Pulsatile Pressure and Flow Through Distensible Vessels

Abstract

The basic differential equations for elastic wall material and for continuity and momentum are derived, including fluid frictional resistance of the wall of the tubes, based on one-dimensional flow. These partial differential equations are transformed into four ordinary differential equations using the theory of characteristics. Then difference equations are developed and by an interpolation method (method of specified time intervals) equations are obtained for computation of velocity and pressure at equally-spaced sections along the vessel at specified equal time intervals. The equations are first applied to a flexible tube of initial constant diameter, with a pulse flow taken from in vivo experiments. Equations are then developed for tapering tubes with distributed outflow along their lengths (to simulate branches). Pressure-time data from femoral artery measurements are then used to compute flow through the artery, and the results are compared with electromagnetic flowmeter data. Computed flow is greater than measured flow if a friction factor for laminar flow is used. Frictional losses of energy in the normal pulsatile flow in the femoral artery are similar to those of turbulent flow.