MATHEMATICAL MODELING OF CARDIAC BLOOD FLOW IN HUMANS

Abstract

Lumped parameter model is a very useful type of mathematical modelling where the physical system is made analogous to an electrical network. Lumped parameter model is represented graphically by a circuit diagram in which vertices represent the voltages and the edges the current in the circuit. The mathematical analysis of such a circuit model is very convenient and eases the analysis of the actual physical system. These models are constructed by building the analogy between cardiovascular system and electrical circuit.This analogy makes use of simple ordinary differential equations in time which can be solved either numerically or analytically.
A mathematical model to model the blood pressure variation in the four chambers of heart at representative altitudes of h= 2 km, h = 4 km and h = 5 kmusing lumped compartments of blood circulation is presented in this paper. This lumped parameter model consists of eight compartments that include the pumping heart, the systemic circulation and the pulmonary circulation. The governing equations for pressure and flow in each compartment are derived from the following three equations: Ohm's law, conservation of volume and the definition of compliances. The g-factor is added to the model in order to accommodate for the effects due to gravitation.