A multiscale modeling study of nanoparticle-based targeting therapy against atherosclerosis.

Although researches on nanoparticle-based (NP-based) drug delivery system for atherosclerosis treatment have grown rapidly in recent years, there are limited studies in quantifying the effects of targeting drugs on plaque components and microenvironment. The purpose of the present study was to quantitatively assess the targeting therapeutic effects against atherosclerosis by establishing a multiscale mathematical model. The multiscale model involved subcellular, cellular and microenvironmental scales to simulate lipid catabolism, macrophage behaviors and dynamics of microenvironmental components, respectively. In vitro and in vivo experimental data were integrated into the mathematical model according to Bayesian statistics, in order to evaluate the therapeutic effects of a proposed NP-based platform for macrophage-specific delivery to simultaneously deliver SR-A siRNA (to reduce LDL uptake) and LXR-L (to stimulate cholesterol efflux). Dosage variation analysis was then performed to investigate the drug efficacy under varied dosage combinations of SR-A siRNA and LXR-L. The simulation results demonstrated that the dynamics of the microenvironmental components presented different developments in Untreated and Treated groups. We also found that the balance of lipid metabolism between uptake and efflux resulted in the improvement of lipid and inflammatory microenvironment, consequently in the plaque regression. In addition, the model predicted optimized dosage combinations according to the co-effect analysis of the two drugs on the lipid microenvironment. This study suggests that multiscale modeling can be a powerful quantitative tool for estimating the therapeutic effects of targeting drugs for plaque regression and designing the enhanced treatment strategies against atherosclerosis.

Shear stress and plaque microenvironment induce heterogeneity: A multiscale microenvironment evolution model.

BACKGROUND: Both clinical images and in vivo observations have demonstrated the heterogeneity in atherosclerotic plaque composition. However, the quantitative mechanisms that contribute to the heterogeneity, such as the wall shear stress (WSS) and the interplays among microenvironmental factors are still unclear. METHODS: We develop a multiscale model coupling computational fluid dynamics, interactions of microenvironmental factors and evolutions of cellular behaviors to investigate the formation of plaque heterogeneity in a three-dimensional vessel segment. The model involves WSS, lipid deposition and inflammatory response to reveal the dynamic balance existed between the lipid metabolism and the phagocytosis of macrophages. RESULTS: The dynamic balance in microenvironment is influenced by both the WSS and the interactions with microenvironmental factors, and consequently results in the longitudinal heterogeneity observed in plaque pathology. In addition, plaque heterogeneity can be reduced by decreasing low WSS area at downstream, as well as by altering the phagocytic abilities of macrophage on lipoproteins, which may be used to develop future plaque regression strategies. CONCLUSIONS: This multiscale modeling provides a framework to understand the mechanisms in dynamics of plaque composition and also provides quantitative information to better risk stratification of plaque vulnerability in future clinical practice.

Macrophage polarization as a potential therapeutic target for atherosclerosis: a dynamic stochastic modelling study.

We proposed a dynamic stochastic mathematical model to evaluate the role of macrophage polarization in plaque development. The dynamic process of macrophages from proliferation to death was simulated under different lipid microenvironments. The probability of macrophage phenotypic switching was described using a Bernoulli distribution where the stochastic variable was determined by the local lipid level. Moreover, the interactions between macrophages and microenvironmental factors vary with macrophage phenotype. We investigated the distribution of key microenvironmental factors, the dynamics of macrophage polarization and its influence on foam cell formation. M1 macrophages were found to predominate in advanced plaque corresponding to the exacerbated inflammation observed in mice experiments. The imbalance between the deposition of oxidized low-density lipoprotein and phagocytic effects of macrophages governed the formation of foam cells. Furthermore, we simulated targeted therapies by either directly inhibiting the polarization probability to M1 macrophages or indirectly regulating macrophage polarization due to high-density lipoprotein levels. Comparison of simulation results with experimental findings in both therapies indicated that the intervention and regulation of macrophage polarization could influence plaque microenvironment and subsequently induce plaque regression, especially in the early stage. The proposed modelling system can facilitate the evaluation of novel therapies targeting macrophage polarization.

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

[This corrects the article DOI: 10.1371/journal.pcbi.1008344.].

Role of vascular smooth muscle cell phenotypic switching in plaque progression: A hybrid modeling study.

Growing genetic lineage mapping experiments have definitively shown a wide-ranging plasticity of vascular smooth muscle cells (VSMCs) in atherosclerotic plaque and suggested that VSMCs can modulate their phenotypes in response to plaque microenvironment. Here, a multiscale hybrid discrete-continuous (HDC) modeling system is established to investigate the complex role of VSMC phenotypic switching within atherosclerotic lesions. The cellular behaviors of VSMCs and macrophages, including proliferation, migration, phenotypic transformation and necrosis, are determined by cellular automata (CA) rules in discrete model. While the dynamics of plaque microenvironmental factors, such as lipid, extracellular matrix (ECM) and chemokines, are described by continuous reaction-diffusion equations in macroscopy. The simulation results demonstrate how the VSMC activities change the extracellular microenvironment and consequently affect the plaque morphology and stability. The regulation of VSMC phenotypes can affect not only the plaque morphology (necrotic core size and fibrous cap thickness) but also the deposition and distribution of microenvironmental factors (lipoprotein, ECM, and chemokines). In addition, it is found that plaque vulnerability can be inhibited by blocking VSMC transdifferentiation to a macrophage-like state and promoting it to a myofibroblastic phenotype, which suggests that targeting VSMC phenotypic switching could be a potential and promising therapeutic strategy for atherosclerosis.

Mathematical modeling of intraplaque neovascularization and hemorrhage in a carotid atherosclerotic plaque.

BACKGROUND: Growing experimental evidence has identified neovascularization from the adventitial vasa vasorum and induced intraplaque hemorrhage (IPH) as critical indicators during the development of vulnerable atherosclerotic plaques. In this study, we propose a mathematical model incorporating intraplaque angiogenesis and hemodynamic calculation of the microcirculation, to obtain the quantitative evaluation of the influences of intraplaque neovascularization and hemorrhage on vulnerable plaque development. A two-dimensional nine-point model of angiogenic microvasculature is generated based on the histology of a patient's carotid plaque. The intraplaque angiogenesis model includes three key cells (endothelial cells, smooth muscle cells, and macrophages) and three key chemical factors (vascular endothelial growth factors, extracellular matrix, and matrix metalloproteinase), which densities and concentrations are described by a series of reaction-diffusion equations. The hemodynamic calculation by coupling the intravascular blood flow, the extravascular plasma flow, and the transvascular transport is carried out on the generated angiogenic microvessel network. We then define the IPH area by using the plasma concentration in the interstitial tissue, as well as the extravascular transport across the capillary wall. RESULTS: The simulational results reproduce a series of pathophysiological phenomena during the atherosclerotic plaque progression. It is found that the high microvessel density region at the shoulder areas and the extravascular flow across the leaky wall of the neovasculature contribute to the IPH observed widely in vulnerable plaques. The simulational results are validated by both the in vivo MR imaging data and in vitro experimental observations and show significant consistency in quantity ground. Moreover, the sensitivity analysis of model parameters reveals that the IPH area and extent can be reduced significantly by decreasing the MVD and the wall permeability of the neovasculature. CONCLUSIONS: The current quantitative model could help us to better understand the roles of microvascular and intraplaque hemorrhage during the carotid plaque progression.

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.

[Biomechanical models and numerical studies of atherosclerotic plaque].

Atherosclerosis is a complex and multi-factorial pathophysiological process. Researches over the past decades have shown that the development of atherosclerotic vulnerable plaque is closely related to its components, morphology, and stress status. Biomechanical models have been developed by combining with medical imaging, biological experiments, and mechanical analysis, to study and analyze the biomechanical factors related to plaque vulnerability. Numerical simulation could quantify the dynamic changes of the microenvironment within the plaque, providing a method to represent the distribution of cellular and acellular components within the plaque microenvironment and to explore the interaction of lipid deposition, inflammation, angiogenesis, and other processes. Studying the pathological mechanism of plaque development would improve our understanding of cardiovascular disease and assist non-invasive inspection and early diagnosis of vulnerable plaques. The biomechanical models and numerical methods may serve as a theoretical support for designing and optimizing treatment strategies for vulnerable atherosclerosis.