A nonlinear multi-scale model for blood circulation in a realistic vascular system

Abstract

In the last decade, numerical models have become an increasingly important tool in biological and medical science. Numerical simulations contribute to a deeper understanding of physiology and are a powerful tool for better diagnostics and treatment. In this paper, a nonlinear multi-scale model framework is developed for blood flow distribution in the full vascular system of an organ. We couple a quasi one-dimensional vascular graph model to represent blood flow in larger vessels and a porous media model to describe flow in smaller vessels and capillary bed. The vascular model is based on Poiseuille’s Law, with pressure correction by elasticity and pressure drop estimation at vessels' junctions. The porous capillary bed is modelled as a two-compartment domain (artery and venous) using Darcy’s Law. The fluid exchange between the artery and venous capillary bed compartments is defined as blood perfusion. The numerical experiments show that the proposed model for blood circulation: (i) is closely dependent on the structure and parameters of both the larger vessels and of the capillary bed, and (ii) provides a realistic blood circulation in the organ. The advantage of the proposed model is that it is complex enough to reliably capture the main underlying physiological function, yet highly flexible as it offers the possibility of incorporating various local effects. Furthermore, the numerical implementation of the model is straightforward and allows for simulations on a regular desktop computer.

Numerical simulation and fast method for the 0D‐1D multi‐scale coupled model and its application in ischemic brain tissue blood flow problems

“…Merging the 1D wave propagation models for the blood vessels with the 0D lumped models for the microcirculation, Kroon et al 17 established a computational method for vascular hemodynamics. Recently, a nonlinear multi‐scale model framework is developed by Qohar et al 18 for blood flow distribution in the full vascular system of an organ. The geometric multi‐scale coupled model provides a comprehensive characterization of ischemic brain tissue blood flow issues, which can help people adopt effective medical measures.…”

A fluid-structure interaction model accounting arterial vessels as a key part of the blood-flow engine for the analysis of cardiovascular diseases

“…FSI theory has been widely used in the study of human blood circulation, especially in the field of hemorheology. There has been great interest in recent research on the effects of vascular elasticity on the distribution of blood flow velocity, wall shear stress and flow velocity (Coccarelli et al, 2021;Chalons et al, 2022), including the effects of different geometric structures (Corti et al, 2020), external conditions (Nardinocchi et al, 2005;Misra et al, 2018), multi-scale factors (Qohar et al, 2021), fluid properties (Shinde et al, 2022) and states (Younis and Berger 2004). There have been many studies on fluidstructure interaction models of blood and arteries, such as the Ventricular-Arterial Coupling model (Pagoulatou et al, 2021), Direct Eulerian Generalized Riemann Problem scheme (Sheng et al, 2021), and Hybrid Windkessel-Womersley coupled model (Aboelkassem and Virag 2019), among others.…”