A theoretical analysis of tumour containment

Abstract

Recent studies have shown that a strategy aiming for containment, not elimination, can control tumour burden more effectively in vitro, in mouse models, and in the clinic. These outcomes are consistent with the hypothesis that emergence of resistance to cancer therapy may be prevented or delayed by exploiting competitive ecological interactions between drug-sensitive and resistant tumour cell subpopulations. However, although various mathematical and computational models have been proposed to explain the superiority of particular containment strategies, this evolutionary approach to cancer therapy lacks a rigorous theoretical foundation. Here we combine extensive mathematical analysis and numerical simulations to establish general conditions under which a containment strategy is expected to control tumour burden more effectively than applying the maximum tolerated dose. We show that containment may substantially outperform more aggressive treatment strategies even if resistance incurs no cellular fitness cost. We further provide formulas for predicting the clinical benefits attributable to containment strategies in a wide range of scenarios, and we compare outcomes of theoretically optimal treatments with those of more practical protocols. Our results strengthen the rationale for clinical trials of evolutionarily-informed cancer therapy, while also clarifying conditions under which containment might fail to outperform standard of care.

Evolutionary Dynamics of Treatment-Induced Resistance in Cancer Informs Understanding of Rapid Evolution in Natural Systems

“…While the first two are strictly qualitative, the last type can also be quantitative in terms of the amount of testosterone produced. Strictly qualitative resistance traits have been explored in detail by modelers (You et al, 2017;Zhang et al, 2017;West et al, 2018;Cunningham et al, 2020;Bayer et al, 2021;Kim et al, 2021;Viossat and Noble, 2021), strictly quantitative less so (Staňková et al, 2019;Reed et al, 2020;Wölfl et al, 2020), and the combination, to our knowledge, has not been explored at all. Our models can be used to consider all three contexts (strictly qualitative, strictly quantitative or both).…”

“…We will also, at times, consider a 20% reduction in tumor volume as the switch threshold. While this has not been tried in any clinical trial, we include it as several authors have shown that it gives superior results as compared to a 50% reduction (Kim et al, 2021;Strobl et al, 2021;Viossat and Noble, 2021).…”

Darwinian Approaches for Cancer Treatment: Benefits of Mathematical Modeling

“…Indeed, a high cell turnover amplifies the effect of competition and therefore the benefits of adaptive therapy. In another study, Viossat et Noble simulated tumors' response to treatment without assuming any costs of resistance, and in spite of that, adaptive therapy was still predicted to outperform MTD-based treatment strategies [43]. Once again, the nature of resistance costs matters, but overall the presence of costs of resistance tends to increase clinical gains.…”

“…Additionally, some ecological phenomena and/or stochasticity events could contribute to making adaptive therapy effective, even without a resistance cost. In brief, it seems that a fitness cost of resistance is not absolutely necessary for adaptive therapy to work, but is certainly helpful [33,43].…”

An Approach to Cell Motility as a Key Mechanism in Oncology

“…As proposed by Kam et al [ 23 ], alternating a fake drug (called ersatzdroges) with a real drug may allow keeping the tumor size constant, without resistance selection. Interestingly, a close strategy promoting tumor containment has been recently proposed by Viossat and Noble [ 24 ] to avoid, or delay, tumor resistances.…”