Mathematical Details on a Cancer Resistance Model

Greene, James M.; Sanchez-Tapia, Cynthia; Sontag, Eduardo D.

doi:10.3389/fbioe.2020.00501

Cited by 19 publications

(11 citation statements)

References 33 publications

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“…We assumed that the tumor cell population was a homogeneous mixture of two genetically fixed drug-sensitive and drug-resistant cell populations. In real tumors, cancer cells can be phonetically plastic and a drug can induce resistance 18,62,63 . In addition, cancer populations are not well-mixed, but rather spatially organized [64][65][66][67] , which can be modulated by heterogeneous tumor microenvironmental factors 68,69 .…”

Section: Discussionmentioning

confidence: 99%

Containing Cancer with Personalized Minimum Effective Dose

Masud

Kim

2022

Preprint

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Resistance to treatment is a challenge in many cancer therapies. This is partly due to the heterogeneous nature of tumors, where drug-sensitive and drug-resistant cells compete for the same resources. This competition is largely shaped by cancer treatment. The rapid reduction of drug-sensitive cell population during therapy with a maximum-tolerated dose relaxes competitive stress on the drug-resistant cell population, promoting relapse. Therefore, maintaining a high level of drug-sensitive cell population with a treatment break or lower dose can impose effective competitive stress on drug-resistant cell populations. Adaptive therapy (AT) exploits the competition between cancer cells. However, given the heterogeneous treatment response of individual patients, determining a personalized optimal treatment that can fine-tune competitive stress remains challenging. Using a deterministic model of cancer cell population competition, this study defines an effective dose window (EDW) as a range of doses that conserve sufficient sensitive cells, while maintaining the tumor volume below a threshold (e.g., initial tumor volume), to maintain a sustained competition against resistant cells. As a proof of concept, we sought to determine the EDW for a small cohort of patients with melanoma (n=8). We first fitted the model to longitudinal tumor response data from each patient. We performed structural and practical identifiability analyses to confirm the reproducibility and uniqueness of the estimated parameters. Then, we considered a subset of the cohort with uniquely identifiable parameters and estimated patient-specific EDW. We demonstrated that if the dose belongs to the EDW, the tumor volume for each patient could be indefinitely contained either using continuous or AT strategy. Using the optimal control theory, we concluded that the lower bound of the EDW approximates the minimum effective dose (MED) for containing cancer. Taken together, using tumor biomarker data, this study provides a proof of concept that there may exist a patient-specific EDW that keeps the tumor below a threshold (e.g., initial volume) by maintaining sustained competition on resistant cells.

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Section: Discussionmentioning

confidence: 99%

Containing Cancer with Personalized Minimum Effective Dose

Masud

Kim

2022

Preprint

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“…Drug-induced resistance thus poses an intrinsic limit to curability of tumors under any treatment that involves cell stress, as is the case with chemotherapy, target-selected therapy or radiation. The role of somatic Darwinian evolution in recurrence relative to that of nongenetic cell state transitions has been analyzed using mathematical models in order to minimize selection pressure during treatment [4,5,[39][40][41]. However, the intrinsic limit that induced resistance places on therapy has only recently been systematically evaluated [39].…”

Section: Introductionmentioning

confidence: 99%

“…The role of somatic Darwinian evolution in recurrence relative to that of nongenetic cell state transitions has been analyzed using mathematical models in order to minimize selection pressure during treatment [4,5,[39][40][41]. However, the intrinsic limit that induced resistance places on therapy has only recently been systematically evaluated [39].…”

Section: Introductionmentioning

confidence: 99%

A model for the intrinsic limit of cancer therapy: Duality of treatment-induced cell death and treatment-induced stemness

et al. 2022

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Intratumor cellular heterogeneity and non-genetic cell plasticity in tumors pose a recently recognized challenge to cancer treatment. Because of the dispersion of initial cell states within a clonal tumor cell population, a perturbation imparted by a cytocidal drug only kills a fraction of cells. Due to dynamic instability of cellular states the cells not killed are pushed by the treatment into a variety of functional states, including a “stem-like state” that confers resistance to treatment and regenerative capacity. This immanent stress-induced stemness competes against cell death in response to the same perturbation and may explain the near-inevitable recurrence after any treatment. This double-edged-sword mechanism of treatment complements the selection of preexisting resistant cells in explaining post-treatment progression. Unlike selection, the induction of a resistant state has not been systematically analyzed as an immanent cause of relapse. Here, we present a generic elementary model and analytical examination of this intrinsic limitation to therapy. We show how the relative proclivity towards cell death versus transition into a stem-like state, as a function of drug dose, establishes either a window of opportunity for containing tumors or the inevitability of progression following therapy. The model considers measurable cell behaviors independent of specific molecular pathways and provides a new theoretical framework for optimizing therapy dosing and scheduling as cancer treatment paradigms move from “maximal tolerated dose,” which may promote therapy induced-stemness, to repeated “minimally effective doses” (as in adaptive therapies), which contain the tumor and avoid therapy-induced progression.

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“…pulsed or continuous) of the MTD-strategy is robust against changes in the mutation rate in a model for targeted cytostatic cancer therapy. Greene et al [ 38 ] on the other hand show that the dose-dependent mutation rate may have a significant impact on which delivery mode is preferable (for more rigorous mathematical treatment of the presented model see [ 39 ]). In contrast, we solve the optimal elimination strategy, which minimises the probability of evolutionary rescue, and demonstrate the potential to improve treatment outcomes by reducing the total cumulative dosage administered.…”

Section: Introductionmentioning

confidence: 99%

“…Only few previous theoretical studies of drug resistance have explicitly accounted for dosedependent mutation rates [37][38][39]. Liu et al [37] find that the optimal delivery mode (e.g.…”

Section: Introductionmentioning

confidence: 99%

Drug-induced resistance evolution necessitates less aggressive treatment

et al. 2021

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Increasing body of experimental evidence suggests that anticancer and antimicrobial therapies may themselves promote the acquisition of drug resistance by increasing mutability. The successful control of evolving populations requires that such biological costs of control are identified, quantified and included to the evolutionarily informed treatment protocol. Here we identify, characterise and exploit a trade-off between decreasing the target population size and generating a surplus of treatment-induced rescue mutations. We show that the probability of cure is maximized at an intermediate dosage, below the drug concentration yielding maximal population decay, suggesting that treatment outcomes may in some cases be substantially improved by less aggressive treatment strategies. We also provide a general analytical relationship that implicitly links growth rate, pharmacodynamics and dose-dependent mutation rate to an optimal control law. Our results highlight the important, but often neglected, role of fundamental eco-evolutionary costs of control. These costs can often lead to situations, where decreasing the cumulative drug dosage may be preferable even when the objective of the treatment is elimination, and not containment. Taken together, our results thus add to the ongoing criticism of the standard practice of administering aggressive, high-dose therapies and motivate further experimental and clinical investigation of the mutagenicity and other hidden collateral costs of therapies.

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Mathematical Details on a Cancer Resistance Model

Cited by 19 publications

References 33 publications

Containing Cancer with Personalized Minimum Effective Dose

Containing Cancer with Personalized Minimum Effective Dose

A model for the intrinsic limit of cancer therapy: Duality of treatment-induced cell death and treatment-induced stemness

Drug-induced resistance evolution necessitates less aggressive treatment

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