Modeling Epithelial-Mesenchymal Transition with Partial Differential Equations: Implications for Metastatic...

Metastatic tumors-secondary malignancies arising from the hematogenous or lymphatic dissemination of cancer cells from primary lesions to distant sites-account for nearly 90% of cancer-associated mortality worldwide. Consequently, studying the effect of epithelial-mesenchymal transition (EMT) on metastatic tumors using experimental data and partial differential equation (PDE) modeling is essential. This study innovatively established a phenotype- and density-regulated chemotaxis coefficient to develop a PDE model characterizing cancer cell migration, proliferation, and EMT, enabling analysis of EMT behavior within the tumor microenvironment and its impact on spreading patterns. Subsequently, incorporating the mechanisms of anti-TGF $\beta$ RII and cyclophosphamide (CTX), three therapeutic models for tumor metastasis were constructed, with parameter estimation based on experimental data. To predict primary tumor distant metastasis risk, we originally established a tumor metastasis incidence index, thereby evaluating the critical roles of EMT-targeting and cytotoxic chemotherapeutic drugs in tumor progression. Our findings demonstrate that appropriate pharmacological intervention effectively suppresses tumor dissemination, with therapeutic efficacy significantly enhanced upon EMT inhibition. This study establishes a theoretical framework for designing cancer treatment strategies and provides foundational insights for developing personalized therapeutic regimens.