Comparison of various zero‐dimensional models to analyze the brachial artery blood flow of an arterio‐venous fistula during hemodialysis procedure

Abstract

Abstract One of the most recommended vascular accesses for hemodialysis is an autogenous arterio‐venous fistula (AVF), which is a surgically created conduit between an artery and a vein. AVFs can be compromised by stenosis‐induced arterial or venous thrombosis. An effective and efficient mathematical fluid mechanical model can provide insight into the mechanisms for stenosis and thrombosis. In an earlier paper, a laminar entry flow model (Shah) was applied to a fifth order lumped parameter zero dimensional (0D) model to predict the inlet flow rate in the brachial artery of an AVF. ODE45, a built in MATLAB ordinary differential equation (ODE) solver, was used to produce the solution. The Shah model showed closer correlation with a computational fluid dynamics model, performed in COMSOL, than did the Poiseuille flow model. In this study, an outlet flow rate in the brachial artery of an AVF is generated with third, fourth, and fifth order lumped parameter zero dimensional models with laminar and turbulent flow conditions within different arterial segments. Butcher's sixth order Runge‐Kutta (RK) method was used as an ODE solver and the results were compared with the MATLAB ODE solvers (ODE45 and ODE113). The lumped parameter model solved with Butcher's sixth order RK method generated less oscillation with a more stable and consistent outlet flow rate in comparison to the other solvers. Brachial artery blood flow, modeled with Shah's entry flow equation in the inlet segment and Blasius turbulent equation modeled at the outlet segment prior to the beginning of the anastomosis, generated an average outlet flow rate similar to that of clinical data. The dependence of brachial artery on the flow equations indicates the importance of wisely selecting flow resistance models and the effect of blood pressure and peripheral resistance on fistula maturation. The average and peak flow rate also depended on the ODE solver. Third and fourth order lumped parameter models generated results similar to the fifth order model only at normal peripheral resistance. Therefore, this study can help to understand the AVF performance in vitro and guide the application of an appropriate lumped parameter model for blood flow prediction.

Keywords

• arterio‐venous fistula (AVF)
• blood flow modeling
• hemodialysis
• lumped parameter