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 solve...

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Bibliographic Details
Published in:Computers in biology and medicine 1996-05, Vol.26 (3), p.255-261
Main Authors: Stern, Ralph H., Rasmussen, Henning
Format: Article
Language:English
Subjects:
Biological and medical sciences
Cardiovascular model
Collocation
Elasticity
Fundamental and applied biological sciences. Psychology
General aspects
Left ventricular ejection
Linear Models
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Models, Cardiovascular
Numerical Analysis, Computer-Assisted
Reproducibility of Results
Simulation
Stroke Volume - physiology
Time Factors
Time-varying elastance
Vascular Resistance
Ventricular Function, Left - physiology
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Summary: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.
ISSN:0010-4825
1879-0534
DOI:10.1016/0010-4825(96)00007-8