Diffusion Process Modeling Based on Partial Differential Equations and its Application in Biological Systems

Haitao Song
Department of Basic Courses, Xinxiang Vocational and Technical College, Xinxiang, Henan, 453006, China
Yulei Wang
Department of Basic Courses, Xinxiang Vocational and Technical College, Xinxiang, Henan, 453006, China

Abstract:

Differences in disease diffusion processes in different parts may directly affect user survival rates. Existing diffusion modeling methods fail to fully consider biological differences and environmental factors in different parts, resulting in the model being unable to accurately reflect changes in user survival and recovery. Therefore, this study aims to analyze the impact of diffusion in different parts on mortality through diffusion modeling based on partial differential equations (PDEs), and provide more accurate predictions and optimized treatment plans. Different diffusion coefficients are set according to the diffusion characteristics of different biological parts (cell density, blood flow, etc.), while considering spatial and temporal changes. This can effectively predict the metastasis of cancer cells in breast cancer patients. The results showed that the metastasis efficiency of cancer cells in tissue environments such as lymph nodes and liver was higher, especially in patients with lymph node metastasis, with a mortality rate as high as 69.23%, while the metastasis efficiency of skin tissue was lower, with a mortality rate of 23.53% in patients with metastasis to the skin. The environmental factors of the experiment found that in a high blood volume concentration environment, the metastasis efficiency of cancer cells increased from the initial 0.12 to 0.88, while in a low blood volume concentration environment, the metastasis efficiency was only 0.58. This study constructs a cell process diffusion model to understand the metastasis characteristics of different tissue environments, providing a theoretical basis for precision treatment and optimization of treatment strategies, and helping clinicians make more scientific decisions during the treatment process.