Left ventricular ejection: model solution by collocation, an approximate analytical method.
A differential equation solution method that does not utilize numerical integration is demonstrated on a physiologic model. A previously proposed model of left ventricular ejection incorporating time-varying elastance, internal resistance, aortic inductance, and a three-component windkessel is solved by collocation. Assuming internal resistance to be constant allows simplification to a third order linear differential equation in left ventricular volume. A trigonometric series is used to approximate the solution and the coefficients of the series as well as the duration of ejection and pre-ejection periods are chosen so that the governing differential equation is exactly satisfied at certain times during ejection (the collocation points), as well as the boundary conditions and steady state condition.
Stern
R H
RH
Department of Medicine, University of Western Ontario, London, Canada.
Rasmussen
H
H
D004548:Elasticity; D016014:Linear Models; D008955:Models, Cardiovascular; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D013318:Stroke Volume / Q000502:physiology*; D013997:Time Factors; D014655:Vascular Resistance; D016277:Ventricular Function, Left / Q000502:physiology*