Mathematical modeling of plaque progression and associated microenvironment: How far from predicting the fate of atherosclerosis?

• We summarize the current ‘state of the art’ on the mathematical modeling of the effects of biomechanical factors and microenvironmental factors on the plaque progression, and its potential help in prediction of plaque development. • We present an outlook on open problems and multiple challenges that require novel modelling techniques and more integrations with experimental and clinical investigations. Mathematical modeling contributes to pathophysiological research of atherosclerosis by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. In turn, the complexity of atherosclerosis is well suited to quantitative approaches as it provides challenges and opportunities for new developments of modeling. In this review, we summarize the current ‘state of the art’ on the mathematical modeling of the effects of biomechanical factors and microenvironmental factors on the plaque progression, and its potential help in prediction of plaque development. We begin with models that describe the biomechanical environment inside and outside the plaque and its influence on its growth and rupture. We then discuss mathematical models that describe the dynamic evolution of plaque microenvironmental factors, such as lipid deposition, inflammation, smooth muscle cells migration and intraplaque hemorrhage, followed by studies on plaque growth and progression using these modelling approaches. Moreover, we present several key questions for future research. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving plaque vulnerability and propose future potential direction in therapy for cardiovascular disease.