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

Objectives: 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.

Conclusions: 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.