Studies on the relations between pressure and flow in the circulation |
| |
Authors: | Robert Macey |
| |
Institution: | (1) Committee on Mathematical Biology, The University of Chicago, Chicago, USA;(2) Present address: Aeromedical and Physical Environment Laboratory, University of Illinois, Chicago 12, Illinois |
| |
Abstract: | Simple theoretical models are proposed for the study of the interdependence between cardiac contraction, arterial pressure,
and capillary drainage. The relation between pressure and flow is derived for a model of branching distensible tubes taking
into account the finite pulse wave velocity. Equations are derived both for the case where the pulse wave is non-distorted
and for the case where the wave is damped and distorted to a limited extent. Following the model of J. W. Remington and W.
F. Hamilton (1947), the former case is applied to the larger arteries. Expressions are developed for the stroke volume, cardiac
ejection, and systolic arterial storage in both the steady and non-steady states. Expressions for the percentage discrepancy
involved in the computation of these quantities from a single tube model as contrasted with a multi-branched model are derived.
For typical cases these discrepancies are small and thus credence is lent to the further use of the simpler single tube model
which requires fewer independent parameters. It is also shown that the formulae for stroke volume and arterial storage are
only slightly sensitive to changes in pulse wave velocities, and that for some purposes it would seem permissible to assume
an infinite velocity.
The problem of capillary drainage is discussed, and the consequences of equations developed for the case of a distorted wave
are shown to compare favorably with published experimental data. An approximate boundary condition for capillary drainage
is derived.
Finally, A. V. Hill's velocity load equation for muscle is used to obtain a first approximation for the velocity of cardiac
contraction in terms of the initial arterial pressure, the heart radius, and the parameters of the heart musculature. It is
shown how methods developed for stroke volume determination from the pressure contour may be used to estimate the heart and
“air chamber” parameters. Use of these parameters and those obtained by other independent measurements permits the principle
variables to be determined numerically. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|