Hemodynamics in stenotic vessels of small diameter under steady state conditions: Effect of viscoelasticity and migration of red blood cells

Dimakopoulos, Yannis; Kelesidis, George; Tsouka, Sofia; Georgiou, Georgios C.; Tsamopoulos, John

doi:10.3233/bir-14033

Cited by 33 publications

(9 citation statements)

References 52 publications

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“…Using the particle migration model of Phillips et al [14] (also used in [16]) along with the Quemada model for blood viscosity [18], Mansour et al [17] found the flux coefficients to depend on H T and dimensionless radial position. The effect of red blood cells' elasticity [19] on RBC migration is addressed in [20][21][22], with the model of Mavrantzas and Beris [23,24], proposed for polymer solutions, adopted for blood flow dynamics by including Fickian cell migration in addition to elastic-stress induced migration instead of shear-induced migration as in the Leighton and Acrivos model [13].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of blood flow: modeling of Fåhraeus and Fåhraeus–Lindqvist effects using a shear-induced red blood cell migration model

Chebbi

2018

J Biol Phys

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Blood flow in micro capillaries of diameter approximately 15-500 μm is accompanied with a lower tube hematocrit level and lower apparent viscosity as the diameter decreases. These effects are termed the Fåhraeus and Fåhraeus-Lindqvist effects, respectively. Both effects are linked to axial accumulation of red blood cells. In the present investigation, we extend previous works using a shear-induced model for the migration of red blood cells and adopt a model for blood viscosity that accounts for the suspending medium viscosity and local hematocrit level. For fully developed hematocrit profiles (i.e., independent of axial location), the diffusion fluxes due to particle collision frequency and viscosity gradients are of equal magnitude and opposite directions. The ratio of the diffusion coefficients for the two fluxes affects both the Fåhraeus and Fåhraeus-Lindqvist effects and is found related to the capillary diameter and discharge hematocrit using a well-known data-fit correlation for apparent blood viscosity. The velocity and hematocrit profiles were determined numerically as functions of radial coordinate, tube diameter, and discharge hematocrit. The velocity profile determined numerically is consistent with the derived analytical expression and the results are in good agreement with published numerical results and experimental data for hematocrit ratio and hematocrit and velocity profiles.

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Section: Introductionmentioning

confidence: 99%

Dynamics of blood flow: modeling of Fåhraeus and Fåhraeus–Lindqvist effects using a shear-induced red blood cell migration model

Chebbi

2018

J Biol Phys

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“…Therefore, the focus has been shifting towards constitutive equations that incorporate plasticity, elasticity and thixotropy. The model of Owens and coworkers [ 50 ], which has been recently revised [ 51 , 52 , 53 ], was derived using ideas drawn from polymer network theory accounting for the agglomeration and deagglomeration of erythrocytes in healthy human blood at different shear rates. Although this model was subsequently applied to simple shear flows as well as to steady, oscillatory, and pulsatile flow in rigid vessels [ 54 ], it lacks explicit accounting for yield stress, the most important manifestation of the viscoplastic nature of blood.…”

Section: Introductionmentioning

confidence: 99%

Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Description of the Model and Rheological Predictions

et al. 2020

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This work focuses on the advanced modeling of the thixotropic nature of blood, coupled with an elasto-visco-plastic formulation by invoking a consistent and validated model for TEVP materials. The proposed model has been verified for the adequate description of the rheological behavior of suspensions, introducing a scalar variable that describes dynamically the level of internal microstructure of rouleaux at any instance, capturing accurately the aggregation and disaggregation mechanisms of the RBCs. Also, a non-linear fitting is adopted for the definition of the model’s parameters on limited available experimental data of steady and transient rheometric flows of blood samples. We present the predictability of the new model in various steady and transient rheometric flows, including startup shear, rectangular shear steps, shear cessation, triangular shear steps and LAOS tests. Our model provides predictions for the elasto-thixotropic mechanism in startup shear flows, demonstrating a non-monotonic relationship of the thixotropic index on the shear-rate. The intermittent shear step test reveals the dynamics of the structural reconstruction, which in turn is associated with the aggregation process. Moreover, our model offers robust predictions for less examined tests such as uniaxial elongation, in which normal stress was found to have considerable contribution. Apart from the integrated modeling of blood rheological complexity, our implementation is adequate for multi-dimensional simulations due to its tensorial formalism accomplished with a single time scale for the thixotropic effects, resulting in a low computational cost compared to other TEVP models.

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“…(i) The shear-induced migration model in Weert [14] Mansour et al [15], and Chebbi [16] using the model of Phillips et al [17], which is an extension of a previous model by Leighton and Acrivos [18] to analyze blood flow (ii) The elastic-stress induced migration model in Moyers-Gonzalez et al [19], Moyers-Gonzalez and Owens [20] and Dimakopoulos et al [21], which is an extension of a previous model by Mavrantzas and Beris [22,23] to examine blood flow.…”

Section: Introductionmentioning

confidence: 99%

A Two-Zone Shear-Induced Red Blood Cell Migration Model for Blood Flow in Microvessels

Chebbi

2019

Front. Phys.

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The Fåhraeus and Fåhraeus-Lindqvist effects are both associated with the concentration of red blood cells (RBCs) in the core region of microvessels. The annular region is a cell-free layer. Blood flow dynamics and both effects are related to the hematocrit level profile. The aim is to propose a model for blood flow in microvessels that is not compute intensive like many other models such as those using finite element methods. Modeling blood flow requires solving for both the hematocrit level and velocity profiles as blood viscosity depends on the hematocrit level. The two-zone shear-induced model for blood flow is adopted while including an annular cell-free layer, as in the marginal zone theory and in consistency with experimental observations. In the core region, the hematocrit level is not considered to be uniform, and the concentration and viscous fluxes are equal in magnitude and opposite in directions in the fully developed velocity and concentration profiles case. The momentum and hematocrit balance equations are solved. Both analytical and numerical solutions for the velocity and hematocrit level profiles are determined. The numerical results are found to exactly match the analytical solutions, and to be in very good agreement with published experimental data for the cell-free layer thickness, the velocity profile, and the hematocrit ratio.

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Hemodynamics in stenotic vessels of small diameter under steady state conditions: Effect of viscoelasticity and migration of red blood cells

Abstract: Viscoelastic effects in blood flow were found to be responsible for steeper decreases of tube and discharge hematocrits as decreasing function of constriction ratio.

Cited by 33 publications

References 52 publications

Dynamics of blood flow: modeling of Fåhraeus and Fåhraeus–Lindqvist effects using a shear-induced red blood cell migration model

Dynamics of blood flow: modeling of Fåhraeus and Fåhraeus–Lindqvist effects using a shear-induced red blood cell migration model

Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Description of the Model and Rheological Predictions

A Two-Zone Shear-Induced Red Blood Cell Migration Model for Blood Flow in Microvessels

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