Unraveling Atherosclerosis: A Nonlinear Coupled Mathematical Model with Dual Free Boundaries - Solution and Numerical Insights

Document Type : Research Paper

Authors
Yarong Zhang 1 , 2 , 3
Xiaoya Mu 1
Ji-Huan He 1 , 4 , 5
1 School of Science, Xi’an University of Architecture and Technology, Caosi East Road, High-Tech Zone, Xi’an, 710055, China
2 Xi’an Special Equipment Inspection Institute, No. 69 Tuanjie South Road, Xi’an High-Tech Zone, Xi’an, 710061, China
3 School of Power and Energy, Northwestern Polytechnical University, No. 1 Dongxiang Road, Chang’an District, Xi’an, 710129, China
4 School of Jia Yang, Zhejiang Shuren University, No. 8 Shuren Street, Gongshu District, Hangzhou, 310015, China
5 School of Mathematics and Big Data, Hohhot Minzu College, No. 56, Tongdao North Road, Xincheng District, Hohhot, 010051, China
10.22055/jacm.2025.48136.5005
Abstract
Atherosclerosis, a major threat to cardiovascular health, encompasses complex nonlinear dynamics in its onset and progression. This study explores a nonlinear coupled free boundary mathematical model for atherosclerosis, featuring dual boundary conditions. The model delineates the interplay of low-density lipoproteins, oxidized low-density lipoproteins, immune cells, and inflammatory factors. The employment of the fixed-point theorem ensures the establishment of both local and global existence and uniqueness of the solution, thereby fortifying the model's theoretical foundation. Furthermore, numerical simulations have been employed to elucidate the nonlinear coupled dynamics between low-density lipoprotein oxidation and immune responses. This provides a quantitative means for probing the molecular mechanisms of atherosclerosis and potential treatments, while also validating the model's accuracy by numerical method. The advancement of the mathematical theory of atherosclerosis models and the provision of novel insights for biomedical research and therapy design are significant contributions of this research.
Keywords
Dual free boundaries
Atherosclerosis
Mathematical modeling
Numerical simulation
Subjects

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Journal of Applied and Computational Mechanics
Volume 11, Issue 4
Autumn 2025
Pages 1162-1171