Effect of the fluid–structure interactions on low-density lipoprotein transport within a multi-layered arterial wall

Plaque heterogeneity and the spatial distributions of its components dictate drug-coated balloon therapy

Drug-coated balloon (DCB) angioplasty is one of the potential approaches to alleviating in-stent restenosis and treating peripheral artery disease. An in-silico model has been developed for sirolimus drug eluted from an inflated balloon in a patient-specific arterial cross-section consisting of fibrous tissue, fibrofatty tissue, dense calcium, necrotic core, and healthy tissue. The convection-diffusion-reaction equation represents the transport of drug, while drug binding, both specific and non-specific, can be modelled as a reaction process. The Brinkman equations describe the interstitial flow in porous tissue. An image processing technique is leveraged for reconstructing the computational domain. The Marker and Cell, and Immersed Boundary Methods are used to solve the set of governing equations. The no-flux interface condition and convection do amplify the tissue content, and the regions of dense calcium and necrotic core limited to or extremely close to the interface pose a clinical threat to DCB therapy. Simulations predict the effects of the positioning and clustering of plaque components in the domain. This study demands extensive intravascular ultrasound-derived virtual histology (VH-IVUS) imaging to understand the plaque morphology and determine the relative positions of different plaque compositions about the lumen-tissue interface, which have a significant impact on arterial pharmacokinetics.

Influence of aortic aneurysm on the local distribution of NO and O2 using image-based computational fluid dynamics

There is a pressing need to establish novel biomarkers to predict the progression of thoracic aortic aneurysm (TAA) dilatation. Aside from hemodynamics, the roles of oxygen (O₂) and nitric oxide (NO) in TAA pathogenesis are potentially significant. As such, it is imperative to comprehend the relationship between aneurysm presence and species distribution in both the lumen and aortic wall. Given the limitations of existing imaging methods, we propose the use of patient-specific computational fluid dynamics (CFD) to explore this relationship. We have performed CFD simulations of O₂ and NO mass transfer in the lumen and aortic wall for two cases: a healthy control (HC) and a patient with TAA, both acquired using 4D-flow magnetic resonance imaging (MRI). The mass transfer of O₂ was based on active transport by hemoglobin, while the local variations of the wall shear stress (WSS) drove NO production. Comparing hemodynamic properties, the time-averaged WSS was considerably lower for TAA, while the oscillatory shear index and endothelial cell activation potential were notably elevated. O₂ and NO showed a non-uniform distribution within the lumen and an inverse correlation between the two species. We identified several locations of hypoxic regions for both cases due to lumen-side mass transfer limitations. In the wall, NO varied spatially, with a clear distinction between TAA and HC. In conclusion, the hemodynamics and mass transfer of NO in the aorta exhibit the potential to serve as a diagnostic biomarker for TAA. Furthermore, hypoxia may provide additional insights into the onset of other aortic pathologies.

On the nonlinear relationship between wall shear stress topology and multi-directionality in coronary atherosclerosis

BACKGROUND AND OBJECTIVE

In this paper we investigate twelve multi-directional/topological wall shear stress (WSS) derived metrics and their relationships with the formation of coronary plaques in both computational fluid dynamics (CFD) and dynamic fluid-structure interaction (FSI) frameworks. While low WSS is one of the most established biomechanical markers associated with coronary atherosclerosis progression, alone it is limited. Multi-directional and topological WSS derived metrics have been shown to be important in atherosclerosis related mechanotransduction and near-wall transport processes. However, the relationships between these twelve WSS metrics and the influence of both FSI simulations and coronary dynamics is understudied.

METHODS

We first investigate the relationships between these twelve WSS derived metrics, stenosis percentage and lesion length through a parametric, transient CFD study. Secondly, we extend the parametric study to FSI, both with and without the addition of coronary dynamics, and assess their correlations. Finally, we present the case of a patient who underwent invasive coronary angiography and optical coherence tomography imaging at two time points 18 months apart. Associations between each of the twelve WSS derived metrics in CFD, static FSI and dynamic FSI simulations were assessed against areas of positive/negative vessel remodelling, and changes in plaque morphology.

RESULTS

22-32% stenosis was the threshold beyond which adverse multi-directional/topological WSS results. Each metric produced a different relationship with changing stenoses and lesion length. Transient haemodynamics was impacted by coronary dynamics, with the topological shear variation index suppressed by up to 94%. These changes appear more critical at smaller stenosis levels, suggesting coronary dynamics could play a role in the earlier stages of atherosclerosis development. In the patient case, both dynamics and FSI vs CFD changes altered associations with measured changes in plaque morphology. An appendix of the linear fits between the various FSI- and CFD-based simulations is provided to assist in scaling CFD-based results to resemble the compliant walled characteristics of FSI more accurately.

CONCLUSIONS

These results highlight the potential for coronary dynamics to alter multi-directional/topological WSS metrics which could impact associations with changes in coronary atherosclerosis over time. These results warrant further investigation in a wider range of morphological settings and longitudinal cohort studies in the future.

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.

Fluid-structure interactions (FSI) based study of low-density lipoproteins (LDL) uptake in the left coronary artery

The purpose of this study is to compare the effect of the different physical factors on low-density lipoproteins (LDL) accumulation from flowing blood to the arterial wall of the left coronary arteries. The three-dimensional (3D) computational model of the left coronary arterial tree is reconstructed from a patient-specific computed tomography angiography (CTA) image. The endothelium of the coronary artery is represented by a shear stress dependent three-pore model. Fluid–structure interaction (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$FSI$$\end{document}FSI) based numerical method is used to study the LDL transport from vascular lumen into the arterial wall. The results show that the high elastic property of the arterial wall decreases the complexity of the local flow field in the coronary bifurcation system. The places of high levels of LDL uptake coincide with the regions of low wall shear stress. In addition, hypertension promotes LDL uptake from flowing blood in the arterial wall, while the thickened arterial wall decreases this process. The present computer strategy combining the methods of coronary CTA image 3D reconstruction, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$FSI$$\end{document}FSI simulation, and three-pore modeling was illustrated to be effective on the simulation of the distribution and the uptake of LDL. This may have great potential for the early prediction of the local atherosclerosis lesion in the human left coronary artery.

Effect of transport parameters on atherosclerotic lesion growth: A parameter sensitivity analysis

BACKGROUND

Atherosclerosis is a degenerative disease of the arterial wall. It results in the formation of progressively growing plaque lesions that can harden and narrow their host arteries. Current computational models of the inflammatory process that govern atherosclerosis growth are reliant on a number of parameters that can freely vary and whose precise values are not well known.

METHODS

To identify the significance of variation in such parameters, a parametric sensitivity study had been conducted on the blood density, blood viscosity, plasma viscosity and bulk flow low density lipoprotein (LDL) concentration. Using computational modeling, the significance of variation in these parameters was assessed on the transport of LDL. The simulation was performed via the 2^k factorial experimental design, which was conducted to identify the significance of the select parameters on the intima LDL concentration and endothelial LDL coverage area.

RESULTS

Results identified the blood viscosity and bulk flow LDL concentration are the dominant parameters for the atherosclerotic lesion growth. The coverage of LDL on the arterial wall surface was strongly dependent on the blood viscosity. The significance of these findings was discussed.

CONCLUSION

This statistical study identifies two dominating blood factors, LDL concentration and blood viscosity, and how they influence atherosclerosis which will serves as a guideline for further investigation on the atherosclerosis topic.

Prediction of the development of coronary atherosclerotic plaques using computational modeling in 3D reconstructed coronary arteries

In this work we present a novel method for the prediction and generation of atherosclerotic plaques. This is performed in a two-step approach, by employing first a multilevel computational plaque growth model and second a correlation between the model's results and the 3D reconstructed follow-up plaques. In particular, computer tomography coronary angiography (CTCA) data and blood tests were collected from patients at two time points. Using the baseline data, the plaque growth is simulated using a multi-level computational model which includes: i) modeling of the blood flow dynamics, ii) modeling of low and high density lipoproteins and monocytes' infiltration in the arterial wall, and the species reactions during the atherosclerotic process, and iii) modeling of the arterial wall thickening. The correlation between the followup plaques and the simulated plaque density distribution resulted to the extraction of a threshold of the plaque density, that can be used to identify plaque areas.Clinical Relevance- The methodology presented in this work is a first step to the prediction of the plaque shape and location of patients with atherosclerosis and could be used as an additional tool for patient-specific risk stratification.

Boundary layer considerations in a multi-layer model for LDL accumulation

Boundary layer effects for Low-Density Lipoprotein (LDL) concentration problems in a multi-layer artery model are analyzed in this work. Both a straight artery and aorta-iliac bifurcation are analyzed. Mass, momentum and species governing equations are based on the porous media theory and solved with the commercial finite-element based code COMSOL Multiphysics. For the straight artery, various inlet velocities, arterial sizes and intramural pressure values are investigated. Results are presented in terms of concentration profiles close to the lumen/endothelium interface and boundary layer thickness. It is shown that the boundary layer is affected by all of the three analyzed parameters. The results in this work will further clarify the concentration polarization effects imposed by the arterial wall.

In vivo mimicking model for solid tumor towards hydromechanics of tissue deformation and creation of necrosis

The present work addresses transvascular and interstitial fluid transport inside a solid tumor surrounded by normal tissue (close to an in vivo mimicking setup). In general, biological tissues behave like a soft porous material and show mechanical behavior towards the fluid motion through the interstitial space. In general, forces like viscous drag that are associated with the fluid flow may compress the tissue material. On the macroscopic level, we try to model the motion of fluids and macromolecules through the interstitial space of solid tumor and the normal tissue layer. The transvascular fluid transport is assumed to be governed by modified Starling's law. The poroelastohydrodynamics (interstitial hydrodynamics and the deformation of tissue material) inside the tumor and normal tissue regions is modeled using linearized biphasic mixture theory. Correspondingly, the velocity distribution of fluid is coupled to the displacement field of the solid phase (mainly cellular phase and extracellular matrix) in both the normal and tumor tissue regions. The corresponding velocity field is used within the transport reaction equation for fluids and macromolecules through interstitial space to get the overall solute (e.g., nutrients, drug, and other macromolecules) distribution. This study justifies that the presence of the normal tissue layer plays a significant role in delaying/assisting necrosis inside the tumor tissue. It is observed that the exchange process of fluids and macromolecules across the interface of the tumor and normal tissue affects the effectiveness factor corresponding to the tumor tissue.

Low density lipoprotein transport through patient-specific thoracic arterial wall

BACKGROUND AND AIMS

The distribution of Low density lipoprotein (LDL) within the arterial wall is helpful in understanding the onset and development of atherosclerosis. The objective of the study is to study the transport and LDL distribution within patient-specific arterial wall using computational analysis under normal and hypertensive conditions.

METHODS

Patient specific model of the thoracic aorta is computationally examined. The arterial wall is treated macroscopically as homogeneous (one layered) porous media of variable thickness. The interfacial lumen-arterial wall (endothelium) coupling is achieved by the Kedem-Katchalsky equation.

RESULTS

High values of LDL are located at areas where WSS values range from 0.4 N/m² to 1.5 N/m² for normal conditions. In this case the Pearson correlation coefficient r between LDL values and WSS is equal to -0.655 denoting a strong negative linear correlation. In the case that hypertension takes place, high LDL values are located at areas where WSS values range from 0.59 N/m² to 1.7 N/m² and the corresponding Pearson correlation coefficient r is equal to -0.808 denoting a very strong negative linear correlation. For the same parabolic intake flow velocity profile, the luminal surface concentration of LDL is 0.2-2.1% higher than that of the bulk flow for the normal pressure and 0.4-3.4% higher than that of the bulk flow for the hypertensive pressure. For normal conditions, the concentration of LDL at the endothelium/media interface is considerably lower (almost 20 times) than the LDL concentration value at lumen/endothelium interface. For hypertensive conditions, the LDL concentration at the endothelium/media interface is only 4.5 times lower than the corresponding luminal (endothelium side) concentration. The lumen/endothelium side locations (mainly the concave parts) of low WSS - high LDL concentration values coincide with those of high wall-side LDL concentration.

CONCLUSIONS

The transport and LDL distribution is affected by elevated transmural pressure which causes higher LDL concentration. Thus, hypertensive conditions theoretically enhance atherosclerosis.

High efficiency fabrication of complex microtube arrays by scanning focused femtosecond laser Bessel beam for trapping/releasing biological cells

In this paper, we present a focused femtosecond laser Bessel beam scanning technique for the rapid fabrication of large-area 3D complex microtube arrays. The femtosecond laser beam is converted into several Bessel beams by two-dimensional phase modulation using a spatial light modulator. By scanning the focused Bessel beam along a designed route, microtubes with variable size and flexible geometry are rapidly fabricated by two-photon polymerization. The fabrication time is reduced by two orders of magnitude in comparison with conventional point-to-point scanning. Moreover, we construct an effective microoperating system for single cell manipulation using microtube arrays, and demonstrate its use in the capture, transfer, and release of embryonic fibroblast mouse cells as well as human breast cancer cells. The new fabrication strategy provides a novel method for the rapid fabrication of functional devices using a flexibly tailored laser beam.

Low-density lipoprotein transport through an arterial wall under hypertension - A model with time and pressure dependent fraction of leaky junction consistent with experiments

The influence of hypertension on low-density lipoproteins intake into the arterial wall is an important factor for understanding mechanisms of atherosclerosis. It has been experimentally observed that the increased pressure leads to the higher level of the LDL inside the wall. In this paper we attempt to construct a model of the LDL transport which reproduces quantitatively experimental outcomes. We supplement the well-known four-layer arterial wall model to include two pressure induced effects: the compression of the intima tissue and the increase of the fraction of leaky junctions. We demonstrate that such model can reach the very good agreement with experimental data.

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.

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

Low-density lipoprotein (LDL), which is recognized as bad cholesterol, typically has been regarded as a main cause of atherosclerosis. LDL infiltration across arterial wall and subsequent formation of Ox-LDL could lead to atherogenesis. In the present study, combined effects of non-Newtonian fluid behavior and fluid-structure interaction (FSI) on LDL mass transfer inside an artery and through its multilayer arterial wall are examined numerically. Navier-Stokes equations for the blood flow inside the lumen and modified Darcy's model for the power-law fluid through the porous arterial wall are coupled with the equations of mass transfer to describe LDL distributions in various segments of the artery. In addition, the arterial wall is considered as a heterogeneous permeable elastic medium. Thus, elastodynamics equation is invoked to examine effects of different wall elasticity on LDL distribution in the artery. Findings suggest that non-Newtonian behavior of filtrated plasma within the wall enhances LDL accumulation meaningfully. Moreover, results demonstrate that at high blood pressure and due to the wall elasticity, endothelium pores expand, which cause significant variations on endothelium physiological properties in a way that lead to higher LDL accumulation. Additionally, results describe that under hypertension, by increasing angular strain, endothelial junctions especially at leaky sites expand more dramatic for the high elastic model, which in turn causes higher LDL accumulation across the intima layer and elevates atherogenesis risk.

Using a Systems Pharmacology Approach to Study the Effect of Statins on the Early Stage of Atherosclerosis in Humans

More than 100,000 people have participated in controlled trials of statins (lowering cholesterol drugs) since the introduction of lovastatin in the 1980s. Meta-analyses of this data have shown that statins have a beneficial effect on treated groups compared to control groups, reducing cardiovascular risk. Inhibiting the HMG-CoA reductase in the liver, statins can reduce cholesterol levels, thus reducing LDL levels in circulation. Published data from intravascular ultrasound studies (IVUS) was used in this work to develop and validate a unique integrative system model; this consisted of analyzing control groups from two randomized controlled statins trials (24/97 subjects respectively), one treated group (40 subjects, simvastatin trial), and 27 male subjects (simvastatin, pharmacokinetic study). The model allows to simulate the pharmacokinetics of statins and its effect on the dynamics of lipoproteins (e.g., LDL) and the inflammatory pathway while simultaneously exploring the effect of flow-related variables (e.g., wall shear stress) on atherosclerosis progression.

Modelling and simulation of low-density lipoprotein transport through multi-layered wall of an anatomically realistic carotid artery bifurcation

A high concentration of low-density lipoprotein (LDL) is recognized as one of the principal risk factors for development of atherosclerosis. This paper reports on modelling and simulations of the coupled mass (LDL concentration) and momentum transport through the arterial lumen and the multi-layered arterial wall of an anatomically realistic carotid bifurcation. The mathematical model includes equations for conservation of mass, momentum and concentration, which take into account a porous layer structure, the biological membranes and reactive source/sink terms in different layers of the arterial wall, as proposed in Yang & Vafai (2006). A four-layer wall model of an arterial wall with constant thickness is introduced and initially tested on a simple cylinder geometry where realistic layer properties are specified. Comparative assessment with previously published results demonstrated proper implementation of the mathematical model. Excellent agreement for the velocity and LDL concentration distributions in the arterial lumen and in the artery wall are obtained. Then, an anatomically realistic carotid artery bifurcation is studied. This is the main novelty of the presented research. We find a strong dependence between underlying blood flow pattern (and consequently the wall shear stress distributions) and the uptake of the LDL concentration in the artery wall. The radial dependency of interactions between the diffusion, convection and chemical reactions within the multi-layered artery wall is crucial for accurate predictions of the LDL concentration in the media. It is shown that a four-layer wall model produced qualitatively good agreement with the experimental results of Meyer et al. (1996) in predicting levels of LDL within the media of a rabbit aorta under identical transmural pressure conditions. Finally, it is demonstrated that the adopted model represents a good initial platform for future numerical investigations of the initial stage of atherosclerosis for patient-specific geometries.

Mathematical modelling of atheroma plaque formation and development in coronary arteries

Atherosclerosis is a vascular disease caused by inflammation of the arterial wall, which results in the accumulation of low-density lipoprotein (LDL) cholesterol, monocytes, macrophages and fat-laden foam cells at the place of the inflammation. This process is commonly referred to as plaque formation. The evolution of the atherosclerosis disease, and in particular the influence of wall shear stress on the growth of atherosclerotic plaques, is still a poorly understood phenomenon. This work presents a mathematical model to reproduce atheroma plaque growth in coronary arteries. This model uses the Navier-Stokes equations and Darcy's law for fluid dynamics, convection-diffusion-reaction equations for modelling the mass balance in the lumen and intima, and the Kedem-Katchalsky equations for the interfacial coupling at membranes, i.e. endothelium. The volume flux and the solute flux across the interface between the fluid and the porous domains are governed by a three-pore model. The main species and substances which play a role in early atherosclerosis development have been considered in the model, i.e. LDL, oxidized LDL, monocytes, macrophages, foam cells, smooth muscle cells, cytokines and collagen. Furthermore, experimental data taken from the literature have been used in order to physiologically determine model parameters. The mathematical model has been implemented in a representative axisymmetric geometrical coronary artery model. The results show that the mathematical model is able to qualitatively capture the atheroma plaque development observed in the intima layer.

Kinetic modeling of low density lipoprotein oxidation in arterial wall and its application in atherosclerotic lesions prediction

Oxidation of low-density lipoprotein (LDL) is one of the major factors in atherogenic process. Trapped oxidized LDL (Ox-LDL) in the subendothelial matrix is taken up by macrophage and leads to foam cell generation creating the first step in atherosclerosis development. Many researchers have studied LDL oxidation using in vitro cell-induced LDL oxidation model. The present study provides a kinetic model for LDL oxidation in intima layer that can be used in modeling of atherosclerotic lesions development. This is accomplished by considering lipid peroxidation kinetic in LDL through a system of elementary reactions. In comparison, characteristics of our proposed kinetic model are consistent with the results of previous experimental models from other researches. Furthermore, our proposed LDL oxidation model is added to the mass transfer equation in order to predict the LDL concentration distribution in intima layer which is usually difficult to measure experimentally. According to the results, LDL oxidation kinetic constant is an important parameter that affects LDL concentration in intima layer so that existence of antioxidants that is responsible for the reduction of initiating rates and prevention of radical formations, have increased the concentration of LDL in intima by reducing the LDL oxidation rate.