On the choice of proper outlet boundary conditions for numerical simulation of cardiovascular flows
Zahra Mirzaiyan, Michele Girfoglio, Gianluigi Rozza
TL;DR
This work investigates how to choose proper outlet boundary conditions for numerical cardiovascular flow simulations governed by the Navier–Stokes equations. It presents two complementary strategies: (i) zero-dimensional lumped-parameter Windkessel models (R_p, C, R_d) to enforce physiologically consistent pressure–flow relationships at outlets, and (ii) an optimal-control framework that minimizes the mismatch between simulated and clinical velocity data by controlling the normal stress at outlets via adjoint equations. The methods are demonstrated on two patient-specific cases: a thoracic-aorta model using Windkessel outlets and a CABG-coronary system using the optimal-control approach, with results showing good agreement to clinical data and highlighting the advantage of spatially varying outlet stresses. The findings suggest that combining 0D lumped models with spatially resolved optimization could yield accurate, clinically relevant boundary conditions for patient-specific cardiovascular simulations, improving the reliability of hemodynamic predictions.
Abstract
It is well known that in the computational fluid dynamics simulations related to the cardiovascular system the enforcement of outflow boundary conditions is a crucial point. In fact, they highly affect the computed flow and a wrong setup could lead to unphysical results. In this chapter we discuss the main features of two different ways for the estimation of proper outlet boundary conditions in the context of hemodynamics simulations: on one side, a lumped parameter model of the downstream circulation and, on the other one, a technique based on optimal control.