Mathematical Modeling of Regulatory Mechanisms for the Distribution of Excitation in the Central Nervous System

Mathematical Modeling of Regulatory Mechanisms for the Distribution of Excitation in the Central Nervous System

Isroilov Shukhrat
Research Institute for the Development of Digital
Technologies and Artificial Intelligence
Tashkent, Uzbekistan
[e-mail]

Abstract— In this article, a mathematical model has been developed based on a system of nonlinear functional differential equations of a lagging type, using the method of regulating the regulatory mechanisms of interaction between the central nervous system and the main vital organs. The developed system of equations is simplified by the reduction and scaling method. There is an opportunity to develop new treatment tactics using mechanisms that regulate the interaction of the central nervous system and various organs, tissues and muscles of a person.
Keywords— mathematical model, regulatory mechanisms, biological systems, central nervous system, functional differential equation, reduction method.

I.Introduction

The normal functioning of many human functions depends on the state of the central nervous system (CNS), and a violation of the regulatory mechanisms of the propagation of excitation can cause many fatal pathologies. In many patients, damage to vital organs occurs in parallel with disorders of the CNS [1-3]. The understanding of these data on neuropathogenesis is still insufficient. The predictive ability of mathematical and computer modeling makes it possible to simulate the main modes of the process under consideration, to determine the regulatory mechanisms and patterns of its action. The CNS is characterized by nervous vibrations, rhythmic nervous activity, and this is usually caused by the vibrational activity of the nerve nodes [4]. In simulating on the basis of functional differential equations of the lagging type, the modeled system has an innate tendency to the state of fluctuating solutions [5-6]. Since these equations allow us to take into account the delayed relationships in the regulatory system, it is most appropriate to use them to model the regulatory mechanisms of excitation distribution in the central nervous system.