广东工业大学学报 ›› 2024, Vol. 41 ›› Issue (01): 11-18.doi: 10.12052/gdutxb.230111

• 智慧医疗 • 上一篇    下一篇

ECM重塑下肿瘤淋巴管生成模型的定性分析与数值模拟

王振友, 黄亚婷   

  1. 广东工业大学 数学与统计学院, 广东 广州 510520
  • 收稿日期:2023-08-23 出版日期:2024-01-25 发布日期:2024-02-01
  • 通信作者: 黄亚婷(1998–)，女，硕士研究生，主要研究方向为肿瘤数学，E-mail：2112114043@mail2.gdut.edu.cn
  • 作者简介:王振友(1979–)，男，教授，博士，主要研究方向为计算生物学、医学数据与统计分析计算等，E-mail：zywang@gdut.edu.cn
  • 基金资助:
    广东省自然科学基金资助项目(2023A1515012891)

Qualitative Analysis and Numerical Simulation of Generative Model of Tumor Lymphatic Vessels Under ECM Remodeling

Wang Zhen-you, Huang Ya-ting   

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2023-08-23 Online:2024-01-25 Published:2024-02-01

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摘要： 肿瘤转移是肿瘤发展过程中的重要环节，也是导致癌症恶化和治疗失败的主要原因之一。以肿瘤转移为背景，本文研究基于肿瘤与细胞外基质(Extracellular Matrix，ECM)相互作用的肿瘤淋巴管生成模型。首先用数学语言梳理肿瘤淋巴管生成的生物原理，其次做出假设，建立数学模型并进行定性分析。主要通过逼近方法、偏微分方程定性理论和Banach不动点定理证明模型局部解的存在唯一性，以及借助局部解的正则性估计和嵌入不等式证明模型整体解的存在唯一性。最后利用差分数值方法进行数值模拟来说明模型的可靠性与准确性。本文对深入理解肿瘤转移机制、指导癌症治疗以及推动相关研究具有重要意义。

关键词: 肿瘤淋巴管生成, 细胞外基质, 反应扩散, 存在性, 唯一性

Abstract: Tumor metastasis is an important link in the process of tumor development, and it is also one of the main reasons for cancer deterioration and treatment failure. Taking tumor metastasis as the background, a study is conducted on the generative model of tumor lymphatics based on the interaction between tumor and extracellular matrix (ECM). First, mathematical language is used to sort out the biological principles of tumor lymphangiogenesis, and then assumptions made and mathematical models established and qualitative analysis carried out. The proof of the uniqueness of the existence of local solutions of the model is mainly carried out by means of approximation methods, the qualitative theory of partial differential equations and Banach's immovable point theorem, as well as the uniqueness of the existence of the overall solution of the model with the help of the regularity estimate of the local solution and the embedding inequality. Finally, the difference numerical method is used to carry out numerical simulation to illustrate the reliability and accuracy of the model. This research is of great significance for in-depth understanding the mechanism of tumor metastasis, guiding cancer treatment, and promoting related research.

Key words: tumor lymphangiogenesis, extracellular matrix(ECM), reaction diffusion, existence, uniqueness

中图分类号: 

  • O175
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