Population dynamics under the Laplace assumption

Attentional effects on local V1 microcircuits explain selective V1-V4 communication

Selective attention implements preferential routing of attended stimuli, likely through increasing the influence of the respective synaptic inputs on higher-area neurons. As the inputs of competing stimuli converge onto postsynaptic neurons, presynaptic circuits might offer the best target for attentional top-down influences. If those influences enabled presynaptic circuits to selectively entrain postsynaptic neurons, this might explain selective routing. Indeed, when two visual stimuli induce two gamma rhythms in V1, only the gamma induced by the attended stimulus entrains gamma in V4. Here, we modelled induced responses with a Dynamic Causal Model for Cross-Spectral Densities and found that selective entrainment can be explained by attentional modulation of intrinsic V1 connections. Specifically, local inhibition was decreased in the granular input layer and increased in the supragranular output layer of the V1 circuit that processed the attended stimulus. Thus, presynaptic attentional influences and ensuing entrainment were sufficient to mediate selective routing.

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.

Neuropharmacological computational analysis of longitudinal electroencephalograms in clozapine-treated patients with schizophrenia using hierarchical dynamic causal modeling

The hierarchical characteristics of the brain are prominent in the pharmacological treatment of psychiatric diseases, primarily targeting cellular receptors that extend upward to intrinsic connectivity within a region, interregional connectivity, and, consequently, clinical observations such as an electroencephalogram (EEG). To understand the long-term effects of neuropharmacological intervention on neurobiological properties at different hierarchical levels, we explored long-term changes in neurobiological parameters of an N-methyl-D-aspartate canonical microcircuit model (CMM-NMDA) in the default mode network (DMN) and auditory hallucination network (AHN) using dynamic causal modeling of longitudinal EEG in clozapine-treated patients with schizophrenia. The neurobiological properties of the CMM-NMDA model associated with symptom improvement in schizophrenia were found across hierarchical levels, from a reduced membrane capacity of the deep pyramidal cell and intrinsic connectivity with the inhibitory population in DMN and intrinsic and extrinsic connectivity in AHN. The medication duration mainly affects the intrinsic connectivity and NMDA time constant in DMN. Virtual perturbation analysis specified the contribution of each parameter to the cross-spectral density (CSD) of the EEG, particularly intrinsic connectivity and membrane capacitances for CSD frequency shifts and progression. It further reveals that excitatory and inhibitory connectivity complements frequency-specific CSD changes, notably the alpha frequency band in DMN. Positive and negative synergistic interactions exist between neurobiological properties primarily within the same region in patients treated with clozapine. The current study shows how computational neuropharmacology helps explore the multiscale link between neurobiological properties and clinical observations and understand the long-term mechanism of neuropharmacological intervention reflected in clinical EEG.

Accurate and Efficient Simulation of Very High-Dimensional Neural Mass Models with Distributed-Delay Connectome Tensors

This paper introduces methods and a novel toolbox that efficiently integrates high-dimensional Neural Mass Models (NMMs) specified by two essential components. The first is the set of nonlinear Random Differential Equations (RDEs) of the dynamics of each neural mass. The second is the highly sparse three-dimensional Connectome Tensor (CT) that encodes the strength of the connections and the delays of information transfer along the axons of each connection. To date, simplistic assumptions prevail about delays in the CT, often assumed to be Dirac-delta functions. In reality, delays are distributed due to heterogeneous conduction velocities of the axons connecting neural masses. These distributed-delay CTs are challenging to model. Our approach implements these models by leveraging several innovations. Semi-analytical integration of RDEs is done with the Local Linearization (LL) scheme for each neural mass model, ensuring dynamical fidelity to the original continuous-time nonlinear dynamic. This semi-analytic LL integration is highly computationally-efficient. In addition, a tensor representation of the CT facilitates parallel computation. It also seamlessly allows modeling distributed delays CT with any level of complexity or realism. This ease of implementation includes models with distributed-delay CTs. Consequently, our algorithm scales linearly with the number of neural masses and the number of equations they are represented with, contrasting with more traditional methods that scale quadratically at best. To illustrate the toolbox's usefulness, we simulate a single Zetterberg-Jansen-Rit (ZJR) cortical column, a single thalmo-cortical unit, and a toy example comprising 1000 interconnected ZJR columns. These simulations demonstrate the consequences of modifying the CT, especially by introducing distributed delays. The examples illustrate the complexity of explaining EEG oscillations, e.g., split alpha peaks, since they only appear for distinct neural masses. We provide an open-source Script for the toolbox.

A mean-field model of glutamate and GABA synaptic dynamics for functional MRS

Advances in functional magnetic resonance spectroscopy (fMRS) have enabled the quantification of activity-dependent changes in neurotransmitter concentrations in vivo. However, the physiological basis of the large changes in GABA and glutamate observed by fMRS (>10%) over short time scales of less than a minute remain unclear as such changes cannot be accounted for by known synthesis or degradation metabolic pathways. Instead, it has been hypothesized that fMRS detects shifts in neurotransmitter concentrations as they cycle from presynaptic vesicles, where they are largely invisible, to extracellular and cytosolic pools, where they are detectable. The present paper uses a computational modelling approach to demonstrate the viability of this hypothesis. A new mean-field model of the neural mechanisms generating the fMRS signal in a cortical voxel is derived. The proposed macroscopic mean-field model is based on a microscopic description of the neurotransmitter dynamics at the level of the synapse. Specifically, GABA and glutamate are assumed to cycle between three metabolic pools: packaged in the vesicles; active in the synaptic cleft; and undergoing recycling and repackaging in the astrocytic or neuronal cytosol. Computational simulations from the model are used to generate predicted changes in GABA and glutamate concentrations in response to different types of stimuli including pain, vision, and electric current stimulation. The predicted changes in the extracellular and cytosolic pools corresponded to those reported in empirical fMRS data. Furthermore, the model predicts a selective control mechanism of the GABA/glutamate relationship, whereby inhibitory stimulation reduces both neurotransmitters, whereas excitatory stimulation increases glutamate and decreases GABA. The proposed model bridges between neural dynamics and fMRS and provides a mechanistic account for the activity-dependent changes in the glutamate and GABA fMRS signals. Lastly, these results indicate that echo-time may be an important timing parameter that can be leveraged to maximise fMRS experimental outcomes.

Space-time resolved inference-based neurophysiological process imaging: application to resting-state alpha rhythm

Neural processes are complex and difficult to image. This paper presents a new space-time resolved brain imaging framework, called Neurophysiological Process Imaging (NPI), that identifies neurophysiological processes within cerebral cortex at the macroscopic scale. By fitting uncoupled neural mass models to each electromagnetic source time-series using a novel nonlinear inference method, population averaged membrane potentials and synaptic connection strengths are efficiently and accurately inferred and imaged across the whole cerebral cortex at a resolution afforded by source imaging. The efficiency of the framework enables return of the augmented source imaging results overnight using high performance computing. This suggests it can be used as a practical and novel imaging tool. To demonstrate the framework, it has been applied to resting-state magnetoencephalographic source estimates. The results suggest that endogenous inputs to cingulate, occipital, and inferior frontal cortex are essential modulators of resting-state alpha power. Moreover, endogenous input and inhibitory and excitatory neural populations play varied roles in mediating alpha power in different resting-state sub-networks. The framework can be applied to arbitrary neural mass models and has broad applicability to image neural processes in different brain states.

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.

Adiabatic dynamic causal modelling

This technical note introduces adiabatic dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity.

Memory and Markov Blankets

In theoretical biology, we are often interested in random dynamical systems-like the brain-that appear to model their environments. This can be formalized by appealing to the existence of a (possibly non-equilibrium) steady state, whose density preserves a conditional independence between a biological entity and its surroundings. From this perspective, the conditioning set, or Markov blanket, induces a form of vicarious synchrony between creature and world-as if one were modelling the other. However, this results in an apparent paradox. If all conditional dependencies between a system and its surroundings depend upon the blanket, how do we account for the mnemonic capacity of living systems? It might appear that any shared dependence upon past blanket states violates the independence condition, as the variables on either side of the blanket now share information not available from the current blanket state. This paper aims to resolve this paradox, and to demonstrate that conditional independence does not preclude memory. Our argument rests upon drawing a distinction between the dependencies implied by a steady state density, and the density dynamics of the system conditioned upon its configuration at a previous time. The interesting question then becomes: What determines the length of time required for a stochastic system to 'forget' its initial conditions? We explore this question for an example system, whose steady state density possesses a Markov blanket, through simple numerical analyses. We conclude with a discussion of the relevance for memory in cognitive systems like us.

Computational models link cellular mechanisms of neuromodulation to large-scale neural dynamics

Decades of neurobiological research have disclosed the diverse manners in which the response properties of neurons are dynamically modulated to support adaptive cognitive functions. This neuromodulation is achieved through alterations in the biophysical properties of the neuron. However, changes in cognitive function do not arise directly from the modulation of individual neurons, but are mediated by population dynamics in mesoscopic neural ensembles. Understanding this multiscale mapping is an important but nontrivial issue. Here, we bridge these different levels of description by showing how computational models parametrically map classic neuromodulatory processes onto systems-level models of neural activity. The ensuing critical balance of systems-level activity supports perception and action, although our knowledge of this mapping remains incomplete. In this way, quantitative models that link microscale neuronal neuromodulation to systems-level brain function highlight gaps in knowledge and suggest new directions for integrating theoretical and experimental work.

Neural Dynamics under Active Inference: Plausibility and Efficiency of Information Processing

Active inference is a normative framework for explaining behaviour under the free energy principle-a theory of self-organisation originating in neuroscience. It specifies neuronal dynamics for state-estimation in terms of a descent on (variational) free energy-a measure of the fit between an internal (generative) model and sensory observations. The free energy gradient is a prediction error-plausibly encoded in the average membrane potentials of neuronal populations. Conversely, the expected probability of a state can be expressed in terms of neuronal firing rates. We show that this is consistent with current models of neuronal dynamics and establish face validity by synthesising plausible electrophysiological responses. We then show that these neuronal dynamics approximate natural gradient descent, a well-known optimisation algorithm from information geometry that follows the steepest descent of the objective in information space. We compare the information length of belief updating in both schemes, a measure of the distance travelled in information space that has a direct interpretation in terms of metabolic cost. We show that neural dynamics under active inference are metabolically efficient and suggest that neural representations in biological agents may evolve by approximating steepest descent in information space towards the point of optimal inference.

Modelling thalamocortical circuitry shows that visually induced LTP changes laminar connectivity in human visual cortex

Neuroplasticity is essential to learning and memory in the brain; it has therefore also been implicated in numerous neurological and psychiatric disorders, making measuring the state of neuroplasticity of foremost importance to clinical neuroscience. Long-term potentiation (LTP) is a key mechanism of neuroplasticity and has been studied extensively, and invasively in non-human animals. Translation to human application largely relies on the validation of non-invasive measures of LTP. The current study presents a generative thalamocortical computational model of visual cortex for investigating and replicating interlaminar connectivity changes using non-invasive EEG recording of humans. The model is combined with a commonly used visual sensory LTP paradigm and fit to the empirical EEG data using dynamic causal modelling. The thalamocortical model demonstrated remarkable accuracy recapitulating post-tetanus changes seen in invasive research, including increased excitatory connectivity from thalamus to layer IV and from layer IV to II/III, established major sites of LTP in visual cortex. These findings provide justification for the implementation of the presented thalamocortical model for ERP research, including to provide increased detail on the nature of changes that underlie LTP induced in visual cortex. Future applications include translating rodent findings to non-invasive research in humans concerning deficits to LTP that may underlie neurological and psychiatric disease.

The brain’s ability to learn and form memories is governed by neuroplasticity. One of the major mechanisms of neuroplasticity is long-term potentiation (LTP). To study LTP in detail necessitates implanting electrodes in the brain of non-human animals. However, to translate this knowledge to humans requires a non-invasive method. Neural mass models use mathematical equations to describe the brain’s neural architecture and function over time. Fitting these models to real data, using methods such as dynamic causal modelling (DCM), helps to elucidate the connectivity and major channel changes that could have plausibly caused the observed effects in electroencephalography data recorded non-invasively from the scalp.

The current study presents a thalamocortical model of the neural architecture of the visual system combined with a thalamic compartment. The model is able to represent the basic transfer of visual information to the cortex, mediated by major receptor types. We combined the thalamocortical model with a visual processing task that uses black and white grating images to induce and measure LTP in visual cortex. We hypothesised that the changes in the model would be consistent with what is seen in animal invasive recordings.

The model demonstrated remarkable accuracy in recapitulating changes to neural architecture consistent with the induction of LTP in visual cortex. Additionally, the result demonstrated specificity to the visual input that induced LTP. Future applications include translating animal findings that are beginning to determine how disordered LTP may underlie neurological and psychiatric disease (for example depression, schizophrenia, autism, and dementia).

Generative modelling of the thalamo-cortical circuit mechanisms underlying the neurophysiological effects of ketamine

Cortical recordings of task-induced oscillations following subanaesthetic ketamine administration demonstrate alterations in amplitude, including increases at high-frequencies (gamma) and reductions at low frequencies (theta, alpha). To investigate the population-level interactions underlying these changes, we implemented a thalamo-cortical model (TCM) capable of recapitulating broadband spectral responses. Compared with an existing cortex-only 4-population model, Bayesian Model Selection preferred the TCM. The model was able to accurately and significantly recapitulate ketamine-induced reductions in alpha amplitude and increases in gamma amplitude. Parameter analysis revealed no change in receptor time-constants but significant increases in select synaptic connectivity with ketamine. Significantly increased connections included both AMPA and NMDA mediated connections from layer 2/3 superficial pyramidal cells to inhibitory interneurons and both GABAA and NMDA mediated within-population gain control of layer 5 pyramidal cells. These results support the use of extended generative models for explaining oscillatory data and provide in silico support for ketamine's ability to alter local coupling mediated by NMDA, AMPA and GABA-A.

Effective immunity and second waves: a dynamic causal modelling study

This technical report addresses a pressing issue in the trajectory of the coronavirus outbreak; namely, the rate at which effective immunity is lost following the first wave of the pandemic. This is a crucial epidemiological parameter that speaks to both the consequences of relaxing lockdown and the propensity for a second wave of infections. Using a dynamic causal model of reported cases and deaths from multiple countries, we evaluated the evidence models of progressively longer periods of immunity. The results speak to an effective population immunity of about three months that, under the model, defers any second wave for approximately six months in most countries. This may have implications for the window of opportunity for tracking and tracing, as well as for developing vaccination programmes, and other therapeutic interventions.

Effective immunity and second waves: a dynamic causal modelling study

This technical report addresses a pressing issue in the trajectory of the coronavirus outbreak; namely, the rate at which effective immunity is lost following the first wave of the pandemic. This is a crucial epidemiological parameter that speaks to both the consequences of relaxing lockdown and the propensity for a second wave of infections. Using a dynamic causal model of reported cases and deaths from multiple countries, we evaluated the evidence models of progressively longer periods of immunity. The results speak to an effective population immunity of about three months that, under the model, defers any second wave for approximately six months in most countries. This may have implications for the window of opportunity for tracking and tracing, as well as for developing vaccination programmes, and other therapeutic interventions.

Dynamic causal modelling of COVID-19

This technical report describes a dynamic causal model of the spread of coronavirus through a population. The model is based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time. The purpose of this model is to quantify the uncertainty that attends predictions of relevant outcomes. By assuming suitable conditional dependencies, one can model the effects of interventions (e.g., social distancing) and differences among populations (e.g., herd immunity) to predict what might happen in different circumstances. Technically, this model leverages state-of-the-art variational (Bayesian) model inversion and comparison procedures, originally developed to characterise the responses of neuronal ensembles to perturbations. Here, this modelling is applied to epidemiological populations-to illustrate the kind of inferences that are supported and how the model per se can be optimised given timeseries data. Although the purpose of this paper is to describe a modelling protocol, the results illustrate some interesting perspectives on the current pandemic; for example, the nonlinear effects of herd immunity that speak to a self-organised mitigation process.

Modules or Mean-Fields?

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

Dynamic causal modelling of COVID-19

This technical report describes a dynamic causal model of the spread of coronavirus through a population. The model is based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time. The purpose of this model is to quantify the uncertainty that attends predictions of relevant outcomes. By assuming suitable conditional dependencies, one can model the effects of interventions (e.g., social distancing) and differences among populations (e.g., herd immunity) to predict what might happen in different circumstances. Technically, this model leverages state-of-the-art variational (Bayesian) model inversion and comparison procedures, originally developed to characterise the responses of neuronal ensembles to perturbations. Here, this modelling is applied to epidemiological populations-to illustrate the kind of inferences that are supported and how the model per se can be optimised given timeseries data. Although the purpose of this paper is to describe a modelling protocol, the results illustrate some interesting perspectives on the current pandemic; for example, the nonlinear effects of herd immunity that speak to a self-organised mitigation process.

Markov blankets, information geometry and stochastic thermodynamics

This paper considers the relationship between thermodynamics, information and inference. In particular, it explores the thermodynamic concomitants of belief updating, under a variational (free energy) principle for self-organization. In brief, any (weakly mixing) random dynamical system that possesses a Markov blanket-i.e. a separation of internal and external states-is equipped with an information geometry. This means that internal states parametrize a probability density over external states. Furthermore, at non-equilibrium steady-state, the flow of internal states can be construed as a gradient flow on a quantity known in statistics as Bayesian model evidence. In short, there is a natural Bayesian mechanics for any system that possesses a Markov blanket. Crucially, this means that there is an explicit link between the inference performed by internal states and their energetics-as characterized by their stochastic thermodynamics. This article is part of the theme issue 'Harmonizing energy-autonomous computing and intelligence'.

Morphogenesis as Bayesian inference: A variational approach to pattern formation and control in complex biological systems

Recent advances in molecular biology such as gene editing [1], bioelectric recording and manipulation [2] and live cell microscopy using fluorescent reporters [3], [4] - especially with the advent of light-controlled protein activation through optogenetics [5] - have provided the tools to measure and manipulate molecular signaling pathways with unprecedented spatiotemporal precision. This has produced ever increasing detail about the molecular mechanisms underlying development and regeneration in biological organisms. However, an overarching concept - that can predict the emergence of form and the robust maintenance of complex anatomy - is largely missing in the field. Classic (i.e., dynamic systems and analytical mechanics) approaches such as least action principles are difficult to use when characterizing open, far-from equilibrium systems that predominate in Biology. Similar issues arise in neuroscience when trying to understand neuronal dynamics from first principles. In this (neurobiology) setting, a variational free energy principle has emerged based upon a formulation of self-organization in terms of (active) Bayesian inference. The free energy principle has recently been applied to biological self-organization beyond the neurosciences [6], [7]. For biological processes that underwrite development or regeneration, the Bayesian inference framework treats cells as information processing agents, where the driving force behind morphogenesis is the maximization of a cell's model evidence. This is realized by the appropriate expression of receptors and other signals that correspond to the cell's internal (i.e., generative) model of what type of receptors and other signals it should express. The emerging field of the free energy principle in pattern formation provides an essential quantitative formalism for understanding cellular decision-making in the context of embryogenesis, regeneration, and cancer suppression. In this paper, we derive the mathematics behind Bayesian inference - as understood in this framework - and use simulations to show that the formalism can reproduce experimental, top-down manipulations of complex morphogenesis. First, we illustrate this 'first principle' approach to morphogenesis through simulated alterations of anterior-posterior axial polarity (i.e., the induction of two heads or two tails) as in planarian regeneration. Then, we consider aberrant signaling and functional behavior of a single cell within a cellular ensemble - as a first step in carcinogenesis as false 'beliefs' about what a cell should 'sense' and 'do'. We further show that simple modifications of the inference process can cause - and rescue - mis-patterning of developmental and regenerative events without changing the implicit generative model of a cell as specified, for example, by its DNA. This formalism offers a new road map for understanding developmental change in evolution and for designing new interventions in regenerative medicine settings.

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.

Ion channels in EEG: isolating channel dysfunction in NMDA receptor antibody encephalitis

See Roberts and Breakspear (doi:10.1093/brain/awy136) for a scientific commentary on this article.Neurological and psychiatric practice frequently lack diagnostic probes that can assess mechanisms of neuronal communication non-invasively in humans. In N-methyl-d-aspartate (NMDA) receptor antibody encephalitis, functional molecular assays are particularly important given the presence of NMDA antibodies in healthy populations, the multifarious symptomology and the lack of radiological signs. Recent advances in biophysical modelling techniques suggest that inferring cellular-level properties of neural circuits from macroscopic measures of brain activity is possible. Here, we estimated receptor function from EEG in patients with NMDA receptor antibody encephalitis (n = 29) as well as from encephalopathic and neurological patient controls (n = 36). We show that the autoimmune patients exhibit distinct fronto-parietal network changes from which ion channel estimates can be obtained using a microcircuit model. Specifically, a dynamic causal model of EEG data applied to spontaneous brain responses identifies a selective deficit in signalling at NMDA receptors in patients with NMDA receptor antibody encephalitis but not at other ionotropic receptors. Moreover, though these changes are observed across brain regions, these effects predominate at the NMDA receptors of excitatory neurons rather than at inhibitory interneurons. Given that EEG is a ubiquitously available clinical method, our findings suggest a unique re-purposing of EEG data as an assay of brain network dysfunction at the molecular level.

Adaptive optimal input design and parametric estimation of nonlinear dynamical systems: application to neuronal modeling

OBJECTIVE

Many physical models of biological processes including neural systems are characterized by parametric nonlinear dynamical relations between driving inputs, internal states, and measured outputs of the process. Fitting such models using experimental data (data assimilation) is a challenging task since the physical process often operates in a noisy, possibly non-stationary environment; moreover, conducting multiple experiments under controlled and repeatable conditions can be impractical, time consuming or costly. The accuracy of model identification, therefore, is dictated principally by the quality and dynamic richness of collected data over single or few experimental sessions. Accordingly, it is highly desirable to design efficient experiments that, by exciting the physical process with smart inputs, yields fast convergence and increased accuracy of the model.

APPROACH

We herein introduce an adaptive framework in which optimal input design is integrated with square root cubature Kalman filters (OID-SCKF) to develop an online estimation procedure that first, converges significantly quicker, thereby permitting model fitting over shorter time windows, and second, enhances model accuracy when only few process outputs are accessible. The methodology is demonstrated on common nonlinear models and on a four-area neural mass model with noisy and limited measurements. Estimation quality (speed and accuracy) is benchmarked against high-performance SCKF-based methods that commonly employ dynamically rich informed inputs for accurate model identification.

MAIN RESULTS

For all the tested models, simulated single-trial and ensemble averages showed that OID-SCKF exhibited (i) faster convergence of parameter estimates and (ii) lower dependence on inter-trial noise variability with gains up to around 1000 ms in speed and 81% increase in variability for the neural mass models. In terms of accuracy, OID-SCKF estimation was superior, and exhibited considerably less variability across experiments, in identifying model parameters of (a) systems with challenging model inversion dynamics and (b) systems with fewer measurable outputs that directly relate to the underlying processes.

SIGNIFICANCE

Fast and accurate identification therefore carries particular promise for modeling of transient (short-lived) neuronal network dynamics using a spatially under-sampled set of noisy measurements, as is commonly encountered in neural engineering applications.

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate under CD-CKF. In conclusion, and with the CKF recently benchmarked against other advanced Bayesian techniques, the CD-CKF framework could provide significant gains in robustness and accuracy when estimating a variety of biological phenomena models where the underlying process dynamics unfold at time scales faster than those seen in collected measurements.

The Space-Clamped Hodgkin-Huxley System with Random Synaptic Input: Inhibition of Spiking by Weak Noise and Analysis with Moment Equations

We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model system obtained by an Euler method, it is found that with excitation only, there is a critical value of the steady-state excitatory conductance for repetitive spiking without noise, and for values of the conductance near the critical value, small noise has a powerfully inhibitory effect. For a given level of inhibition, there is also a critical value of the steady-state excitatory conductance for repetitive firing, and it is demonstrated that noise in either the excitatory or inhibitory processes or both can powerfully inhibit spiking. Furthermore, near the critical value, inverse stochastic resonance was observed when noise was present only in the inhibitory input process. The system of deterministic differential equations for the approximate first- and second-order moments of the model is derived. They are solved using Runge-Kutta methods, and the solutions are compared with the results obtained by simulation for various sets of parameters, including some with conductances obtained by experiment on pyramidal cells of rat prefrontal cortex. The mean and variance obtained from simulation are in good agreement when there is spiking induced by strong stimulation and relatively small noise or when the voltage is fluctuating at subthreshold levels. In the occasional spike mode sometimes exhibited by spinal motoneurons and cortical pyramidal cells, the assumptions underlying the moment equation approach are not satisfied. The simulation results show that noisy synaptic input of either an excitatory or inhibitory character or both may lead to the suppression of firing in neurons operating near a critical point and this has possible implications for cortical networks. Although suppression of firing is corroborated for the system of moment equations, there seem to be substantial differences between the dynamical properties of the original system of stochastic differential equations and the much larger system of moment equations.

Profiling neuronal ion channelopathies with non-invasive brain imaging and dynamic causal models: Case studies of single gene mutations

Clinical assessments of brain function rely upon visual inspection of electroencephalographic waveform abnormalities in tandem with functional magnetic resonance imaging. However, no current technology proffers in vivo assessments of activity at synapses, receptors and ion-channels, the basis of neuronal communication. Using dynamic causal modeling we compared electrophysiological responses from two patients with distinct monogenic ion channelopathies and a large cohort of healthy controls to demonstrate the feasibility of assaying synaptic-level channel communication non-invasively. Synaptic channel abnormality was identified in both patients (100% sensitivity) with assay specificity above 89%, furnishing estimates of neurotransmitter and voltage-gated ion throughput of sodium, calcium, chloride and potassium. This performance indicates a potential novel application as an adjunct for clinical assessments in neurological and psychiatric settings. More broadly, these findings indicate that biophysical models of synaptic channels can be estimated non-invasively, having important implications for advancing human neuroimaging to the level of non-invasive ion channel assays.

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Dynamic causal modeling (DCM) for M/EEG includes ion channel parameter estimates.

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Parameter estimates from patients with monogenic ion channelopathies were compared.

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Synaptic channel abnormality was identified in patients, with specificity above 89%.

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DCM could serve as a platform for non-invasively assaying brain molecular dynamics.

Losing control under ketamine: suppressed cortico-hippocampal drive following acute ketamine in rats

Systemic doses of the psychotomimetic ketamine alter the spectral characteristics of hippocampal and prefrontal cortical network activity. Using dynamic causal modeling (DCM) of cross-spectral densities, we quantify the putative synaptic mechanisms underlying ketamine effects in terms of changes in directed, effective connectivity between dorsal hippocampus and medial prefrontal (dCA1-mPFC) cortex of freely moving rats. We parameterize dose-dependent changes in spectral signatures of dCA1-mPFC local field potential recordings, using neural mass models of glutamatergic and GABAergic circuits. Optimizing DCMs of theta and gamma frequency range responses, model comparisons suggest that both enhanced gamma and depressed theta power result from a reduction in top-down connectivity from mPFC to the hippocampus, mediated by postsynaptic NMDA receptors (NMDARs). This is accompanied by an alteration in the bottom-up pathway from dCA1 to mPFC, which exhibits a distinct asymmetry: here, feed-forward drive at AMPA receptors increases in the presence of decreased NMDAR-mediated inputs. Setting these findings in the context of predictive coding suggests that NMDAR antagonism by ketamine in recurrent hierarchical networks may result in the failure of top-down connections from higher cortical regions to signal predictions to lower regions in the hierarchy, which consequently fail to respond consistently to errors. Given that NMDAR dysfunction has a central role in pathophysiological theories of schizophrenia and that theta and gamma rhythm abnormalities are evident in schizophrenic patients, the approach followed here may furnish a framework for the study of aberrant hierarchical message passing (of prediction errors) in schizophrenia-and the false perceptual inferences that ensue.

Self-organization, free energy minimization, and optimal grip on a field of affordances

In this paper, we set out to develop a theoretical and conceptual framework for the new field of Radical Embodied Cognitive Neuroscience. This framework should be able to integrate insights from several relevant disciplines: theory on embodied cognition, ecological psychology, phenomenology, dynamical systems theory, and neurodynamics. We suggest that the main task of Radical Embodied Cognitive Neuroscience is to investigate the phenomenon of skilled intentionality from the perspective of the self-organization of the brain-body-environment system, while doing justice to the phenomenology of skilled action. In previous work, we have characterized skilled intentionality as the organism's tendency toward an optimal grip on multiple relevant affordances simultaneously. Affordances are possibilities for action provided by the environment. In the first part of this paper, we introduce the notion of skilled intentionality and the phenomenon of responsiveness to a field of relevant affordances. Second, we use Friston's work on neurodynamics, but embed a very minimal version of his Free Energy Principle in the ecological niche of the animal. Thus amended, this principle is helpful for understanding the embeddedness of neurodynamics within the dynamics of the system "brain-body-landscape of affordances." Next, we show how we can use this adjusted principle to understand the neurodynamics of selective openness to the environment: interacting action-readiness patterns at multiple timescales contribute to the organism's selective openness to relevant affordances. In the final part of the paper, we emphasize the important role of metastable dynamics in both the brain and the brain-body-environment system for adequate affordance-responsiveness. We exemplify our integrative approach by presenting research on the impact of Deep Brain Stimulation on affordance responsiveness of OCD patients.

Engineering a thalamo-cortico-thalamic circuit on SpiNNaker: a preliminary study toward modeling sleep and wakefulness

We present a preliminary study of a thalamo-cortico-thalamic (TCT) implementation on SpiNNaker (Spiking Neural Network architecture), a brain inspired hardware platform designed to incorporate the inherent biological properties of parallelism, fault tolerance and energy efficiency. These attributes make SpiNNaker an ideal platform for simulating biologically plausible computational models. Our focus in this work is to design a TCT framework that can be simulated on SpiNNaker to mimic dynamical behavior similar to Electroencephalogram (EEG) time and power-spectra signatures in sleep-wake transition. The scale of the model is minimized for simplicity in this proof-of-concept study; thus the total number of spiking neurons is ≈1000 and represents a "mini-column" of the thalamocortical tissue. All data on model structure, synaptic layout and parameters is inspired from previous studies and abstracted at a level that is appropriate to the aims of the current study as well as computationally suitable for model simulation on a small 4-chip SpiNNaker system. The initial results from selective deletion of synaptic connectivity parameters in the model show similarity with EEG power spectra characteristics of sleep and wakefulness. These observations provide a positive perspective and a basis for future implementation of a very large scale biologically plausible model of thalamo-cortico-thalamic interactivity-the essential brain circuit that regulates the biological sleep-wake cycle and associated EEG rhythms.

Resting-state functional connectivity emerges from structurally and dynamically shaped slow linear fluctuations

Brain fluctuations at rest are not random but are structured in spatial patterns of correlated activity across different brain areas. The question of how resting-state functional connectivity (FC) emerges from the brain's anatomical connections has motivated several experimental and computational studies to understand structure-function relationships. However, the mechanistic origin of resting state is obscured by large-scale models' complexity, and a close structure-function relation is still an open problem. Thus, a realistic but simple enough description of relevant brain dynamics is needed. Here, we derived a dynamic mean field model that consistently summarizes the realistic dynamics of a detailed spiking and conductance-based synaptic large-scale network, in which connectivity is constrained by diffusion imaging data from human subjects. The dynamic mean field approximates the ensemble dynamics, whose temporal evolution is dominated by the longest time scale of the system. With this reduction, we demonstrated that FC emerges as structured linear fluctuations around a stable low firing activity state close to destabilization. Moreover, the model can be further and crucially simplified into a set of motion equations for statistical moments, providing a direct analytical link between anatomical structure, neural network dynamics, and FC. Our study suggests that FC arises from noise propagation and dynamical slowing down of fluctuations in an anatomically constrained dynamical system. Altogether, the reduction from spiking models to statistical moments presented here provides a new framework to explicitly understand the building up of FC through neuronal dynamics underpinned by anatomical connections and to drive hypotheses in task-evoked studies and for clinical applications.

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.

Combined neurostimulation and neuroimaging in cognitive neuroscience: past, present, and future

Modern neurostimulation approaches in humans provide controlled inputs into the operations of cortical regions, with highly specific behavioral consequences. This enables causal structure–function inferences, and in combination with neuroimaging, has provided novel insights into the basic mechanisms of action of neurostimulation on distributed networks. For example, more recent work has established the capacity of transcranial magnetic stimulation (TMS) to probe causal interregional influences, and their interaction with cognitive state changes. Combinations of neurostimulation and neuroimaging now face the challenge of integrating the known physiological effects of neurostimulation with theoretical and biological models of cognition, for example, when theoretical stalemates between opposing cognitive theories need to be resolved. This will be driven by novel developments, including biologically informed computational network analyses for predicting the impact of neurostimulation on brain networks, as well as novel neuroimaging and neurostimulation techniques. Such future developments may offer an expanded set of tools with which to investigate structure–function relationships, and to formulate and reconceptualize testable hypotheses about complex neural network interactions and their causal roles in cognition.

Functional and effective connectivity: a review

Over the past 20 years, neuroimaging has become a predominant technique in systems neuroscience. One might envisage that over the next 20 years the neuroimaging of distributed processing and connectivity will play a major role in disclosing the brain's functional architecture and operational principles. The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. I accepted the invitation to write this review with great pleasure and hope to celebrate and critique the achievements to date, while addressing the challenges ahead.

Analysing connectivity with Granger causality and dynamic causal modelling

This review considers state-of-the-art analyses of functional integration in neuronal macrocircuits. We focus on detecting and estimating directed connectivity in neuronal networks using Granger causality (GC) and dynamic causal modelling (DCM). These approaches are considered in the context of functional segregation and integration and--within functional integration--the distinction between functional and effective connectivity. We review recent developments that have enjoyed a rapid uptake in the discovery and quantification of functional brain architectures. GC and DCM have distinct and complementary ambitions that are usefully considered in relation to the detection of functional connectivity and the identification of models of effective connectivity. We highlight the basic ideas upon which they are grounded, provide a comparative evaluation and point to some outstanding issues.

Post-hoc selection of dynamic causal models

Dynamic causal modelling (DCM) was originally proposed as a hypothesis driven procedure in which a small number of neurobiologically motivated models are compared. Model comparison in this context usually proceeds by individually fitting each model to data and then approximating the corresponding model evidence with a free energy bound. However, a recent trend has emerged for comparing very large numbers of models in a more exploratory manner. This led Friston and Penny (2011) to propose a post-hoc approximation to the model evidence, which is computed by optimising only the largest (full) model of a set of models. The evidence for any (reduced) submodel is then obtained using a generalisation of the Savage-Dickey density ratio (Dickey, 1971). The benefit of this post-hoc approach is a huge reduction in the computational time required for model fitting. This is because only a single model is fitted to data, allowing a potentially huge model space to be searched relatively quickly. In this paper, we explore the relationship between the free energy bound and post-hoc approximations to the model evidence in the context of deterministic (bilinear) dynamic causal models (DCMs) for functional magnetic resonance imaging data.

A neuronal model of predictive coding accounting for the mismatch negativity

The mismatch negativity (MMN) is thought to index the activation of specialized neural networks for active prediction and deviance detection. However, a detailed neuronal model of the neurobiological mechanisms underlying the MMN is still lacking, and its computational foundations remain debated. We propose here a detailed neuronal model of auditory cortex, based on predictive coding, that accounts for the critical features of MMN. The model is entirely composed of spiking excitatory and inhibitory neurons interconnected in a layered cortical architecture with distinct input, predictive, and prediction error units. A spike-timing dependent learning rule, relying upon NMDA receptor synaptic transmission, allows the network to adjust its internal predictions and use a memory of the recent past inputs to anticipate on future stimuli based on transition statistics. We demonstrate that this simple architecture can account for the major empirical properties of the MMN. These include a frequency-dependent response to rare deviants, a response to unexpected repeats in alternating sequences (ABABAA…), a lack of consideration of the global sequence context, a response to sound omission, and a sensitivity of the MMN to NMDA receptor antagonists. Novel predictions are presented, and a new magnetoencephalography experiment in healthy human subjects is presented that validates our key hypothesis: the MMN results from active cortical prediction rather than passive synaptic habituation.

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.

Distributed processing; distributed functions?

After more than twenty years busily mapping the human brain, what have we learned from neuroimaging? This review (coda) considers this question from the point of view of structure-function relationships and the two cornerstones of functional neuroimaging; functional segregation and integration. Despite remarkable advances and insights into the brain's functional architecture, the earliest and simplest challenge in human brain mapping remains unresolved: We do not have a principled way to map brain function onto its structure in a way that speaks directly to cognitive neuroscience. Having said this, there are distinct clues about how this might be done: First, there is a growing appreciation of the role of functional integration in the distributed nature of neuronal processing. Second, there is an emerging interest in data-driven cognitive ontologies, i.e., that are internally consistent with functional anatomy. We will focus this review on the growing momentum in the fields of functional connectivity and distributed brain responses and consider this in the light of meta-analyses that use very large data sets to disclose large-scale structure-function mappings in the human brain.

Computational psychiatry

Computational ideas pervade many areas of science and have an integrative explanatory role in neuroscience and cognitive science. However, computational depictions of cognitive function have had surprisingly little impact on the way we assess mental illness because diseases of the mind have not been systematically conceptualized in computational terms. Here, we outline goals and nascent efforts in the new field of computational psychiatry, which seeks to characterize mental dysfunction in terms of aberrant computations over multiple scales. We highlight early efforts in this area that employ reinforcement learning and game theoretic frameworks to elucidate decision-making in health and disease. Looking forwards, we emphasize a need for theory development and large-scale computational phenotyping in human subjects.

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 models and physiological inference: a validation study using isoflurane anaesthesia in rodents

Generative models of neuroimaging and electrophysiological data present new opportunities for accessing hidden or latent brain states. Dynamic causal modeling (DCM) uses Bayesian model inversion and selection to infer the synaptic mechanisms underlying empirically observed brain responses. DCM for electrophysiological data, in particular, aims to estimate the relative strength of synaptic transmission at different cell types and via specific neurotransmitters. Here, we report a DCM validation study concerning inference on excitatory and inhibitory synaptic transmission, using different doses of a volatile anaesthetic agent (isoflurane) to parametrically modify excitatory and inhibitory synaptic processing while recording local field potentials (LFPs) from primary auditory cortex (A1) and the posterior auditory field (PAF) in the auditory belt region in rodents. We test whether DCM can infer, from the LFP measurements, the expected drug-induced changes in synaptic transmission mediated via fast ionotropic receptors; i.e., excitatory (glutamatergic) AMPA and inhibitory GABA(A) receptors. Cross- and auto-spectra from the two regions were used to optimise three DCMs based on biologically plausible neural mass models and specific network architectures. Consistent with known extrinsic connectivity patterns in sensory hierarchies, we found that a model comprising forward connections from A1 to PAF and backward connections from PAF to A1 outperformed a model with forward connections from PAF to A1 and backward connections from A1 to PAF and a model with reciprocal lateral connections. The parameter estimates from the most plausible model indicated that the amplitude of fast glutamatergic excitatory postsynaptic potentials (EPSPs) and inhibitory postsynaptic potentials (IPSPs) behaved as predicted by previous neurophysiological studies. Specifically, with increasing levels of anaesthesia, glutamatergic EPSPs decreased linearly, whereas fast GABAergic IPSPs displayed a nonlinear (saturating) increase. The consistency of our model-based in vivo results with experimental in vitro results lends further validity to the capacity of DCM to infer on synaptic processes using macroscopic neurophysiological data.

Alterations in brain connectivity underlying beta oscillations in Parkinsonism

Cortico-basal ganglia-thalamocortical circuits are severely disrupted by the dopamine depletion of Parkinson's disease (PD), leading to pathologically exaggerated beta oscillations. Abnormal rhythms, found in several circuit nodes are correlated with movement impairments but their neural basis remains unclear. Here, we used dynamic causal modelling (DCM) and the 6-hydroxydopamine-lesioned rat model of PD to examine the effective connectivity underlying these spectral abnormalities. We acquired auto-spectral and cross-spectral measures of beta oscillations (10-35 Hz) from local field potential recordings made simultaneously in the frontal cortex, striatum, external globus pallidus (GPe) and subthalamic nucleus (STN), and used these data to optimise neurobiologically plausible models. Chronic dopamine depletion reorganised the cortico-basal ganglia-thalamocortical circuit, with increased effective connectivity in the pathway from cortex to STN and decreased connectivity from STN to GPe. Moreover, a contribution analysis of the Parkinsonian circuit distinguished between pathogenic and compensatory processes and revealed how effective connectivity along the indirect pathway acquired a strategic importance that underpins beta oscillations. In modelling excessive beta synchrony in PD, these findings provide a novel perspective on how altered connectivity in basal ganglia-thalamocortical circuits reflects a balance between pathogenesis and compensation, and predicts potential new therapeutic targets to overcome dysfunctional oscillations.

An in vivo assay of synaptic function mediating human cognition

The contribution of dopamine to working memory has been studied extensively [1-3]. Here, we exploited its well characterized effects [1-3] to validate a novel human in vivo assay of ongoing synaptic [4, 5] processing. We obtained magnetoencephalographic (MEG) measurements from subjects performing a working memory (WM) task during a within-subject, placebo-controlled, pharmacological (dopaminergic) challenge. By applying dynamic causal modeling (DCM), a Bayesian technique for neuronal system identification [6], to MEG signals from prefrontal cortex, we demonstrate that it is possible to infer synaptic signaling by specific ion channels in behaving humans. Dopamine-induced enhancement of WM performance was accompanied by significant changes in MEG signal power, and a DCM assay disclosed related changes in synaptic signaling. By estimating the contribution of ionotropic receptors (AMPA, NMDA, and GABA(A)) to the observed spectral response, we demonstrate changes in their function commensurate with the synaptic effects of dopamine. The validity of our model is reinforced by a striking quantitative effect on NMDA and AMPA receptor signaling that predicted behavioral improvement over subjects. Our results provide a proof-of-principle demonstration of a novel framework for inferring, noninvasively, neuromodulatory influences on ion channel signaling via specific ionotropic receptors, providing a window on the hidden synaptic events mediating discrete psychological processes in humans.

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).

Dynamics underlying spontaneous human alpha oscillations: a data-driven approach

Although the cognitive and clinical correlates of spontaneous human alpha oscillations as recorded with electroencephalography (EEG) or magnetoencephalography (MEG) are well documented, the dynamics underlying these oscillations is still a matter of debate. This study proposes a data-driven method to reveal the dynamics of these oscillations. It demonstrates that spontaneous human alpha oscillations as recorded with MEG can be viewed as noise-perturbed damped harmonic oscillations. This provides evidence for the hypothesis that these oscillations reflect filtered noise and hence do not possess limit-cycle dynamics. To illustrate the use of the model, we apply it to two data-sets in which a decrease in alpha power can be observed across conditions. The associated differences in the estimated model parameters show that observed decreases in alpha power are associated with different kinds of changes in the dynamics. Thus, the model parameters are useful dynamical biomarkers for spontaneous human alpha oscillations.

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.