Imposing Ratios of Outlet Flow Rates on Large Arterial Networks with Two-Element Windkessel Model: Parametric Analysis

Abstract

Substantial effort is being invested in the creation of a virtual human — a model which will improve our understanding of human physiology and diseases and assist clinicians in the design of personalised medical treatments. A central challenge of achieving blood flow simulations at full-human scale is the development of an efficient and accurate approach to imposing boundary conditions on many outlets. A previous study proposed an efficient method for implementing the two-element Windkessel model to control the flow rate ratios at outlets. However, no study to date has examined the conditions for this approach to hold in complex geometries. Here we clarify the general role of the resistance and capacitance in this approach. We show that the error of the flow rate ratios decreases exponentially as the resistance increases. The errors fall below 4% in a simple five-outlets model and 7% in a human artery model comprising 10 outlets. Moreover, the flow rate ratios converge faster and suffer from weaker fluctuations as the capacitance decreases. Our findings also establish constraints on the parameters controlling the numerical stability of the simulations. The findings from this work are directly applicable to larger and more complex vascular domains encountered at full-human scale.

Uncertainty quantification of the impact of peripheral arterial disease on abdominal aortic aneurysms in blood flow simulations

“…Supplementary materials including the supplementary text, the arterial model, the code used to perform the campaigns of uncertainty quantification and all the results of the campaigns is available from the Figshare repository: [ 85 ].…”

Development and performance of a HemeLB GPU code for human-scale blood flow simulation

“…Moreover, another challenge of simulations at full-human scale is the development of an efficient and accurate approach to imposing BCs on multiple outlets. Lo et al [44] recently implemented a two-element Windkessel model in HemeLB_CPU to control the flow rate ratios at the outlets.…”