A Review of Biologically Plausible Neuron Models for Spiking Neural Networks

Abstract

In this paper, five mathematical models of single neurons are discussed and compared. The physical meanings, derivations, and differential equations of each model are provided. Since for many applications the spiking rates of neurons are of great importance, we compare the spiking rate patterns under different sustained current inputs. Numerical stability and accuracy are also considered. The computational cost and storage requirements needed to numerically solve each of the models are also discussed.

How the Accuracy and Computational Cost of Spiking Neuron Simulation are Affected by the Time Span and Firing Rate

“…Although several works are tackling the SN simulation problem on different fronts, a framework to test the SN simulation optimality is inexistent. This study and the preceding ones [77,50,79,72,81,82] Besides, our findings are in agreement with other authors suggesting that the Izhikevich statements could be mistaken. In most cases when the efficient simulations are compared, the HH shows the highest efficiency for any time span and firing rate whereas the IZH shows the lowest.…”

“…There is a significant number of SNs [22,39]. For simplicity, the LIF, IZH, and HH were reviewed because they are used in many simulation studies [38,74,67,50,72,81,82,61] that is widely used owing to its low computational cost and implementation ease [1,9]. The HH is the most biologically plausible model that works at the particle dynamics and electrical current levels.…”

“…Even though there are several open issues in the single SN simulation, this paper focuses on the time span and firing rate influence. It is thought that the firing rate changes the accuracy that some studies [50,72,81] have included it, but its impact has not been measured. The influence of the time span variability has been ignored and, in consequence, remains unknown.…”

AN EFFICIENT STOCHASTIC BASED MODEL FOR SIMULATING MICROELECTRODE RECORDINGS OF THE DEEP BRAIN - Modelling and Analysis

“…Dynamic models of neurons and neural networks are common for simulating brain structures (Feng, Shea-Brown, Greenwald, Kosut, & Rabitz, 2007;Izhikevich, 2007aIzhikevich, , 2007bRubin & Terman, 2004;Terman, Rubin, Yew, & Wilson, 2002). These types of models, using synaptic connections between neurons with dynamical neuron models, can be very computationally intensive (Long & Fang, 2010). To reduce the computational burden of modelling individual neurons with synaptic connections, the firing times of each neuron can be characterized by a stochastic variable.…”

A Parametric Simulation of Neuronal Noise From Microelectrode Recordings

“…Current STN models involving a large number of individual neurons are computationally intensive [17]. DBS MER models that simulate a single neuron with background noise are computationally efficcient but do not reflect neuronal noise processes.…”