Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies

TL;DR

This paper models how different chemotherapy strategies influence the evolution of drug resistance in cancer cells, using mathematical tools to predict long-term outcomes and optimize treatment levels.

Contribution

It introduces a continuous-variable model based on mutation-selection theory to analyze resistance evolution under various chemotherapeutic actions.

Findings

Different treatments induce varying resistance levels.

Optimal drug dosing can be more effective than maximum tolerated dose.

Mathematical framework predicts long-term resistance dynamics.

Abstract

Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death rates, effects of chemotherapies (both cytotoxic and cytostatic) and mutations. We extend previous work by demonstrating how qualitatively different actions of chemotherapeutic and cytostatic treatments may induce different levels of resistance. The mathematical interest of our study is in the formalism of constrained Hamilton-Jacobi equations in the framework of viscosity solutions. We derive the long-term temporal dynamics of the fittest traits in the regime of small mutations. In the context of adaptive cancer management, we also analyse whether an optimal drug level is better than the maximal tolerated dose.