Dynamics of cancer recurrence

TL;DR

This paper models the stochastic dynamics of cancer recurrence driven by mutation-induced resistance, providing mathematical approximations for key times and processes involved in tumor regrowth after treatment.

Contribution

It introduces a mathematical framework for understanding the timing and dynamics of cancer recurrence due to mutation-driven resistance, with uniform in-time approximations.

Findings

Derived uniform in-time approximations for escape paths

Characterized the timing of tumor rebound and resistance dominance

Provided insights into mutation-driven cancer recurrence dynamics

Abstract

Mutation-induced drug resistance in cancer often causes the failure of therapies and cancer recurrence, despite an initial tumor reduction. The timing of such cancer recurrence is governed by a balance between several factors such as initial tumor size, mutation rates and growth kinetics of drug-sensitive and resistance cells. To study this phenomenon we characterize the dynamics of escape from extinction of a subcritical branching process, where the establishment of a clone of escape mutants can lead to total population growth after the initial decline. We derive uniform in-time approximations for the paths of the escape process and its components, in the limit as the initial population size tends to infinity and the mutation rate tends to zero. In addition, two stochastic times important in cancer recurrence will be characterized: (i) the time at which the total population size first begins to rebound (i.e., become supercritical) during treatment, and (ii) the first time at which the resistant cell population begins to dominate the tumor.