南方医科大学学报

南方医科大学学报 ›› 2025, Vol. 45 ›› Issue (8): 1768-1776.doi: 10.12122/j.issn.1673-4254.2025.08.21

• • 上一篇    

基于耦合扩散的肿瘤转移与骨髓来源的抑制细胞相互作用模型

黄亚婷(), 王振友()   

  1. 广东工业大学数学与统计学院，广东 广州 510520
  • 收稿日期:2025-03-15 出版日期:2025-08-20 发布日期:2025-09-05
  • 通讯作者: 王振友 E-mail:1112414003@mail2.gdut.edu.cn;zywang@gdut.edu.cn
  • 作者简介:黄亚婷，在读博士研究生，E-mail: 1112414003@mail2.gdut.edu.cn
  • 基金资助:
    广东省自然科学基金(2023A1515012891)

A coupled diffusion-based model of interaction between tumor metastasis and myeloid-derived suppressive cells

Yating HUANG(), Zhenyou WANG()   

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2025-03-15 Online:2025-08-20 Published:2025-09-05
  • Contact: Zhenyou WANG E-mail:1112414003@mail2.gdut.edu.cn;zywang@gdut.edu.cn

RichHTML

2

PDF

12

摘要：

目的 探讨骨髓来源的抑制细胞（MDSCs）在肿瘤转移前微环境（PMN）中的关键作用，并建立数学模型分析其与微环境内主要参与成分之间的相互关系。 方法 运用数学描述系统地分析MDSCs在肿瘤转移过程中的功能，阐明其与肿瘤转移前微环境形成过程中主要成分（如血管内皮细胞、间质细胞、癌症相关巨噬细胞等）的关联。基于肿瘤转移前微环境的形成原理，假设关键生物学过程，构建耦合的偏微分扩散方程模型。通过逼近方法、偏微分方程定性理论和Banach不动点定理，研究模型解的存在性和唯一性，并采用差分数值方法进行数值模拟，以验证模型的可靠性与精确性。 结果 逼近方法、偏微分方程定性理论和Banach不动点定理结合局部解的正则性估计和嵌入不等式证明了模型局部解和整体解的存在性与唯一性。数值模拟结果进一步验证了模型的可靠性，MDSCs在肿瘤转移前微环境中，尤其是在血管生成和免疫抑制方面发挥了重要作用。 结论 本研究通过数学建模与数值模拟，深入揭示了MDSCs在肿瘤转移前微环境中的重要功能，为理解肿瘤转移机制、制定癌症治疗策略及相关研究提供了重要的理论依据。

关键词: 肿瘤转移, 耦合扩散, 偏微分, 存在唯一性, 抑制细胞

Abstract:

Objective To explore the key role of myeloid-derived suppressive cells (MDSCs) in pre-metastatic niche (PMN) and analyze their interrelationships with the main components in the microenvironment using a mathematical model. Methods Mathematical descriptions were used to systematically analyze the functions of MDSCs in tumor metastasis and elucidate their association with the major components (vascular endothelial cells, mesenchymal stromal cells, and cancer-associated macrophages) contributing to the formation of the pre-metastatic microenvironment. Based on the formation principle of the pre-metastatic microenvironment of tumors, the key biological processes were assumed to construct a coupled partial differential diffusion equation model. The existence and uniqueness of the model solutions were investigated using approximation methods, the qualitative theory of partial differential equations and Banach's immovable point theorem, and numerical simulations were carried out by differential numerical methods to verify the reliability and accuracy of the model. Results The existence and uniqueness of the local and overall solutions of the model were proved using the approximation method, the qualitative theory of partial differential equations and Banach's immovable point theorem in combination with the regularity estimation of the local solutions and the embedding inequality. Numerical simulation results further validated the reliability of the model and demonstrated the important role of MDSCs in the pre-metastatic microenvironment of tumors, especially in angiogenesis and immunosuppression. Conclusion This study reveals the important functions of MDSCs in the pre-metastatic microenvironment of tumors through mathematical modeling and numerical simulation, which provides an important theoretical basis for understanding the mechanism of tumor metastasis and devising cancer treatment strategies.

Key words: tumor metastasis, coupled diffusion, partial differentiation, existence uniqueness, suppressive cells