Hemodynamic Analysis in an Idealized Artery Tree: Differences in Wall Shear Stress between Newtonian and Non-Newtonian Blood Models

Abstract

Development of many conditions and disorders, such as atherosclerosis and stroke, are dependent upon hemodynamic forces. To accurately predict and prevent these conditions and disorders hemodynamic forces must be properly mapped. Here we compare a shear-rate dependent fluid (SDF) constitutive model, based on the works by Yasuda et al in 1981, against a Newtonian model of blood. We verify our stabilized finite element numerical method with the benchmark lid-driven cavity flow problem. Numerical simulations show that the Newtonian model gives similar velocity profiles in the 2-dimensional cavity given different height and width dimensions, given the same Reynolds number. Conversely, the SDF model gave dissimilar velocity profiles, differing from the Newtonian velocity profiles by up to 25% in velocity magnitudes. This difference can affect estimation in platelet distribution within blood vessels or magnetic nanoparticle delivery. Wall shear stress (WSS) is an important quantity involved in vascular remodeling through integrin and adhesion molecule mechanotransduction. The SDF model gave a 7.3-fold greater WSS than the Newtonian model at the top of the 3-dimensional cavity. The SDF model gave a 37.7-fold greater WSS than the Newtonian model at artery walls located immediately after bifurcations in the idealized femoral artery tree. The pressure drop across arteries reveals arterial sections highly resistive to flow which correlates with stenosis formation. Numerical simulations give the pressure drop across the idealized femoral artery tree with the SDF model which is approximately 2.3-fold higher than with the Newtonian model. In atherosclerotic lesion models, the SDF model gives over 1 Pa higher WSS than the Newtonian model, a difference correlated with over twice as many adherent monocytes to endothelial cells from the Newtonian model compared to the SDF model.

Influence of shear stress magnitude and direction on atherosclerotic plaque composition

“…The Newtonian fluid assumption is justified as mean shear rates are greater than 1000 s −1 in both the instrumented and control mouse carotid arteries (the Reynolds number is approx. 40), where Newtonian and non-Newtonian models of blood behave similarly [22]. Simulations imposed a pulsatile flow of the blood at the inlet of the vessel by assigning a plug flow profile equal to the peak velocity measured at each point in the cardiac cycle, as has been reported previously [23].…”

Stationary Flow of Blood in a Rigid Vessel in the Presence of an External Magnetic Field: Considerations about the Forces and Wall Shear Stresses

“…Evaluating these quantities at the wall should allow to see whether the stresses reach some levels that could be at risk: 1) for the vessel wall (plaque rupture in case of atherosclerotic lesion [18], severity of some aneurysms [19], ...), 2) for the mechanotransduction in the endothelial cells, 3) for other cells attachment and/or transmigration (white blood cells, tumor cells, cells seeded in vascular substitutes [20], ...). Estimation of shear stresses at the wall may also have important implications in magnetic nanoparticle delivery and drug targeting [6] [21].…”

Cell isolation via spiral microfluidics and the secondary anchor targeted cell release system

“…Fluid dynamics within the microfluidic device were simulated based on the incompressible Navier–Stokes equations for Newtonian fluids: Equations are the momentum‐balance and incompressibility equations, respectively, where ρ is the density, v is the velocity field, v , t is the time derivative of the velocity field, μ is the fluid viscosity, and p is the pressure field. The fluid is assumed to be Newtonian with fluid properties of blood: ρ = 1, 060 kg/m 3 and μ = 0.0035 Pa/s . The three‐dimensional (3D) microfluidic device geometry was developed as a rigid wall geometry with six concentric cylindrical spirals in Autodesk inventor (Figure ) and meshed using Abaqus/CAE.…”

“…The maximum velocity is calculated as twice the average velocity across the inlet of the microfluidic device: where Q is the applied flow rate. Simulations quantifying fluid velocity and pressure profiles were carried out with the FEAP software modified with the stabilized finite element method for shear‐rate‐dependent fluids, as described previously . Postprocessing and visualization of numerical data were carried out with Paraview.…”