Exploration on the spiking response of a single compartment neuron with multiple active properties under electrical stimuli

The study of modulating the neuronal signals by electrical stimuli is important to intervene the abnormal neuronal firing and bring them to a normal state. Spike trains, which are the highest quality of brain signals, have been deficiently explored and analyzed owing to the challenges of obtaining them in reality. In this regard, this paper aims to investigate and analyze the effect of electrical stimuli on the spiking response of neurons, and the following work is to be carried out. The relationships between the spiking response and three parameters (namely, the amplitude of the electrode current (EC), the angular velocity of the electric field current (EFC), and the signal-noise ratio (SNR)) are examined on a neuronal model with spatial length and multiple active properties. When specific currents with different SNRs are imposed on the neurons, their influence on the spiking response is further explored. With regard to the spiking response, the main focus is on three characteristics, i.e., the spiking pattern, the spike count (SC), and the spiking arrangement. An algorithm, called the return map distance (RMD) algorithm, is proposed in this paper, and gives the classification of spiking patterns a quantitative criterion. Based on it, the spiking patterns are classified in this paper as busting spike train, regular spike train (RST), and meager spike train (MST). Simulation results indicate that both the amplitude of the EC and the angular velocity of the EFC change the neuronal spiking patterns. As the amplitude (angular velocity) of the EC (EFC) increases, the spiking pattern of the Soldado-Magraner model (SMM) eventually tends to RST (MST). In addition, the SC increases with the amplitude of the EC, while it does not hold for the SC with respect to the angular velocity of the EFC. Furthermore, the spiking arrangement and the SC are severely destroyed for the EC with low SNRs, while three spiking features of the SMM under EFC are all robust to the different SNRs, which implies that compared with the EC, the spiking responses of the SMM under EFC are more stable. The findings in this paper may provide some theoretical guidance to the fields related to neuronal firing, such as brain-computer interfaces and electrotherapy. The RMD algorithm proposed here can be applied to more individual neurons, and the spiking arrangement discussed here could be regarded as an effective encoding way for spike trains.