Mixed quantitative/qualitative modeling and simulation of the cardiovascular system

Abstract

The cardiovascular system is composed of the hemodynamical system and the central nervous system (CNS) control. Whereas the structure and functioning of the hemodynamical system are well known and a number of quantitative models have already been developed that capture the behavior of the hemodynamical system fairly accurately, the CNS control is, at present, still not completely understood and no good deductive models exist that are able to describe the CNS control from physical and physiological principles. The use of qualitative methodologies may offer an interesting alternative to quantitative modeling approaches for inductively capturing the behavior of the CNS control. In this paper, a qualitative model of the CNS control of the cardiovascular system is developed by means of the fuzzy inductive reasoning (FIR) methodology. FIR is a fairly new modeling technique that is based on the general system problem solving (GSPS) methodology developed by G.J. Klir (Architecture of Systems Problem Solving, Plenum Press, New York, 1985). Previous investigations have demonstrated the applicability of this approach to modeling and simulating systems, the structure of which is partially or totally unknown. In this paper, five separate controller models for different control actuations are described that have been identified independently using the FIR methodology. Then the loop between the hemodynamical system, modeled by means of differential equations, and the CNS control, modeled in terms of five FIR models, is closed, in order to study the behavior of the cardiovascular system as a whole. The model described in this paper has been validated for a single patient only.