ISSN:
1741-0444
Schlagwort(e):
Haemodynamics
;
Modelling
;
Pulsatile flow
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Biologie
,
Chemie und Pharmazie
,
Medizin
Notizen:
Abstract The purpose of this paper is to present standard results on the effect of nonlinearities on the computed pulsatile flow in a cylindrical distensible tube as a first stage in the calculation of flow in a tapered tube and blood flow in arteries. The calculations are made using the pressure-radius relationship of a rubber tube with no longitudinal motion and for a linearised relationship. The one-dimensional equations of motion are solved by the method of finite differences. The values of skin friction that are incorporated are determined from the vorticity and continuity equations for a rigid tube and a correction made to the current diameter at each time step. The accuracy of the results is assessed and the effect of varying parameters investigated. The method is applied to a segment of an infinite tube for which the linear analytical solution is available. The characteristics of the velocity wave calculated from an input pressure wave are presented as departures from the linear theory values of these characteristics, the wave speed, flux and transmission factor per wavelength. Computations are made at values of non-dimensional frequency (Stokes number α) of about 3 and 10. It is concluded that as far as physiological application is concerned (i.e. small amplitude and long wavelength) the results of linear theory are a very good first approximation for the cylindrical tube. At α=10, the relative departure of wave speed is about 0·5 times the relative diameter amplitude ( $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ amplitude/mean diameter) when the pressure-radius relation is linear and the pressure and velocity waves have the same characteristics. At α=3 the corresponding wave speed departure is about 0·1 $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ . The relative departure of the flux is less than 0·05 $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ at α=3 and about 0·5 $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ at α=10. The transmission coefficient has a relative departure of less than 0·05 $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ at α=10 and its relative increase at α=3 is about 0·3 $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ .
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF02441850
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