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.
Keywords: mathematical model; morphoelasticity; necrotic core; simulation; vulnerable plaque.