Tumor containment for Norton-Simon models

TL;DR

This paper extends a mathematical model of tumor containment by incorporating mutations from sensitive to resistant cells, providing a more realistic framework for optimizing treatment strategies that delay resistance and improve survival.

Contribution

It introduces a novel mathematical analysis that removes previous assumptions, allowing for mutations from sensitive to resistant cells in tumor growth models.

Findings

Model now accounts for mutations from sensitive to resistant cells.

Analysis compares tumor sizes based on resistant population, not time.

Supports potential benefits of containment strategies in treatment.

Abstract

Some clinical and pre-clinical data suggests that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells identified conditions under which a treatment aiming at tumor containment rather than eradication is indeed optimal. This model however neglected mutations from sensitive to resistant cells, and assumed that the growth-rate of sensitive cells is non-increasing in the size of the resistant population. The latter is not true in standard models of chemotherapy. This article shows how to dispense with this assumption and allow for mutations from sensitive to resistant cells. This is achieved by a novel mathematical analysis comparing tumor sizes across treatments not as a function of time, but as a function of the resistant population size.