Publications

Bridging the Gap: Dynamic Causal Modeling and Granger Causality Analysis of Resting State Functional Magnetic Resonance Imaging

Granger causality (GC) and dynamic causal modeling (DCM) are the two key approaches used to determine the directed interactions among brain areas. Recent discussions have provided a constructive account of the merits and demerits. GC, on one side, considers dependencies among measured responses, whereas DCM, on the other, models how neuronal activity in one brain area causes dynamics in another. In this study, our objective was to establish construct validity between GC and DCM in the context of resting state functional magnetic resonance imaging (fMRI). We first established the face validity of both approaches using simulated fMRI time series, with endogenous fluctuations in two nodes. Crucially, we tested both unidirectional and bidirectional connections between the two nodes to ensure that both approaches give veridical and consistent results, in terms of model comparison. We then applied both techniques to empirical data and examined their consistency in terms of the (quantitative) in-degree of key nodes of the default mode. Our simulation results suggested a (qualitative) consistency between GC and DCM. Furthermore, by applying nonparametric GC and stochastic DCM to resting-state fMRI data, we confirmed that both GC and DCM infer similar (quantitative) directionality between the posterior cingulate cortex (PCC), the medial prefrontal cortex, the left middle temporal cortex, and the left angular gyrus. These findings suggest that GC and DCM can be used to estimate directed functional and effective connectivity from fMRI measurements in a consistent manner.

Schizophrenia and the disconnection hypothesis

This article reviews the disconnection hypothesis of schizophrenia and presents a mechanistic account of how dysfunctional integration among neuronal systems might arise. This neurobiological account is based on some simple observations about schizophrenia and the central role that neuronal plasticity plays in shaping the connections, and the ensuing dynamics, that underlie brain function. The particular hypothesis put forward here is that the pathophysiology of schizophrenia is expressed at the level of modulation of associative changes in synaptic efficacy, specifically the modulation of plasticity in those brain systems that are responsible for learning, memory and emotion. This modulation is mediated by ascending neurotransmitter systems that (i) have been implicated in schizophrenia and (ii) are known to be involved in consolidating synaptic connections during learning. The proposed pathophysiology would translate, in functional terms, into a disruption of the reinforcement of adaptive behaviour that is consistent with the disintegrative aspects of schizophrenic neuropsychology.

Methods for mapping and modeling the human brain: Proceedings of the BrainMap '96 workshop, San Antonio, December 1996

Spectral dynamic causal modeling: A didactic introduction and its relationship with functional connectivity

Abstract We present a didactic introduction to spectral dynamic causal modeling (DCM), a Bayesian state-space modeling approach used to infer effective connectivity from noninvasive neuroimaging data. Spectral DCM is currently the most widely applied DCM variant for resting-state functional MRI analysis. Our aim is to explain its technical foundations to an audience with limited expertise in state-space modeling and spectral data analysis. Particular attention will be paid to cross-spectral density, which is the most distinctive feature of spectral DCM and is closely related to functional connectivity, as measured by (zero-lag) Pearson correlations. In fact, the model parameters estimated by spectral DCM are those that best reproduce the cross-correlations between all measurements—at all time lags—including the zero-lag correlations that are usually interpreted as functional connectivity. We derive the functional connectivity matrix from the model equations and show how changing a single effective connectivity parameter can affect all pairwise correlations. To complicate matters, the pairs of brain regions showing the largest changes in functional connectivity do not necessarily coincide with those presenting the largest changes in effective connectivity. We discuss the implications and conclude with a comprehensive summary of the assumptions and limitations of spectral DCM.

A brain network model for depression: From symptom understanding to disease intervention

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.

Canonical Microcircuits for Predictive Coding

This Perspective considers the influential notion of a canonical (cortical) microcircuit in light of recent theories about neuronal processing. Specifically, we conciliate quantitative studies of microcircuitry and the functional logic of neuronal computations. We revisit the established idea that message passing among hierarchical cortical areas implements a form of Bayesian inference—paying careful attention to the implications for intrinsic connections among neuronal populations. By deriving canonical forms for these computations, one can associate specific neuronal populations with specific computational roles. This analysis discloses a remarkable correspondence between the microcircuitry of the cortical column and the connectivity implied by predictive coding. Furthermore, it provides some intuitive insights into the functional asymmetries between feedforward and feedback connections and the characteristic frequencies over which they operate.

Detecting bilateral abnormalities with voxel‐based morphometry

In this article we describe a new method, using SPM99, that searches explicitly for bilateral structural abnormalities.Children with bilateral pathology have a poorer prognosis than children with unilateral damage.After brain injury or disease in childhood, it is thought that rescue of function is only possible if the neuronal substrates of that function are preserved and operational in at least one hemisphere [Vargha-Khadem and Mishkin, 1997].If this is the case, the detection of bilateral abnormalities would greatly facilitate more accurate prognosis in children with brain injury or developmental disorders.We have therefore developed a technique to detect bilateral abnormalities that uses conjunction analysis with voxel based morphometry.It is illustrated using a group of patients with bilateral hypoxicischaemic damage to the hippocampus.The approach is shown to have enhanced specificity and sensitivity relative to conventional unilateral characterisations.Hum.

Increasing spectral DCM flexibility and speed by leveraging Julia’s ModelingToolkit and automated differentiation

Abstract Using neuroimaging and electrophysiological data to infer neural parameter estimations from theoretical circuits requires solving the inverse problem. Here, we provide a new Julia language package designed to i) compose complex dynamical models in a simple and modular way with ModelingToolkit.jl, ii) implement parameter fitting based on spectral dynamic causal modeling (sDCM) using the Laplace approximation, analogous to MATLAB implementation in SPM, and iii) leverage Julia’s unique strengths to increase accuracy and speed by employing Automatic Differentiation during the fitting procedure. To illustrate the utility of our flexible modular approach, we provide a method to improve correction for fMRI scanner field strengths (1.5T, 3T, 7T) when fitting models to real data.

Subtractions, conjunctions, and interactions in experimental design of activation studies

This paper contrasts different experimental designs for revealing the neural correlates of phonological retrieval (i.e., naming). Cognitive subtraction designs require a minimum of one task pair and the comparison between tasks reveals the differing functional task components. Conjunction analysis requires a minimum of two task pairs, each differing by the same component, and this component is revealed as the difference which is common to both task pairs. Two different limitations of cognitive subtraction are highlighted: 1) the difficulty of finding baseline tasks that activate all but the process of interest, and 2) activation differences (between the two tasks of a pair) include the interaction term, i.e., the effect that the added component in the activation task has on preexisting components. The problem of baseline selection can be overcome by conjunction analysis, for which there may be many processing differences for each task pair, providing that the only common difference between pairs is the component of interest. The problem of interactions can be overcome when the experimental design is factorial. This permits the effect that an added component has on the expression of preexisting components (i.e., the interaction term) to be evaluated explicitly. We demonstrate that when the design is factorial, conjunction analysis reveals commonalities in activation, while the interactions reveal task-specific effects.

Time-Varying Dynamic Causal Modelling for Sequential Responses: Neural Mechanisms of Slow Cortical Potentials, Preparation, Planning and Beyond

Abstract Cognitive processes such as decision-making, working memory, and motor planning operate across a hierarchy of timescales, manifesting as rapid neural transients alongside slower physiological mechanisms like short-term plasticity. Conventional Dynamic Causal Modelling (DCM) limits our ability to study these dynamics by assuming stationary parameters, whilst recent time-varying approaches often rely on segmenting data into epochs. This segmentation artificially resets neural states between windows, fundamentally obscuring the continuous hysteresis essential to sequential processing. To address this limitation, we introduce DCM for Sequential Responses (DCM-SR), a generative framework that embeds parameter evolution directly within the first-level model whilst employing a continuous state-space formulation that removes the requirement for epoching. This approach generalises non-stationarity to all neural mass parameters, including synaptic gains and time constants, modelling them as piecewise smooth trajectories that evolve alongside continuous neural states. Consequently, the model explicitly captures two distinct forms of temporal memory: transient history dependence, where responses are shaped by the carryover effect of recent perturbations, and path dependence, where the system’s trajectory through parameter space determines its responsiveness. The framework accommodates both exogenous, stimulus-locked transitions and endogenous, autonomous state changes, permitting inference on both external perturbations and internal drivers of network evolution. Simulations establish the model’s face validity, demonstrating robust parameter recovery and conservative model selection that accurately discriminates between genuine parameter evolution and spurious complexity. We applied the framework to empirical data from an auditory go/no-go task, modelling a full sequence of cognitive phases from initial cue processing and anticipation through to motor preparation and execution. This analysis established construct validity by resolving the biophysical generators of the contingent negative variation, attributing this slow potential to sustained thalamocortical drive and deep-layer hyperpolarisation rather than superficial-layer activity. Furthermore, the model captured trial-specific modulations of the hyperdirect pathway during motor inhibition, tracking the dynamic interplay between prefrontal executive control and basal ganglia gating. DCM-SR offers the first principled approach to decomposing compound signals such as slow cortical potentials into evolving synaptic mechanisms and continuous state trajectories, and provides a necessary bridge for investigating the biophysical implementation of extended cognitive phenomena including evidence accumulation and physiological hysteresis.

Dynamic diaschisis: Anatomically remote and task specific effects of human brain lesions

Collective behavior from surprise minimization

Collective motion is ubiquitous in nature; groups of animals, such as fish, birds, and ungulates appear to move as a whole, exhibiting a rich behavioral repertoire that ranges from directed movement to milling to disordered swarming. Typically, such macroscopic patterns arise from decentralized, local interactions among constituent components (e.g., individual fish in a school). Preeminent models of this process describe individuals as self-propelled particles, subject to self-generated motion and 'social forces' such as short-range repulsion and long-range attraction or alignment. However, organisms are not particles; they are probabilistic decision-makers. Here, we introduce an approach to modelling collective behavior based on active inference. This cognitive framework casts behavior as the consequence of a single imperative: to minimize surprise. We demonstrate that many empirically-observed collective phenomena, including cohesion, milling and directed motion, emerge naturally when considering behavior as driven by active Bayesian inference -- without explicitly building behavioral rules or goals into individual agents. Furthermore, we show that active inference can recover and generalize the classical notion of social forces as agents attempt to suppress prediction errors that conflict with their expectations. By exploring the parameter space of the belief-based model, we reveal non-trivial relationships between the individual beliefs and group properties like polarization and the tendency to visit different collective states. We also explore how individual beliefs about uncertainty determine collective decision-making accuracy. Finally, we show how agents can update their generative model over time, resulting in groups that are collectively more sensitive to external fluctuations and encode information more robustly.

Predictive Coding and Pitch Processing in the Auditory Cortex

In this work, we show that electrophysiological responses during pitch perception are best explained by distributed activity in a hierarchy of cortical sources and, crucially, that the effective connectivity between these sources is modulated with pitch strength. Local field potentials were recorded in two subjects from primary auditory cortex and adjacent auditory cortical areas along the axis of Heschl's gyrus (HG) while they listened to stimuli of varying pitch strength. Dynamic causal modeling was used to compare system architectures that might explain the recorded activity. The data show that representation of pitch requires an interaction between nonprimary and primary auditory cortex along HG that is consistent with the principle of predictive coding.

Deep active inference agents using Monte-Carlo methods

Active inference is a Bayesian framework for understanding biological intelligence. The underlying theory brings together perception and action under one single imperative: minimizing free energy. However, despite its theoretical utility in explaining intelligence, computational implementations have been restricted to low-dimensional and idealized situations. In this paper, we present a neural architecture for building deep active inference agents operating in complex, continuous state-spaces using multiple forms of Monte-Carlo (MC) sampling. For this, we introduce a number of techniques, novel to active inference. These include: i) selecting free-energy-optimal policies via MC tree search, ii) approximating this optimal policy distribution via a feed-forward `habitual' network, iii) predicting future parameter belief updates using MC dropouts and, finally, iv) optimizing state transition precision (a high-end form of attention). Our approach enables agents to learn environmental dynamics efficiently, while maintaining task performance, in relation to reward-based counterparts. We illustrate this in a new toy environment, based on the dSprites data-set, and demonstrate that active inference agents automatically create disentangled representations that are apt for modeling state transitions. In a more complex Animal-AI environment, our agents (using the same neural architecture) are able to simulate future state transitions and actions (i.e., plan), to evince reward-directed navigation - despite temporary suspension of visual input. These results show that deep active inference - equipped with MC methods - provides a flexible framework to develop biologically-inspired intelligent agents, with applications in both machine learning and cognitive science.

Dissociable neural responses associated with reward, punishment and risk-taking

How vaccination and contact isolation might interact to suppress transmission of Covid-19: a DCM study

Abstract This report describes a dynamic causal model that could be used to address questions about the rollout and efficacy of vaccines in the United Kingdom. For example, is suppression of community transmission a realistic aspiration? And, if not, what kind of endemic equilibrium might be achieved? What percentage of the population needs to be vaccinated? And over what timescale? It focuses on the synergies among (i) vaccination , (ii) the supported isolation of contacts of confirmed cases and (iii) restrictions on contact rates (i.e., lockdown and social distancing). To model these mitigations, we used a dynamic causal model that embeds an epidemiological model into agent-based behavioural model. The model structure and parameters were optimised to best explain responses—to the first and subsequent waves—enabling predictions over the forthcoming year under counterfactual scenarios. Illustrative analyses suggest that the full potential of vaccination is realised by increasing the efficacy of contact tracing: for example, under idealised (best case) assumptions—of an effective vaccine and efficient isolation of infected pre-symptomatic cases— suppression of community transmission would require 50% herd immunity by vaccinating 22% by the end of 2021; i.e., 15 million people or about 50,000 per day. With no change in the isolation of contacts, 36% would require vaccination, i.e., 25 million people. These figures should not be read as estimates of the actual number of people requiring vaccination; however, they illustrate the potential of this kind of model to quantify interactions among public health interventions. We anticipate using this model in a few months—to estimate the average effectiveness of vaccines when more data become available.

Attention or salience?

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 traveled 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.