Low-density lipoprotein accumulation within a carotid artery with multilayer elastic porous wall: fluid-structure interaction and non-Newtonian considerations

Impact of geometric and hemodynamic changes on a mechanobiological model of atherosclerosis

BACKGROUND AND OBJECTIVE

In this work, the analysis of the importance of hemodynamic updates on a mechanobiological model of atheroma plaque formation is proposed.

METHODS

For that, we use an idealized and axisymmetric model of carotid artery. In addition, the behavior of endothelial cells depending on hemodynamical changes is analyzed too. A total of three computational simulations are carried out and their results are compared: an uncoupled model and two models that consider the opposite behavior of endothelial cells caused by hemodynamic changes. The model considers transient blood flow using the Navier-Stokes equation. Plasma flow across the endothelium is determined with Darcy's law and the Kedem-Katchalsky equations, considering the three-pore model, which is also employed for the flow of substances across the endothelium. The behavior of the considered substances in the arterial wall is modeled with convection-diffusion-reaction equations, and the arterial wall is modeled as a hyperelastic Yeoh's material.

RESULTS

Significant variations are noted in both the morphology and stenosis ratio of the plaques when comparing the uncoupled model to the two models incorporating updates for geometry and hemodynamic stimuli. Besides, the phenomenon of double-stenosis is naturally reproduced in the models that consider both geometric and hemodynamical changes due to plaque growth, whereas it cannot be predicted in the uncoupled model.

CONCLUSIONS

The findings indicate that integrating the plaque growth model with geometric and hemodynamic settings is essential in determining the ultimate shape and dimensions of the carotid plaque.

Simulation of LDL permeation into multilayer wall of a coronary bifurcation using WSS-dependent model: effects of hemorheology

Atherosclerosis, due to the permeation of low-density lipoprotein (LDL) particles into the arterial wall, is one of the most common and deadly diseases in today's world. Due to its importance, numerous studies have been conducted on the factors affecting this disease. In this study, using numerical simulation, the effects of Wall Shear Stress (WSS), non-Newtonian behavior of blood, different values of hematocrit and blood pressure on LDL permeation into the arterial wall layers are investigated in a 4-layer wall model of a coronary bifurcation. To obtain the velocity and concentration fields in the fluid domain, the Navier-Stokes, Brinkman, and mass transfer equations are numerically solved in the lumen and wall layers. Results show that it is important to consider the effects of WSS on transport properties of endothelium layer in bifurcations and this leads to completely different concentration profiles compared to the constant properties model. Our computations show that a giant accumulation of LDL in the intima layer of the outer wall of the left anterior descending artery, especially in low WSS regions, may lead to atherosclerosis. It is also, necessary to consider the non-Newtonian behavior of blood in bifurcations due to its direct effect on WSS. A pressure-induced increase in the half-width of leaky junctions may be responsible for the higher risk of atherosclerosis in hypertension. In addition, it is shown that the dominant mechanism in LDL permeation into the wall is convection, and also, hypertension increases the effect of mass transfer by convection mechanism more than the diffusion mechanism. Furthermore, our results are consistent with various clinical studies.

Steady-state solutions of one-dimensional equations of non-Newtonian hemodynamics

This paper is devoted to obtaining and analysis of steady-state solutions of one-dimensional equations for the simulation of blood flow when the non-Newtonian nature of blood is taken into account. The models, based on the rheological relations, widely used for the blood, are considered. The expressions for the nonlinear frictional term are presented. For the Power Law, Simplified Cross, and Quemada models, the exact integrals of the nonlinear ordinary differential equation, obtained from the averaged momentum equation, are obtained. It is demonstrated that several solutions exist for every rheological model, but the physically relevant solutions can be selected by the appropriate value of Mach number. The effects of the velocity profile and the value of hematocrit on the steady-state solutions are analyzed. It is demonstrated that the flattening of the velocity profile, which is typical for the blood, leads to the diminishing of the length of the interval, where the solution exists. The same effect is observed when the hematocrit value is increased.

Modeling cholesterol metabolism and atherosclerosis

Atherosclerotic cardiovascular disease (ASCVD) is the leading cause of morbidity and mortality among Western populations. Many risk factors have been identified for ASCVD; however, elevated low-density lipoprotein cholesterol (LDL-C) remains the gold standard. Cholesterol metabolism at the cellular and whole-body level is maintained by an array of interacting components. These regulatory mechanisms have complex behavior. Likewise, the mechanisms which underpin atherogenesis are nontrivial and multifaceted. To help overcome the challenge of investigating these processes mathematical modeling, which is a core constituent of the systems biology paradigm has played a pivotal role in deciphering their dynamics. In so doing models have revealed new insights about the key drivers of ASCVD. The aim of this review is fourfold; to provide an overview of cholesterol metabolism and atherosclerosis, to briefly introduce mathematical approaches used in this field, to critically discuss models of cholesterol metabolism and atherosclerosis, and to highlight areas where mathematical modeling could help to investigate in the future. This article is categorized under: Cardiovascular Diseases > Computational Models.

Comparison of Non-Newtonian Models of One-Dimensional Hemodynamics

The paper is devoted to the comparison of different one-dimensional models of blood flow. In such models, the non-Newtonian property of blood is considered. It is demonstrated that for the large arteries, the small parameter is observed in the models, and the perturbation method can be used for the analytical solution. In the paper, the simplified nonlinear problem for the semi-infinite vessel with constant properties is solved analytically, and the solutions for different models are compared. The effects of the flattening of the velocity profile and hematocrit value on the deviation from the Newtonian model are investigated.

Effects of Ageing on Aortic Circulation During Atrial Fibrillation; a Numerical Study on Different Aortic Morphologies

Atrial fibrillation (AF) can alter intra-cardiac flow and cardiac output that subsequently affects aortic flow circulation. These changes may become more significant where they occur concomitantly with ageing. Aortic ageing is accompanied with morphological changes such as dilation, lengthening, and arch unfolding. While the recognition of AF mechanism has been the subject of numerous studies, less focus has been devoted to the aortic circulation during the AF and there is a lack of such investigation at different ages. The current work aims to address the present gap. First, we analyse aortic flow distribution in three configurations, which attribute to young, middle and old people, using geometries constructed via clinical data. We then introduce two transient inlet flow conditions representative of key AF-associated defects. Results demonstrate that both AF and ageing negatively affect flow circulation. The main consequence of concomitant occurrence is enhancement of endothelial cell activation potential (ECAP) throughout the vascular domain, mainly at aortic arch and descending thoracic aorta, which is consistent with some clinical observations. The outcome of the current study suggests that AF exacerbates the vascular defects occurred due to the ageing, which increases the possibility of cardiovascular diseases per se.

Analysis of non-Newtonian effects on Low-Density Lipoprotein accumulation in an artery

In this work, non-Newtonian effects on Low-Density Lipoprotein (LDL) transport across an artery are analyzed with a multi-layer model. Four rheological models (Carreau, Carreau-Yasuda, power-law and Newtonian) are used for the blood flow through the lumen. For the non-Newtonian cases, the arterial wall is modeled with a generalized momentum equation. Convection-diffusion equation is used for the LDL transport through the lumen, while Staverman-Kedem-Katchalsky, combined with porous media equations, are used for the LDL transport through the wall. Results are presented in terms of filtration velocity, Wall Shear Stresses (WSS) and concentration profiles. It is shown that non-Newtonian effects on mass transport are negligible for a healthy intramural pressure value. Non-Newtonian effects increase slightly with intramural pressure, but Newtonian assumption can still be considered reliable. Effects of arterial size are also analyzed, showing that Newtonian assumption can be considered valid for both medium and large arteries, in predicting LDL deposition. Finally, non-Newtonian effects are also analyzed for an aorta-common iliac bifurcation, showing that Newtonian assumption is valid for mass transport at low Reynolds numbers. At a high Reynolds number, it has been shown that a non-Newtonian fluid model can have more impact due to the presence of flow recirculation.