Model Of non-Newtonian Blood Flow Research Articles

Study of Non-Newtonian blood flow - heat transfer characteristics in the human coronary system with an external magnetic field.

This paper proposes a novel mathematical model of non-Newtonian blood flow and heat transfer in the human coronary system with an external magnetic field. As the blood viscosity is assumed to depend not only on shear rate but also on temperature and magnet strength, the modified Carreau-Yasuda viscosity model is formulated. The computational domain includes the base of the aorta, the right coronary artery, and the left coronary artery, with the left circumflex and left anterior descending arteries. The element-based finite volume method is derived for the solution of the proposed model. Numerical simulations are carried out to investigate the magnetic field effect on the blood flow-heat transfer characteristic in the human coronary system. It is found that the magnetic field has a significant impact on fluid viscosity, leading to enhanced fluid velocity.

Non-Newtonian heat and mass transfer on MHD blood flow through a stenosed artery in the presence of body exercise and chemical reaction

A mathematical model of non-Newtonian blood flow, heat and mass transfer through a stenosed artery is studied. The non-Newtonian model is chosen to suit the Herschel-Bulkley fluid characteristics, taking into account the presence of body acceleration, magnetic fields and chemical reaction. The study assumed that, the flow is unsteady, laminar, two-dimensional and axisymmetric. The governing flow equations of motion were solved numerically using explicit finite difference schemes. The study found that velocity profile diminishes with increase in Hartman number and increases with body acceleration. The temperature profile is raised by the increase of body acceleration and the Eckert number, while it diminishes with the increase of the Peclet number. It was found also that the concentration profile increases with the increase of the Soret number and decreases with the increase of the chemical reaction. It was further observed that the shear stress deviates more when n > 1 than when n < 1. Shear stress for power law fluid when n > 1 exhibited higher magnitude value than Newtonian, Bingham and Herschel-Bulkley fluids.

Influence of non-Newtonian blood flow models on drug deposition in the arterial wall

In this paper, we investigate the influence of non-Newtonian blood flow models on drug diffusion from a coronary drug-eluting-stent (DES). We consider the Oldroyd-B, Phan-Thien-Tanner (PTT) and Giesekus viscoelastic models for the description of fluid dynamics of blood. The model for blood flow is coupled with plasma filtration and mass transport from a DES. The model for the transport problem takes into consideration non-Fickian diffusion, drug dissolution, polymer degradation and binding. We propose an Implicit-Explicit (IMEX) finite element method and show numerical experiments that confirm the effectiveness and order of convergence of the employed methodology. The numerical results indicate that an increase in the elastic properties of the blood leads to an increase of the concentration of free drug in the arterial wall. Finally, we present unsteady simulations comparing the Newtonian and non-Newtonian blood flow models.

Permeability and fluid flow-induced wall shear stress of bone tissue scaffolds: Computational fluid dynamic analysis using Newtonian and non-Newtonian blood flow models

Among the factors that are important in successful bone tissue regeneration through scaffolds are permeability and fluid flow-induced wall shear stress (WSS) because of the direct contribution of these factors to cell bioactivities. The permeability of scaffolds is usually measured using fluids such as water, which are characterized as Newtonian materials with constant viscosity. However, using the fluid properties of blood as bases in measuring permeability can lead to more realistic results given that scaffolds are implanted in the body, where the only flowing fluid (i.e., blood) is a non-Newtonian fluid. Moreover, the linear relationship of WSS with fluid viscosity challenges the use of Newtonian fluids in determining WSS magnitude. With consideration for these issues, we investigated permeability and WSS through computational fluid dynamics (CFD) analyses of lattice-based and gyroid scaffold architectures with Newtonian and non-Newtonian blood flow properties. With reference to geometrical parameters and the pressure drops derived from the CFD analyses, the permeability levels of the Newtonian and non-Newtonian models were calculated by exploiting the classic and modified Darcy's equations, respectively. Results showed that both scaffold architectures were several times more permeable in the Newtonian blood flow models than in their non-Newtonian counterparts. Within the scaffolds, the non-Newtonian flow of blood caused almost twice the magnitude of WSS originating from Newtonian blood flow. These striking discrepancies in permeability and WSS between the two blood models were due to differences in their viscosity behaviors.

Mathematical modeling of power law and Herschel - Buckley non-Newtonian fluid of blood flow through a stenosed artery with permeable wall: Effects of slip velocity

A mathematical model of non-Newtonian blood flow through a stenosed artery is considered. The steadynon-Newtonian model is chosen characterized by the generalized power-law model and Herschel-Bulkley model incorporating the effect of slip velocity due to steanosed artery with permeable wall. The effects of slip velocity for non-Newtonian nature of blood on velocity, flow rate and wall shear stress of the stenosed artery with permeable wall are solved analytically. The effects of various parameters such as slip parameter (λ), power index (m) and different thickness of the stenosis (δ) on velocity, volumetric flow rate and wall shear stress are discussed through graphs.

Newtonian and Non-Newtonian Pulsatile Flows through an Artery with Stenosis

The current study presents three-dimensional modeling and analysis of blood flow through artery stenosis under several variants of pulsatile flow to mimic the atherosclerosis artery disease. The study considered Newtonian and non-Newtonian blood flow models and solved the three-dimensional laminar and unsteady Navier-Stokes (NS) equations for different inlet velocity profiles. The Carreau Yasuda model was used for hemodynamics modeling of fluid viscosity. A comparative analysis was carried out for Newtonian and non-Newtonian fluid models under several simple pulsatile, equivalent pulsatile and physiological velocity profiles. The non-Newtonian fluid exhibited a higher centerline velocity. Wall shear stresses, shear strain rates, velocity fields, and vortex distribution for Newtonian and non-Newtonian fluid flows show significant differences. A higher wall shear was noticed near the stenosis. The vortex formed near the stenosis shifts to upstream and downstream of the stenosis with the change of velocity pulse. The velocity profile deflates more for non-Newtonian flows than the Newtonian flows.

PEG-albumin supraplasma expansion is due to increased vessel wall shear stress induced by blood viscosity shear thinning

We studied the extreme hemodilution to a hematocrit of 11% induced by three plasma expanders: polyethylene glycol (PEG)-conjugated albumin (PEG-Alb), 6% 70-kDa dextran, and 6% 500-kDa dextran. The experimental component of our study relied on microelectrodes and cardiac output to measure both the rheological properties of plasma-expander blood mixtures and nitric oxide (NO) bioavailability in vessel walls. The modeling component consisted of an analysis of the distribution of wall shear stress (WSS) in the microvessels. Our experiments demonstrated that plasma expansion with PEG-Alb caused a state of supraperfusion with cardiac output 40% above baseline, significantly increased NO vessel wall bioavailability, and lowered peripheral vascular resistance. We attributed this behavior to the shear thinning nature of blood and PEG-Alb mixtures. To substantiate this hypothesis, we developed a mathematical model of non-Newtonian blood flow in a vessel. Our model used the Quemada rheological constitutive relationship to express blood viscosity in terms of both hematocrit and shear rate. The model revealed that the net effect of the hemodilution induced by relatively low-viscosity shear thinning PEG-Alb plasma expanders is to reduce overall blood viscosity and to increase the WSS, thus intensifying endothelial NO production. These changes act synergistically, significantly increasing cardiac output and perfusion due to lowered overall peripheral vascular resistance.

A power-law model of blood flow through a tapered overlapping stenosed artery

A mathematical model of non-Newtonian blood flow through a tapered stenotic artery is considered. The non-Newtonian model chosen is characterized by the generalized power-law model incorporating the effect of tapering due to the pulsatile nature of blood flow. The flow is assumed to be unsteady, laminar, two-dimensional and axisymmetric. The governing equations of motion in terms of the viscous shear stress in the cylindrical coordinate system are solved numerically using a finite difference scheme. Numerical results obtained for the positive taper angle show that the blood flow characteristics such as the axial velocity profiles, flow rate and wall shear stress have lower values, while the resistive impedances have higher values than the Newtonian model.

A two-fluid model of non-Newtonian blood flow induced by peristaltic waves

The problem of blood flow induced by peristaltic waves in a uniform small diameter tube has been investigated. Blood has been represented by a two-fluid model consisting of a core region of suspension of all the erythrocytes, assumed to be a Casson fluid, and a peripheral layer of plasma as a Newtonian fluid. The expressions for dimensionless pressure drop and friction force have been obtained. The results obtained in the analysis have been evaluated numerically and discussed briefly. The significance of the present model over the existing models has been pointed out by comparing the results with other theories both analytically and numerically.