# Golfvoortplanting in slagaderen

Golfvoortplanting in slagaderen

Author Faculty Department Date1975-06-01

AbstractPlease note that only this summary is in english. The rest of the report is in dutch only. This paper deals with the wave propagation of harmonic travelling waves through an incompressible, Newtonian fluid contained within an elastic tube with homogeneous and isotropic wall material. In particular the next questions are considered: 1) What is the difference between the one-dimensional and the two-dimensional blood flow approach? 2) Is it possible to derive an expression for the wave velocity c without making important restrictions as a thin or an incrompessible wall? 3) What is the influence of vascular tethering on blood flow and wave propagation? After a historical review and some physiological aspects, an one-dimensional approach is considered. The equations for (axisymmetric) long waves are derived and linearized. From these equations the expressions for the wave velocity c, the phase velocity c_p, the damping number d and the longitudinal impedance per length Z_l are realised. In the next part of this paper, a two-dimensional flow is considered. The motion of the fluid is described by the linearized form of the Navier-Stoker equations. The motion of the wall is described by the equations of classical elasticity theory, the equations of Navier. Boundary conditions are used describing the continuity of stress and velocity components in the fluid and the tube. From these boundary conditions a set of six simultaneous equations in six unknown constants has been obtained. Because it is not possible to solve the set of six equations, asymptotic methods have been introduced. Furthermore, one boundary condition is strongly dependent on the tethering of the blood vessels to the surrounding tissues. Therefore two cases are considered. In the first case the longitudinal constraint of the blood vessels is very strong, the second case deals with the study of a freely moving tube. For both cases expressions are realised for the wave velocity c, the phase velocity c_p, the damping number d and the longitudinal impedance per length Z_l are compared with each other and with the one-dimensional approach. The next conclusions follow from this work: 1) It is not possible to describe quite satisfactory blood flow and wave propagation in blood vessels with an one-dimensional harmonic theory. 2) The influence of vascular tethering on blood flow and wave propagation is rather small. 3) The longitudinally constrained blood vessel conception approaches reality much better than the freely moving conception.

Subjectgolfvoortplanting

wave propagation

blood flow

blood vessels

vascular tethering

Navier-Stokes

bloedstroming

http://resolver.tudelft.nl/uuid:3c81a957-c073-48bf-8ebc-992557320e74

PublisherTU Delft, Department of Hydraulic Engineering

SourceReport no. 4-75

Part of collectionInstitutional Repository

Document typereport

Rights(c) 1975 TU Delft, Department of Hydraulic Engineering