Modeling blood flow in networks of viscoelastic vessels with the 1-D augmented fluid-structure interaction system

Abstract

A noteworthy aspect in blood flow modeling is the definition of the mechanical interaction between the fluid flow and the biological structure that contains it, namely the vessel wall. Particularly, it has been demonstrated that the addition of a viscous contribution to the mechanical characterization of vessels brings positive results when compared to in-vivo measurements. In this context, the implementation of boundary conditions able to keep memory of the viscoelastic contribution of vessel walls assumes an important role, especially when dealing with large circulatory systems. In this work, viscoelasticity is taken into account in entire networks via the Standard Linear Solid Model. The implementation of the viscoelastic contribution at boundaries, namely inlet, outlet and junction, is carried out considering the natively hyperbolic nature of the mathematical model. Specifically, a non-linear system is established based on the definition of the Riemann Problem at junctions, characterized by rarefaction waves separated by contact discontinuity waves, among which the mass and the total energy are conserved. Basic junction test cases are analyzed, such as a trivial 2vessels junction, for both a generic artery and a generic vein, and a simple 3-vessels junction, considering an aortic bifurcation scenario. The chosen IMEX-SSP2 Finite Volume scheme is demonstrated to be second-order accurate in the whole domain and well-balanced, even when including junctions. Two benchmark arterial networks are then implemented, differing in number of vessels and in viscoelastic parameters. Comparison of the results obtained in the two networks underlines the high sensitivity of the model to the chosen viscoelastic parameters. In these numerical tests, the network-wise conservation of the contribution provided by the viscoelastic characterization of vessel walls is assessed. Finally, numerical results of pressure waveforms in the common carotid artery and in the femoral artery of the second network simulated are compared with in-vivo data recorded from different healthy subjects.

Assessment of cardiac function by pulse wave analysis. A computational study

“…The vascular network model has been thoroughly tested in previous studies 3,5,33 . Here, we focused on verifying the ability of the cardiac contractility model coupled to the vas- presenting its characteristic double-peaked morphology 19,38 .…”

“…Virtual subjects are characterised by haemodynamic variables spanning the physiological range, even in disease-related conditions 15,35 . Different numerical models can be employed to accomplish this task: zerodimensional (0-D) lumped-parameters models for simulating blood flow in distal vessels 8 and specific organs such as the heart 25 , one-dimensional (1-D) models for simulating blood flow in the large arteries of the human circulation 33 , and three-dimensional (3-D) models 15 , which are often used to simulate blood flow in localised regions of the vasculature, such as arterial bifurcations, due to their high computational cost. 1-D models can simulate pulse wave signals with a reasonable accuracy compared with both 3-D models 47,15 and experimental data 21 , and at much lower computational cost compared to 3-D models.…”

“…The aim of this study is to investigate the effect of cardiac properties on pulse wave morphology using a 1-D model of the arterial vasculature 33 coupled to a 0-D model of cardiac contraction. The 1-D model considers the viscoelastic behaviour of vessel walls 3,5 .…”

“…The treatment of internal BCs, i.e. vessel junctions, and external BCs followed the methodology presented by Piccioli et al 33 .…”

“…The flow rate through the aortic valve, q AV (t), was computed at every time step and prescribed as the inflow to the aortic root. The coupling between the cardiac model and the arterial domain was accomplished using the following Riemann invariants associated with the genuinely non-linear field at the proximal boundary of the physical domain 33 ,…”