A memristive model of spatio-temporal excitability

TL;DR

The paper addresses the challenge of modeling neuronal excitability across disparate scales by proposing a memristive framework that unifies temporal and spatial mechanisms. By retaining the Hodgkin–Huxley circuit structure and Amari's neural-field ideas while introducing memductances that depend on the history of the field, the authors present a single, cross-scale mechanism capable of capturing both cellular and population dynamics. They demonstrate temporal excitability via a fast-acting memductance with rapid positive feedback and slower negative feedback, and spatial excitability via short-range excitation with longer-range inhibition, all cast within a memristive, CNN-like operator framework. The resulting spatio-temporal model preserves biophysical interpretability, supports scalable simulations, and offers a pathway to extend excitability to more complex behaviors such as bursting, with potential implications for neuromorphic design and cross-scale neuroscience analysis.

Abstract

This paper introduces a model of excitability that unifies the mechanism of an important neuronal property both in time and in space. As a starting point, we revisit both a key model of temporal excitability, proposed by Hodgkin and Huxley, and a key model of spatial excitability, proposed by Amari. We then propose a novel model that captures the temporal and spatial properties of both models. Our aim is to regard neuronal excitability as a property across scales, and to explore the benefits of modeling excitability with one and the same mechanism, whether at the cellular or the population level.

Figures (9)

• Figure 1: Temporal excitability in the Hodgkin-Huxley model. A small difference in $i_\text{app}$ (bottom) can cause a large difference in the voltage response (top).
• Figure 2: Block diagram of the mixed temporal monotone structure of the Hodgkin-Huxley model.
• Figure 3: Sketch of $w(x)$ as used in Amari's model.
• Figure 4: Spatial excitability in Amari's model. Left: the subthreshold steady-state voltage response $u^{ss}(x)$ (top) to Gaussian input current (bottom). Right: The superthreshold steady-state voltage response $u^{ss}(x)$ (top) to a Gaussian input current (bottom). The first applied pulse does not lead to spatial excitation, whereas the second applied pulse does,
• Figure 5: Block diagram of the mixed spatial monotone structure of Amari's model. We require $\sigma_E < \sigma_I$ to ensure that the excitatory interactions given by $i_E$ operate on shorter length scales than the inhibitory interactions given by $i_I$.