Control Structures of Drug Resistance in Cancer Chemotherapy

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

doi:10.1109/cdc.2018.8618653

Cited by 5 publications

(16 citation statements)

References 19 publications

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“…Feizabadi (17) used mathematical modeling to show that certain chemotherapy strategies are highly unsuccessful, and even damaging to the patient, under the assumption that the drug can induce resistance during the treatment period. Greene et al (18,19) developed mathematical approach to differentiate between spontaneous and induced resistance to drugs and proposed in vitro experiments that can determine weather treatment can induce resistance. The authors also designed optimized treatment protocols that can prolong the time before resistance develops.…”

Section: Introductionmentioning

confidence: 99%

Drug-induced resistance in micrometastases: analysis of spatio-temporal cell lineages

Pérez-Velázquez

Rejniak

2020

Preprint

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AbstractResistance to anti-cancer drugs is a major cause of treatment failure. While several intracellular mechanisms of resistance have been postulated, the role of extrinsic factors in the development of resistance in individual tumor cells is still not fully understood. Here we used a hybrid agent-based model to investigate how sensitive tumor cells develop drug resistance in the heterogeneous tumor microenvironment. We characterized the spatio-temporal evolution of lineages of the resistant cells and examined how resistance at the single-cell level contributes to the overall tumor resistance. We also developed new methods to track tumor cell adaptation, to trace cell viability trajectories and to examine the three-dimensional spatio-temporal lineage trees. Our findings indicate that drug-induced resistance can result from cells adaptation to the changes in drug distribution. Two modes of cell adaptation were identified that coincide with microenvironmental niches—areas sheltered by cell micro-communities (protectorates) or regions with limited drug penetration (refuga or sanctuaries). We also recognized that certain cells gave rise to lineages of resistant cells (precursors of resistance) and pinpointed three temporal periods and spatial locations at which such cells emerged. This supports the hypothesis that tumor micrometastases do not need to harbor cell populations with pre-existing resistance, but that individual tumor cells can adapt and develop resistance induced by the drug during the treatment.

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Section: Introductionmentioning

confidence: 99%

Drug-induced resistance in micrometastases: analysis of spatio-temporal cell lineages

Pérez-Velázquez

Rejniak

2020

Preprint

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“…In this work, we demonstrated that induced resistance may play a crucial role in therapy outcome, and also discussed methods by which a treatment's mutagenic potential may be identified via biological assays. An extension of the work was presented in [10], where a formal optimal control problem was introduced, and an initial mathematical analysis was performed. The aim of this work is to both formalize the identifiability properties of our theoretical framework, establish the existence of the optimal control introduced in [10], and to precisely classify the optimal control structure utilizing the Pontryagin Maximum Principle and differential-geometric techniques.…”

Section: Introductionmentioning

confidence: 99%

“…An extension of the work was presented in [10], where a formal optimal control problem was introduced, and an initial mathematical analysis was performed. The aim of this work is to both formalize the identifiability properties of our theoretical framework, establish the existence of the optimal control introduced in [10], and to precisely classify the optimal control structure utilizing the Pontryagin Maximum Principle and differential-geometric techniques. A numerical investigation of both the control structure and corresponding objective is also undertaken as a function of patient-specific parameters, and clinical conclusions are emphasized.…”

Section: Introductionmentioning

confidence: 99%

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mentioning

confidence: 99%

“…We have recently introduced a framework for quantifying the effects of induced and non-induced resistance to cancer chemotherapy [11,10]. In this work, we expound on the details relating to an optimal control problem outlined in [10]. The control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie algebra techniques.…”

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confidence: 99%

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Mathematical Details on a Cancer Resistance Model

Greene

Sanchez-Tapia

Sontag

2018

Preprint

Self Cite

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The primary factor limiting the success of chemotherapy in cancer treatment is the phenomenon of drug resistance. We have recently introduced a framework for quantifying the effects of induced and non-induced resistance to cancer chemotherapy [11,10]. In this work, we expound on the details relating to an optimal control problem outlined in [10]. The control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie algebra techniques. A structural identifiability analysis is also presented, demonstrating that patient-specific parameters may be measured and thus utilized in the design of optimal therapies prior to the commencement of therapy. For completeness, a detailed analysis of existence results is also included.

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Optimal chemotherapy counteracts cancer adaptive resistance in a cell-based, spatially-extended, evolutionary model

2022

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Most aggressive cancers are incurable due to their fast evolution of drug resistance. We model cancer growth and adaptive response in a simplified cell-based (CB) setting, assuming a genetic resistance to two chemotherapeutic drugs. We show that optimal administration protocols can steer cells resistance and turned it into a weakness for the disease. Our work extends the population-based (PB) model proposed by Orlando et al. (Physical Biology, 2012), in which a homogeneous population of cancer cells evolves according to a fitness landscape. The landscape models three types of trade-offs, differing on whether the cells are more, less, or equal effective when generalizing resistance to two drugs as opposed to specializing to a single one. The CB framework allows us to include genetic heterogeneity, spatial competition, and drugs diffusion, as well as realistic administration protocols. By calibrating our model on Orlando et al.'s assumptions, we show that dynamical protocols that alternate the two drugs minimize the cancer size at the end of (or at mid-points during) treatment. These results significantly differ from those obtained with the homogeneous model---suggesting static protocols under the pro-generalizing and neutral allocation trade-offs---highlighting the important role of spatial and genetic heterogeneities. Our work is the first attempt to search for optimal treatments in a CB setting, a step forward toward realistic clinical applications.

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Control Structures of Drug Resistance in Cancer Chemotherapy

Cited by 5 publications

References 19 publications

Drug-induced resistance in micrometastases: analysis of spatio-temporal cell lineages

Drug-induced resistance in micrometastases: analysis of spatio-temporal cell lineages

Mathematical Details on a Cancer Resistance Model

Optimal chemotherapy counteracts cancer adaptive resistance in a cell-based, spatially-extended, evolutionary model

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