WELL-POSEDNESS OF A MATHEMATICAL MODEL OF DIABETIC ATHEROSCLEROSIS

Area of Science:

• Cardiovascular Science
• Mathematical Biology
• Diabetes Research

Background:

• Atherosclerosis is a major global cause of death, driven by complex cellular processes.
• Diabetes exacerbates atherosclerosis by increasing inflammation and altering cellular functions, leading to higher risks of heart attack and stroke.
• Existing knowledge of diabetic vascular disease lacks a mathematical model for plaque growth.

Purpose of the Study:

• To propose a novel mathematical model for diabetic atherosclerosis.
• To incorporate the effects of diabetes on plaque growth within a dynamic system.
• To analyze the mathematical underpinnings of diabetic atherosclerosis progression.

Main Methods:

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

Main Results:

• Established the local existence and uniqueness of solutions for the proposed mathematical model.
• Provided a rigorous mathematical framework for studying diabetic atherosclerosis.
• Demonstrated the feasibility of using advanced mathematical techniques to model complex biological processes.

Conclusions:

• The developed mathematical model offers a new tool for understanding diabetic atherosclerosis.
• This work bridges the gap between the pathophysiology of diabetic vascular disease and mathematical modeling.
• The methodology provides a foundation for future research into diabetes-related cardiovascular complications.