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

Abstract

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

On the relevance of boundary conditions and viscosity models in blood flow simulations in patient‐specific aorto‐coronary bypass models

“…Namely, it is the belief of the authors of this article that the aforementioned issues with LPM‐1 (unnatural flow waveforms) and LPM‐3 (decrease in total blood volume) were partially caused by the incorrect estimation of lumped parameters or, to be more specific, the unsuitable distribution of resistance and compliance values among the corresponding lumped elements (Table 2). To resolve this issue, an improvement could be attained either by using a robust estimation methodology that would take into consideration the complex geometry of patient‐specific vascular models 55,58 or by applying an alternative approach such as the one developed in the paper by Baker et al, 74 where only one coefficient needs to be estimated for each distal boundary condition.…”

Patient-Specific Blood Flow Analysis for Cerebral Arteriovenous Malformation Based on Digital Subtraction Angiography Images

“…Having capacitors and inductors included for the large arteries may improve the simulations, but will inevitably increase the complexity of the model. Another development direction is to apply a coupled or hybrid electrical analog and one dimensional (0D-1D) model, which has been presented in recent multidimensional modeling works, e.g., in Baker et al (2020) and Yu et al (2018). Specifically, the CBF re-distribution in the CoW could be analyzed from a 1D flow model coupled with 0D models at vessel outlets (Yu et al, 2018).…”

Multiscale Modeling Is Required for the Patent Ductus Arteriosus in Preterm Infants

“…Concerning modeling techniques, the in silico blood flow models mentioned above range from lumped parameter (or 0D) models to the transmission line and 1D models where the vessel geometry (length and diameter) is incorporated. If the purpose of the simulation is to reproduce the velocity waveform observed in echocardiography and the impedance of the vascular bed, then a coupled 1D and lumped parameter model, e.g., of ( 17 ), or coupled 1D and transmission line model, e.g., of ( 18 ) could serve the purpose. On the other hand, if the modeling goal is to investigate the detailed 3D flow patterns, e.g., the formation of vortex and flow separations after constriction in PDA, and the wall shear stress, then a 3D flow model should be applied ( 19 , 20 ).…”