NEUR Subgroup Contributed Talks

Sishu Shankar Muni

School of Fundamental Sciences, Massey University, New Zealand

"Dynamics of the discretised Izhikevich neuron model"

When analyzing neuron models, ODE(Ordinary Differential Equation)-based models are used to study the characteristics of neurons and in turn understand the various complexities of neurons and their relations with abnormalities and hazards. But the biggest challenge of ODE-based models are its computational complexities and hence researchers started focusing on less complex models resulting in discrete models of neurons. A neuron exhibits bursting and spiking behavior depending on the resetting process which happens in every iteration step. In ODE models this iteration step decides the accuracy of the neuron models while in discrete models the iteration step is one and hence the accuracy is not affected. In this talk, I am going to introduce the discrete Izhikevich model which is modified version of the well-known ODE based Izhikevich neuron model. I analyze the complete dynamical properties and bifurcation patterns of the discretised model. It is found that a careful application of electric field on embryonic neuronal cells have led to their growth in cultures. Therefore, it is of interest to consider the effect of external electromagnetic field on the dynamical behavior of the neurons. I will show how the dynamics changes when external electromagnetic field is applied.

Marina Chugunova

University of Waterloo, Canada

"Calcium dynamics in the gonadotropin-releasing hormone neurons"

Located in hypothalamus, the gonadotropin-releasing hormone (GNRH) neurons trigger the reproductive axis by the synchronized release of gonadotropin-releasing hormone. The action potential propagating along the neuron's membrane activates the voltage-gated calcium channels, and the influx of the extracellular calcium activates the internal calcium stores. The resulting increase of the calcium ion concentration is crucial for the hormone exocytosis. The existing models of this phenomenon successfully explain the calcium transients along the dendrite of the GnRH neuron. However, the latest experimental results show a dramatic increase in the amplitude of the calcium concentration transients with the propagation along the dendrite. We conjecture that this amplitude increase is, in fact, the main reason for the synchronized release of the GnRH hormone and offer a new model for the calcium dynamics. The computational results based on the suggested model correlate with the experimental data.

John Parker

University of New Hampshire

"Existence of Cupolets in Chaotic Hindmarsh-Rose Neural Model"

This talk focuses on the Hindmarsh-Rose neuron model in a chaotic regime, and we consider a mechanism by which the system enters into a periodic state when driven by a signal from a chain of neurons. Previous work in nonlinear dynamics has shown that chaotic systems may be driven into periodic states (called cupolets) when driven by instantaneous impulses, using information theoretic and graph theoretic methods. In related work studying a coupled two cell FitzHugh-Nagumo neural model, it was possible for the combined system to enter into chaotic behavior, and through interaction and neural learning, mutually stabilized periodic states could be achieved. However, cupolet states were not possible because of the low dimensionality of the individual neurons. Here, we show that the Hindmarsh-Rose model, in a chaotic regime, may exhibit stabilized cupolets when impulses are applied on two Poincare surfaces. We report on several interesting properties of the cupolets. We then show how certain interactions between cupolets lead to chaotic stabilization in neural systems, with examples including a bidirectional neural system, a chain of neurons, and a feedback network. We conclude with a discussion of the implications and future directions of this research.

Christina Pospisil

USA

"Mathematical Models for Living Forms in Medical Physics Submodel 2: Information-Coding and Information-Processing through Nerves"

This talk continues the presentation Mathematical Models for Living Forms in Medical Physics Submodel 1: The information processing from teeth to Nerves from the Biophysics Annual Meeting 2020 Conference and American Physical Society Conferences. In the Submodel 1 the information processing from teeth to the nerves is modeled. The information is passed via p-waves through the tooth layers enamel and dentin. Odontoblasts located in the liquid in the tubules of the tooth dentin layer perform finally the transformation into electrical information (an electrical signal) that passes along nerves. The Submodel 2 of the project is dedicated to the information coding of the information from an entity hitting/touching a tooth and to the information processing of the coded unit through the nerves. Emphasized are the information representation as an electrical code and the coded information flow in the living system.