Well-posedness of a mathematical model of diabetic atherosclerosis with advanced glycation end-products

Abstract

Atherosclerosis is a leading cause of death worldwide; it emerges as a result of multiple dynamical cell processes, including hemodynamics, endothelial damage, innate immunity and sterol biochemistry. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation, diabetic patients are twice as likely to have a heart attack or stroke. The pathophysiology of diabetic vascular disease is generally understood. Dyslipidemia with increased levels of atherogenic low-density lipoprotein, hyperglycemia, oxidative stress and increased inflammation are factors that increase the risk and accelerate development of atherosclerosis. In a recent paper, Xie [Well-posedness of a mathematical model of diabetic atherosclerosis. J Math Anal Appl. 2022;505(2):125606], we have developed a mathematical model that includes the effect of hyperglycemia and insulin resistance on plaque growth. In this paper, we propose a more comprehensive mathematical model for diabetic atherosclerosis which include more variables; in particular, it includes the variable for Advanced Glycation End-Products (AGEs) concentration. Hyperglycemia trigger vascular damage by forming AGEs, which are not easily metabolized and may accelerate the progression of vascular disease in diabetic patients. The model is given by a system of partial differential equations (PDEs) with a free boundary. We also establish the local existence and uniqueness of solution to the model. The methodology is to reduce the free boundary to a fixed boundary and the system of PDEs to an abstract evolution equation in Banach spaces, and apply the theory of analytic semigroup.

Keywords:

• Diabetes
• atherosclerosis
• free boundary problem
• abstract evolution equation

1991 Mathematics Subject Classifications:

• Primary: 35Q35
• 92C50

Acknowledgments

The content is solely the responsibility of the author and does not necessarily represent the official views of the National Institute of Health.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Research reported in this paper was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number UL1GM118973.