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Steady solution and its stability of a mathematical model of diabetic atherosclerosis

Xuming Xie1

  • 1Department of Mathematics, Morgan State University, Baltimore, MD, USA.

Journal of Biological Dynamics
|September 15, 2023
PubMed

Insights

Diabetes significantly elevates atherosclerosis risk, increasing inflammation and cardiovascular events. Mathematical modeling confirms plaque persistence due to hyperglycemia, even with normal cholesterol levels, highlighting diabetes as a critical risk factor.

Area of Science:

  • Cardiovascular Science
  • Diabetology
  • Mathematical Biology

Background:

  • Atherosclerosis is a major global cause of mortality.
  • Diabetes exacerbates atherosclerosis by increasing inflammation.
  • Diabetic individuals face a doubled risk of heart attack and stroke.

Purpose of the Study:

  • To analyze diabetic atherosclerosis using a simplified mathematical model.
  • To investigate the role of hyperglycemia in plaque persistence.
  • To establish the existence and stability of stationary solutions.

Main Methods:

  • Development of a mathematical model for diabetic atherosclerosis.
  • Inclusion of key biological factors: LDL, HDL, glucose, insulin, ROS, beta cells, macrophages, foam cells.
  • Analysis of a system of partial differential equations with a free boundary.

Main Results:

  • Existence of small, radially symmetric stationary solutions was established.
  • The model demonstrates plaque persistence driven by hyperglycemia.
  • Hyperglycemia's role in atherosclerosis is confirmed even with normal LDL/HDL levels.

Conclusions:

  • Diabetes significantly increases atherosclerosis risk and related inflammation.
  • Hyperglycemia is a key driver for persistent atherosclerotic plaque.
  • Mathematical modeling provides insights into diabetic atherosclerosis mechanisms.

Keywords:
35Q9292C50Atherosclerosisdiabetesfree boundary problemstabilitysteady solution

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