title: 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.
authors.affiliation: Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Ks. Trojdena 4, 02-109 Warsaw, Poland.
authors.forename: Leszek
authors.initials: L
authors.lastname: Pstras
authors.affiliation: Institute of Electronics, Computer and Telecommunication Engineering, National Research Council, c/o Department of Information Engineering (DEI), Via G. Gradenigo 6/b, 35131 Padova, Italy.
authors.forename: Karl
authors.initials: K
authors.lastname: Thomaseth
authors.affiliation: Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Ks. Trojdena 4, 02-109 Warsaw, Poland.
authors.forename: Jacek
authors.initials: J
authors.lastname: Waniewski
authors.affiliation: Department of Medicine, Sant'Antonio Hospital, Via Jacopo Facciolati 71, 35127 Padova, Italy.
authors.forename: Italo
authors.initials: I
authors.lastname: Balzani
authors.affiliation: Provincial Agency for Health Services (APSS), Via Alcide Degasperi 79, 38123 Trento, Italy.
authors.forename: Federico
authors.initials: F
authors.lastname: Bellavere
mesh_terms: D001341:Autonomic Nervous System / Q000502:physiology; D017704:Baroreflex; D001794:Blood Pressure; D001810:Blood Volume; D002302:Cardiac Output; D003198:Computer Simulation; D006339:Heart Rate; D006439:Hemodynamics; D006801:Humans; D055641:Mathematical Concepts; D008955:Models, Cardiovascular; D017711:Nonlinear Dynamics; D014636:Valsalva Maneuver; D014655:Vascular Resistance
keywords: afterload; autonomic function; baroreflex; blood pressure; cardiovascular homeostasis; haemodynamics; heart rate variations; mathematical model; nonlinear pressure-volume curves