Development of a cardiopulmonary mathematical model incorporating a baro–chemoreceptor reflex control system

Abstract

This article describes the development of a comprehensive mathematical model of the human cardiopulmonary system that combines the respiratory and cardiovascular systems and their associated autonomous nervous control actions. The model is structured to allow the complex interactions between the two systems and the responses of the combined system to be predicted under different physiological conditions. The cardiovascular system model contains 13 compartments, including the heart chambers operating as a pump and the blood vessels represented as distensible tubes configured in a serial and parallel arrangement. The accurate representation of the hemodynamics in the system and the good fit to published pressure and flow waveforms gave confidence in the modelling approach adopted for the cardiovascular system prior to the incorporation of the baroreflex control and the respiratory models. An improved baroreceptor reflex model is developed in this research, incorporating afferent, central and efferent compartments. A sigmoid function is included in the efferent compartment to produce sympathetic and parasympathetic nerve outflow to the effector sites. The baroreflex action is modelled using physiological data, its interaction with the chemoreflex control is explained and the simulation results presented show the ability of the model to predict the static and dynamic hemodynamic responses to environmental disturbances. A previously published respiratory model that includes the mechanics of breathing, gas exchange process and the regulation of the system is then combined with the cardiovascular model to form the cardiopulmonary model. Through comparison with published data, the cardiopulmonary model with the baro–chemoreflex control is validated during hypoxia and hypercapnia. The percentage difference between the predicted and measured changes in the heart rates and the mean arterial pressures are within 3% in both cases. The total peripheral resistance correlates well for hypoxia but is less good for hypercapnia, where the predicted change from normal condition is around 7% compared with a measured change of 23%. An example showing the application of the proposed model in sport science is also included.