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

Wang Zhen-you; Huang Ya-ting

doi:10.12052/gdutxb.230111

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

更新时间：2026-05-27

- Qualitative Analysis and Numerical Simulation of Generative Model of Tumor Lymphatic Vessels Under ECM Remodeling
- Vol. 41, Issue 1, Pages: 11-18(2024)
- 作者机构：
  
  广东工业大学数学与统计学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.230111
  CLC： O175
- Online First：25 January 2024，
  
  Published：2024
- 稿件说明：
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王振友, 黄亚婷. ECM重塑下肿瘤淋巴管生成模型的定性分析与数值模拟[J]. 广东工业大学学报, 2024, 41(1): 11-18.

Wang Zhen-you, Huang Ya-ting. Qualitative Analysis and Numerical Simulation of Generative Model of Tumor Lymphatic Vessels Under ECM Remodeling[J]. 2024, 41(1): 11-18.
王振友, 黄亚婷. ECM重塑下肿瘤淋巴管生成模型的定性分析与数值模拟[J]. 广东工业大学学报, 2024, 41(1): 11-18. DOI： 10.12052/gdutxb.230111.

Wang Zhen-you, Huang Ya-ting. Qualitative Analysis and Numerical Simulation of Generative Model of Tumor Lymphatic Vessels Under ECM Remodeling[J]. 2024, 41(1): 11-18. DOI： 10.12052/gdutxb.230111.

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。

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.

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references

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