmacological modulation, from electroencephalography data.

Neural masses and fields in dynamic causal modeling

Dynamic causal modeling (DCM) provides a framework for the analysis of effective connectivity among neuronal subpopulations that subtend invasive (electrocorticograms and local field potentials) and non-invasive (electroencephalography and magnetoencephalography) electrophysiological responses. This paper reviews the suite of neuronal population models including neural masses, fields and conductance-based models that are used in DCM. These models are expressed in terms of sets of differential equations that allow one to model the synaptic underpinnings of connectivity. We describe early developments using neural mass models, where convolution-based dynamics are used to generate responses in laminar-specific populations of excitatory and inhibitory cells. We show that these models, though resting on only two simple transforms, can recapitulate the characteristics of both evoked and spectral responses observed empirically. Using an identical neuronal architecture, we show that a set of conductance based models-that consider the dynamics of specific ion-channels-present a richer space of responses; owing to non-linear interactions between conductances and membrane potentials. We propose that conductance-based models may be more appropriate when spectra present with multiple resonances. Finally, we outline a third class of models, where each neuronal subpopulation is treated as a field; in other words, as a manifold on the cortical surface. By explicitly accounting for the spatial propagation of cortical activity through partial differential equations (PDEs), we show that the topology of connectivity-through local lateral interactions among cortical layers-may be inferred, even in the absence of spatially resolved data. We also show that these models allow for a detailed analysis of structure-function relationships in the cortex. Our review highlights the relationship among these models and how the hypothesis asked of empirical data suggests an appropriate model class.

Dynamic causal modeling suggests serial processing of tactile vibratory stimuli in the human somatosensory cortex--an fMRI study

Sensitivity to location and frequency of tactile stimuli is a characterizing feature of human primary (S1), and secondary (S2) somatosensory cortices. Recent evidence suggests that S1 is predominantly receptive to stimulus location, while S2 is attuned to stimulus frequency. Although it is well established in humans that tactile frequency information is relayed serially from S1 to S2, a recent study, using functional magnetic resonance imaging (fMRI) in combination with dynamic causal modeling (DCM), suggested that somatosensory inputs are processed in parallel in S1 and S2. In the present fMRI/DCM study, we revisited this controversy and investigated the specialization of the human somatosensory cortical areas with regard to tactile stimulus representations, as well as their effective connectivity. During brain imaging, 14 participants performed a somatosensory discrimination task on vibrotactile stimuli. Importantly, the model space for DCM was chosen to allow for direct inference on the question of interest by systematically varying the information transmission from pure parallel to pure serial implementations. Bayesian model comparison on the level of model families strongly favors a serial, instead of a parallel processing route for tactile stimulus information along the somatosensory pathway. Our fMRI/DCM data thus support previous suggestions of a sequential information transmission from S1 to S2 in humans.

Neural field theory with variance dynamics

Previous neural field models have mostly been concerned with prediction of mean neural activity and with second order quantities such as its variance, but without feedback of second order quantities on the dynamics. Here the effects of feedback of the variance on the steady states and adiabatic dynamics of neural systems are calculated using linear neural field theory to estimate the neural voltage variance, then including this quantity in the total variance parameter of the nonlinear firing rate-voltage response function, and thus into determination of the fixed points and the variance itself. The general results further clarify the limits of validity of approaches with and without inclusion of variance dynamics. Specific applications show that stability against a saddle-node bifurcation is reduced in a purely cortical system, but can be either increased or decreased in the corticothalamic case, depending on the initial state. Estimates of critical variance scalings near saddle-node bifurcation are also found, including physiologically based normalizations and new scalings for mean firing rate and the position of the bifurcation.

Effects of transcranial Direct Current Stimulation (tDCS) on cortical activity: a computational modeling study

Although it is well-admitted that transcranial Direct Current Stimulation (tDCS) allows for interacting with brain endogenous rhythms, the exact mechanisms by which externally-applied fields modulate the activity of neurons remain elusive. In this study a novel computational model (a neural mass model including subpopulations of pyramidal cells and inhibitory interneurons mediating synaptic currents with either slow or fast kinetics) of the cerebral cortex was elaborated to investigate the local effects of tDCS on neuronal populations based on an in-vivo experimental study. Model parameters were adjusted to reproduce evoked potentials (EPs) recorded from the somatosensory cortex of the rabbit in response to air-puffs applied on the whiskers. EPs were simulated under control condition (no tDCS) as well as under anodal and cathodal tDCS fields. Results first revealed that a feed-forward inhibition mechanism must be included in the model for accurate simulation of actual EPs (peaks and latencies). Interestingly, results revealed that externally-applied fields are also likely to affect interneurons. Indeed, when interneurons get polarized then the characteristics of simulated EPs become closer to those of real EPs. In particular, under anodal tDCS condition, more realistic EPs could be obtained when pyramidal cells were depolarized and, simultaneously, slow (resp. fast) interneurons became de- (resp. hyper-) polarized. Geometrical characteristics of interneurons might provide some explanations for this effect.

Estimating the unmeasured membrane potential of neuronal populations from the EEG using a class of deterministic nonlinear filters

We present a model-based estimation method to reconstruct the unmeasured membrane potential of neuronal populations from a single-channel electroencephalographic (EEG) measurement. We consider a class of neural mass models that share a general structure, specifically the models by Stam et al (1999 Clin. Neurophysiol. 110 1801-13), Jansen and Rit (1995 Biol. Cybern. 73 357-66) and Wendling et al (2005 J. Clin. Neurophysiol. 22 343). Under idealized assumptions, we prove the global exponential convergence of our filter. Then, under more realistic assumptions, we investigate the robustness of our filter against model uncertainties and disturbances. Analytic proofs are provided for all results and our analyses are further illustrated via simulations.

Cross validation for selection of cortical interaction models from scalp EEG or MEG

A cross-validation (CV) method based on state-space framework is introduced for comparing the fidelity of different cortical interaction models to the measured scalp electroencephalogram (EEG) or magnetoencephalography (MEG) data being modeled. A state equation models the cortical interaction dynamics and an observation equation represents the scalp measurement of cortical activity and noise. The measured data are partitioned into training and test sets. The training set is used to estimate model parameters and the model quality is evaluated by computing test data innovations for the estimated model. Two CV metrics normalized mean square error and log-likelihood are estimated by averaging over different training/test partitions of the data. The effectiveness of this method of model selection is illustrated by comparing two linear modeling methods and two nonlinear modeling methods on simulated EEG data derived using both known dynamic systems and measured electrocorticography data from an epilepsy patient.

EEG and MEG data analysis in SPM8

SPM is a free and open source software written in MATLAB (The MathWorks, Inc.). In addition to standard M/EEG preprocessing, we presently offer three main analysis tools: (i) statistical analysis of scalp-maps, time-frequency images, and volumetric 3D source reconstruction images based on the general linear model, with correction for multiple comparisons using random field theory; (ii) Bayesian M/EEG source reconstruction, including support for group studies, simultaneous EEG and MEG, and fMRI priors; (iii) dynamic causal modelling (DCM), an approach combining neural modelling with data analysis for which there are several variants dealing with evoked responses, steady state responses (power spectra and cross-spectra), induced responses, and phase coupling. SPM8 is integrated with the FieldTrip toolbox , making it possible for users to combine a variety of standard analysis methods with new schemes implemented in SPM and build custom analysis tools using powerful graphical user interface (GUI) and batching tools.

Consistent spectral predictors for dynamic causal models of steady-state responses

Dynamic causal modelling (DCM) for steady-state responses (SSR) is a framework for inferring the mechanisms that underlie observed electrophysiological spectra, using biologically plausible generative models of neuronal dynamics. In this paper, we examine the dynamic repertoires of nonlinear conductance-based neural population models and propose a generative model of their power spectra. Our model comprises an ensemble of interconnected excitatory and inhibitory cells, where synaptic currents are mediated by fast, glutamatergic and GABAergic receptors and slower voltage-gated NMDA receptors. We explore two formulations of how hidden neuronal states (depolarisation and conductances) interact: through their mean and variance (mean-field model) or through their mean alone (neural-mass model). Both rest on a nonlinear Fokker–Planck description of population dynamics, which can exhibit bifurcations (phase transitions). We first characterise these phase transitions numerically: by varying critical model parameters, we elicit both fixed points and quasiperiodic dynamics that reproduce the spectral characteristics (~ 2–100 Hz) of real electrophysiological data. We then introduce a predictor of spectral activity using centre manifold theory and linear stability analysis. This predictor is based on sampling the system's Jacobian over the orbits of hidden neuronal states. This predictor behaves consistently and smoothly in the region of phase transitions, which permits the use of gradient descent methods for model inversion. We demonstrate this by inverting generative models (DCMs) of SSRs, using simulated data that entails phase transitions.

On meta-analyses of imaging data and the mixture of records

Neumann et al. (2010) aim to find directed graphical representations of the independence and dependence relations among activities in brain regions by applying a search procedure to merged fMRI activity records from a large number of contrasts obtained under a variety of conditions. To that end, Neumann et al., obtain three graphical models, justifying their search procedure with simulations that find that merging the data sampled from probability distributions characterized by two distinct Bayes net graphs results in a graphical object that combines the edges in the individual graphs. We argue that the graphical objects they obtain cannot be interpreted as representations of conditional independence and dependence relations among localized neural activities; specifically, directed edges and directed pathways in their graphical results may be artifacts of the manner in which separate studies are combined in the meta-analytic procedure. With a larger simulation study, we argue that their simulation results with combined data sets are an artifact of their choice of examples. We provide sufficient conditions and necessary conditions for the merger of two or more probability distributions, each characterized by the Markov equivalence class of a directed acyclic graph, to be describable by a Markov equivalence class whose edges are a union of those for the individual distributions. Contrary to Neumann et al., we argue that the scientific value of searches for network representations from imaging data lies in attempting to characterize large scaled neural mechanisms, and we suggest several alternative strategies for combining data from multiple experiments.