A Critical Evaluation of Dynamical Systems Models of Bipolar Disorder

Bipolar disorder (BD) is a mood disorder involving recurring (hypo)manic and depressive episodes. The inherently temporal nature of BD has inspired its conceptualization using dynamical systems theory, which is a mathematical framework for understanding systems that evolve over time. In this paper we provide a critical review of dynamical systems models of BD. Owing to heterogeneity of methodologies and experimental designs in computational modeling, we designed a structured approach to guide our review in a fashion that parallels the appraisal of animal models by their Face, Predictive, and Construct Validity. This tool, the Validity Appraisal Guide for Computational Models (VAG-CM) is not an absolute estimate of validity, but rather a guide for more objective appraisal of models in this review. We identified 26 studies published before November 18, 2021 that proposed generative dynamical systems models of time-varying signals in BD. Two raters independently applied the VAG-CM to included studies, obtaining a mean Cohen's kappa of 0.55 (95% CI [0.45, 0.64]) prior to establishing consensus ratings. Consensus VAG-CM ratings revealed three model/study clusters: data-driven models with face validity, theory-driven models with predictive validity, and theory-driven models lacking all forms of validity. We conclude that future models should be developed using a hybrid approach that first operationalizes BD features of interest using empirical data (a data-driven approach), followed by explanations of those features using generative models with components that are homologous to physiological or psychological systems involved in BD (a theory-driven approach).

Rise-to-threshold and dynamical systems views of proactive inhibition

Successful models of movement should encompass the flexibility of the human motor system to execute movements under different contexts. One such context-dependent modulation is proactive inhibition, a type of behavioural inhibition concerned with responding with restraint. Whilst movement has classically been modelled as a rise-to-threshold process, there exists a lack of empirical evidence for this in limb movements. Alternatively, the dynamical systems view conceptualises activity during motor preparation as setting the initial state of a dynamical system, that evolves into the movement upon receipt of a trigger. We tested these models by measuring how proactive inhibition influenced movement preparation and execution in humans. We changed the orientation (PA: postero-anterior and AP: antero-posterior flowing currents) and pulse width (120 μs and 30 μs) of motor cortex transcranial magnetic stimulation to probe different corticospinal interneuron circuits. PA and AP interneuron circuits represent the dimensions of a state space upon which motor cortex activity unfolds during motor preparation and execution. AP30 inputs were inhibited at the go cue, regardless of proactive inhibition, whereas PA120 inputs scaled inversely with the probability of successful inhibition. When viewed through a rise-to-threshold model, proactive inhibition was implemented by delaying the trigger to move, suggesting that motor preparation and execution are independent. A dynamical systems perspective showed that proactive inhibition was marked by a shift in the distribution of interneuron networks (trajectories) during movement execution, despite normalisation for reaction time. Viewing data through the rise-to-threshold and dynamical systems models reveal complimentary mechanisms by which proactive inhibition is implemented.Key pointsWe view proactive inhibition through the rise-to-threshold and dynamical systems models.We change the orientation (PA: postero-anterior and AP: antero-posterior flowing currents) and pulse width (120 μs and 30 μs) of transcranial magnetic stimulation to probe interneuron networks in motor cortex during behavioural tasks employing proactive inhibition.When viewed through a rise-to-threshold model, proactive inhibition was implemented by delaying the trigger to move, suggesting that motor preparation and execution are independent.A dynamical systems perspective showed that despite normalisation for reaction time, the trajectory/balance between PA120 and AP30 interneuron inputs during movement execution depended on proactive inhibition.Viewing data through the rise-to-threshold and dynamical systems models reveal complimentary mechanisms by which proactive inhibition is implemented.

Recurrent Switching Dynamical Systems Models for Multiple Interacting Neural Populations

Modern recording techniques can generate large-scale measurements of multiple neural populations over extended time periods. However, it remains a challenge to model non-stationary interactions between high-dimensional populations of neurons. To tackle this challenge, we develop recurrent switching linear dynamical systems models for multiple populations. Here, each high-dimensional neural population is represented by a unique set of latent variables, which evolve dynamically in time. Populations interact with each other through this low-dimensional space. We allow the nature of these interactions to change over time by using a discrete set of dynamical states. Additionally, we parameterize these discrete state transition rules to capture which neural populations are responsible for switching between interaction states. To fit the model, we use variational expectation-maximization with a structured mean-field approximation. After validating the model on simulations, we apply it to two different neural datasets: spiking activity from motor areas in a non-human primate, and calcium imaging from neurons in the nematode C. elegans. In both datasets, the model reveals behaviorally-relevant discrete states with unique inter-population interactions and different populations that predict transitioning between these states.

Validation of System-level Properties at Code Level

This chapter claims that code generation can be adapted to enable the expression of system-level properties at code level, and be later proved with respect to the code semantics. All previous analyses were performed on discrete dynamical systems models. However, once the control-level properties have been expressed and analyzed at model level, their validity must be asserted on the code artifact extracted from the model. Luckily, this extraction of code from models is largely automatized thanks to autocoding framework generating embedded code from dataflow models. Indeed, code generation from dataflow language is now effective and widely used in the industry. With these in mind, the chapter first gives an overview of the modeling framework, enabling the expression of properties at model and code level. A second part explains the generation of such code annotations, while a last part focuses on their verification.