Quantifying wave propagation in a chain of FitzHugh–Nagumo neurons

Abstract

Understanding how external stimuli propagate in neural systems is an important challenge in the fields of neuroscience and nonlinear dynamics. Despite extensive studies over several decades, this problem remains poorly understood. In this work, we examine a simple "toy model" of an excitable medium, a linear chain of diffusely coupled FitzHugh-Nagumo neurons, and analyze the transmission of a sinusoidal signal injected into one of the neurons at the ends of the chain. We measure to what extent the propagation of the wave reaching the opposite end is affected by the frequency and amplitude of the signal, the number of neurons in the chain, and the strength of their mutual diffusive coupling. To quantify these effects, we measure the cross correlation between the time series of the membrane potentials of the end neurons. This measure allows us to detect the values of the parameters that delimit different propagation regimes.