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

Abstract

Physiologically realistic results are the aim of every blood flow simulation. This is not different in aorto‐coronary bypasses where the properties of the coronary circulation may significantly affect the relevance of the performed simulations. By considering three patient‐specific bypass geometries, the present article focuses on two aspects of the coronary blood flow – its phasic flow pattern and its behaviour affected by blood rheology. For the phasic flow property, a multiscale modelling approach is chosen as a means to assess the ability of five different types of coronary boundary conditions (mean arterial pressure, Windkessel model and three lumped parameter models) to attain realistic coronary haemodynamics. From the analysed variants of boundary conditions, the best option in terms of physiological characteristics and its potential for use in patient‐based simulations, is utilised to account for the effect of shear‐dependent viscosity on the resulting haemodynamics and wall shear stress stimulation. Aside from the Newtonian model, the blood rheology is approximated by two non‐Newtonian models in order to determine whether the choice of a viscosity model is important in simulations involving coronary circulation. A comprehensive analysis of obtained results demonstrated notable superiority of all lumped parameter models, especially in comparison to the constant outlet pressure, which regardless of bypass type gave overestimated and physiologically misleading results. In terms of rheology, it was noted that blood in undamaged coronary arteries behaves as a Newtonian fluid, whereas in vessels with atypical lumen geometry, such as that of anastomosis or stenosis, its shear‐thinning behaviour should not be ignored.

Parametric analysis of an efficient boundary condition to control outlet flow rates in large arterial networks

“…For example, the WK2 model may lead to non-physiological reflections of pulse waves because it lacks a resistance connected to the outlet vessel in series 46 . The addition of such a resistance gives rise to the popular three-element Windkessel model 10, 15,19,[47][48][49][50] . We note that such reflections occur in incompressible flows only if the wall motions are considered, but this study does not consider such motions.…”

A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models

“…A typical example is the three-element Windkessel model (3WK) [ 10 ], a circuit containing only one reactive component (the capacitor), and thus defined as a circuit of order one. Higher order Windkessel models, defined as circuits containing a total number of capacitors and inductors higher than one, have also been proposed [ 11 ]. The choice of the best model for outlet boundary conditions is generally the result of a trade-off between accuracy, model complexity, and number of parameters to estimate.…”

“…A typical example is the three-element Windkessel model (3WK) [ 10 ], a circuit containing only one reactive component (the capacitor), and thus defined as a circuit of order one. Higher order Windkessel models, defined as circuits containing a total number of capacitors and inductors higher than one, have also been proposed [ 11 ].…”

Modeling the Five-Element Windkessel Model with Simultaneous Utilization of Blood Viscoelastic Properties for FFR Achievement: A Proof-of-Concept Study

“…Applying these models as boundary conditions allows for the creation of a pressure distribution profile along the entire vessel, eliminating the need to model the full circulatory system. Jonášová et al (2021) utilized several accurate Windkessel models with 3, 5, and 7 elements, to numerically assess coronary circulation, but they used the Newtonian and shear-thinning blood models, and did not evaluate the fractional flow reserve [11]. Kim et al (2014) compared the invasive and the computed FFR measures of patient-specific left coronary arteries and found remarkably similar results.…”

“…The blood suspensions grant blood its non-Newtonian characteristics, that lead to very complex behavior [16]. In the literature, blood is frequently modeled as a shear-thinning fluid that does not factor in the viscoelasticity [11,[17][18][19]. In the study conducted by Pinto et al (2020), three different viscoelastic constitutive models were used to model blood and the results using a Newtonian and a Carreau model for numerical simulations in right coronary arteries (RCAs) were compared.…”