Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes

Numerical analysis of blood flow through stenosed microvessels using a multi-phase model

Blood flow in arterioles have attracted considerable research attention due to their clinical implications. However, the fluid structure interaction between red blood cells and plasma in the blood poses formidable difficulty to the computational efforts. In this contribution, we seek to represent the red blood cells in the blood as a continuous non-Newtonian phase and construct a multi-phase model for the blood flow in microvessels. The methods are presented and validated using a channel with sudden expansion. And the resulting blood flow inside a stenosed microvessel is investigated at different inlet velocity amplitudes and hematocrits. It is show that the increase of both inlet velocity amplitude and inlet hematocrit leads to longer and thicker cell-rich layer downstream the stenosis. Besides, it is found that the maximum values of wall shear stress scales up with inlet velocity amplitudes and hematocrits. These results show the validity of the proposed computational model and provide helpful insights into blood flow behaviors inside stenosed vessels.

Numerical simulation of the fractional Maxwell fluid flow in locally narrow artery

Research on hemorheology and blood flow behavior in non-uniform vessels is of extreme significance for diagnosis and treatment of many cardiovascular diseases. The aim of this study is to reveal the hemodynamics in stenotic vessels, and provide a reference for formulating a clinical operation plan. A set of rheological data of human blood at 37° is utilized in the paper to construct the fractional Maxwell constitutive equation of blood. Consequently, the continuity and momentum equations of a fractional Maxwell fluid passing through a stenosis artery in a two-dimensional cylindrical coordinate system are established. With the help of the vorticity and stream function, the finite difference method combined with the fractional order derivative L1 algorithm is applied to acquire the numerical solutions of the velocity, wall shear stress and intravascular pressure gradient, and the validity of the algorithm is verified. Furthermore, the effects of the stenosis degree, stenosis shoulder length, various Reynolds numbers and fractional parameter α on the blood flow characteristics in stenosis are analyzed.

Semi-automated red blood cell core detection in blood micro-flow

In microcirculation, red blood cells (RBCs) tend to migrate toward the centre of the vessel leaving a region of a cell depleted layer or cell-free layer (CFL) at the vessel wall and a core of RBCs at the centre. This heterogenous distribution of cells has an effect on the blood apparent viscosity and the exchanges of gases and nutrients between the RBCs and the vessel. Understanding the formation of the CFL and obtaining accurate measurement of it is paramount for furthering development of devices such as drug administration. This paper presents a general semi-automatic method to quantify the thickness of the CFL for different channel geometries and image quality. It enables the use of a method based on intensity, a method using the gradient of the intensity, or a method based on spatiotemporal variation. The main features are reported, the performance is demonstrated on experimentally obtained image sets and accuracy is validated using synthetic images with known CFL thickness. A pure automatic detection is limited by the most visually correct using the spatiotemporal method, however proposed thresholding through automatic detection allows for quality controls through manual adjustments. With a semi-automatic approach RBC core variability between 3 % to 8 % was found when the test user was tasked with repeating the analysis of the same set. The presented method provides, users without programming ability with a user-friendly interface that can extract CFL automatically with quality control through manual adjustments.

Shear stress and intravascular pressure effects on vascular dynamics: two-phase blood flow in elastic microvessels accounting for the passive stresses

We study the steady hemodynamics in physiological elastic microvessels proposing an advanced fluid-structure interaction model. The arteriolar tissue is modeled as a two-layer fiber-reinforced hyperelastic material representing its Media and Adventitia layers. The constitutive model employed (Holzapfel et al. in J Elast 61:1-48, 2000) is parametrized via available data on stress-strain experiments for arterioles. The model is completed by simulating the blood/plasma flow in the lumen, using the thixotropic elasto-viscoplastic model in its core, and the linear Phan-Thien and Tanner viscoelastic model in its annular part. The Cell-Free Layer (CFL) and the Fåhraeus and Fåhraeus-Lindqvist effects are considered via analytical expressions based on experimental data (Giannokostas et al. in Materials (Basel) 14:367, 2021b). The coupling between tissue deformation and blood flow is achieved through the experimentally verified pressure-shear hypothesis (Pries et al. Circ Res 77:1017-1023, 1995). Our calculations confirm that the increase in the reference inner radius produces larger expansion. Also, by increasing the intraluminal pressure, the thinning of the walls is more pronounced and it may reach 40% of the initial thickness. Comparing our predictions with those in rigid-wall microtubes, we conclude that apart from the vital importance of vasodilation, there is an up to 25% reduction in wall shear stress. The passive vasodilation contributes to the decrease in the tissue stress fields and affects the hemodynamic features such as the CFL thickness, reducing the plasma layer when blood flows in vessels with elastic walls, in quantitative agreement with previous experiments. Our calculations verify the correctness of the pressure-shear hypothesis but not that of the Laplace law.

Continuum microhaemodynamics modelling using inverse rheology

Modelling blood flow in microvascular networks is challenging due to the complex nature of haemorheology. Zero- and one-dimensional approaches cannot reproduce local haemodynamics, and models that consider individual red blood cells (RBCs) are prohibitively computationally expensive. Continuum approaches could provide an efficient solution, but dependence on a large parameter space and scarcity of experimental data for validation has limited their application. We describe a method to assimilate experimental RBC velocity and concentration data into a continuum numerical modelling framework. Imaging data of RBCs were acquired in a sequentially bifurcating microchannel for various flow conditions. RBC concentration distributions were evaluated and mapped into computational fluid dynamics simulations with rheology prescribed by the Quemada model. Predicted velocities were compared to particle image velocimetry data. A subset of cases was used for parameter optimisation, and the resulting model was applied to a wider data set to evaluate model efficacy. The pre-optimised model reduced errors in predicted velocity by 60% compared to assuming a Newtonian fluid, and optimisation further reduced errors by 40%. Asymmetry of RBC velocity and concentration profiles was demonstrated to play a critical role. Excluding asymmetry in the RBC concentration doubled the error, but excluding spatial distributions of shear rate had little effect. This study demonstrates that a continuum model with optimised rheological parameters can reproduce measured velocity if RBC concentration distributions are known a priori. Developing this approach for RBC transport with more network configurations has the potential to provide an efficient approach for modelling network-scale haemodynamics.