Numerical simulation of blood flow through a capillary using a non-linear viscoelastic model

Recent advances in blood rheology: a review

Due to the potential impact on the diagnosis and treatment of various cardiovascular diseases, work on the rheology of blood has significantly expanded in the last decade, both experimentally and theoretically. Experimentally, blood has been confirmed to demonstrate a variety of non-Newtonian rheological characteristics, including pseudoplasticity, viscoelasticity, and thixotropy. New rheological experiments and the development of more controlled experimental protocols on more extensive, broadly physiologically characterized, human blood samples demonstrate the sensitivity of aspects of hemorheology to several physiological factors. For example, at high shear rates the red blood cells elastically deform, imparting viscoelasticity, while at low shear rates, they form "rouleaux" structures that impart additional, thixotropic behavior. In addition to the advances in experimental methods and validated data sets, significant advances have also been made in both microscopic simulations and macroscopic, continuum, modeling, as well as novel, multiscale approaches. We outline and evaluate the most promising of these recent developments. Although we primarily focus on human blood rheology, we also discuss recent observations on variations observed across some animal species that provide some indication on evolutionary effects.

Pulsatile flow of non-Newtonian blood fluid inside stenosed arteries: Investigating the effects of viscoelastic and elastic walls, arteriosclerosis, and polycythemia diseases

BACKGROUND AND OBJECTIVE

In this study, the interaction of pulsatile blood flow with the viscoelastic walls of the axisymmetric artery is numerically investigated for different severities of stenosis. The geometry of artery is modeled by an axisymmetric cylindrical tube with a symmetric stenosis in a two-dimensional case. The effects of stenosis severity on the axial velocity profile, pressure distribution, streamlines, wall shear stress, and wall radial displacement for the viscoelastic artery are also compared to the elastics artery. Furthermore, the effects of atherosclerosis and polycythemia diseases on the hemodynamics and the mechanical behavior of arterial walls are investigated.

METHODS

The pulsatile flow of non-Newtonian blood is simulated inside the viscoelastic artery using the COMSOL Multiphysics software (version 5) and by employing the fluid-structure interaction (FSI) method and the arbitrary Lagrangian-Eulerian (ALE) method. Moreover, finite element method (FEM) is used to solve the governing equations on the unstructured grids. For modeling the non-Newtonian blood fluid and the viscoelastic arterial wall, the modified Casson model, and generalized Maxwell model are used, respectively.

RESULTS

According to the results, with stenosis severity increasing from 25% to 75% at the time of maximum volumetric flow rate, the maximum value of axial velocity and its gradient increase 7.9 and 19.6 times, and the maximum wall shear stress of viscoelastic wall increases 24.2 times in the constriction zone. With the progression of the atherosclerosis disease (fivefold growth of arterial elastic modulus), the wall radial displacement of viscoelastic arterial walls decreases nearly 40%.

CONCLUSIONS

In this study, axial velocity profile, pressure distribution, streamlines, wall radial displacement, and wall shear stress were examined for different percentages of stenosis (25%, 50%, and 75%). The atherosclerosis disease was investigated by the fivefold growth of viscoelastic arterial elastic modulus and polycythemia disease was examined by the 21-fold increase in the yield stress of the blood fluid. Furthermore, the comparison of results between the elastic and viscoelastic arterial walls shows that the wall radial displacement for viscoelastic artery is lower than that for the elastic artery as much as 21.7% for the severe stenosis of 75%.

Numerical investigation on red blood cell dynamics in microflow: Effect of cell deformability

The radial dispersion of red blood cells (RBCs) near the vessel wall can significantly affect the transport dynamics in small vessels. The radial dispersion of RBCs is mainly caused by collisions between RBCs and this can be enhanced by aggregation. The objective of this study is to numerically investigate on the effect of RBC deformability on the radial motion of individual RBCs in a range of flow rates. Immersed Boundary - Lattice Boltzmann Method was utilized to study the radial motion of RBCs in a two-dimensional flow domain. The RBC flow simulations were performed at 40% hematocrit in a microvessel with diameter of 25μm and length of 100μm. The dispersion of less deformable RBCs was notably greater than that of normal RBCs at all flow rates and this effect seemed to be more pronounced when the flow rate was increased. The cell dispersion was higher near the vessel wall than the flow center regardless of flow rate and RBCs deformability. Thus, the dispersion of RBCs could be enhanced with flow rate and RBC rigidity. Our findings would be especially useful in investigating blood flows in arterioles and venules.