A review on non-Newtonian fluid models for multi-layered blood rheology in constricted arteries

Abstract

Haemodynamics is a branch of fluid mechanics which investigates the features of blood when it flows not only via blood vessels of smaller/larger diameter, but also under normal as well as abnormal flow states, such as in the presence of stenosis, aneurysm, and thrombosis. This review aims to discuss the rheological properties of blood, geometry of constrictions, dilations and the emergence of single-layered fluid to four-layered fluid models. To discuss further the influence of the aforesaid parameters on the physiologically important flow quantities, the mathematical formulation and solution methodology of the two-layered and four layered arterial blood flow problems studied by the authors (Afiqah and Sankar in ARPN J Eng Appl Sci 15:1129--1143, 2020, Comput Methods Programs Biomed 199:105907, 2021. 10.1016/j.cmpb.2020.105907) are recalled. It should be pointed out that the increasing resistive impedance to flow in three distinct states encompassing healthy, anaemic, and diabetic demonstrates that the greater the restriction in the artery, very few blood is carried to the pathetic organs, leading to subjects’ death. It is also discovered that the pulsatile nature of blood movement produces a dynamic environment that poses a slew of intriguing and unstable fluid mechanical state. It is hoped that the intriguing results gathered from this literature survey and review conducted may help the medical practitioners to forecast blood behaviour mobility in stenotic arteries. Furthermore, the physiological information gathered from the available clinical data from the literature on patients diagnosed with diabetes and anaemia may be beneficial to doctors in deciding the therapeutic procedure for treating some particular cardiovascular disease.

Hydrodynamics simulation of red blood cells: Employing a penalty method with double jump composition of lower order time integrator

“…This complex behavior has a strong impact on the hemorheology on a global scale and gives blood a non-Newtonian rheology, particularly in the microcirculation, damaged vessels, or aneurysm sites [5]. While healthy blood can be assumed to be Newtonian in large arteries, non-Newtonian hemorheological properties (shear thinning, viscoelasticity, thixotropy, and yield stress) cannot be overlooked in the microcirculation [6][7][8]. The inherently non-trivial spatio-temporal behaviors of individual RBCs and biomembranes continue to pose a formidable challenge to numerical modeling [9][10][11].…”

Investigation of Erying–Powell fluid flow in the elliptical multi‐stenosed artery: Application of perturbation method via polynomial solutions

“…More theoretical investigations on the blood flow via stenotic arteries of the circular cross-section are provided in Refs. [7][8][9][10][11][12][13].…”