Stability and reachability analysis for a controlled heterogeneous population of cells

Carrère, Cécile; Zidani, Hasnaa

doi:10.1002/oca.2627

Cited by 7 publications

(7 citation statements)

References 31 publications

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“…Third, all else being equal, the larger the subpopulation of sensitive cells, the lower the growth-rate of resistant cells (g r is non-increasing in S). This is a standard assumption in the adaptive therapy literature (see Supplementary Information, Section 1), which might result from density-dependence (the larger the tumour, the larger its doubling time [13,14,26], as in the Gompertzian Model 3), frequency-dependence (the rarer resistant cells, the larger their doubling time [8,9]), a combination of those two factors [4,8,15,17,18,21], or some other form of inhibition of resistant cells by sensitive cells. It is important to note that this assumption does not imply a fitness cost of resistance; we permit the possibility that resistant cells are as fit or even fitter than sensitive cells in the absence of treatment.…”

Section: Assumptionsmentioning

confidence: 99%

“…Yet, the underlying evolutionary theory remains only imprecisely characterized in the cancer context. With the exception of [13], previous mathematical and simulation studies [4,[8][9][10][14][15][16][17][18][19][20][21][22] have focussed on particular model formulations, specific therapeutic protocols, and typically untested assumptions about tumour growth rate, cell-cell interactions, treatment effects and resistance costs. Many previous findings are not readily generalizable because they are based on simulations, rather than mathematical analysis.…”

Section: Introductionmentioning

confidence: 99%

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A theoretical analysis of tumour containment

Viossat

Noble

2021

Nat Ecol Evol

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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.

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Section: Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A theoretical analysis of tumour containment

Viossat

Noble

2021

Nat Ecol Evol

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“…The fact that these policies are recovered in feedback form makes this approach particularly suitable for optimization of adaptive therapies. But even though the use of general optimal control in cancer treatment is by now common [55], the same is not true for the more robust HJB-based methods, which so far have been used in only a handful of cancer-related applications [1, 7, 19, 25, 36, 42, 53]. This is partly due to the HJBs’ well-known curse of dimensionality : the rapid increase in computational costs when the system state becomes higher-dimensional.…”

Section: Discussionmentioning

confidence: 99%

“…Tumor heterogeneity is increasingly viewed as a key aspect that can be leveraged to improve therapies through the use of optimal control theory [55]. Most researchers using this perspective focus on deterministic models of tumor evolution, with typical optimization objectives of maximizing the survival time [46], minimizing the tumor size [6], or minimizing the time until the tumor size is stabilized [7]. In models that address the stochasticity in tumor evolution, a typical optimization goal is to find treatment policies that maximize the likelihood of patient’s eventual cure (e.g., [10, 13, 37]) or minimize the likelihood of negative events (e.g., metastasis) after specified time [19].…”

Section: Introductionmentioning

confidence: 99%

Threshold-awareness in adaptive cancer therapy

Wang

Scott

Vladimirsky

2022

Preprint

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While adaptive cancer therapy is beginning to prove a promising approach of building evolutionary dynamics into therapeutic scheduling, the stochastic nature of cancer evolution has rarely been incorporated. Various sources of random perturbations can impact the evolution of heterogeneous tumors. In this paper, we propose a method that can effectively select optimal adaptive treatment policies under randomly evolving tumor dynamics based on Stochastic Optimal Control theory. We first construct a stochastic model of cancer dynamics under drug therapy based on Evolutionary Game theory. That model is then used to improve the cumulative ''cost'', a combination of the total amount of drugs used and the time to recovery. As this cost becomes random in a stochastic setting, we maximize the probability of recovery under a pre-specified cost threshold (or a ''budget''). We can achieve our goal for a range of threshold values simultaneously using the tools of dynamic programming. We then compare our threshold-aware policies with the policies previously shown to be optimal in the deterministic setting. We show that this threshold-awareness yields a significant improvement in the probability of under-the-budget recovery, which is correlated with a lower general drug usage. The particular model underlying our discussion has originated in [Kaznatcheev et al. 2017], but the presented approach is far more general and provides a new tool for optimizing adaptive therapies based on a broad range of stochastic cancer models.

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“…Many mathematical models emphasize competition between sensitive and highly resistant cells and assume that the larger the tumor size, the stronger the competition ( Martin et al, 1992b ; Monro and Gaffney, 2009 ; Zhang et al, 2017 ; Carrère, 2017 ; Carrère and Zidani, 2020 ; Martin et al, 1992a ; Strobl et al, 2020 ; Viossat and Noble, 2021 ). Such models suggest maintaining the tumor at the maximal acceptable size in order to maximize competitive suppression of resistance ( Hansen and Read, 2020b ; Viossat and Noble, 2021 ).…”

Section: Introductionmentioning

confidence: 99%

A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation

West

Adler

Gallaher

et al. 2023

eLife

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Adaptive therapy is a dynamic cancer treatment protocol that updates (or ‘adapts’) treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.

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Stability and reachability analysis for a controlled heterogeneous population of cells

Cited by 7 publications

References 31 publications

A theoretical analysis of tumour containment

A theoretical analysis of tumour containment

Threshold-awareness in adaptive cancer therapy

A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation

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