A stochastic mean field model for an excitatory and inhibitory synaptic drive cortical neuronal network

A Computational Study of a Spatiotemporal Mean Field Model Capturing the Emergence of Alpha and Gamma Rhythmic Activity in the Neocortex

In this paper, we analyze the spatiotemporal mean field model developed by Liley et al. in order to advance our understanding of the wide effects of pharmacological agents and anesthetics. Specifically, we use the spatiotemporal mean field model for capturing the electrical activity in the neocortex to computationally study the emergence of α - and γ -band rhythmic activity in the brain. We show that α oscillations in the solutions of the model appear globally across the neocortex, whereas γ oscillations can emerge locally as a result of a bifurcation in the dynamics of the model. We solve the dynamic equations of the model using a finite element solver package and show that our results verify the predictions made by bifurcation analysis.

Estimating Sensorimotor Mapping From Stimuli to Behaviors to Infer C. elegans Movements by Neural Transmission Ability Through Connectome Databases

One of the ultimate goals of computational neuroscience is to quantitatively connect between complex neural circuits and behaviors. In the past decades, the touch response circuit in Caenorhabditis elegans (C. elegans) has extensively been investigated in studies using genetically modified or laser-ablated worms. Synaptic connections, including chemical and electrical synapses, have been identified for most neurons in the C. elegans. However, we still do not know whether the empirically observed touch responses can be derived from connectome reconstructed from databases. To address this issue, we defined the transmission abilities (or levels) of neurons in a rate model in order to infer the behaviors of wild-type and ablated worms in response to posterior/nose/anterior touch stimuli. Our analysis showed that transmission abilities can be used to identify sensorimotor mapping from stimuli to movements and then to infer the C. elegans behaviors under simulations based on the perspective of decision-making, and provide useful information about how chemical and electronic synapses should be combined in the neural network movement analysis. This paper reveals an efficient tool that provided insights into the functions of complex neural circuits.

A Mechanistic Neural Field Theory of How Anesthesia Suppresses Consciousness: Synaptic Drive Dynamics, Bifurcations, Attractors, and Partial State Equipartitioning

With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus on how the molecular properties of anesthetic agents lead to the observed macroscopic property that defines the anesthetic state, that is, lack of responsiveness to noxious stimuli. In this paper, we use dynamical system theory to develop a mechanistic mean field model for neural activity to study the abrupt transition from consciousness to unconsciousness as the concentration of the anesthetic agent increases. The proposed synaptic drive firing-rate model predicts the conscious-unconscious transition as the applied anesthetic concentration increases, where excitatory neural activity is characterized by a Poincaré-Andronov-Hopf bifurcation with the awake state transitioning to a stable limit cycle and then subsequently to an asymptotically stable unconscious equilibrium state. Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions. This is done by focusing on a postulated subset of inhibitory neurons that are not themselves connected to other inhibitory neurons. Finally, several numerical experiments are presented to illustrate the different aspects of the proposed theory.

From data patterns to mechanistic models in acute critical illness

The complexity of the physiologic and inflammatory response in acute critical illness has stymied the accurate diagnosis and development of therapies. The Society for Complex Acute Illness was formed a decade ago with the goal of leveraging multiple complex systems approaches to address this unmet need. Two main paths of development have characterized the society's approach: (i) data pattern analysis, either defining the diagnostic/prognostic utility of complexity metrics of physiologic signals or multivariate analyses of molecular and genetic data and (ii) mechanistic mathematical and computational modeling, all being performed with an explicit translational goal. Here, we summarize the progress to date on each of these approaches, along with pitfalls inherent in the use of each approach alone. We suggest that the next decade holds the potential to merge these approaches, connecting patient diagnosis to treatment via mechanism-based dynamical system modeling and feedback control and allowing extrapolation from physiologic signals to biomarkers to novel drug candidates. As a predicate example, we focus on the role of data-driven and mechanistic models in neuroscience and the impact that merging these modeling approaches can have on general anesthesia.