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<p>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<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> 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.</p>

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Modeling Epithelial-Mesenchymal Transition with Partial Differential Equations: Implications for Metastatic Progression and Treatment Strategies

  • 期刊论文

  • 发表日期：

    2026年3月31日

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  • Ruixuan Sun,
  • Yongzhen Pei,
  • Changguo Li,
  • Han Lu,
  • Yonghui Liu

摘要

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 \(\beta \) β 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.