Velocity profile method for time varying resistance in minimal cardiovascular system models

Abstract

This paper investigates the fluid dynamics governing arterial flow used in lumped parameter cardiovascular system (CVS) models, particularly near the heart where arteries are large. Assumptions made in applying equations conventionally used in lumped parameter models are investigated, specifically that of constant resistance to flow. The Womersley number is used to show that the effects of time varying resistance must be modelled in the pulsatile flow through the large arteries near the heart. It is shown that the equation commonly used to include inertial effects in fluid flow calculations is inappropriate for including time varying resistance. A method of incorporating time varying resistance into a lumped parameter model is developed that uses the Navier-Stokes equations to track the velocity profile. Tests on a single-chamber model show a 17.5% difference in cardiac output for a single-chamber ventricle model when comparing constant resistance models with the velocity profile tracking method modelling time varying resistance. This increase in precision can be achieved using 20 nodes with only twice the computational time required. The method offers a fluid dynamically and physiologically accurate method of calculating large Womersley number pulsatile fluid flows in large arteries around the heart and valves. The proposed velocity profile tracking method can be easily incorporated into existing lumped parameter CVS models, improving their clinical application by increasing their accuracy.