A multiphysics approach for modeling early atherosclerosis

HDL and plaque regression in a multiphase model of early atherosclerosis

Atherosclerosis is a chronic disease of the arteries characterised by the accumulation of lipids and lipid-engorged cells in the artery wall. Early plaque growth is aggravated by the deposition of low density lipoproteins (LDL) in the wall and the subsequent immune response. High density lipoproteins (HDL) counterbalance the effects of LDL by accepting cholesterol from macrophages and removing it from the plaque. In this paper, we develop a free boundary multiphase model to investigate the effects of LDL and HDL on early plaque development. We examine how the rates of LDL and HDL deposition affect cholesterol accumulation in macrophages, and how this impacts cell death rates and emigration. We identify a region of LDL-HDL parameter space where plaque growth stabilises for low LDL and high HDL influxes, due to macrophage emigration and HDL clearance that counterbalances the influx of new cells and cholesterol. We explore how the efferocytic uptake of dead cells and the recruitment of new macrophages affect plaque development for a range of LDL and HDL influxes. Finally, we consider how changes in the LDL-HDL profile can change the course of plaque development. We show that changes towards lower LDL and higher HDL can slow plaque growth and even induce regression. We find that these changes have less effect on larger, more established plaques, and that temporary changes will only slow plaque growth in the short term.

Haemodynamic Effects on the Development and Stability of Atherosclerotic Plaques in Arterial Blood Vessel

Studying the formation and stability of atherosclerotic plaques in the hemodynamic field is essential for understanding the growth mechanism and preventive treatment of atherosclerotic plaques. In this paper, based on a multiplayer porous wall model, we established a two-way fluid-solid interaction with time-varying inlet flow. The lipid-rich necrotic core (LRNC) and stress in atherosclerotic plaque were described for analyzing the stability of atherosclerotic plaques during the plaque growth by solving advection-diffusion-reaction equations with finite-element method. It was found that LRNC appeared when the lipid levels of apoptotic materials (such as macrophages, foam cells) in the plaque reached a specified lower concentration, and increased with the plaque growth. LRNC was positively correlated with the blood pressure and was negatively correlated with the blood flow velocity. The maximum stress was mainly located at the necrotic core and gradually moved toward the left shoulder of the plaque with the plaque growth, which increases the plaque instability and the risk of the plaque shedding. The computational model may contribute to understanding the mechanisms of early atherosclerotic plaque growth and the risk of instability in the plaque growth.

Macrophage Anti-inflammatory Behaviour in a Multiphase Model of Atherosclerotic Plaque Development

Atherosclerosis is an inflammatory disease characterised by the formation of plaques, which are deposits of lipids and cholesterol-laden macrophages that form in the artery wall. The inflammation is often non-resolving, due in large part to changes in normal macrophage anti-inflammatory behaviour that are induced by the toxic plaque microenvironment. These changes include higher death rates, defective efferocytic uptake of dead cells, and reduced rates of emigration. We develop a free boundary multiphase model for early atherosclerotic plaques, and we use it to investigate the effects of impaired macrophage anti-inflammatory behaviour on plaque structure and growth. We find that high rates of cell death relative to efferocytic uptake results in a plaque populated mostly by dead cells. We also find that emigration can potentially slow or halt plaque growth by allowing material to exit the plaque, but this is contingent on the availability of live macrophage foam cells in the deep plaque. Finally, we introduce an additional bead species to model macrophage tagging via microspheres, and we use the extended model to explore how high rates of cell death and low rates of efferocytosis and emigration prevent the clearance of macrophages from the plaque.

Microbiota Effect on Trimethylamine N-Oxide Production: From Cancer to Fitness-A Practical Preventing Recommendation and Therapies

Trimethylamine N-oxide (TMAO) is a microbial metabolite derived from nutrients, such as choline, L-carnitine, ergothioneine and betaine. Recently, it has come under the spotlight for its close interactions with gut microbiota and implications for gastrointestinal cancers, cardiovascular disease, and systemic inflammation. The culprits in the origin of these pathologies may be food sources, in particular, high fat meat, offal, egg yolk, whole dairy products, and fatty fish, but intercalated between these food sources and the production of pro-inflammatory TMAO, the composition of gut microbiota plays an important role in modulating this process. The aim of this review is to explain how the gut microbiota interacts with the conversion of specific compounds into TMA and its oxidation to TMAO. We will first cover the correlation between TMAO and various pathologies such as dysbiosis, then focus on cardiovascular disease, with a particular emphasis on pro-atherogenic factors, and then on systemic inflammation and gastrointestinal cancers. Finally, we will discuss primary prevention and therapies that are or may become possible. Possible treatments include modulation of the gut microbiota species with diets, physical activity and supplements, and administration of drugs, such as metformin and aspirin.

The Need to Shift from Morphological to Structural Assessment for Carotid Plaque Vulnerability

Degree of luminal stenosis is generally considered to be an important indicator for judging the risk of atherosclerosis burden. However, patients with the same or similar degree of stenosis may have significant differences in plaque morphology and biomechanical factors. This study investigated three patients with carotid atherosclerosis within a similar range of stenosis. Using our developed fluid-structure interaction (FSI) modelling method, this study analyzed and compared the morphological and biomechanical parameters of the three patients. Although their degrees of carotid stenosis were similar, the plaque components showed a significant difference. The distribution range of time-averaged wall shear stress (TAWSS) of patient 2 was wider than that of patient 1 and patient 3. Patient 2 also had a much smaller plaque stress compared to the other two patients. There were significant differences in TAWSS and plaque stresses among three patients. This study suggests that plaque vulnerability is not determined by a single morphological factor, but rather by the combined structure. It is necessary to transform the morphological assessment into a structural assessment of the risk of plaque rupture.

A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation

Development of in silico models that capture progression of diseases in soft biological tissues are intrinsic in the validation of the hypothesized cellular and molecular mechanisms involved in the respective pathologies. In addition, they also aid in patient-specific adaptation of interventional procedures. In this regard, a fully-coupled high-fidelity Lagrangian finite element framework is proposed within this work which replicates the pathology of in-stent restenosis observed post stent implantation in a coronary artery. Advection-reaction-diffusion equations are set up to track the concentrations of the platelet-derived growth factor, the transforming growth factor-β, the extracellular matrix, and the density of the smooth muscle cells. A continuum mechanical description of volumetric growth involved in the restenotic process, coupled to the evolution of the previously defined vessel wall constituents, is presented. Further, the finite element implementation of the model is discussed, and the behavior of the computational model is investigated via suitable numerical examples. Qualitative validation of the computational model is presented by emulating a stented artery. Patient-specific data are intended to be integrated into the model to predict the risk of in-stent restenosis, and thereby assist in the tuning of stent implantation parameters to mitigate the risk.

Fluid-structure interaction (FSI) simulation for studying the impact of atherosclerosis on hemodynamics, arterial tissue remodeling, and initiation risk of intracranial aneurysms

The biomechanical and hemodynamic effects of atherosclerosis on the initiation of intracranial aneurysms (IA) are not yet clearly discovered. Also, studies for the observation of hemodynamic variation due to atherosclerotic stenosis and its impact on arterial remodeling and aneurysm genesis remain a controversial field of vascular engineering. The majority of studies performed are relevant to computational fluid dynamic (CFD) simulations. CFD studies are limited in consideration of blood and arterial tissue interactions. In this work, the interaction of the blood and vessel tissue because of atherosclerotic occlusions is studied by developing a fluid and structure interaction (FSI) analysis for the first time. The FSI presents a semi-realistic simulation environment to observe how the blood and vessels' structural interactions can increase the accuracy of the biomechanical study results. In the first step, many different intracranial vessels are modeled for an investigation of the biomechanical and hemodynamic effects of atherosclerosis in arterial tissue remodeling. Three physiological conditions of an intact artery, the artery with intracranial atherosclerosis (ICAS), and an atherosclerotic aneurysm (ACA) are employed in the models with required assumptions. Finally, the obtained outputs are studied with comparative and statistical analyses according to the intact model in a normal physiological condition. The results show that existing occlusions in the cross-sectional area of the arteries play a determinative role in changing the hemodynamic behavior of the arterial segments. The undesirable variations in blood velocity and pressure throughout the vessels increase the risk of arterial tissue remodeling and aneurysm formation.

A Hybrid Reactive Multiphasic Mixture With a Compressible Fluid Solvent

Mixture theory is a general framework that has been used to model mixtures of solid, fluid, and solute constituents, leading to significant advances in modeling the mechanics of biological tissues and cells. Though versatile and applicable to a wide range of problems in biomechanics and biophysics, standard multiphasic mixture frameworks incorporate neither dynamics of viscous fluids nor fluid compressibility, both of which facilitate the finite element implementation of computational fluid dynamics solvers. This study formulates governing equations for reactive multiphasic mixtures where the interstitial fluid has a solvent which is viscous and compressible. This hybrid reactive multiphasic framework uses state variables that include the deformation gradient of the porous solid matrix, the volumetric strain and rate of deformation of the solvent, the solute concentrations, and the relative velocities between the various constituents. Unlike standard formulations which employ a Lagrange multiplier to model fluid pressure, this framework requires the formulation of a function of state for the pressure, which depends on solvent volumetric strain and solute concentrations. Under isothermal conditions the formulation shows that the solvent volumetric strain remains continuous across interfaces between hybrid multiphasic domains. Apart from the Lagrange multiplier-state function distinction for the fluid pressure, and the ability to accommodate viscous fluid dynamics, this hybrid multiphasic framework remains fully consistent with standard multiphasic formulations previously employed in biomechanics. With these additional features, the hybrid multiphasic mixture theory makes it possible to address a wider range of problems that are important in biomechanics and mechanobiology.

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.

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.

Numerical analysis of the hemodynamics of rat aorta based on magnetic resonance imaging and fluid-structure interaction

Murine models have been widely used to investigate the mechanobiology of aortic atherosclerosis and dissections, which develop preferably at different anatomic locations of aorta. Based MRI and finite element analysis with fluid-structure interaction, we numerically investigated factors that may affect the blood flow and structural mechanics of rat aorta. The results indicated that aortic root motion greatly increases time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), relative residence time (RRT), displacement of the aorta, and enhances helical flow pattern but has limited influence on effective stress, which is highly modulated by blood pressure. Moreover, the influence of the motion component on these indicators is different with axial motion more obvious than planar motion. Surrounding fixation of the intercostal arteries and the branch vessels on aortic arch would reduce the influence of aortic root motion. The compliance of the aorta has different influences at different regions, leading to decrease in TAWSS and helical flow, increase in OSI, RRT at the aortic arch, but has reversed effects on the branch vessels. When compared with the steady flow, the pulsatile blood flow would obviously increase the WSS, the displacement, and the effective stress in most regions. In conclusion, to accurately quantify the blood flow and structural mechanics of rat aorta, the motion of the aortic root, the compliance of aortic wall, and the pulsation of blood flow should be considered. However, when only focusing on the effective stress in rat aorta, the motion of the aortic root may be neglected.

Simultaneous measurements of 3D wall shear stress and pulse wave velocity in the murine aortic arch

PURPOSE

Wall shear stress (WSS) and pulse wave velocity (PWV) are important parameters to characterize blood flow in the vessel wall. Their quantification with flow-sensitive phase-contrast (PC) cardiovascular magnetic resonance (CMR), however, is time-consuming. Furthermore, the measurement of WSS requires high spatial resolution, whereas high temporal resolution is necessary for PWV measurements. For these reasons, PWV and WSS are challenging to measure in one CMR session, making it difficult to directly compare these parameters. By using a retrospective approach with a flexible reconstruction framework, we here aimed to simultaneously assess both PWV and WSS in the murine aortic arch from the same 4D flow measurement.

METHODS

Flow was measured in the aortic arch of 18-week-old wildtype (n = 5) and ApoE-/- mice (n = 5) with a self-navigated radial 4D-PC-CMR sequence. Retrospective data analysis was used to reconstruct the same dataset either at low spatial and high temporal resolution (PWV analysis) or high spatial and low temporal resolution (WSS analysis). To assess WSS, the aortic lumen was labeled by semi-automatically segmenting the reconstruction with high spatial resolution. WSS was determined from the spatial velocity gradients at the lumen surface. For calculation of the PWV, segmentation data was interpolated along the temporal dimension. Subsequently, PWV was quantified from the through-plane flow data using the multiple-points transit-time method. Reconstructions with varying frame rates and spatial resolutions were performed to investigate the influence of spatiotemporal resolution on the PWV and WSS quantification.

RESULTS

4D flow measurements were conducted in an acquisition time of only 35 min. Increased peak flow and peak WSS values and lower errors in PWV estimation were observed in the reconstructions with high temporal resolution. Aortic PWV was significantly increased in ApoE-/- mice compared to the control group (1.7 ± 0.2 versus 2.6 ± 0.2 m/s, p < 0.001). Mean WSS magnitude values averaged over the aortic arch were (1.17 ± 0.07) N/m2 in wildtype mice and (1.27 ± 0.10) N/m2 in ApoE-/- mice.

CONCLUSION

The post processing algorithm using the flexible reconstruction framework developed in this study permitted quantification of global PWV and 3D-WSS in a single acquisition. The possibility to assess both parameters in only 35 min will markedly improve the analyses and information content of in vivo measurements.

Preclinical techniques to investigate exercise training in vascular pathophysiology

Atherosclerosis is a dynamic process starting with endothelial dysfunction and inflammation and eventually leading to life-threatening arterial plaques. Exercise generally improves endothelial function in a dose-dependent manner by altering hemodynamics, specifically by increased arterial pressure, pulsatility, and shear stress. However, athletes who regularly participate in high-intensity training can develop arterial plaques, suggesting alternative mechanisms through which excessive exercise promotes vascular disease. Understanding the mechanisms that drive atherosclerosis in sedentary versus exercise states may lead to novel rehabilitative methods aimed at improving exercise compliance and physical activity. Preclinical tools, including in vitro cell assays, in vivo animal models, and in silico computational methods, broaden our capabilities to study the mechanisms through which exercise impacts atherogenesis, from molecular maladaptation to vascular remodeling. Here, we describe how preclinical research tools have and can be used to study exercise effects on atherosclerosis. We then propose how advanced bioengineering techniques can be used to address gaps in our current understanding of vascular pathophysiology, including integrating in vitro, in vivo, and in silico studies across multiple tissue systems and size scales. Improving our understanding of the antiatherogenic exercise effects will enable engaging, targeted, and individualized exercise recommendations to promote cardiovascular health rather than treating cardiovascular disease that results from a sedentary lifestyle.

Image-based morphometric studies of human coronary artery bifurcations with/without coronary artery disease

It is of great clinical significance to study the relationship between coronary bifurcation's morphometrical feature change and coronary artery disease (CAD) lesion. The purpose of this study is to determine the morphological changes in patients with CAD lesion when compared with non-CAD subjects and to find indicators that may be used for cardiovascular disease diagnosis. Computed tomography angiography images from Southern Chinese populations were used to reconstruct three-dimensional coronary arterial trees. Murray's law was introduced to assess the level of deviation of the realistic vascular networks from their optimal state. The results showed CAD Left had the highest deviation values of ARR (0.2552 ± 0.0071 ) and DERR (0.5059 ± 0.0098 ), while non-CAD Right had the lowest values (ARR : 0.1892 ± 0.0066 and DERR : 0.3733 ± 0.0092 , respectively). Moreover, the slope values of the ratio between D m 3 and D s 3 + D l 3 for non-CAD Left, CAD Left, non-CAD Right, and CAD Right were 0.7428, 0.7004, 0.7628, and 0.7577, respectively. Theoretically, the slope value should equal to 1 when the bifurcation structure is in its optimal state. Therefore, these results indicated that coronary bifurcations with CAD lesion deviated from the optimal structure further than those without CAD lesion and coronary bifurcations in right were closer to the optimal structure than those in left. More importantly, the present study found that DERR and AER depended only on the diseased state, but not age, suggesting that DERR and AER were potentially used as two novel indicators for early CAD diagnosis.

Phenethyl Isothiocyanate Protects against High Fat/Cholesterol Diet-Induced Obesity and Atherosclerosis in C57BL/6 Mice

This study concerns obesity-related atherosclerosis, hyperlipidemia, and chronic inflammation. We studied the anti-obesity and anti-atherosclerosis effects of phenethyl isothiocyanate (PEITC) and explored their underlying mechanisms. We established an animal model of high fat/cholesterol-induced obesity in C57BL/6 mice fed for 13 weeks. We divided the mice into five groups: control (CON), high fat/cholesterol (HFCD), HFCD with 3 mg/kg/day gallic acid (HFCD + G), and HFCD with PEITC (30 and 75 mg/kg/day; HFCD + P30 and P75). The body weight, total cholesterol, and triglyceride were significantly lower in the HFCD + P75 group than in the HFCD group. Hepatic lipid accumulation and atherosclerotic plaque formation in the aorta were significantly lower in both HFCD + PEITC groups than in the HFCD group, as revealed by hematoxylin and eosin (H&E) staining. To elucidate the mechanism, we identified the expression of genes related to inflammation, reverse cholesterol transport, and lipid accumulation pathway in the liver. The expression levels of peroxisome proliferator activated receptor gamma (PPARγ), liver-X-receptor α (LXR-α), and ATP binding cassette subfamily A member 1 (ABCA1) were increased, while those of scavenger receptor A (SR-A1), cluster of differentiation 36 (CD36), and nuclear factor-kappa B (NF-κB) were decreased in the HFCD + P75 group compared with those in the HFCD group. Moreover, PEITC modulated H3K9 and H3K27 acetylation, H3K4 dimethylation, and H3K27 di-/trimethylation in the HFCD + P75 group. We, therefore, suggest that supplementation with PEITC may be a potential candidate for the treatment and prevention of atherosclerosis and obesity.

An integrated approach to simulating the vulnerable atherosclerotic plaque

Analyses of individual atherosclerotic plaques are mostly descriptive, relying, for example, on histological classification by spectral analysis of ultrasound waves or staining and observing particular cellular components. Such passive methods have proved useful for characterizing the structure and vulnerability of plaques but have little quantitative predictive power. Our aim is to introduce and discuss a computational framework to provide insight to clinicians and help them visualize internal plaque dynamics. We use partial differential equations (PDEs) with macrophages, necrotic cells, oxidized lipids, oxygen concentration, and platelet-derived growth factor (PDGF) as primary variables coupled to a biomechanical model to describe vessel growth. The model is deterministic, providing mechanical, morphological, and histological characteristics of an atherosclerotic vessel at any desired future time point. We use our model to create computer-generated animations of a plaque evolution that are in qualitative agreement with published serial ultrasound images and hypothesize possible atherogenic mechanisms. A systems biology model consisting of five differential equations is able to capture the morphology of necrotic cores residing within vulnerable atherosclerotic plaque. In the context of the model, the distribution of oxidized low-density lipoprotein (Ox-LDL) particles, endothelial inflammation, plaque oxygenation (via the presence of vasa vasora), and intimal oxygenation are four important factors that drive changes in core morphology.NEW & NOTEWORTHY In this article, we propose a quantitative framework to describe the evolution of atherosclerotic plaque. We use partial differential equations (PDEs) with macrophages, necrotic cells, oxidized lipids, oxygen concentration, and PDGF as primary variables coupled to a biomechanical model to describe vessel growth. A feature of our method is that it outputs color-coded vessel sections corresponding to regions of the plaque that are necrotic and fibrous, qualitatively similar to images generated by enhanced intravascular ultrasound.

Gut microbiota in atherosclerosis: focus on trimethylamine N-oxide

The increasing prevalence of cardiovascular diseases cannot adequately be explained by traditional risk factors. Recently, accumulating evidence has suggested that gut microbiota‐derived numerous metabolites are contributors to atherosclerotic events. Among them, the role of trimethylamine N‐oxide (TMAO) in promoting atherosclerosis has gained attention. TMAO is reported to exert the proatherogenic effects by impacting on the traditional risk factors of atherosclerosis and is associated with high risk of cardiovascular events. Besides that, TMAO is involved in the complex pathological processes of atherosclerotic lesion formation, such as endothelial dysfunction, platelet activation and thrombus generation. In light of these promising findings, TMAO may serve as a potential target for atherosclerosis prevention and treatment, which is conceptually novel, when compared with existing traditional treatments. It is likely that regulating TMAO production and associated gut microbiota may become a promising strategy for the anti‐atherosclerosis therapy.

Coronary artery plaque growth: A two-way coupled shear stress-driven model

Atherosclerosis in coronary arteries can lead to plaque growth, stenosis formation, and blockage of the blood flow supplying the heart tissue. Several studies have shown that hemodynamics play an important role in the growth of coronary artery plaques. Specifically, low wall shear stress (WSS) appears to be the leading hemodynamic parameter promoting atherosclerotic plaque growth, which in turn influences the blood flow and WSS distribution. Therefore, a two-way coupled interaction exists between WSS and atherosclerosis growth. In this work, a computational framework was developed to study the coupling between WSS and plaque growth in coronary arteries. Computational fluid dynamics (CFD) was used to quantify WSS distribution. Surface mesh nodes were moved in the inward normal direction according to a growth model based on WSS. After each growth stage, the geometry was updated and the CFD simulation repeated to find updated WSS values for the next growth stage. One hundred twenty growth stages were simulated in an idealized tube and an image-based left anterior descending artery. An automated framework was developed using open-source software to couple CFD simulations with growth. Changes in plaque morphology and hemodynamic patterns during different growth stages are presented. The results show larger plaque growth towards the downstream segment of the plaque, agreeing with the reported clinical observations. The developed framework could be used to establish hemodynamic-driven growth models and study the interaction between these processes.

A Spatially Resolved and Quantitative Model of Early Atherosclerosis

Atherosclerosis is a major burden for all societies, and there is a great need for a deeper understanding of involved key inflammatory, immunological and biomechanical processes. A decisive step for the prevention and medical treatment of atherosclerosis is to predict what conditions determine whether early atherosclerotic plaques continue to grow, stagnate or become regressive. The driving biological and mechanobiological mechanisms that determine the stability of plaques are yet not fully understood. We develop a spatially resolved and quantitative mathematical model of key contributors of early atherosclerosis. The stability of atherosclerotic model plaques is assessed to identify and classify progression-prone and progression-resistant atherosclerotic regions based on measurable or computable in vivo inputs, such as blood cholesterol concentrations and wall shear stresses. The model combines Darcy's law for the transmural flow through vessels walls, the Kedem-Katchalsky equations for endothelial fluxes of lipoproteins, a quantitative model of early plaque formation from a recent publication and a novel submodel for macrophage recruitment. The parameterization and analysis of the model suggest that the advective flux of lipoproteins through the endothelium is decisive, while the influence of the advective transport within the artery wall is negligible. Further, regions in arteries with an approximate wall shear stress exposure below 20% of the average exposure and their surroundings are potential regions where progression-prone atherosclerotic plaques develop.