Mathematical modelling of cardiovascular response to the Valsalva manoeuvre

Abstract

The Valsalva manoeuvre (VM) used for clinical autonomic testing results in a complex cardiovascular response with a concomitant action of several regulatory mechanisms whose nonlinear interactions are difficult to analyse without the aid of a mathematical model. The article presents a new non-pulsatile compartmental model of the human cardiovascular system with a variable intrathoracic pressure enabling the simulation of the haemodynamic response to the VM. The model is based on physiological data and includes three baroreflex mechanisms acting on heart rate, systemic resistance and venous unstressed volume. New nonlinear functions have been proposed to model cardiac output dependence on preload and afterload. Following the individual fitting of some parameters with a clear physiological meaning, the model is able to fit clinical data from patients with both typical and abnormal haemodynamic response to the VM. The sensitivity analysis showed that the model is most sensitive to the parameters describing the vascular pressure–volume relationships (the maximal volume of systemic veins and the relative level of vascular compliance). The use of nonlinear pressure–volume relationships for systemic veins proved crucial for the accurate modelling of the VM. On the contrary, the introduction of aroreflex time delays did not change significantly the haemodynamic response to the manoeuvre. The model can be a useful tool for aiding the interpretation of patient's response to the VM and provides a framework for analysing the interactions between the cardiovascular system and autonomic regulatory mechanisms.