Simulation of Dynamic Processes in the Human Body using Differential Equations with Discontinuous Right-Hand Side

Abstract

this study considers the simulation of the human body’s functional systems as part of the research into the parameter variation dynamics in subsystems with a chaotic, self-organizing structure. The problem is significant as we need to study the interaction between the subsystems of a complex system, the human body, and find the causes of pathologies. The proposed simulation method uses differential equations with a discontinuous right-hand side. It enables us to account for self-organization in dynamic subsystems. The stationary state is maintained as the solution approaches a unique discontinuity line in the system, as it correctly reproduces the dynamics of a subsystem in the human body. The discontinuity line is generated during the simulation and adjusted to match the current state of the subsystem and the stationary state, which is a much better representation of the dynamics of a real living system. The paper includes the simulation results of a human biomechanical system (a special case). The tests proved the simulation results are in good agreement with the experiments. The biomechanical system motion simulation results show stability in a series of computational experiments.