Structured tree outflow condition for blood flow in larger systemic arteries

TLDR

A central problem in modeling blood flow and pressure in the larger systemic arteries is determining a physiologically based boundary condition so that the arterial tree can be truncated after a few generations. The authors use a structured tree attached to the terminal branches of the truncated arterial tree, estimating root impedance via a semianalytical approach based on linearized viscous Navier–Stokes equations, and validate the model by comparing it with pure resistance, windkessel models, and measured data. The structured tree provides a dynamic boundary condition that preserves the phase lag and high‑frequency oscillations in impedance spectra, accommodates wave propagation throughout the systemic arterial tree, and yields a model that is both physiologically adequate and computationally feasible.

Abstract

A central problem in modeling blood flow and pressure in the larger systemic arteries is determining a physiologically based boundary condition so that the arterial tree can be truncated after a few generations. We have used a structured tree attached to the terminal branches of the truncated arterial tree in which the root impedance is estimated using a semianalytical approach based on a linearization of the viscous axisymmetric Navier-Stokes equations. This provides a dynamic boundary condition that maintains the phase lag between blood flow and pressure as well as the high-frequency oscillations present in the impedance spectra. Furthermore, it accommodates the wave propagation effects for the entire systemic arterial tree. The result is a model that is physiologically adequate as well as computationally feasible. For validation, we have compared the structured tree model with a pure resistance and a windkessel model as well as with measured data.