Publications

Assessing interactions among neuronal systems using functional neuroimaging

Mapping conservative Fokker–Planck entropy in neural systems

Mapping the flow of information through the networks of the brain remains one of the most important challenges in computational neuroscience. In certain cases, this flow can be approximated by considering just two contributing factors—a predictable drift and a randomized diffusion. We show here that the uncertainty associated with such a drift-diffusion process can be calculated in terms of the entropy associated with the Fokker–Planck equation. This entropic evolution comprises two components: an irreversible entropic spread that always increases over time and a reversible entropic current that can increase or decrease locally within the system. We apply this dynamic entropy decomposition to two-photon imaging data collected in the murine visual cortex. Our analysis reveals maps of conserved entropic flow emanating from lateromedial, anterolateral, and rostrolateral regions toward the primary visual cortex (V1). These results highlight the role of V1 as an entropic sink, facilitating the redistribution of information throughout the visual cortex. These findings offer new insights into the hierarchical organization of cortical processing and provide a framework for exploring information dynamics in complex dynamical systems.

Rendering neuronal state equations compatible with the principle of stationary action

Abstract The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in classical mechanics through to quantum field theory. However, computational neuroscience, despite its heavy reliance on concepts in physics, is anomalous in this regard as its main equations of motion are not compatible with a Lagrangian formulation and hence with the principle of stationary action. Taking the Dynamic Causal Modelling (DCM) neuronal state equation as an instructive archetype of the first-order linear differential equations commonly found in computational neuroscience, we show that it is possible to make certain modifications to this equation to render it compatible with the principle of stationary action. Specifically, we show that a Lagrangian formulation of the DCM neuronal state equation is facilitated using a complex dependent variable, an oscillatory solution, and a Hermitian intrinsic connectivity matrix. We first demonstrate proof of principle by using Bayesian model inversion to show that both the original and modified models can be correctly identified via in silico data generated directly from their respective equations of motion. We then provide motivation for adopting the modified models in neuroscience by using three different types of publicly available in vivo neuroimaging datasets, together with open source MATLAB code, to show that the modified (oscillatory) model provides a more parsimonious explanation for some of these empirical timeseries. It is our hope that this work will, in combination with existing techniques, allow people to explore the symmetries and associated conservation laws within neural systems – and to exploit the computational expediency facilitated by direct variational techniques.

Uncovering the underlying mechanisms and whole-brain dynamics of deep brain stimulation for Parkinson’s disease

Deep brain stimulation (DBS) for Parkinson's disease is a highly effective treatment in controlling otherwise debilitating symptoms. Yet the underlying brain mechanisms are currently not well understood. Whole-brain computational modeling was used to disclose the effects of DBS during resting-state functional Magnetic Resonance Imaging in ten patients with Parkinson's disease. Specifically, we explored the local and global impact that DBS has in creating asynchronous, stable or critical oscillatory conditions using a supercritical bifurcation model. We found that DBS shifts global brain dynamics of patients towards a Healthy regime. This effect was more pronounced in very specific brain areas such as the thalamus, globus pallidus and orbitofrontal regions of the right hemisphere (with the left hemisphere not analyzed given artifacts arising from the electrode lead). Global aspects of integration and synchronization were also rebalanced. Empirically, we found higher communicability and coherence brain measures during DBS-ON compared to DBS-OFF. Finally, using our model as a framework, artificial in silico DBS was applied to find potential alternative target areas for stimulation and whole-brain rebalancing. These results offer important insights into the underlying large-scale effects of DBS as well as in finding novel stimulation targets, which may offer a route to more efficacious treatments.

Observing the Observer (II): Deciding When to Decide

In a companion paper [1], we have presented a generic approach for inferring how subjects make optimal decisions under uncertainty. From a Bayesian decision theoretic perspective, uncertain representations correspond to "posterior" beliefs, which result from integrating (sensory) information with subjective "prior" beliefs. Preferences and goals are encoded through a "loss" (or "utility") function, which measures the cost incurred by making any admissible decision for any given (hidden or unknown) state of the world. By assuming that subjects make optimal decisions on the basis of updated (posterior) beliefs and utility (loss) functions, one can evaluate the likelihood of observed behaviour. In this paper, we describe a concrete implementation of this meta-Bayesian approach (i.e. a Bayesian treatment of Bayesian decision theoretic predictions) and demonstrate its utility by applying it to both simulated and empirical reaction time data from an associative learning task. Here, inter-trial variability in reaction times is modelled as reflecting the dynamics of the subjects' internal recognition process, i.e. the updating of representations (posterior densities) of hidden states over trials while subjects learn probabilistic audio-visual associations. We use this paradigm to demonstrate that our meta-Bayesian framework allows for (i) probabilistic inference on the dynamics of the subject's representation of environmental states, and for (ii) model selection to disambiguate between alternative preferences (loss functions) human subjects could employ when dealing with trade-offs, such as between speed and accuracy. Finally, we illustrate how our approach can be used to quantify subjective beliefs and preferences that underlie inter-individual differences in behaviour.

The Feature-Based Model of Semantic Memory

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Updating Beliefs Beyond the Here-and-Now: The Counter-factual Self in Anosognosia for Hemiplegia

The syndrome of anosognosia for hemiplegia (AHP), or the lack of awareness for one’s paralysis following right hemisphere stroke, can provide unique insights into the neurocognitive mechanisms of self-awareness. Yet it remains unclear whether AHP is a modality-specific deficit of sensorimotor monitoring, or whether domain-general processes of attention and belief-updating converge to cause AHP. Using a Bayesian learning framework, we formalised and empirically investigated the hypothesis that failures to update anosognosic beliefs can be explained by abnormalities in the relative uncertainty (i.e. precision) ascribed to prior beliefs versus sensory information in different contexts. We designed a new motor belief-updating task that manipulated both the temporal (prospective and retrospective) and spatial (hemispace most affected by inattention and hemispace less affected by inattention) conditions in which beliefs had to be updated, and we validated its sensitivity to AHP in 26 patients with right hemisphere stroke. We then computed and empirically tested two different Bayesian predictors of prospective beliefs using two proxies for precision in AHP patients: (i) standardised, neuropsychological measures of objective attention abilities, i.e. visuospatial neglect scores, and (ii) subjective uncertainty reports, i.e. confidence ratings. Our results suggest that while neglect does not affect local, sensorimotor error monitoring, it does seem to affect the degree to which observed errors are used to update more general, prospective beliefs about counterfactual motor abilities in AHP. Difficulties in such ‘counterfactual’ belief-updating were associated with disruptions in tracts of the ventral attentional network (i.e. superior longitudinal fasciculus connecting the temporo-parietal junction and ventral frontal cortex) and associated lesions to the insula, inferior parietal cortex and superior temporal regions. These results suggest that self-awareness extends beyond local, retrospective monitoring, requiring also salience-based, convergence of beliefs about the self that go beyond the ‘here-and-now’ of sensorimotor experience.

Waking and Dreaming Consciousness: Neurobiological and Functional Considerations

Is predictability salient? A study of attentional capture by auditory patterns

In this series of behavioural and electroencephalography (EEG) experiments, we investigate the extent to which repeating patterns of sounds capture attention. Work in the visual domain has revealed attentional capture by statistically predictable stimuli, consistent with predictive coding accounts which suggest that attention is drawn to sensory regularities. Here, stimuli comprised rapid sequences of tone pips, arranged in regular (REG) or random (RAND) patterns. EEG data demonstrate that the brain rapidly recognizes predictable patterns manifested as a rapid increase in responses to REG relative to RAND sequences. This increase is reminiscent of the increase in gain on neural responses to attended stimuli often seen in the neuroimaging literature, and thus consistent with the hypothesis that predictable sequences draw attention. To study potential attentional capture by auditory regularities, we used REG and RAND sequences in two different behavioural tasks designed to reveal effects of attentional capture by regularity. Overall, the pattern of results suggests that regularity does not capture attention. This article is part of the themed issue ‘Auditory and visual scene analysis’.

PsPM-SCRV6: Skin conductance responses to pain by electric stimulation

This dataset includes skin conductance response (SCR) measurements for each of 20 healthy unmedicated participants (10 males and 10 females aged 21.8+/-3.3 years) in response to 10 discomforting electric shocks. Stimuli are 0.5ms wide square current pulse repeated at 500Hz for 100ms. Amplitude is varied (mean +/- SD: 0.78mA +/- 0.43mA). ITI is selected randomly on each trial from 29s, 34s or 39s.

Tractography-based priors for dynamic causal models

Functional integration in the brain rests on anatomical connectivity (the presence of axonal connections) and effective connectivity (the causal influences mediated by these connections). The deployment of anatomical connections provides important constraints on effective connectivity, but does not fully determine it, because synaptic connections can be expressed functionally in a dynamic and context-dependent fashion. Although it is generally assumed that anatomical connectivity data is important to guide the construction of neurobiologically realistic models of effective connectivity; the degree to which these models actually profit from anatomical constraints has not yet been formally investigated. Here, we use diffusion weighted imaging and probabilistic tractography to specify anatomically informed priors for dynamic causal models (DCMs) of fMRI data. We constructed 64 alternative DCMs, which embodied different mappings between the probability of an anatomical connection and the prior variance of the corresponding of effective connectivity, and fitted them to empirical fMRI data from 12 healthy subjects. Using Bayesian model selection, we show that the best model is one in which anatomical probability increases the prior variance of effective connectivity parameters in a nonlinear and monotonic (sigmoidal) fashion. This means that the higher the likelihood that a given connection exists anatomically, the larger one should set the prior variance of the corresponding coupling parameter; hence making it easier for the parameter to deviate from zero and represent a strong effective connection. To our knowledge, this study provides the first formal evidence that probabilistic knowledge of anatomical connectivity can improve models of functional integration.

Multi-modal and multi-model interrogation of large-scale functional brain networks

Existing whole-brain models are generally tailored to the modelling of a particular data modality (e.g., fMRI or MEG/EEG). We propose that despite the differing aspects of neural activity each modality captures, they originate from shared network dynamics. Building on the universal principles of self-organising delay-coupled nonlinear systems, we aim to link distinct features of brain activity - captured across modalities - to the dynamics unfolding on a macroscopic structural connectome. To jointly predict connectivity, spatiotemporal and transient features of distinct signal modalities, we consider two large-scale models - the Stuart Landau and Wilson and Cowan models - which generate short-lived 40 Hz oscillations with varying levels of realism. To this end, we measure features of functional connectivity and metastable oscillatory modes (MOMs) in fMRI and MEG signals - and compare them against simulated data. We show that both models can represent MEG functional connectivity (FC), functional connectivity dynamics (FCD) and generate MOMs to a comparable degree. This is achieved by adjusting the global coupling and mean conduction time delay and, in the WC model, through the inclusion of balance between excitation and inhibition. For both models, the omission of delays dramatically decreased the performance. For fMRI, the SL model performed worse for FCD and MOMs, highlighting the importance of balanced dynamics for the emergence of spatiotemporal and transient patterns of ultra-slow dynamics. Notably, optimal working points varied across modalities and no model was able to achieve a correlation with empirical FC higher than 0.4 across modalities for the same set of parameters. Nonetheless, both displayed the emergence of FC patterns that extended beyond the constraints of the anatomical structure. Finally, we show that both models can generate MOMs with empirical-like properties such as size (number of brain regions engaging in a mode) and duration (continuous time interval during which a mode appears). Our results demonstrate the emergence of static and dynamic properties of neural activity at different timescales from networks of delay-coupled oscillators at 40 Hz. Given the higher dependence of simulated FC on the underlying structural connectivity, we suggest that mesoscale heterogeneities in neural circuitry may be critical for the emergence of parallel cross-modal functional networks and should be accounted for in future modelling endeavours.

Active Inference and Intentional Behaviour

Recent advances in theoretical biology suggest that basal cognition and sentient behaviour are emergent properties of in vitro cell cultures and neuronal networks, respectively. Such neuronal networks spontaneously learn structured behaviours in the absence of reward or reinforcement. In this paper, we characterise this kind of self-organisation through the lens of the free energy principle, i.e., as self-evidencing. We do this by first discussing the definitions of reactive and sentient behaviour in the setting of active inference, which describes the behaviour of agents that model the consequences of their actions. We then introduce a formal account of intentional behaviour, that describes agents as driven by a preferred endpoint or goal in latent state-spaces. We then investigate these forms of (reactive, sentient, and intentional) behaviour using simulations. First, we simulate the aforementioned in vitro experiments, in which neuronal cultures spontaneously learn to play Pong, by implementing nested, free energy minimising processes. The simulations are then used to deconstruct the ensuing predictive behaviour, leading to the distinction between merely reactive, sentient, and intentional behaviour, with the latter formalised in terms of inductive planning. This distinction is further studied using simple machine learning benchmarks (navigation in a grid world and the Tower of Hanoi problem), that show how quickly and efficiently adaptive behaviour emerges under an inductive form of active inference.

The Effect of Prior Visual Information on Recognition of Speech and Sounds

To identify and categorize complex stimuli such as familiar objects or speech, the human brain integrates information that is abstracted at multiple levels from its sensory inputs. Using cross-modal priming for spoken words and sounds, this functional magnetic resonance imaging study identified 3 distinct classes of visuoauditory incongruency effects: visuoauditory incongruency effects were selective for 1) spoken words in the left superior temporal sulcus (STS), 2) environmental sounds in the left angular gyrus (AG), and 3) both words and sounds in the lateral and medial prefrontal cortices (IFS/mPFC). From a cognitive perspective, these incongruency effects suggest that prior visual information influences the neural processes underlying speech and sound recognition at multiple levels, with the STS being involved in phonological, AG in semantic, and mPFC/IFS in higher conceptual processing. In terms of neural mechanisms, effective connectivity analyses (dynamic causal modeling) suggest that these incongruency effects may emerge via greater bottom-up effects from early auditory regions to intermediate multisensory integration areas (i.e., STS and AG). This is consistent with a predictive coding perspective on hierarchical Bayesian inference in the cortex where the domain of the prediction error (phonological vs. semantic) determines its regional expression (middle temporal gyrus/STS vs. AG/intraparietal sulcus).

Computing average shaped tissue probability templates

The brain network for emotional body language reading: Combined structural and effective connectivity

Conservation laws by virtue of scale symmetries in neural systems

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, 1t. 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.