A lipid-structured model for macrophage populations in atherosclerotic plaques

Genesis of intimal thickening due to hemodynamical shear stresses

This paper investigates intimal growth in arteries, induced by hemodynamical shear stress, through finite element simulation using the FEniCS computational environment. In our model, the growth of the intima depends on cross-section geometry and shear stress. In this work, the arterial wall is modeled as three distinct layers: the intima, the media and the adventitia, each with different mechanical properties. We assume that the cross-section of the vessel does not change in the axial direction. We further assume that the blood flow is steady, non-turbulent and unidirectional. Blood flow induces shear stress on the endothelium and stimulates the release of platelet derived growth factor (PDGF) which drives the growth. We simulate intimal growth for three distinct arterial cross section geometries. We show that the qualitative nature of intimal thickening varies depending on arterial geometry. For cross section geometries that are annular, the growth of the intima is uniform in the angular direction, and the endothelium stays circular as the intima grows. For non-annular cross section geometries, the intima grows more quickly where it is thicker, and shear stress and intimal thickening are negatively correlated with the distance from the flow center, where the flow velocity is maximal. Over time, the maxima and minima of the curvature increase and decrease, respectively, the PDGF concentration increases and the lumen becomes more polygonal. The model provides a framework for coupling hemodynamics simulations to mathematical descriptions of atherosclerosis, both of which have been modeled separately in great detail.

Exploring relationship between hypercholesterolemia and instability of atherosclerotic plaque - An approach based on a matrix population model

Background: Cardiovascular diseases have long been studied to identify their causal factors and counteract them effectively. Atherosclerosis, an inflammatory process of the blood vessel wall, is a common cardiovascular disease. Among the many well-known risk factors, hypercholesterolemia is undoubtedly a significant condition for atherosclerotic plaque formation and is linked to atherosclerosis on many levels, i.e. cell interactions, cytokines levels, diet, and lifestyle. Current studies suggest that controlling balance between proinflammatory (M1) and anti-inflammatory (M2) types of macrophages may be used for patient condition improvement and necrotic core reduction. Methods: This study considered the effects of hypercholesterolemia on the population dynamics of macrophages (M0, M1, M2, foam cells) in atherosclerotic plaque. A mathematical model using a matrix approach to population dynamics was proposed and tested in various scenarios. In order to check model sensitivity and variability associated with error propagation, the uncertainty analysis was performed based on the Monte Carlo approach. Results: Simulations of macrophage population dynamics provided the assessment of necrotic core development and plaque instability. Excess lipid levels emerged as the most critical factor for necrotic core development. However, plaque growth can be significantly slowed if macrophages and foam cells can maintain proper lipid levels. This balance may be disrupted by proinflammatory lipids that eventually will increase plaque size, what is also reflected by M1/M2 dynamics. Conclusion: Hypercholesterolemia accelerates atherosclerosis development, leading to earlier cardiovascular incidents. In silico results suggest that reducing lipid intake and portion of proinflammatory lipids is crucial to slowing plaque development and reducing rupture risk, all of which requires preserving fragile M1/M2 balance. Targeting the inflammatory microenvironment and macrophage polarization represents a promising approach for atherosclerosis management.

Blood Lipoproteins Shape the Phenotype and Lipid Content of Early Atherosclerotic Lesion Macrophages: A Dual-Structured Mathematical Model

Macrophages in atherosclerotic lesions exhibit a spectrum of behaviours or phenotypes. The phenotypic distribution of monocyte-derived macrophages (MDMs), its correlation with MDM lipid content, and relation to blood lipoprotein densities are not well understood. Of particular interest is the balance between low density lipoproteins (LDL) and high density lipoproteins (HDL), which carry bad and good cholesterol respectively. To address these issues, we have developed a mathematical model for early atherosclerosis in which the MDM population is structured by phenotype and lipid content. The model admits a simpler, closed subsystem whose analysis shows how lesion composition becomes more pathological as the blood density of LDL increases relative to the HDL capacity. We use asymptotic analysis to derive a power-law relationship between MDM phenotype and lipid content at steady-state. This relationship enables us to understand why, for example, lipid-laden MDMs have a more inflammatory phenotype than lipid-poor MDMs when blood LDL lipid density greatly exceeds HDL capacity. We show further that the MDM phenotype distribution always attains a local maximum, while the lipid content distribution may be unimodal, adopt a quasi-uniform profile or decrease monotonically. Pathological lesions exhibit a local maximum in both the phenotype and lipid content MDM distributions, with the maximum at an inflammatory phenotype and near the lipid content capacity respectively. These results illustrate how macrophage heterogeneity arises in early atherosclerosis and provide a framework for future model validation through comparison with single-cell RNA sequencing data.

A Lipid-Structured Model of Atherosclerosis with Macrophage Proliferation

Atherosclerotic plaques are fatty deposits that form in the walls of major arteries and are one of the major causes of heart attacks and strokes. Macrophages are the main immune cells in plaques and macrophage dynamics influence whether plaques grow or regress. Macrophage proliferation is a key process in atherosclerosis, particularly in the development of mid-stage plaques, but very few mathematical models include proliferation. In this paper we reframe the lipid-structured model of Ford et al. (J Theor Biol 479:48-63, 2019. https://doi.org/10.1016/j.jtbi.2019.07.003 ) to account for macrophage proliferation. Proliferation is modelled as a non-local decrease in the lipid structural variable. Steady state analysis indicates that proliferation assists in reducing eventual necrotic core lipid content and spreads the lipid load of the macrophage population amongst the cells. The contribution of plaque macrophages from proliferation relative to recruitment from the bloodstream is also examined. The model suggests that a more proliferative plaque differs from an equivalent (defined as having the same lipid content and cell numbers) recruitment-dominant plaque in the way lipid is distributed amongst the macrophages. The macrophage lipid distribution of an equivalent proliferation-dominant plaque is less skewed and exhibits a local maximum near the endogenous lipid content.

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.

Cluster of Differentiation-44-Targeting Prussian Blue Nanoparticles Onloaded with Colchicine for Atherosclerotic Plaque Regression in a Mice Model

Atherosclerosis management heavily relies on the suppression of the inflammatory response of macrophages. Colchicine's potent anti-inflammatory properties make it a promising candidate for secondary prevention against cardiovascular disease. However, its high toxicity and numerous adverse effects limit its clinical use. To address this, there is an urgent need for specific drug delivery systems to boost the level of accumulation of colchicine within atherosclerotic plaques. In this study, the cluster of differentiation-44 receptor was verified to be overexpressed in inflammatory macrophages within plaques both in vitro and in vivo. Subsequently, a Prussian blue-based nanomedical loading system with hyaluronic acid (HA) coating was constructed, and its effects were observed on the atherosclerosis regression. Colchicine and Cy5.5 were encapsulated within Prussian blue nanoparticles through self-assembly, followed by conjugation with hyaluronic acid to create col@PBNP@HA. The formulated col@PBNP@HA displayed a cubic shape and scattered distribution. Importantly, col@PBNP@HA demonstrated specific cellular uptake into lipopolysaccharide-stimulated macrophages. In vitro experiments showed that col@PBNP@HA more effectively inhibited expression of inflammatory factors and scavenged reactive oxygen species compared with the control group, which were treated with colchicine. Furthermore, col@PBNP@HA exhibited its specific and higher accumulation in aortic plaque analysis via fluorescence imaging of aortas. After 4 weeks, administration of col@PBNP@HA resulted in significant atherosclerosis regression in the mice model, with therapeutic effects superior to those of free colchicine. Similar to colchicine, col@PBNP@HA inhibited the secretion of inflammation factors and scavenged ROS through the regulation of the toll-like receptor 4 (TLR4)/myeloid differentiation factor 88 (Myd88)/nuclear factor kappa-B (NF-κB) and peroxisome proliferator-activated receptor-gamma coactivator-1α (PGC-1α) signaling pathway. In summary, col@PBNP@HA demonstrated specific targeting ability to inflammatory plaques and exerted beneficial effects on atherosclerosis regression through TLR4/Myd88/NF-κB and PGC-1α modulation.

High-Density Lipoprotein Metabolism and Function in Cardiovascular Diseases: What about Aging and Diet Effects?

Cardiovascular diseases (CVDs) have become the leading global cause of mortality, prompting a heightened focus on identifying precise indicators for their assessment and treatment. In this perspective, the plasma levels of HDL have emerged as a pivotal focus, given the demonstrable correlation between plasma levels and cardiovascular events, rendering them a noteworthy biomarker. However, it is crucial to acknowledge that HDLs, while intricate, are not presently a direct therapeutic target, necessitating a more nuanced understanding of their dynamic remodeling throughout their life cycle. HDLs exhibit several anti-atherosclerotic properties that define their functionality. This functionality of HDLs, which is independent of their concentration, may be impaired in certain risk factors for CVD. Moreover, because HDLs are dynamic parameters, in which HDL particles present different atheroprotective properties, it remains difficult to interpret the association between HDL level and CVD risk. Besides the antioxidant and anti-inflammatory activities of HDLs, their capacity to mediate cholesterol efflux, a key metric of HDL functionality, represents the main anti-atherosclerotic property of HDL. In this review, we will discuss the HDL components and HDL structure that may affect their functionality and we will review the mechanism by which HDL mediates cholesterol efflux. We will give a brief examination of the effects of aging and diet on HDL structure and function.

A stochastic lipid structured model for macrophage dynamics in atherosclerotic plaques

We propose to model certain aspects of the dynamics of a macrophage that moves randomly in a one dimensional space in arterial wall tissue and grows by accumulating localized lipid particles, thus reducing its motility. This phenomenon has been observed in the context of atherosclerotic plaque formation. For this purpose, we use a system of stochastic differential equations satisfied by the position and diffusion coefficient of a Brownian particle whose diffusion coefficient is modified at each visit to the origin and with a dumping coefficient. The novelty of the model, with respect to Bénichou et al. (Phys Rev E 85(2):021137, 2012), Meunier et al. (Acta Appl Math 161:107-126, 2019), is to include offloading of lipids through the dumping term. We find explicit necessary and sufficient conditions for macrophage trapping in the locally enriched region.

A Lipid-Structured Model of Atherosclerotic Plaque Macrophages with Lipid-Dependent Kinetics

Atherosclerotic plaques are fatty growths in artery walls that cause heart attacks and strokes. Plaque formation is driven by macrophages that are recruited to the artery wall. These cells consume and remove blood-derived lipids, such as modified low-density lipoprotein. Ineffective lipid removal, due to macrophage death and other factors, leads to the accumulation of lipid-loaded macrophages and formation of a necrotic lipid core. Experimental observations suggest that macrophage functionality varies with the extent of lipid loading. However, little is known about the influence of macrophage lipid loads on plaque fate. Extending work by Ford et al. (J Theor Biol 479:48-63, 2019) and Chambers et al. (A lipid-structured model of atherosclerosis with macrophage proliferation, 2022), we develop a plaque model where macrophages are structured by their ingested lipid load and behave in a lipid-dependent manner. The model considers several macrophage behaviours, including recruitment to and emigration from the artery wall; proliferation and apotosis; ingestion of plaque lipids; and secondary necrosis of apoptotic cells. We consider apoptosis, emigration and proliferation to be lipid-dependent and we model these effects using experimentally informed functions of the internalised lipid load. Our results demonstrate that lipid-dependent macrophage behaviour can substantially alter plaque fate by changing both the total quantity of lipid in the plaque and the distribution of lipid between the live cells, dead cells and necrotic core. The consequences of macrophage lipid-dependence are often unpredictable because lipid-dependent effects introduce subtle, nonlinear interactions between the modelled cell behaviours. These observations highlight the importance of mathematical modelling in unravelling the complexities of macrophage lipid accumulation during atherosclerotic plaque formation.

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.

A new lipid-structured model to investigate the opposing effects of LDL and HDL on atherosclerotic plaque macrophages

Atherosclerotic plaques form in artery walls due to a chronic inflammatory response driven by lipid accumulation. A key component of the inflammatory response is the interaction between monocyte-derived macrophages and extracellular lipid. Although concentrations of low-density lipoprotein (LDL) and high-density lipoprotein (HDL) particles in the blood are known to affect plaque progression, their impact on the lipid load of plaque macrophages remains unexplored. In this paper, we develop a lipid-structured mathematical model to investigate the impact of blood LDL/HDL levels on plaque composition, and lipid distribution in plaque macrophages. A reduced subsystem, derived by summing the equations of the full model, describes the dynamics of biophysical quantities relating to plaque composition (e.g. total number of macrophages, total amount of intracellular lipid). We also derive a continuum approximation of the model to facilitate analysis of the macrophage lipid distribution. The results, which include time-dependent numerical solutions and asymptotic analysis of the unique steady state solution, indicate that plaque lipid content is sensitive to the influx of LDL relative to HDL capacity. The macrophage lipid distribution evolves in a wave-like manner towards an equilibrium profile which may be monotone decreasing, quasi-uniform or unimodal, attaining its maximum value at a non-zero lipid level. Our model also reveals that macrophage uptake may be severely impaired by lipid accumulation. We conclude that lipid accumulation in plaque macrophages may serve as a partial explanation for the defective uptake of apoptotic cells (efferocytosis) often reported in atherosclerotic plaques.

Phenotypic and functional characterization of first-trimester human placental macrophages, Hofbauer cells

Hofbauer cells (HBCs) are a population of macrophages found in high abundance within the stroma of the first-trimester human placenta. HBCs are the only fetal immune cell population within the stroma of healthy placenta. However, the functional properties of these cells are poorly described. Aligning with their predicted origin via primitive hematopoiesis, we find that HBCs are transcriptionally similar to yolk sac macrophages. Phenotypically, HBCs can be identified as HLA-DR-FOLR2+ macrophages. We identify a number of factors that HBCs secrete (including OPN and MMP-9) that could affect placental angiogenesis and remodeling. We determine that HBCs have the capacity to play a defensive role, where they are responsive to Toll-like receptor stimulation and are microbicidal. Finally, we also identify a population of placenta-associated maternal macrophages (PAMM1a) that adhere to the placental surface and express factors, such as fibronectin, that may aid in repair.

Modelling Preferential Phagocytosis in Atherosclerosis: Delineating Timescales in Plaque Development

Atherosclerotic plaques develop over a long time and can cause heart attacks and strokes. There are no simple mathematical models that capture the different timescales of rapid macrophage and lipid dynamics and slow plaque growth. We propose a simple ODE model for lipid dynamics that includes macrophage preference for ingesting apoptotic material and modified low-density lipoproteins (modLDL) over ingesting necrotic material. We use multiple timescale analysis to show that if the necrosis rate is small then the necrotic core in the model plaque may continue to develop slowly even when the lipid levels in plaque macrophages, apoptotic material and modLDL appear to have reached equilibrium. We use the model to explore the effect of macrophage emigration, apoptotic cell necrosis, total rate of macrophage phagocytosis and modLDL influx into the plaque on plaque lipid accumulation.

Macrophage Plasticity and Atherosclerosis Therapy

Atherosclerosis is a chronic disease starting with the entry of monocytes into the subendothelium and the subsequent differentiation into macrophages. Macrophages are the major immune cells in atherosclerotic plaques and are involved in the dynamic progression of atherosclerotic plaques. The biological properties of atherosclerotic plaque macrophages determine lesion size, composition, and stability. The heterogenicity and plasticity of atherosclerotic macrophages have been a hotspot in recent years. Studies demonstrated that lipids, cytokines, chemokines, and other molecules in the atherosclerotic plaque microenvironment regulate macrophage phenotype, contributing to the switch of macrophages toward a pro- or anti-atherosclerosis state. Of note, M1/M2 classification is oversimplified and only represent two extreme states of macrophages. Moreover, M2 macrophages in atherosclerosis are not always protective. Understanding the phenotypic diversity and functions of macrophages can disclose their roles in atherosclerotic plaques. Given that lipid-lowering therapy cannot completely retard the progression of atherosclerosis, macrophages with high heterogeneity and plasticity raise the hope for atherosclerosis regression. This review will focus on the macrophage phenotypic diversity, its role in the progression of the dynamic atherosclerotic plaque, and finally discuss the possibility of treating atherosclerosis by targeting macrophage microenvironment.

A prediction tool for plaque progression based on patient-specific multi-physical modeling

Atherosclerotic plaque rupture is responsible for a majority of acute vascular syndromes and this study aims to develop a prediction tool for plaque progression and rupture. Based on the follow-up coronary intravascular ultrasound imaging data, we performed patient-specific multi-physical modeling study on four patients to obtain the evolutional processes of the microenvironment during plaque progression. Four main pathophysiological processes, i.e., lipid deposition, inflammatory response, migration and proliferation of smooth muscle cells (SMCs), and neovascularization were coupled based on the interactions demonstrated by experimental and clinical observations. A scoring table integrating the dynamic microenvironmental indicators with the classical risk index was proposed to differentiate their progression to stable and unstable plaques. The heterogeneity of plaque microenvironment for each patient was demonstrated by the growth curves of the main microenvironmental factors. The possible plaque developments were predicted by incorporating the systematic index with microenvironmental indicators. Five microenvironmental factors (LDL, ox-LDL, MCP-1, SMC, and foam cell) showed significant differences between stable and unstable group (p < 0.01). The inflammatory microenvironments (monocyte and macrophage) had negative correlations with the necrotic core (NC) expansion in the stable group, while very strong positive correlations in unstable group. The inflammatory microenvironment is strongly correlated to the NC expansion in unstable plaques, suggesting that the inflammatory factors may play an important role in the formation of a vulnerable plaque. This prediction tool will improve our understanding of the mechanism of plaque progression and provide a new strategy for early detection and prediction of high-risk plaques.

Besides the traditional systematic factors, the influences of the local microenvironmental factors on atherosclerotic plaque progression have been demonstrated. Mathematical and computational modeling is an important tool to investigate the complex interplay between plaque progression and the microenvironment, and provides a potential way toward the prediction of plaque vulnerability according to the comprehensive evaluation of both morphological and/or biochemical factors in tissue level with microenvironmental factors in cellular level. We performed patient-specific multi-physical modeling study on four patients to obtain the evolutional processes of the microenvironment during plaque progression and predicted the possible plaque developments. A scoring table integrating the dynamic microenvironmental indicators with the classical risk index was proposed to differentiate their progression to stable and unstable plaques. Based on patient-specific imaging data, the mathematical model will provide a novel method to predict the changes of plaque microenvironment and improve ability to access the personal therapeutic strategy for atherosclerotic plaque.

A multiphase model of growth factor-regulated atherosclerotic cap formation

Atherosclerosis is characterised by the growth of fatty plaques in the inner artery wall. In mature plaques, vascular smooth muscle cells (SMCs) are recruited from adjacent tissue to deposit a collagenous cap over the fatty plaque core. This cap isolates the thrombogenic plaque content from the bloodstream and prevents the clotting cascade that leads to myocardial infarction or stroke. Despite the protective role of the cap, the mechanisms that regulate cap formation and maintenance are not well understood. It remains unclear why some caps become stable, while others become vulnerable to rupture. We develop a multiphase PDE model with non-standard boundary conditions to investigate collagen cap formation by SMCs in response to diffusible growth factor signals from the endothelium. Platelet-derived growth factor stimulates SMC migration, proliferation and collagen degradation, while transforming growth factor (TGF)-[Formula: see text] stimulates SMC collagen synthesis and inhibits collagen degradation. The model SMCs respond haptotactically to gradients in the collagen phase and have reduced rates of migration and proliferation in dense collagenous tissue. The model, which is parameterised using in vivo and in vitro experimental data, reproduces several observations from plaque growth in mice. Numerical and analytical results demonstrate that a stable cap can be formed by a relatively small SMC population and emphasise the critical role of TGF-[Formula: see text] in effective cap formation. These findings provide unique insight into the mechanisms that may lead to plaque destabilisation and rupture. This work represents an important step towards the development of a comprehensive in silico plaque model.