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Mathematical model of atherosclerotic aneurysm

Guoyi Ke1, Chetan Hans2, Gunjan Agarwal3

  • 1Department of Mathematics and Physical Sciences, Louisiana State University at Alexandria, Alexandria, LA 71302, USA.

Mathematical Biosciences and Engineering : MBE
|March 24, 2021
PubMed

Insights

Atherosclerosis significantly contributes to abdominal aortic aneurysms (AAA). A new mathematical model identifies a cholesterol and DDR1 biomarker for AAA risk and evaluates treatments, suggesting drug dosage is key to slowing progression.

Area of Science:

  • Biomedical Engineering
  • Cardiovascular Research
  • Mathematical Modeling

Background:

  • Atherosclerosis is a primary driver of abdominal aortic aneurysms (AAA), affecting up to 80% of patients.
  • Understanding the interplay between atherosclerosis and AAA is crucial for effective patient treatment.

Purpose of the Study:

  • To develop a mathematical model simulating atherosclerotic aneurysm progression.
  • To identify biomarkers for assessing atherosclerotic aneurysm risk.
  • To evaluate the efficacy of potential treatment strategies.

Main Methods:

  • Development of a mathematical model using partial differential equations with free boundaries.
  • Incorporation of multi-layered arterial wall structure and atherosclerotic pathophysiology.
  • Analysis of cholesterol ratio and DDR1 levels as risk biomarkers.

Main Results:

  • Identification of a 2D biomarker (cholesterol ratio and DDR1 level) for atherosclerotic aneurysm risk.
  • The model demonstrates that anti-cholesterol drug dosage is critical for slowing disease progression.
  • Combined anti-cholesterol therapy with anti-DDR1 injections shows potential for further risk reduction.

Conclusions:

  • The developed mathematical model provides insights into atherosclerotic aneurysm progression.
  • Cholesterol ratio and DDR1 levels serve as valuable biomarkers for risk assessment.
  • Treatment strategies involving cholesterol-lowering drugs and DDR1 inhibition are promising for managing atherosclerotic aneurysms.

Keywords:
anti-DDR1 injectionanti-cholesterol drugsatherosclerotic aneurysmscholesterol ratio and DDR1 levelfree boundariesmathematical model

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