A Mathematical Model of Breast Cancer Growth and Drug Resistance Evolution Under Chemotherapy

Precision medicine aims to tailor treatments to individual patients based on their unique characteristics and disease pathophysiology. This study presents a novel mathematical model of breast tumor growth, specifically focusing on implanted breast tumors in mice treated with Pegylated Liposomal Doxorubicin (PLD). The model describes drug pharmacokinetics, drug resistance development, and the evolution of tumor mass over time. The introduction of a compartment for drug resistance development represents the novel aspect of this work, providing a straightforward description of this critical process. The model was adapted to observed data on two mice and model parameters were estimated. To assess the qualitative properties of the model solutions and to investigate its potential limitations, a stability analysis was conducted to identify equilibrium points. The analysis revealed that if the tumor cell spontaneous elimination rate exceeds the growth rate, then the tumor is stable, preventing any form of treatment. On the contrary, the pathological case occurs, the equilibrium becomes unstable, and the tumor requires treatment. By accurately modeling drug pharmacokinetics and resistance development, this model can inform clinical decisions by predicting patient-specific responses to PLD treatment, thereby guiding personalized therapeutic strategies. The findings from this study contribute to a deeper understanding of tumor growth dynamics and provide valuable insights for the development of personalized treatment strategies.