Mathematical modelling of extracorporeal circulation: simulation of different perfusion regimens

Abstract

Computer- and sensor-aided control of the heart-lung machine is considered a major goal for perfusion sciences for the next few years. At present, control of perfusion is achieved by surgeons, anaesthesiologists and perfusionists making short-term decisions, which leads to variations of the perfusion regimens between different centres and even between different teams in the operating theatre. As the basis for an integrated control of extracorporeal circulation (ECC), we proposed a mathematical model for simulating haemodynamics during pulsatile perfusion. This model was then modified to allow it to simulate the effects of different perfusion regimens on arterial haemodynamics and whole body oxygen consumption. The model was constructed on a PC using MATLAB/SIMULINK. The human arterial tree was divided into a multibranch structure consisting of 128 segments characterized by their particular physical properties. Peripheral branches were terminated by a resistance term representing smaller vessels like arterioles and capillaries. Flow and pressure were expressed by the intensity of current and voltage in an electrotechnical analogon; inductivity, resistance and capacitance were implemented according to the physical properties of the arterial tree and the rheology of blood. The effects of different perfusion regimens (pulsatility, flow amount, acid-base regulation) were studied. After introducing an input signal to the model, flow and pressure waves established themselves throughout the simulated arterial tree. During the simulation experiments, marked differences among different perfusion regimens were displayed by the model. Variations in acid-base management mainly influenced the distribution of perfusion: during simulation of low-flow perfusion (1.2 l/min/m2), cerebral blood flow was 6.2 ml/s using an alpha-stat regimen, while it was increased to 9.4 ml/s during pH-stat, caused by an implementation of reduced cerebral resistance. Whole body oxygen consumption was predominantly regulated by the perfusion rate. While central venous oxygen saturation was calculated to be 84.7% during simulation of high-flow perfusion (2.4 l/min/m2), it dropped to 70% during simulation of low-flow perfusion regimens. The model proved to be useful for a realistic simulation of different perfusion regimens. Therefore it can be considered a continuing step for the derivation of a ‘state’ observer leading to the realization of an automatically controlled heart-lung machine.