Mirror Oncology: A History-Dependent Mathematical Framework for Predicting Cancer Cell Adaptation and Drug Resistance

Cancer drug resistance is a major challenge in modern oncology. Although conventional mathematical models describe tumor growth and treatment response, cancer cells may undergo adaptive changes that depend not only on current drug exposure but also on their previous environmental and therapeutic conditions. This proposal introduces Mirror Oncology, a history-dependent mathematical framework designed to investigate how previous therapeutic exposures influence subsequent cancer-cell adaptation and drug resistance. The framework extends the conceptual principles of Mirror Dynamics by incorporating a memory-dependent internal state into a mathematical representation of cancer-cell populations. The model will investigate whether treatment history, adaptive state transitions, and recovery dynamics can explain differences in drug response between cells exposed to identical current conditions. A computational approach based on differential equations, numerical simulations, sensitivity analysis, and comparison with established mathematical models will be developed. Publicly available experimental datasets may be used for calibration and validation. The principal objective is to determine whether a history-dependent model can improve the representation and prediction of cancer-cell adaptation compared with memoryless models. The proposed framework is intended as a theoretical and computational research platform for future investigations in mathematical oncology and adaptive drug-delivery systems.