WELL-POSEDNESS OF A MATHEMATICAL MODEL OF DIABETIC ATHEROSCLEROSIS WITH ADVANCED GLYCATION END-PRODUCTS

Area of Science:

• Biomedical Engineering
• Mathematical Biology
• Cardiovascular Research

Background:

• Atherosclerosis is a major global cause of death, influenced by hemodynamics, immunity, and biochemistry.
• Diabetes significantly exacerbates atherosclerosis, increasing inflammation and cardiovascular event risk.
• Existing models inadequately capture the full complexity of diabetic atherosclerosis.

Purpose of the Study:

• To develop a comprehensive mathematical model for diabetic atherosclerosis.
• To incorporate the role of Advanced Glycation End-Products (AGEs) in diabetic vascular disease progression.
• To analyze the impact of hyperglycemia-induced AGEs on plaque growth.

Main Methods:

• Developed a mathematical model using partial differential equations with a free boundary.
• Employed Hanzawa transformation to convert the free boundary to a fixed boundary.
• Reduced the system to an abstract evolution equation in Banach spaces, applying analytic semigroup theory.

Main Results:

• Established local existence and uniqueness of solutions for the proposed model.
• The model accounts for hyperglycemia, insulin resistance, and AGEs concentration.
• Provides a framework for studying diabetic atherosclerosis dynamics.

Conclusions:

• The new mathematical model offers a more comprehensive understanding of diabetic atherosclerosis.
• Advanced Glycation End-Products (AGEs) play a crucial role in accelerating vascular disease in diabetic patients.
• The mathematical framework supports further investigation into diabetic vascular complications.