Analysis of Low Density Lipoprotein (LDL) Transport Within a Curved Artery

Numerical simulation of the blood flow through a pre-stenotic aneurysm in coronary artery: effects of varying heart rate

The left anterior descending artery (LAD) is a significant coronary artery and a facilitator of oxygenated blood to the heart muscles. Thus, any occurrence of an aneurysm in LAD requires immediate medical attention. It is often inclined toward fatality if coupled with a blockage due to stenosis. Given the high relevance of understanding such models, invasive techniques under all parametric circumstances are hard to achieve. So, a theoretical approach with a cost-effective intervention of mathematical modeling becomes essential. In our current work, we analyze the model with the numerical technique of a modified form of SIMPLE pressure-correction based algorithm and perform parametric studies for the flow field with degree of stenosis, degree of aneurysm, heart rate, and distance separating aneurysm and stenosis as parameters. The study reveals a direct proportionality relation between the number of recirculation zones and heart rate through instantaneous streamline plots. Alongside this, the demonstration of an increase in the risk of rupture of the aneurysm with a decrease in the distance between stenosis and aneurysm, using the physical parameters associated with blood flow, is another key finding. Further, we examine the effect of the flow field on heat transfer and the consequent temperature profiles.

Numerical study of the effect of hemodynamic variables on LDL concentration through the single layer of the Left Anterior Descending coronary artery (LAD) under the heart pulse

Heart attack is one of the most common causes of death in the world. Coronary artery disease is the most recognized cause of heart attack whose onset and progression have been attributed to low-density lipoprotein (LDL) passing through the wall of the artery. In this paper, hemodynamic variables as well as the concentration of LDL through the coronary porous artery at the Left Anterior Descending coronary artery (LAD), and its first diagonal branch (D1) under the heart motion investigated using computational simulation. The geometry that has been studied in this paper is the first bifurcation of Left Anterior Descending (LAD) that has been placed on a perimeter of hypothetical sphere representative of the heart geometry. Sinusoidal variations of sphere radii, simulated pulsating movement of the heart. Blood has been considered as a Newtonian and incompressible flow with pulsatile flow rate and real physiological profile. The plasma filtration boundary condition used over the walls in order to simulate the concentration of LDL to a one-layer artery wall. Variations in the concentration of LDL on the artery wall and its relation to oscillation on shear stress on the artery wall under different conditions are presented. Moreover, the effects of the pulsating inlet flow and dynamic movement of the artery are explored. The results declared that minimum shear stress and maximum LDL concentration take place at the bifurcation and on the myocardial wall which is in complete agreement with clinical studies. Furthermore, it has been shown that the heart pulse has a slight effect on the average time of concentration (0.1% increase); however, by analyzing all time steps, one could observe that the maximum concentration rises in some time steps; where this increases the possibility of LDL presence and helps them diffuse inside the artery wall.

Multiscale Computational Modeling of Vascular Adaptation: A Systems Biology Approach Using Agent-Based Models

The widespread incidence of cardiovascular diseases and associated mortality and morbidity, along with the advent of powerful computational resources, have fostered an extensive research in computational modeling of vascular pathophysiology field and promoted in-silico models as a support for biomedical research. Given the multiscale nature of biological systems, the integration of phenomena at different spatial and temporal scales has emerged to be essential in capturing mechanobiological mechanisms underlying vascular adaptation processes. In this regard, agent-based models have demonstrated to successfully embed the systems biology principles and capture the emergent behavior of cellular systems under different pathophysiological conditions. Furthermore, through their modular structure, agent-based models are suitable to be integrated with continuum-based models within a multiscale framework that can link the molecular pathways to the cell and tissue levels. This can allow improving existing therapies and/or developing new therapeutic strategies. The present review examines the multiscale computational frameworks of vascular adaptation with an emphasis on the integration of agent-based approaches with continuum models to describe vascular pathophysiology in a systems biology perspective. The state-of-the-art highlights the current gaps and limitations in the field, thus shedding light on new areas to be explored that may become the future research focus. The inclusion of molecular intracellular pathways (e.g., genomics or proteomics) within the multiscale agent-based modeling frameworks will certainly provide a great contribution to the promising personalized medicine. Efforts will be also needed to address the challenges encountered for the verification, uncertainty quantification, calibration and validation of these multiscale frameworks.

Influence of vessel curvature and plaque composition on drug transport in the arterial wall following drug-eluting stent implantation

In the last decade, many computational models have been developed to describe the transport of drug eluted from stents and the subsequent uptake into arterial tissue. Each of these models has its own set of limitations: for example, models typically employ simplified stent and arterial geometries, some models assume a homogeneous arterial wall, and others neglect the influence of blood flow and plasma filtration on the drug transport process. In this study, we focus on two common limitations. Specifically, we provide a comprehensive investigation of the influence of arterial curvature and plaque composition on drug transport in the arterial wall following drug-eluting stent implantation. The arterial wall is considered as a three-layered structure including the subendothelial space, the media and the adventitia, with porous membranes separating them (endothelium, internal and external elastic lamina). Blood flow is modelled by the Navier-Stokes equations, while Darcy's law is used to calculate plasma filtration through the porous layers. Our findings demonstrate that arterial curvature and plaque composition have important influences on the spatiotemporal distribution of drug, with potential implications in terms of effectiveness of the treatment. Since the majority of computational models tend to neglect these features, these models are likely to be under- or over-estimating drug uptake and redistribution in arterial tissue.

Inflammatory Cytokines and Atherosclerotic Plaque Progression. Therapeutic Implications

PURPOSE OF THE REVIEW

Inflammatory cytokines play a major role in atherosclerotic plaque progression. This review summarizes the rationale for personalized anti-inflammatory therapy.

RECENT FINDINGS

Systemic inflammatory parameters may be used to follow the clinical outcome in primary and secondary prevention. Medical therapy, both in patients with stable cardiovascular disease, or with acute events, may be tailored taking into consideration the level and course of systemic inflammatory mediators. There is significant space for improvement in primary prevention and in the treatment of patients who have suffered from severe cardiovascular events, paying attention to not only blood pressure and cholesterol levels but also including inflammatory parameters in our clinical analysis. The potential exists to alter the course of atherosclerosis with anti-inflammatory drugs. With increased understanding of the specific mechanisms that regulate the relationship between inflammation and atherosclerosis, new, more effective and specific anti-inflammatory treatment may become available.

Hydraulic conductivity and low-density lipoprotein transport of the venous graft wall in an arterial bypass

Background

Blood flow condition may have influence upon the hydraulic conductivity of venous graft (L_p,vein) in an arterial bypass, then affecting the accumulation of low-density lipoproteins (LDLs) within the graft wall. To probe this possibility, we first measured in vitro the filtration rates of swine lateral saphenous vein segments under different flow rates, and the correlation of L_p,vein with wall shear stress (WSS) was then obtained.

Results

The experimental results showed that when WSS was very low, L_p,vein would increase drastically with WSS from 1.16 ± 0.15 × 10⁻¹¹ m/s Pa at 0 dyn/cm² to 2.17 ± 0.20 × 10⁻¹¹ m/s Pa at 0.7 dyn/cm², then became constant of approximately 2.33 × 10⁻¹¹ m/s Pa as the WSS increased further. Based on the experimental results, we assumed three different cases of L_p,vein and numerically simulated the LDLs transport in an arterial bypass model with venous graft. Case A: L_p,vein = 2.33 × 10⁻¹¹ m/s Pa; Case B: L_p,vein = 1.16 × 10⁻¹¹ m/s Pa (static condition with WSS of 0); Case C: L_p,vein was shear dependent. The simulation showed that the deposition/accumulation of LDLs within the venous graft wall in Case A was greatly enhanced when compared with that in Case B. However, the LDL accumulation in the graft wall was similar for Case A and Case C.

Conclusions

Our study, therefore, indicates that when the venous graft was implanted as a bypass graft, the L_p,vein might remain nearly constant along its whole length except for very few areas where the value of WSS was extremely low (less than 0.7 dyn/cm²) and the effects of L_p,vein modulated by blood flow on LDL transport may be neglected.

Mathematical Modelling and Simulation of Atherosclerosis Formation and Progress: A Review

Cardiovascular disease (CVD) is a major threat to human health since it is the leading cause of death in western countries. Atherosclerosis is a type of CVD related to hypertension, diabetes, high levels of cholesterol, smoking, oxidative stress, and age. Atherosclerosis primarily occurs in medium and large arteries, such as coronary and the carotid artery and, in particular, at bifurcations and curvatures. Atherosclerosis is compared to an inflammatory disease where a thick, porous material comprising cholesterol fat, saturated sterols, proteins, fatty acids, calcium etc., is covered by an endothelial membrane and a fragile fibrous tissue which makes atheromatic plaque prone to rupture that could lead to the blockage of the artery due to the released plaque material. Despite the great progress achieved, the nature of the disease is not fully understood. This paper reviews the current state of modelling of all levels of atherosclerosis formation and progress and discusses further challenges in atherosclerosis modelling. The objective is to pave a way towards more precise computational tools to predict and eventually reengineer the fate of atherosclerosis.

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.

Numerical simulation of haemodynamics and low-density lipoprotein transport in the rabbit aorta and their correlation with atherosclerotic plaque thickness

Two mechanisms of shear stress and mass transport have been recognized to play an important role in the development of localized atherosclerosis. However, their relationship and roles in atherogenesis are still obscure. It is necessary to investigate quantitatively the correlation among low-density lipoproteins (LDL) transport, haemodynamic parameters and plaque thickness. We simulated blood flow and LDL transport in rabbit aorta using computational fluid dynamics and evaluated plaque thickness in the aorta of a high-fat-diet rabbit. The numerical results show that regions with high luminal LDL concentration tend to have severely negative haemodynamic environments (HEs). However, for regions with moderately and slightly high luminal LDL concentration, the relationship between LDL concentration and the above haemodynamic indicators is not clear cut. Point-by-point correlation with experimental results indicates that severe atherosclerotic plaque corresponds to high LDL concentration and seriously negative HEs, less severe atherosclerotic plaque is related to either moderately high LDL concentration or moderately negative HEs, and there is almost no atherosclerotic plaque in regions with both low LDL concentration and positive HEs. In conclusion, LDL distribution is closely linked to blood flow transport, and the synergetic effects of luminal surface LDL concentration and wall shear stress-based haemodynamic indicators may determine plaque thickness.

Semi-Empirical Estimation of Dean Flow Velocity in Curved Microchannels

Curved and spiral microfluidic channels are widely used in particle and cell sorting applications. However, the average Dean velocity of secondary vortices which is an important design parameter in these devices cannot be estimated precisely with the current knowledge in the field. In this paper, we used co-flows of dyed liquids in curved microchannels with different radii of curvatures and monitored the lateral displacement of fluids using optical microscopy. A quantitative Switching Index parameter was then introduced to calculate the average Dean velocity in these channels. Additionally, we developed a validated numerical model to expand our investigations to elucidating the effects of channel hydraulic diameter, width, and height as well as fluid kinematic viscosity on Dean velocity. Accordingly, a non-dimensional comprehensive correlation was developed based on our numerical model and validated against experimental results. The proposed correlation can be used extensively for the design of curved microchannels for manipulation of fluids, particles, and biological substances in spiral microfluidic devices.

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.