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Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models; including stationary points and limit cycles and the possibility for bifurcations and transitions among different modes of activity. This complexity allows neural mass models to describe the itinerant features of brain dynamics. However, expressive, nonlinear neural mass models are often difficult to fit to empirical data without additional simplifying assumptions: e.g., that the system can be modelled as linear perturbations around a fixed point. In this study we offer a mathematical analysis of neural mass models, specifically the canonical microcircuit model, providing analytical solutions describing slow changes in the type of cortical activity, i.e. dynamical itinerancy. We derive a perturbation analysis up to second order of the phase flow, together with adiabatic approximations. This allows us to describe amplitude modulations in a relatively simple mathematical format providing analytic proof-of-principle for the existence of semi-stable states of cortical dynamics at the scale of a cortical column. This work allows for model inversion of neural mass models, not only around fixed points, but over regions of phase space that encompass transitions among semi or multi-stable states of oscillatory activity. Crucially, these theoretical results speak to model inversion in the context of multiple semi-stable brain states, such as the transition between interictal, pre-ictal and ictal activity in epilepsy., Competing Interests: There are no competing interests for any of the authors., (Copyright: © 2023 Cooray et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

An isotropic dynamical system is one that looks the same in every direction, i.e., if we imagine standing somewhere within an isotropic system, we would not be able to differentiate between different lines of sight. Conversely, anisotropy is a measure of the extent to which a system deviates from perfect isotropy, with larger values indicating greater discrepancies between the structure of the system along its axes. Here, we derive the form of a generalised scalable (mechanically similar) discretized field theoretic Lagrangian that allows for levels of anisotropy to be directly estimated via timeseries of arbitrary dimensionality. We generate synthetic data for both isotropic and anisotropic systems and, by using Bayesian model inversion and reduction, show that we can discriminate between the two datasets - thereby demonstrating proof of principle. We then apply this methodology to murine calcium imaging data collected in rest and task states, showing that anisotropy can be estimated directly from different brain states and cortical regions in an empirical in vivo biological setting. We hope that this theoretical foundation, together with the methodology and publicly available MATLAB code, will provide an accessible way for researchers to obtain new insight into the structural organization of neural systems in terms of how scalable neural regions grow - both ontogenetically during the development of an individual organism, as well as phylogenetically across species., (© 2022. The Author(s).)

Neurophysiological measurements suggest that human information processing is evinced by neuronal activity. However, the quantitative relationship between the activity of a brain region and its information processing capacity remains unclear. We introduce and validate a mathematical model of the information processing capacity of a brain region in terms of neuronal activity, input storage capacity, and the arrival rate of afferent information. We applied the model to fMRI data obtained from a flanker paradigm in young and old subjects. Our analysis showed that-for a given cognitive task and subject-higher information processing capacity leads to lower neuronal activity and faster responses. Crucially, processing capacity-as estimated from fMRI data-predicted task and age-related differences in reaction times, speaking to the model's predictive validity. This model offers a framework for modelling of brain dynamics in terms of information processing capacity, and may be exploited for studies of predictive coding and Bayes-optimal decision-making., (© 2022. The Author(s).)

This work considers a class of canonical neural networks comprising rate coding models, wherein neural activity and plasticity minimise a common cost function-and plasticity is modulated with a certain delay. We show that such neural networks implicitly perform active inference and learning to minimise the risk associated with future outcomes. Mathematical analyses demonstrate that this biological optimisation can be cast as maximisation of model evidence, or equivalently minimisation of variational free energy, under the well-known form of a partially observed Markov decision process model. This equivalence indicates that the delayed modulation of Hebbian plasticity-accompanied with adaptation of firing thresholds-is a sufficient neuronal substrate to attain Bayes optimal inference and control. We corroborated this proposition using numerical analyses of maze tasks. This theory offers a universal characterisation of canonical neural networks in terms of Bayesian belief updating and provides insight into the neuronal mechanisms underlying planning and adaptive behavioural control., (© 2022. The Author(s).)

The clinical syndromes caused by frontotemporal lobar degeneration are heterogeneous, including the behavioural variant frontotemporal dementia (bvFTD) and progressive supranuclear palsy. Although pathologically distinct, they share many behavioural, cognitive and physiological features, which may in part arise from common deficits of major neurotransmitters such as γ-aminobutyric acid (GABA). Here, we quantify the GABAergic impairment and its restoration with dynamic causal modelling of a double-blind placebo-controlled crossover pharmaco-magnetoencephalography study. We analysed 17 patients with bvFTD, 15 patients with progressive supranuclear palsy, and 20 healthy age- and gender-matched controls. In addition to neuropsychological assessment and structural MRI, participants undertook two magnetoencephalography sessions using a roving auditory oddball paradigm: once on placebo and once on 10 mg of the oral GABA reuptake inhibitor tiagabine. A subgroup underwent ultrahigh-field magnetic resonance spectroscopy measurement of GABA concentration, which was reduced among patients. We identified deficits in frontotemporal processing using conductance-based biophysical models of local and global neuronal networks. The clinical relevance of this physiological deficit is indicated by the correlation between top-down connectivity from frontal to temporal cortex and clinical measures of cognitive and behavioural change. A critical validation of the biophysical modelling approach was evidence from parametric empirical Bayes analysis that GABA levels in patients, measured by spectroscopy, were related to posterior estimates of patients' GABAergic synaptic connectivity. Further evidence for the role of GABA in frontotemporal lobar degeneration came from confirmation that the effects of tiagabine on local circuits depended not only on participant group, but also on individual baseline GABA levels. Specifically, the phasic inhibition of deep cortico-cortical pyramidal neurons following tiagabine, but not placebo, was a function of GABA concentration. The study provides proof-of-concept for the potential of dynamic causal modelling to elucidate mechanisms of human neurodegenerative disease, and explains the variation in response to candidate therapies among patients. The laminar- and neurotransmitter-specific features of the modelling framework, can be used to study other treatment approaches and disorders. In the context of frontotemporal lobar degeneration, we suggest that neurophysiological restoration in selected patients, by targeting neurotransmitter deficits, could be used to bridge between clinical and preclinical models of disease, and inform the personalized selection of drugs and stratification of patients for future clinical trials., (© The Author(s) (2021). Published by Oxford University Press on behalf of the Guarantors of Brain.)

We propose a computational neurology of movement based on the convergence of theoretical neurobiology and clinical neurology. A significant development in the former is the idea that we can frame brain function as a process of (active) inference, in which the nervous system makes predictions about its sensory data. These predictions depend upon an implicit predictive (generative) model used by the brain. This means neural dynamics can be framed as generating actions to ensure sensations are consistent with these predictions-and adjusting predictions when they are not. We illustrate the significance of this formulation for clinical neurology by simulating a clinical examination of the motor system using an upper limb coordination task. Specifically, we show how tendon reflexes emerge naturally under the right kind of generative model. Through simulated perturbations, pertaining to prior probabilities of this model's variables, we illustrate the emergence of hyperreflexia and pendular reflexes, reminiscent of neurological lesions in the corticospinal tract and cerebellum. We then turn to the computational lesions causing hypokinesia and deficits of coordination. This in silico lesion-deficit analysis provides an opportunity to revisit classic neurological dichotomies (e.g. pyramidal versus extrapyramidal systems) from the perspective of modern approaches to theoretical neurobiology-and our understanding of the neurocomputational architecture of movement control based on first principles., (© The Author(s) (2021). Published by Oxford University Press on behalf of the Guarantors of Brain.)

The aim of this paper is to leverage the free-energy principle and its corollary process theory, active inference, to develop a generic, generalizable model of the representational capacities of living creatures; that is, a theory of phenotypic representation. Given their ubiquity, we are concerned with distributed forms of representation (e.g., population codes), whereby patterns of ensemble activity in living tissue come to represent the causes of sensory input or data. The active inference framework rests on the Markov blanket formalism, which allows us to partition systems of interest, such as biological systems, into internal states, external states, and the blanket (active and sensory) states that render internal and external states conditionally independent of each other. In this framework, the representational capacity of living creatures emerges as a consequence of their Markovian structure and nonequilibrium dynamics, which together entail a dual-aspect information geometry. This entails a modest representational capacity: internal states have an intrinsic information geometry that describes their trajectory over time in state space, as well as an extrinsic information geometry that allows internal states to encode (the parameters of) probabilistic beliefs about (fictive) external states. Building on this, we describe here how, in an automatic and emergent manner, information about stimuli can come to be encoded by groups of neurons bound by a Markov blanket; what is known as the neuronal packet hypothesis. As a concrete demonstration of this type of emergent representation, we present numerical simulations showing that self-organizing ensembles of active inference agents sharing the right kind of probabilistic generative model are able to encode recoverable information about a stimulus array., (Copyright © 2020 The Authors. Published by Elsevier Ltd.. All rights reserved.)

This letter considers a class of biologically plausible cost functions for neural networks, where the same cost function is minimized by both neural activity and plasticity. We show that such cost functions can be cast as a variational bound on model evidence under an implicit generative model. Using generative models based on partially observed Markov decision processes (POMDP), we show that neural activity and plasticity perform Bayesian inference and learning, respectively, by maximizing model evidence. Using mathematical and numerical analyses, we establish the formal equivalence between neural network cost functions and variational free energy under some prior beliefs about latent states that generate inputs. These prior beliefs are determined by particular constants (e.g., thresholds) that define the cost function. This means that the Bayes optimal encoding of latent or hidden states is achieved when the network's implicit priors match the process that generates its inputs. This equivalence is potentially important because it suggests that any hyperparameter of a neural network can itself be optimized-by minimization with respect to variational free energy. Furthermore, it enables one to characterize a neural network formally, in terms of its prior beliefs.

The notions of degeneracy and redundancy are important constructs in many areas, ranging from genomics through to network science. Degeneracy finds a powerful role in neuroscience, explaining key aspects of distributed processing and structure-function relationships in the brain. For example, degeneracy accounts for the superadditive effect of lesions on functional deficits in terms of a "many-to-one" structure-function mapping. In this paper, we offer a principled account of degeneracy and redundancy, when function is operationalized in terms of active inference, namely, a formulation of perception and action as belief updating under generative models of the world. In brief, "degeneracy" is quantified by the "entropy" of posterior beliefs about the causes of sensations, while "redundancy" is the "complexity" cost incurred by forming those beliefs. From this perspective, degeneracy and redundancy are complementary: Active inference tries to minimize redundancy while maintaining degeneracy. This formulation is substantiated using statistical and mathematical notions of degenerate mappings and statistical efficiency. We then illustrate changes in degeneracy and redundancy during the learning of a word repetition task. Finally, we characterize the effects of lesions-to intrinsic and extrinsic connections-using in silico disconnections. These numerical analyses highlight the fundamental difference between degeneracy and redundancy-and how they score distinct imperatives for perceptual inference and structure learning that are relevant to synthetic and biological intelligence., (© The Author(s) 2020. Published by Oxford University Press.)

In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, a special case exists in which the action is scale invariant if it satisfies the following two constraints: 1) it must depend upon a scale-free Lagrangian, and 2) the Lagrangian must change under scale in the same way as the inverse time, [Formula: see text]. Our contribution lies in the derivation of a generalised Lagrangian, in the form of a power series expansion, that satisfies these constraints. This generalised Lagrangian furnishes a normal form for dynamic causal models-state space models based upon differential equations-that can be used to distinguish scale symmetry from scale freeness in empirical data. We establish face validity with an analysis of simulated data, in which we show how scale symmetry can be identified and how the associated conserved quantities can be estimated in neuronal time series., Competing Interests: The authors have declared that no competing interests exist.

The prefrontal cortex is vital for a range of cognitive processes, including working memory, attention, and decision-making. Notably, its absence impairs the performance of tasks requiring the maintenance of information through a delay period. In this paper, we formulate a rodent task-which requires maintenance of delay-period activity-as a Markov decision process and treat optimal task performance as an (active) inference problem. We simulate the behavior of a Bayes optimal mouse presented with 1 of 2 cues that instructs the selection of concurrent visual and auditory targets on a trial-by-trial basis. Formulating inference as message passing, we reproduce features of neuronal coupling within and between prefrontal regions engaged by this task. We focus on the micro-circuitry that underwrites delay-period activity and relate it to functional specialization within the prefrontal cortex in primates. Finally, we simulate the electrophysiological correlates of inference and demonstrate the consequences of lesions to each part of our in silico prefrontal cortex. In brief, this formulation suggests that recurrent excitatory connections-which support persistent neuronal activity-encode beliefs about transition probabilities over time. We argue that attentional modulation can be understood as the contextualization of sensory input by these persistent beliefs., (© The Author(s) 2019. Published by Oxford University Press.)

Active inference is an approach to understanding behaviour that rests upon the idea that the brain uses an internal generative model to predict incoming sensory data. The fit between this model and data may be improved in two ways. The brain could optimise probabilistic beliefs about the variables in the generative model (i.e. perceptual inference). Alternatively, by acting on the world, it could change the sensory data, such that they are more consistent with the model. This implies a common objective function (variational free energy) for action and perception that scores the fit between an internal model and the world. We compare two free energy functionals for active inference in the framework of Markov decision processes. One of these is a functional of beliefs (i.e. probability distributions) about states and policies, but a function of observations, while the second is a functional of beliefs about all three. In the former (expected free energy), prior beliefs about outcomes are not part of the generative model (because they are absorbed into the prior over policies). Conversely, in the second (generalised free energy), priors over outcomes become an explicit component of the generative model. When using the free energy function, which is blind to future observations, we equip the generative model with a prior over policies that ensure preferred (i.e. priors over) outcomes are realised. In other words, if we expect to encounter a particular kind of outcome, this lends plausibility to those policies for which this outcome is a consequence. In addition, this formulation ensures that selected policies minimise uncertainty about future outcomes by minimising the free energy expected in the future. When using the free energy functional-that effectively treats future observations as hidden states-we show that policies are inferred or selected that realise prior preferences by minimising the free energy of future expectations. Interestingly, the form of posterior beliefs about policies (and associated belief updating) turns out to be identical under both formulations, but the quantities used to compute them are not.

To exhibit social intelligence, animals have to recognize whom they are communicating with. One way to make this inference is to select among internal generative models of each conspecific who may be encountered. However, these models also have to be learned via some form of Bayesian belief updating. This induces an interesting problem: When receiving sensory input generated by a particular conspecific, how does an animal know which internal model to update? We consider a theoretical and neurobiologically plausible solution that enables inference and learning of the processes that generate sensory inputs (e.g., listening and understanding) and reproduction of those inputs (e.g., talking or singing), under multiple generative models. This is based on recent advances in theoretical neurobiology-namely, active inference and post hoc (online) Bayesian model selection. In brief, this scheme fits sensory inputs under each generative model. Model parameters are then updated in proportion to the probability that each model could have generated the input (i.e., model evidence). The proposed scheme is demonstrated using a series of (real zebra finch) birdsongs, where each song is generated by several different birds. The scheme is implemented using physiologically plausible models of birdsong production. We show that generalized Bayesian filtering, combined with model selection, leads to successful learning across generative models, each possessing different parameters. These results highlight the utility of having multiple internal models when making inferences in social environments with multiple sources of sensory information.

This technical note describes a variational or Bayesian implementation of representational similarity analysis (RSA) and pattern component modelling (PCM). It considers RSA and PCM as Bayesian model comparison procedures that assess the evidence for stimulus or condition-specific patterns of responses distributed over voxels or channels. On this view, one can use standard variational inference procedures to quantify the contributions of particular patterns to the data, by evaluating second-order parameters or hyperparameters. Crucially, this allows one to use parametric empirical Bayes (PEB) to infer which patterns are consistent among subjects. At the between-subject level, one can then assess the evidence for different (combinations of) hypotheses about condition-specific effects using Bayesian model comparison. Alternatively, one can select a single hypothesis that best explains the pattern of responses using Bayesian model selection. This note rehearses the technical aspects of within and between-subject RSA using a worked example, as implemented in the Statistical Parametric Mapping (SPM) software. En route, we highlight the connection between univariate and multivariate analyses of neuroimaging data and the sorts of analyses that are possible using component modelling and representational similarity analysis., (Copyright © 2019 The Authors. Published by Elsevier Inc. All rights reserved.)

Predictive processing (e.g., predictive coding) is a predominant paradigm in cognitive neuroscience. This Primer considers the various levels of commitment neuroscientists have to the neuronal process theories that accompany the principles of predictive processing. Specifically, it reviews and contextualises a recent PLOS Biology study of alpha oscillations and travelling waves. We will see that alpha oscillations emerge naturally under the computational architectures implied by predictive coding-and may tell us something profound about recurrent message passing in brain hierarchies. Specifically, the bidirectional nature of forward and backward waves speaks to opportunities to understand attention and how it nuances bottom-up and top-down influences., Competing Interests: The author has declared that no competing interests exist.

In this paper, we draw from recent theoretical work on active perception, which suggests that the brain makes use of an internal (i.e., generative) model to make inferences about the causes of sensations. This view treats visual sensations as consequent on action (i.e., saccades) and implies that visual percepts must be actively constructed via a sequence of eye movements. Oculomotor control calls on a distributed set of brain sources that includes the dorsal and ventral frontoparietal (attention) networks. We argue that connections from the frontal eye fields to ventral parietal sources represent the mapping from "where", fixation location to information derived from "what" representations in the ventral visual stream. During scene construction, this mapping must be learned, putatively through changes in the effective connectivity of these synapses. Here, we test the hypothesis that the coupling between the dorsal frontal cortex and the right temporoparietal cortex is modulated during saccadic interrogation of a simple visual scene. Using dynamic causal modeling for magnetoencephalography with (male and female) human participants, we assess the evidence for changes in effective connectivity by comparing models that allow for this modulation with models that do not. We find strong evidence for modulation of connections between the two attention networks; namely, a disinhibition of the ventral network by its dorsal counterpart. SIGNIFICANCE STATEMENT This work draws from recent theoretical accounts of active vision and provides empirical evidence for changes in synaptic efficacy consistent with these computational models. In brief, we used magnetoencephalography in combination with eye-tracking to assess the neural correlates of a form of short-term memory during a dot cancellation task. Using dynamic causal modeling to quantify changes in effective connectivity, we found evidence that the coupling between the dorsal and ventral attention networks changed during the saccadic interrogation of a simple visual scene. Intuitively, this is consistent with the idea that these neuronal connections may encode beliefs about "what I would see if I looked there", and that this mapping is optimized as new data are obtained with each fixation., (Copyright © 2019 Parr et al.)

Many physiological and pathological changes in brain function manifest in eye-movement control. As such, assessment of oculomotion is an invaluable part of a clinical examination and affords a non-invasive window on several key aspects of neuronal computation. While oculomotion is often used to detect deficits of the sort associated with vascular or neoplastic events; subtler (e.g. pharmacological) effects on neuronal processing also induce oculomotor changes. We have previously framed oculomotor control as part of active vision, namely, a process of inference comprising two distinct but related challenges. The first is inferring where to look, and the second is inferring how to implement the selected action. In this paper, we draw from recent theoretical work on the neuromodulatory control of active inference. This allows us to simulate the sort of changes we would expect in oculomotor behaviour, following pharmacological enhancement or suppression of key neuromodulators-in terms of deciding where to look and the ensuing trajectory of the eye movement itself. We focus upon the influence of cholinergic and GABAergic agents on the speed of saccades, and consider dopaminergic and noradrenergic effects on more complex, memory-guided, behaviour. In principle, a computational approach to understanding the relationship between pharmacology and oculomotor behaviour affords the opportunity to estimate the influence of a given pharmaceutical upon neuronal function, and to use this to optimise therapeutic interventions on an individual basis.

Parkinson's disease (PD) is a neurodegenerative condition in which aberrant oscillatory synchronization of neuronal activity at beta frequencies (15-35 Hz) across the cortico-basal ganglia-thalamocortical circuit is associated with debilitating motor symptoms, such as bradykinesia and rigidity. Mounting evidence suggests that the magnitude of beta synchrony in the parkinsonian state fluctuates over time, but the mechanisms by which thalamocortical circuitry regulates the dynamic properties of cortical beta in PD are poorly understood. Using the recently developed generic Dynamic Causal Modelling (DCM) framework, we recursively optimized a set of plausible models of the thalamocortical circuit (n = 144) to infer the neural mechanisms that best explain the transitions between low and high beta power states observed in recordings of field potentials made in the motor cortex of anesthetized Parkinsonian rats. Bayesian model comparison suggests that upregulation of cortical rhythmic activity in the beta-frequency band results from changes in the coupling strength both between and within the thalamus and motor cortex. Specifically, our model indicates that high levels of cortical beta synchrony are mainly achieved by a delayed (extrinsic) input from thalamic relay cells to deep pyramidal cells and a fast (intrinsic) input from middle pyramidal cells to superficial pyramidal cells. From a clinical perspective, our study provides insights into potential therapeutic strategies that could be utilized to modulate the network mechanisms responsible for the enhancement of cortical beta in PD. Specifically, we speculate that cortical stimulation aimed to reduce the enhanced excitatory inputs to either the superficial or deep pyramidal cells could be a potential non-invasive therapeutic strategy for PD., (Copyright © 2019 The Authors. Published by Elsevier Inc. All rights reserved.)

The selective attention for identification model (SAIM) is an established model of selective visual attention. SAIM implements translation-invariant object recognition, in scenes with multiple objects, using the parallel distributed processing (PDP) paradigm. Here, we show that SAIM can be formulated as Bayesian inference. Crucially, SAIM uses excitatory feedback to combine top-down information (i.e. object knowledge) with bottom-up sensory information. By contrast, predictive coding implementations of Bayesian inference use inhibitory feedback. By formulating SAIM as a predictive coding scheme, we created a new version of SAIM that uses inhibitory feedback. Simulation studies showed that both types of architectures can reproduce the response time costs induced by multiple objects-as found in visual search experiments. However, due to the different nature of the feedback, the two SAIM schemes make distinct predictions about the motifs of microcircuits mediating the effects of top-down afferents. We discuss empirical (neuroimaging) methods to test the predictions of the two inference architectures.

Successful behaviour depends on the right balance between maximising reward and soliciting information about the world. Here, we show how different types of information-gain emerge when casting behaviour as surprise minimisation. We present two distinct mechanisms for goal-directed exploration that express separable profiles of active sampling to reduce uncertainty. 'Hidden state' exploration motivates agents to sample unambiguous observations to accurately infer the (hidden) state of the world. Conversely, 'model parameter' exploration, compels agents to sample outcomes associated with high uncertainty, if they are informative for their representation of the task structure. We illustrate the emergence of these types of information-gain, termed active inference and active learning, and show how these forms of exploration induce distinct patterns of 'Bayes-optimal' behaviour. Our findings provide a computational framework for understanding how distinct levels of uncertainty systematically affect the exploration-exploitation trade-off in decision-making., Competing Interests: PS, JP, TH, TF, MK, KF No competing interests declared, (© 2019, Schwartenbeck et al.)

This paper considers the emergence of a generalised synchrony in ensembles of coupled self-organising systems, such as neurons. We start from the premise that any self-organising system complies with the free energy principle, in virtue of placing an upper bound on its entropy. Crucially, the free energy principle allows one to interpret biological systems as inferring the state of their environment or external milieu. An emergent property of this inference is synchronisation among an ensemble of systems that infer each other. Here, we investigate the implications of neuronal dynamics by simulating neuronal networks, where each neuron minimises its free energy. We cast the ensuing ensemble dynamics in terms of inference and show that cardinal behaviours of neuronal networks - both in vivo and in vitro - can be explained by this framework. In particular, we test the hypotheses that (i) generalised synchrony is an emergent property of free energy minimisation; thereby explaining synchronisation in the resting brain: (ii) desynchronisation is induced by exogenous input; thereby explaining event-related desynchronisation and (iii) structure learning emerges in response to causal structure in exogenous input; thereby explaining functional segregation in real neuronal systems.

Despite the potential for better understanding functional neuroanatomy, the complex relationship between neuroimaging measures of brain structure and function has confounded integrative, multimodal analyses of brain connectivity. This is particularly true for task-related effective connectivity, which describes the causal influences between neuronal populations. Here, we assess whether measures of structural connectivity may usefully inform estimates of effective connectivity in larger scale brain networks. To this end, we introduce an integrative approach, capitalising on two recent statistical advances: Parametric Empirical Bayes, which provides group-level estimates of effective connectivity, and Bayesian model reduction, which enables rapid comparison of competing models. Crucially, we show that structural priors derived from high angular resolution diffusion imaging on a dynamic causal model of a 12-region network-based on functional MRI data from the same subjects-substantially improve model evidence (posterior probability 1.00). This provides definitive evidence that structural and effective connectivity depend upon each other in mediating distributed, large-scale interactions in the brain. Furthermore, this work offers novel perspectives for understanding normal brain architecture and its disintegration in clinical conditions.

In this work, we address the neuronal encoding problem from a Bayesian perspective. Specifically, we ask whether neuronal responses in an in vitro neuronal network are consistent with ideal Bayesian observer responses under the free energy principle. In brief, we stimulated an in vitro cortical cell culture with stimulus trains that had a known statistical structure. We then asked whether recorded neuronal responses were consistent with variational message passing based upon free energy minimisation (i.e., evidence maximisation). Effectively, this required us to solve two problems: first, we had to formulate the Bayes-optimal encoding of the causes or sources of sensory stimulation, and then show that these idealised responses could account for observed electrophysiological responses. We describe a simulation of an optimal neural network (i.e., the ideal Bayesian neural code) and then consider the mapping from idealised in silico responses to recorded in vitro responses. Our objective was to find evidence for functional specialisation and segregation in the in vitro neural network that reproduced in silico learning via free energy minimisation. Finally, we combined the in vitro and in silico results to characterise learning in terms of trajectories in a variational information plane of accuracy and complexity.

Understanding the neural substrates of depression is crucial for diagnosis and treatment. Here, we review recent studies of functional and effective connectivity in depression, in terms of functional integration in the brain. Findings from these studies, including our own, point to the involvement of at least four networks in patients with depression. Elevated connectivity of a ventral limbic affective network appears to be associated with excessive negative mood (dysphoria) in the patients; decreased connectivity of a frontal-striatal reward network has been suggested to account for loss of interest, motivation, and pleasure (anhedonia); enhanced default mode network connectivity seems to be associated with depressive rumination; and diminished connectivity of a dorsal cognitive control network is thought to underlie cognitive deficits especially ineffective top-down control of negative thoughts and emotions in depressed patients. Moreover, the restoration of connectivity of these networks-and corresponding symptom improvement-following antidepressant treatment (including medication, psychotherapy, and brain stimulation techniques) serves as evidence for the crucial role of these networks in the pathophysiology of depression., (© 2018 John Wiley & Sons Ltd.)

Context-sensitive and activity-dependent fluctuations in connectivity underlie functional integration in the brain and have been studied widely in terms of synaptic plasticity, learning and condition-specific (e.g., attentional) modulations of synaptic efficacy. This dynamic aspect of brain connectivity has recently attracted a lot of attention in the resting state fMRI community. To explain dynamic functional connectivity in terms of directed effective connectivity among brain regions, we introduce a novel method to identify dynamic effective connectivity using spectral dynamic causal modelling (spDCM). We used parametric empirical Bayes (PEB) to model fluctuations in directed coupling over consecutive windows of resting state fMRI time series. Hierarchical PEB can model random effects on connectivity parameters at the second (between-window) level given connectivity estimates from the first (within-window) level. In this work, we used a discrete cosine transform basis set or eigenvariates (i.e., expression of principal components) to model fluctuations in effective connectivity over windows. We evaluated the ensuing dynamic effective connectivity in terms of the consistency of baseline connectivity within default mode network (DMN), using the resting state fMRI from Human Connectome Project (HCP). To model group-level baseline and dynamic effective connectivity for DMN, we extended the PEB approach by conducting a multilevel PEB analysis of between-session and between-subject group effects. Model comparison clearly spoke to dynamic fluctuations in effective connectivity - and the dynamic functional connectivity these changes explain. Furthermore, baseline effective connectivity was consistent across independent sessions - and notably more consistent than estimates based upon conventional models. This work illustrates the advantage of hierarchical modelling with spDCM, in characterizing the dynamics of effective connectivity., (Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.)

Our behavior entails a flexible and context-sensitive interplay between brain areas to integrate information according to goal-directed requirements. However, the neural mechanisms governing the entrainment of functionally specialized brain areas remain poorly understood. In particular, the question arises whether observed changes in the regional activity for different cognitive conditions are explained by modifications of the inputs to the brain or its connectivity? We observe that transitions of fMRI activity between areas convey information about the tasks performed by 19 subjects, watching a movie versus a black screen (rest). We use a model-based framework that explains this spatiotemporal functional connectivity pattern by the local variability for 66 cortical regions and the network effective connectivity between them. We find that, among the estimated model parameters, movie viewing affects to a larger extent the local activity, which we interpret as extrinsic changes related to the increased stimulus load. However, detailed changes in the effective connectivity preserve a balance in the propagating activity and select specific pathways such that high-level brain regions integrate visual and auditory information, in particular boosting the communication between the two brain hemispheres. These findings speak to a dynamic coordination underlying the functional integration in the brain., (Copyright © 2017. Published by Elsevier Inc.)

The free-energy principle is an attempt to explain the structure of the agent and its brain, starting from the fact that an agent exists (Friston and Stephan, 2007; Friston et al., 2010). More specifically, it can be regarded as a systematic attempt to understand the 'fit' between an embodied agent and its niche, where the quantity of free-energy is a measure for the 'misfit' or disattunement (Bruineberg and Rietveld, 2014) between agent and environment. This paper offers a proof-of-principle simulation of niche construction under the free-energy principle. Agent-centered treatments have so far failed to address situations where environments change alongside agents, often due to the action of agents themselves. The key point of this paper is that the minimum of free-energy is not at a point in which the agent is maximally adapted to the statistics of a static environment, but can better be conceptualized an attracting manifold within the joint agent-environment state-space as a whole, which the system tends toward through mutual interaction. We will provide a general introduction to active inference and the free-energy principle. Using Markov Decision Processes (MDPs), we then describe a canonical generative model and the ensuing update equations that minimize free-energy. We then apply these equations to simulations of foraging in an environment; in which an agent learns the most efficient path to a pre-specified location. In some of those simulations, unbeknownst to the agent, the 'desire paths' emerge as a function of the activity of the agent (i.e. niche construction occurs). We will show how, depending on the relative inertia of the environment and agent, the joint agent-environment system moves to different attracting sets of jointly minimized free-energy., (Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Using predictions based on environmental regularities is fundamental for adaptive behavior. While it is widely accepted that predictions across different stimulus attributes (e.g., time and content) facilitate sensory processing, it is unknown whether predictions across these attributes rely on the same neural mechanism. Here, to elucidate the neural mechanisms of predictions, we combine invasive electrophysiological recordings (human electrocorticography in 4 females and 2 males) with computational modeling while manipulating predictions about content ("what") and time ("when"). We found that "when" predictions increased evoked activity over motor and prefrontal regions both at early (∼180 ms) and late (430-450 ms) latencies. "What" predictability, however, increased evoked activity only over prefrontal areas late in time (420-460 ms). Beyond these dissociable influences, we found that "what" and "when" predictability interactively modulated the amplitude of early (165 ms) evoked responses in the superior temporal gyrus. We modeled the observed neural responses using biophysically realistic neural mass models, to better understand whether "what" and "when" predictions tap into similar or different neurophysiological mechanisms. Our modeling results suggest that "what" and "when" predictability rely on complementary neural processes: "what" predictions increased short-term plasticity in auditory areas, whereas "when" predictability increased synaptic gain in motor areas. Thus, content and temporal predictions engage complementary neural mechanisms in different regions, suggesting domain-specific prediction signaling along the cortical hierarchy. Encoding predictions through different mechanisms may endow the brain with the flexibility to efficiently signal different sources of predictions, weight them by their reliability, and allow for their encoding without mutual interference. SIGNIFICANCE STATEMENT Predictions of different stimulus features facilitate sensory processing. However, it is unclear whether predictions of different attributes rely on similar or different neural mechanisms. By combining invasive electrophysiological recordings of cortical activity with experimental manipulations of participants' predictions about content and time of acoustic events, we found that the two types of predictions had dissociable influences on cortical activity, both in terms of the regions involved and the timing of the observed effects. Further, our biophysical modeling analysis suggests that predictability of content and time rely on complementary neural processes: short-term plasticity in auditory areas and synaptic gain in motor areas, respectively. This suggests that predictions of different features are encoded with complementary neural mechanisms in different brain regions., (Copyright © 2018 the authors 0270-6474/18/388681-14$15.00/0.)

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.

Given that eye movement control can be framed as an inferential process, how are the requisite forces generated to produce anticipated or desired fixation? Starting from a generative model based on simple Newtonian equations of motion, we derive a variational solution to this problem and illustrate the plausibility of its implementation in the oculomotor brainstem. We show, through simulation, that the Bayesian filtering equations that implement 'planning as inference' can generate both saccadic and smooth pursuit eye movements. Crucially, the associated message passing maps well onto the known connectivity and neuroanatomy of the brainstem - and the changes in these messages over time are strikingly similar to single unit recordings of neurons in the corresponding nuclei. Furthermore, we show that simulated lesions to axonal pathways reproduce eye movement patterns of neurological patients with damage to these tracts., (Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Biological systems-like ourselves-are constantly faced with uncertainty. Despite noisy sensory data, and volatile environments, creatures appear to actively maintain their integrity. To account for this remarkable ability to make optimal decisions in the face of a capricious world, we propose a generative model that represents the beliefs an agent might possess about their own uncertainty. By simulating a noisy and volatile environment, we demonstrate how uncertainty influences optimal epistemic (visual) foraging. In our simulations, saccades were deployed less frequently to regions with a lower sensory precision, while a greater volatility led to a shorter inhibition of return. These simulations illustrate a principled explanation for some cardinal aspects of visual foraging-and allow us to propose a correspondence between the representation of uncertainty and ascending neuromodulatory systems, complementing that suggested by Yu & Dayan (Yu & Dayan 2005 Neuron 46 , 681-692. (doi:10.1016/j.neuron.2005.04.026))., (© 2017 The Authors.)

The development of large-scale network models that infer the effective (directed) connectivity among neuronal populations from neuroimaging data represents a key challenge for computational neuroscience. Dynamic causal models (DCMs) of neuroimaging and electrophysiological data are frequently used for inferring effective connectivity but are presently restricted to small graphs (typically up to 10 regions) in order to keep model inversion computationally feasible. Here, we present a novel variant of DCM for functional magnetic resonance imaging (fMRI) data that is suited to assess effective connectivity in large (whole-brain) networks. The approach rests on translating a linear DCM into the frequency domain and reformulating it as a special case of Bayesian linear regression. This paper derives regression DCM (rDCM) in detail and presents a variational Bayesian inversion method that enables extremely fast inference and accelerates model inversion by several orders of magnitude compared to classical DCM. Using both simulated and empirical data, we demonstrate the face validity of rDCM under different settings of signal-to-noise ratio (SNR) and repetition time (TR) of fMRI data. In particular, we assess the potential utility of rDCM as a tool for whole-brain connectomics by challenging it to infer effective connection strengths in a simulated whole-brain network comprising 66 regions and 300 free parameters. Our results indicate that rDCM represents a computationally highly efficient approach with promising potential for inferring whole-brain connectivity from individual fMRI data., (Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.)

Effective connectivity is commonly assessed using blood oxygenation level-dependent (BOLD) signals. In (Havlicek et al., 2015), we presented a novel, physiologically informed dynamic causal model (P-DCM) that extends current generative models. We demonstrated the improvements afforded by P-DCM in terms of the ability to model commonly observed neuronal and vascular transients in single regions. Here, we assess the ability of the novel and previous DCM variants to estimate effective connectivity among a network of five ROIs driven by a visuo-motor task. We demonstrate that connectivity estimates depend sensitively on the DCM used, due to differences in the modeling of hemodynamic response transients; such as the post-stimulus undershoot or adaptation during stimulation. In addition, using a novel DCM for arterial spin labeling (ASL) fMRI that measures BOLD and CBF signals simultaneously, we confirmed our findings (by using the BOLD data alone and in conjunction with CBF). We show that P-DCM provides better estimates of effective connectivity, regardless of whether it is applied to BOLD data alone or to ASL time-series, and that all new aspects of P-DCM (i.e. neuronal, neurovascular, hemodynamic components) constitute an improvement compared to those in the previous DCM variants. In summary, (i) accurate modeling of fMRI response transients is crucial to obtain valid effective connectivity estimates and (ii) any additional hemodynamic data, such as provided by ASL, increases the ability to disambiguate neuronal and vascular effects present in the BOLD signal., (Copyright © 2017 Elsevier Inc. All rights reserved.)

The neural processing and experience of pain are influenced by both expectations and attention. For example, the amplitude of event-related pain responses is enhanced by both novel and unexpected pain, and by moving the focus of attention towards a painful stimulus. Under predictive coding, this congruence can be explained by appeal to a precision-weighting mechanism, which mediates bottom-up and top-down attentional processes by modulating the influence of feedforward and feedback signals throughout the cortical hierarchy. The influence of expectation and attention on pain processing can be mapped onto changes in effective connectivity between or within specific neuronal populations, using a canonical microcircuit (CMC) model of hierarchical processing. We thus implemented a CMC within dynamic causal modelling for magnetoencephalography in human subjects, to investigate how expectation violation and attention to pain modulate intrinsic (within-source) and extrinsic (between-source) connectivity in the somatosensory hierarchy. This enabled us to establish whether both expectancy and attentional processes are mediated by a similar precision-encoding mechanism within a network of somatosensory, frontal and parietal sources. We found that both unexpected and attended pain modulated the gain of superficial pyramidal cells in primary and secondary somatosensory cortex. This modulation occurred in the context of increased lateralized recurrent connectivity between somatosensory and fronto-parietal sources, driven by unexpected painful occurrences. Finally, the strength of effective connectivity parameters in S1, S2 and IFG predicted individual differences in subjective pain modulation ratings. Our findings suggest that neuromodulatory gain control in the somatosensory hierarchy underlies the influence of both expectation violation and attention on cortical processing and pain perception., (Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.)

The neuronal mechanisms underlying arithmetic calculations are not well understood but the differences between mental addition and subtraction could be particularly revealing. Using fMRI and dynamic causal modeling (DCM), this study aimed to identify the distinct neuronal architectures engaged by the cognitive processes of simple addition and subtraction. Our results revealed significantly greater activation during subtraction in regions along the dorsal pathway, including the left inferior frontal gyrus (IFG), middle portion of dorsolateral prefrontal cortex (mDLPFC), and supplementary motor area (SMA), compared with addition. Subsequent analysis of the underlying changes in connectivity - with DCM - revealed a common circuit processing basic (numeric) attributes and the retrieval of arithmetic facts. However, DCM showed that addition was more likely to engage (numeric) retrieval-based circuits in the left hemisphere, while subtraction tended to draw on (magnitude) processing in bilateral parietal cortex, especially the right intraparietal sulcus (IPS). Our findings endorse previous hypotheses about the differences in strategic implementation, dominant hemisphere, and the neuronal circuits underlying addition and subtraction. Moreover, for simple arithmetic, our connectivity results suggest that subtraction calls on more complex processing than addition: auxiliary phonological, visual, and motor processes, for representing numbers, were engaged by subtraction, relative to addition. Hum Brain Mapp 38:3210-3225, 2017. © 2017 Wiley Periodicals, Inc., (© 2017 Wiley Periodicals, Inc.)

In this opinion paper, we describe a combined view of functional and effective brain connectivity along with the free-energy principle for investigating persistent disruptions in brain networks of patients with focal epilepsy. These changes are likely reflected in effective connectivity along the cortical hierarchy and construct the basis of increased local functional connectivity in focal epilepsy. We propose a testable framework based on dynamic causal modelling and functional connectivity analysis with the capacity of explaining commonly observed connectivity changes during interictal periods. We then hypothesise their possible relation with disrupted free-energy minimisation in the Bayesian brain. This may offer a new approach for neuroimaging to specifically develop and address hypotheses regarding the network pathomechanisms underlying epileptic phenotypes.

Biological phenomena arise through interactions between an organism's intrinsic dynamics and stochastic forces-random fluctuations due to external inputs, thermal energy, or other exogenous influences. Dynamic processes in the brain derive from neurophysiology and anatomical connectivity; stochastic effects arise through sensory fluctuations, brainstem discharges, and random microscopic states such as thermal noise. The dynamic evolution of systems composed of both dynamic and random effects can be studied with stochastic dynamic models (SDMs). This article, Part I of a two-part series, offers a primer of SDMs and their application to large-scale neural systems in health and disease. The companion article, Part II, reviews the application of SDMs to brain disorders. SDMs generate a distribution of dynamic states, which (we argue) represent ideal candidates for modeling how the brain represents states of the world. When augmented with variational methods for model inversion, SDMs represent a powerful means of inferring neuronal dynamics from functional neuroimaging data in health and disease. Together with deeper theoretical considerations, this work suggests that SDMs will play a unique and influential role in computational psychiatry, unifying empirical observations with models of perception and behavior., (Copyright © 2017 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.)

Brain activity derives from intrinsic dynamics (due to neurophysiology and anatomical connectivity) in concert with stochastic effects that arise from sensory fluctuations, brainstem discharges, and random microscopic states such as thermal noise. The dynamic evolution of systems composed of both dynamic and random fluctuations can be studied with stochastic dynamic models (SDMs). This article, Part II of a two-part series, reviews applications of SDMs to large-scale neural systems in health and disease. Stochastic models have already elucidated a number of pathophysiological phenomena, such as epilepsy and hypoxic ischemic encephalopathy, although their use in biological psychiatry remains rather nascent. Emerging research in this field includes phenomenological models of mood fluctuations in bipolar disorder and biophysical models of functional imaging data in psychotic and affective disorders. Together with deeper theoretical considerations, this work suggests that SDMs will play a unique and influential role in computational psychiatry, unifying empirical observations with models of perception and behavior., (Copyright © 2017 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.)

This paper presents a physiological account of seizure activity and its evolution over time using a rat model of induced epilepsy. We analyse spectral activity recorded in the hippocampi of three rats who received kainic acid injections in the right hippocampus. We use dynamic causal modelling of seizure activity and Bayesian model reduction to identify the key synaptic and connectivity parameters that underlie seizure onset. Using recent advances in hierarchical modelling (parametric empirical Bayes), we characterise seizure onset in terms of slow fluctuations in synaptic excitability of specific neuronal populations. Our results suggest differences in the pathophysiology - of seizure activity in the lesioned versus the non-lesioned hippocampus - with pronounced changes in excitation-inhibition balance and temporal summation on the lesioned side. In particular, our analyses suggest that marked reductions in the synaptic time constant of the deep pyramidal cells and the self-inhibition of inhibitory interneurons (in the lesioned hippocampus) are sufficient to explain changes in spectral activity. Although these synaptic changes are consistent over rats, the resulting electrophysiological phenotype can be quite diverse., (Copyright © 2016 Elsevier Inc. All rights reserved.)

Tinnitus is a common disorder that often complicates hearing loss. Its mechanisms are incompletely understood. Current theories proposing pathophysiology from the ear to the cortex cannot individually - or collectively - explain the range of experimental evidence available. We propose a new framework, based on predictive coding, in which spontaneous activity in the subcortical auditory pathway constitutes a 'tinnitus precursor' which is normally ignored as imprecise evidence against the prevailing percept of 'silence'. Extant models feature as contributory mechanisms acting to increase either the intensity of the precursor or its precision. If precision (i.e., postsynaptic gain) rises sufficiently then tinnitus is perceived. Perpetuation arises through focused attention, which further increases the precision of the precursor, and resetting of the default prediction to expect tinnitus., (Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Twenty years have passed since the dysconnection hypothesis was first proposed (Friston and Frith, 1995; Weinberger, 1993). In that time, neuroscience has witnessed tremendous advances: we now live in a world of non-invasive neuroanatomy, computational neuroimaging and the Bayesian brain. The genomics era has come and gone. Connectomics and large-scale neuroinformatics initiatives are emerging everywhere. So where is the dysconnection hypothesis now? This article considers how the notion of schizophrenia as a dysconnection syndrome has developed - and how it has been enriched by recent advances in clinical neuroscience. In particular, we examine the dysconnection hypothesis in the context of (i) theoretical neurobiology and computational psychiatry; (ii) the empirical insights afforded by neuroimaging and associated connectomics - and (iii) how bottom-up (molecular biology and genetics) and top-down (systems biology) perspectives are converging on the mechanisms and nature of dysconnections in schizophrenia., (Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.)

The neural substrate of bodily ownership can be disclosed by the rubber hand illusion (RHI); namely, the illusory self-attribution of an artificial hand that is induced by synchronous tactile stimulation of the subject's hand that is hidden from view. Previous studies have pointed to the premotor cortex (PMC) as a pivotal area in such illusions. To investigate the effective connectivity between - and within - sensory and premotor areas involved in bodily perceptions, we used dynamic causal modeling of touch-evoked responses in 13 healthy subjects. Each subject's right hand was stroked while viewing their own hand ("REAL"), or an artificial hand presented in an anatomically plausible ("CONGRUENT") or implausible ("INCONGRUENT") position. Bayesian model comparison revealed strong evidence for a differential involvement of the PMC in the generation of touch-evoked responses under the three conditions, confirming a crucial role of PMC in bodily self-attribution. In brief, the extrinsic (forward) connection from left occipital cortex to left PMC was stronger for CONGRUENT and INCONGRUENT as compared to REAL, reflecting the augmentation of bottom-up visual input when multisensory integration is challenged. Crucially, intrinsic connectivity in the primary somatosensory cortex (S1) was attenuated in the CONGRUENT condition, during the illusory percept. These findings support predictive coding models of the functional architecture of multisensory integration (and attenuation) in bodily perceptual experience., (Copyright © 2016 Elsevier Inc. All rights reserved.)

Degeneracy is a fundamental source of biological robustness, complexity and evolvability in many biological systems. However, degeneracy is often confused with redundancy. Furthermore, the quantification of degeneracy has not been addressed for realistic neuronal networks. The objective of this paper is to characterize degeneracy in neuronal network models via quantitative mathematic measures. Firstly, we establish Hodgkin-Huxley neuronal networks with Newman-Watts small world network architectures. Secondly, in order to calculate the degeneracy, redundancy and complexity in the ensuing networks, we use information entropy to quantify the information a neuronal response carries about the stimulus - and mutual information to measure the contribution of each subset of the neuronal network. Finally, we analyze the interdependency of degeneracy, redundancy and complexity - and how these three measures depend upon network architectures. Our results suggest that degeneracy can be applied to any neuronal network as a formal measure, and degeneracy is distinct from redundancy. Qualitatively degeneracy and complexity are more highly correlated over different network architectures, in comparison to redundancy. Quantitatively, the relationship between both degeneracy and redundancy depends on network coupling strength: both degeneracy and redundancy increase with complexity for small coupling strengths; however, as coupling strength increases, redundancy decreases with complexity (in contrast to degeneracy, which is relatively invariant). These results suggest that the degeneracy is a general topologic characteristic of neuronal networks, which could be applied quantitatively in neuroscience and connectomics., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

This paper presents a review of theoretical and empirical work on repetition suppression in the context of predictive coding. Predictive coding is a neurobiologically plausible scheme explaining how biological systems might perform perceptual inference and learning. From this perspective, repetition suppression is a manifestation of minimising prediction error through adaptive changes in predictions about the content and precision of sensory inputs. Simulations of artificial neural hierarchies provide a principled way of understanding how repetition suppression - at different time scales - can be explained in terms of inference and learning implemented under predictive coding. This formulation of repetition suppression is supported by results of numerous empirical studies of repetition suppression and its contextual determinants., (Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Oscillatory activity in the beta range, in human primary motor cortex (M1), shows interesting dynamics that are tied to behaviour and change systematically in disease. To investigate the pathophysiology underlying these changes, we must first understand how changes in beta activity are caused in healthy subjects. We therefore adapted a canonical (repeatable) microcircuit model used in dynamic causal modelling (DCM) previously used to model induced responses in visual cortex. We adapted this model to accommodate cytoarchitectural differences between visual and motor cortex. Using biologically plausible connections, we used Bayesian model selection to identify the best model of measured MEG data from 11 young healthy participants, performing a simple handgrip task. We found that the canonical M1 model had substantially more model evidence than the generic canonical microcircuit model when explaining measured MEG data. The canonical M1 model reproduced measured dynamics in humans at rest, in a manner consistent with equivalent studies performed in mice. Furthermore, the changes in excitability (self-inhibition) necessary to explain beta suppression during handgrip were consistent with the attenuation of sensory precision implied by predictive coding. These results establish the face validity of a model that can be used to explore the laminar interactions that underlie beta-oscillatory dynamics in humans in vivo. Our canonical M1 model may be useful for characterising the synaptic mechanisms that mediate pathophysiological beta dynamics associated with movement disorders, such as stroke or Parkinson's disease., (Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.)

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., (Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.)

Seizure activity in EEG recordings can persist for hours with seizure dynamics changing rapidly over time and space. To characterise the spatiotemporal evolution of seizure activity, large data sets often need to be analysed. Dynamic causal modelling (DCM) can be used to estimate the synaptic drivers of cortical dynamics during a seizure; however, the requisite (Bayesian) inversion procedure is computationally expensive. In this note, we describe a straightforward procedure, within the DCM framework, that provides efficient inversion of seizure activity measured with non-invasive and invasive physiological recordings; namely, EEG/ECoG. We describe the theoretical background behind a Bayesian belief updating scheme for DCM. The scheme is tested on simulated and empirical seizure activity (recorded both invasively and non-invasively) and compared with standard Bayesian inversion. We show that the Bayesian belief updating scheme provides similar estimates of time-varying synaptic parameters, compared to standard schemes, indicating no significant qualitative change in accuracy. The difference in variance explained was small (less than 5%). The updating method was substantially more efficient, taking approximately 5-10min compared to approximately 1-2h. Moreover, the setup of the model under the updating scheme allows for a clear specification of how neuronal variables fluctuate over separable timescales. This method now allows us to investigate the effect of fast (neuronal) activity on slow fluctuations in (synaptic) parameters, paving a way forward to understand how seizure activity is generated., (Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.)

The functional MRI (fMRI) signal is an indirect measure of neuronal activity. In order to deconvolve the neuronal activity from the experimental fMRI data, biophysical generative models have been proposed describing the link between neuronal activity and the cerebral blood flow (the neurovascular coupling), and further the hemodynamic response and the BOLD signal equation. These generative models have been employed both for single brain area deconvolution and to infer effective connectivity in networks of multiple brain areas. In the current paper, we introduce a new fMRI model inspired by experimental observations about the physiological underpinnings of the BOLD signal and compare it with the generative models currently used in dynamic causal modeling (DCM), a widely used framework to study effective connectivity in the brain. We consider three fundamental aspects of such generative models for fMRI: (i) an adaptive two-state neuronal model that accounts for a wide repertoire of neuronal responses during and after stimulation; (ii) feedforward neurovascular coupling that links neuronal activity to blood flow; and (iii) a balloon model that can account for vascular uncoupling between the blood flow and the blood volume. Finally, we adjust the parameterization of the BOLD signal equation for different magnetic field strengths. This paper focuses on the form, motivation and phenomenology of DCMs for fMRI and the characteristics of the various models are demonstrated using simulations. These simulations emphasize a more accurate modeling of the transient BOLD responses - such as adaptive decreases to sustained inputs during stimulation and the post-stimulus undershoot. In addition, we demonstrate using experimental data that it is necessary to take into account both neuronal and vascular transients to accurately model the signal dynamics of fMRI data. By refining the models of the transient responses, we provide a more informed perspective on the underlying neuronal process and offer new ways of inferring changes in local neuronal activity and effective connectivity from fMRI., (Copyright © 2015. Published by Elsevier Inc.)

We review a theory of homeostatic regulation and adaptive behavioural control within the Active Inference framework. Our aim is to connect two research streams that are usually considered independently; namely, Active Inference and associative learning theories of animal behaviour. The former uses a probabilistic (Bayesian) formulation of perception and action, while the latter calls on multiple (Pavlovian, habitual, goal-directed) processes for homeostatic and behavioural control. We offer a synthesis these classical processes and cast them as successive hierarchical contextualisations of sensorimotor constructs, using the generative models that underpin Active Inference. This dissolves any apparent mechanistic distinction between the optimization processes that mediate classical control or learning. Furthermore, we generalize the scope of Active Inference by emphasizing interoceptive inference and homeostatic regulation. The ensuing homeostatic (or allostatic) perspective provides an intuitive explanation for how priors act as drives or goals to enslave action, and emphasises the embodied nature of inference., (Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.)

We characterised the pathophysiology of seizure onset in terms of slow fluctuations in synaptic efficacy using EEG in patients with anti-N-methyl-d-aspartate receptor (NMDA-R) encephalitis. EEG recordings were obtained from two female patients with anti-NMDA-R encephalitis with recurrent partial seizures (ages 19 and 31). Focal electrographic seizure activity was localised using an empirical Bayes beamformer. The spectral density of reconstructed source activity was then characterised with dynamic causal modelling (DCM). Eight models were compared for each patient, to evaluate the relative contribution of changes in intrinsic (excitatory and inhibitory) connectivity and endogenous afferent input. Bayesian model comparison established a role for changes in both excitatory and inhibitory connectivity during seizure activity (in addition to changes in the exogenous input). Seizures in both patients were associated with a sequence of changes in inhibitory and excitatory connectivity; a transient increase in inhibitory connectivity followed by a transient increase in excitatory connectivity and a final peak of excitatory-inhibitory balance at seizure offset. These systematic fluctuations in excitatory and inhibitory gain may be characteristic of (anti NMDA-R encephalitis) seizures. We present these results as a case study and replication to motivate analyses of larger patient cohorts, to see whether our findings generalise and further characterise the mechanisms of seizure activity in anti-NMDA-R encephalitis., (Copyright © 2015. Published by Elsevier Inc.)