Mathematical Modelling of the Cardiovascular System Haemodynamics

Abstract

In this paper we propose a model of the cardiovascular system, where stressed blood volume is a model parameter instead of an initial condition. Stressed blood volume (SBV) is an important indicator of fluid responsiveness, i.e., this term can help to classify patients between responders and non-responders to fluid therapy. We study a six compartment model, then using the conservation of total blood volume, one differential equation of the original model is omitted and a new model is obtained. Comparing the haemodynamic signals of the previous model and the new version, we show that the simulations are qualitatively similar. One important difference with the original model is that the initial conditions for solving the proposed model are arbitrary. This allows us to perform a sensitivity analysis using automatic differentiation of the reduced model for all model parameters without excluding any parameter a priori, unlike the authors of the original formulation have done. This analysis showed that two parameters, the heart period and the stressed blood volume, have a major effect on the performance of the model.