A coupled one dimension and transmission line model for arterial flow simulation

A broad choice of numerical schemes and methods currently exists for blood flow simulations. The results rely critically on the prescription of boundary conditions. The outflow boundary condition for a one-dimensional (1D) flow solver is usually prescribed via a Windkessel or lumped parameter model. The weakness of such an approach is the determination of the parameters. In the present work, we use an alternative approach, that is, a reflection coefficient (RC), to lumped parameter models for distal boundary conditions. With such a RC, the number of parameters required is reduced to one. We derive the theoretical foundation for the RC. Specifically, we couple a transmission line theory for peripheral resistance with a 1D arterial flow solver. We apply this method to a healthy and a stenosed virtual aorta, and show this method can reproduce some subtle features in arterial pressure propagation, such as the steepened pressure waveform and the reflection from the stenosed site. In summary, the RC parameter has strong physical implications in the theory of wave propagation and may be used in flow simulations where reflections need to be explicitly modeled. Novelty Statement A novel coupled one-dimensional-transimission line model has been developed in this work with detailed implementations. Only one outflow boundary condition, that is, the refection coefficient is required in the model. Reflections for a pulse wave from aortic terminals as well as from a stenotic site are numerically simulated.