Outflow Boundary Conditions for Blood Flow in Arterial Trees

Abstract

In the modeling of the pulse wave in the systemic arterial tree, it is necessary to truncate small arterial crowns representing the networks of small arteries and arterioles. Appropriate boundary conditions at the truncation points are required to represent wave reflection effects of the truncated arterial crowns. In this work, we provide a systematic method to extract parameters of the three-element Windkessel model from the impedance of a truncated arterial tree or from experimental measurements of the blood pressure and flow rate at the inlet of the truncated arterial crown. In addition, we propose an improved three-element Windkessel model with a complex capacitance to accurately capture the fundamental-frequency time lag of the reflection wave with respect to the incident wave. Through our numerical simulations of blood flow in a single artery and in a large arterial tree, together with the analysis of the modeling error of the pulse wave in large arteries, we show that both a small truncation radius and the complex capacitance in the improved Windkessel model play an important role in reducing the modeling error, defined as the difference in dynamics induced by the structured tree model and the Windkessel models.

Patient-specific structural effects on hemodynamics in the ischemic lower limb artery

“…The DFA, SFA, PA branches can be found clearly in all models. Distinct from the arterial tree models, our geometric models showed more detailed structures, which enabled us to study the impact of geometric characteristics on hemodynamics2223.…”

Non-dimensional physics of pulsatile cardiovascular networks and energy efficiency

“…carotid bifurcation (one inlet, two outlets), aortic arch (one inlet, four outlets), venous confluence (two inlets, one outlet) and hepatic confluence (three inlets, one outlet)), with fixed flow and pressure BCs as well as more complex BCs, which are determined by upstream and downstream vascular structures. For a more general power loss estimation, improved impedance calculations using the reduced-order, variable morphometric and fractal approaches [78][79][80] will be considered.…”

A fast algorithm for the simulation of arterial pulse waves

“…In downstream arteries, these ratios become even smaller because, with decreasing vessel radius, the flow velocity u decreases and the pulse wave speed increases. As a result, for an arterial crown with small root-vessel radius (e.g., smaller than 1.5mm [53]), the nonlinearity is negligible. As a consequence of this weak nonlinearity and the short duration of time for the pulse wave to propagate through the arterial system, there would be no formation of shock waves in the arterial system.…”

“…where R = ρc0 A0 is the characteristic resistance of the vessel [4,53]. Using £ ± , we can also rewrite Eq.…”

“…The cardiac output q c (t), which is the blood flow rate pumped into the aorta by the heart and can usually be measured experimentally, is used to determine the boundary condition at the inlet of an arterial tree [15,33,53],…”