Mathematical Modelling of Pancreatic Adenocarcinoma Progression: Integrating Microenvironmental Influences on Tumor Dynamics

Abstract

Pancreatic ductal adenocarcinoma (PDAC) is a highly treatment‑refractory malignancy characterized by a dense desmoplastic microenvironment that actively shields malignant cells from immune attacks and pharmacological interventions. This paper presents a deterministic mathematical model that modifies the intrinsic proliferation rate of neoplasms using a composite environmental constant ( ). This dimensionless modulator integrates the cumulative effects of hypoxia, immune response, nutrient blockade, and therapeutic dose. Using both analytical solutions and fourth‑order Runge‑Kutta numerical methods, we demonstrate that  is a critical determinant of growth rate and terminal tumor burden, often outweighing the intrinsic growth rate. Simulations indicate that high‑dose monotherapy targeting only cell proliferation cannot alter disease progression in a permissive microenvironment. These findings support an ecology‑based therapeutic strategy combining microenvironment neutralization with specific cytotoxic targeting to achieve meaningful clinical outcomes.