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

doi:10.12052/gdutxb.230111

欢迎来到能源电力期刊网！

English Version 期刊登录

您当前的位置：

首页 >

文章列表页 >

ECM重塑下肿瘤淋巴管生成模型的定性分析与数值模拟

智慧医疗 | 更新时间：2026-05-27

- ECM重塑下肿瘤淋巴管生成模型的定性分析与数值模拟
- Qualitative Analysis and Numerical Simulation of Generative Model of Tumor Lymphatic Vessels Under ECM Remodeling
- 广东工业大学学报 2024年41卷第1期页码：11-18
- 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：
  
  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
  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
- 基金信息：
  
  广东省自然科学基金资助项目(2023A1515012891)
- DOI：10.12052/gdutxb.230111
  中图分类号： O175
- 网络首发：2024-01-25，
  
  纸质出版：2024
- 稿件说明：
移动端阅览
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.

关键词

Keywords

references

DILLEKS H, ROGERS M S, STRAUME O. Are 90% of deaths from cancer caused by metastases? [J]. Cancer Medicine, 2019, 8(12): 5574-5576.

LIU P, DING P, SUN C, et al . Lymphangiogenesis in gastric cancer: function and mechanism [J ] . European Journal of Medical Research, 2023, 28( 1): 405.

ALEJANDRA G L, TATIANA V, PETROVA. Development and aging of the lymphatic vascular system [J]. Advanced Drug Delivery Reviews, 2021, 169: 63-78.

YANG Y L, CAO Y H. The impact of VEGF on cancer metastasis and systemic disease [J]. Seminars in Cancer Biology, 2022, 86(3): 251-261.

KAI F B, DRAIN A P, WEAVER V M. The extracellular matrix modulates the metastatic Journey [J]. Developmental Cell, 2019, 49(3): 332-346.

LE X N, NILSSON M, GOLDMAN J, et al . Dual EGFR-VEGF pathway inhibition: a promising strategy for patients with EGFR-mutant NSCLC [J ] . Journal of Thoracic Oncology, 2021, 16(2): 205-215.

LIU Y, CAO X T. Characteristics and significance of the pre-metastatic niche [J]. Cancer Cell, 2016, 30(5): 668-681.

QUINTERO-FABIÁN S, RODRIGO A, ECERRIL-VILLANUEVA, et al . Role of matrix metalloproteinases in angiogenesis and cancer [J ] . Frontiers in Oncology, 2019, 9: 1307.

ZHOU Y, WEI X M. A qualitative analysis of a hyperbolic tumor growth model with robin free boundary [J]. Journal of Guangdong University of Technology, 2021, 38(2): 60-65.

LIANG X Z, WEI X M. Existence of the solution to the metabolic model of colon cancer cells [J]. Journal of Guangdong University of Technology, 2019, 36(5): 38-42.

CUI S B. Analysis of a free boundary problem modeling tumor growth [J]. Acta Mathematica Sinica, 2005, 21(5): 1071-1082.

LADYZHENSKAYA O A, SOLONNIKOV V A, URAL'TSEVA N N. Linear and quasi-linear equations of parabolic type[M]. Translations of Mathematical Monographs. USA: Am Math Soc, 1968: 23.

FRIEDMAN A, LOLAS G. Analysis of a mathematical model of tumor lymphangiogenesis [J]. Mathematical Models Methods in Applied Sciences, 2005, 15(1): 95-107.

WEI X, CUI S. Existence and uniqueness of global solutions for a mathematical model of antiangiogenesis in tumor growth [J]. Nonlinear Analysis:Real World Applications, 2008, 9(5): 1827-1836.

WEI X, GUO C. Global existence for a mathematical model of the immune response to cancer [J]. Nonlinear Analysis Real World Applications, 2010, 11(5): 3903-3911.

王术. Sobolev空间与偏微分方程引论[M]. 北京: 科学出版社, 2009.

LAI X, FRIEDMAN A. Combination therapy for melanoma with braf/mek inhibitor and immune checkpoint inhibitor: a mathematical model [J]. BMC Systems Biology, 2017, 11(1): 70.

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

一个视网膜血管肿瘤数学模型整体解的存在唯一性

结肠癌细胞代谢模型解的存在性

一类四阶边值问题解的存在性

一类反应扩散方程的整体吸引子

人工噪声辅助无人机太赫兹安全通信的鲁棒设计