Physiological outflow boundary conditions methodology for small arteries with multiple outlets: a patient-specific hepatic artery haemodynamics case study

Abstract

Physiological outflow boundary conditions are necessary to carry out computational fluid dynamics simulations that reliably represent the blood flow through arteries. When dealing with complex three-dimensional trees of small arteries, and therefore with multiple outlets, the robustness and speed of convergence are also important. This study derives physiological outflow boundary conditions for cases in which the physiological values at those outlets are not known (neither in vivo measurements nor literature-based values are available) and in which the tree exhibits symmetry to some extent. The inputs of the methodology are the three-dimensional domain and the flow rate waveform and the systolic and diastolic pressures at the inlet. The derived physiological outflow boundary conditions, which are a physiological pressure waveform for each outlet, are based on the results of a zero-dimensional model simulation. The methodology assumes symmetrical branching and is able to tackle the flow distribution problem when the domain outlets are at branches with a different number of upstream bifurcations. The methodology is applied to a group of patient-specific arteries in the liver. The methodology is considered to be valid because the pulsatile computational fluid dynamics simulation with the inflow flow rate waveform (input of the methodology) and the derived outflow boundary conditions lead to physiological results, that is, the resulting systolic and diastolic pressures at the inlet match the inputs of the methodology, and the flow split is also physiological.

Keywords: Arterial tree; computational fluid dynamics; liver; lumped model; three-dimensional model.