Oscillatory Flow in Arteries: the Constrained Elastic Tube as a Model of Arterial Flow and Pulse Transmission

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Abstract
In the consideration of pulsatile flow in arteries, the conditions of oscillatory flow in a thin-walled elastic tube have to be modified owing to the tethering effect of the connective tissue and the mass of the adjacent organs. It is shown that by modification of a single parameter (the ratio of the wall-thickness to the radius of the tube) the equations of an earlier paper can be used to describe the motion when the tube is constrained as in the living body. If the longitudinal constraint is very still the solution is a simple one, for the relationship between pressure-gradient and rate of flow reduces to that of the rigid tube but the wave velocity remains finite. The application of the theory to the relation of arterial dilation and pressure show that it predicts the data as accurately as the experimental measurements allow.