Optimisation of Cancer Drug Treatments Using Cell Population Dynamics

Billy, Frédérique; Clairambault, Jean; Fercoq, Olivier

doi:10.1007/978-1-4614-4178-6_10

Cited by 24 publications

(33 citation statements)

References 128 publications

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“…becomes a problem with two populations, healthy and cancer, that are partly proliferating, partly dying, both evolving under the same drug insult, however with structural dynamic differences between them. This question has been the object of several studies [17,27,30,50,51,52], taking into account for some of them heterogeneity with respect to age phases in the cell division cycle [27,28,29,30], but so far heterogeneity with respect to phenotypes determining drug resistance had only been sketched as prospective work [27,51].…”

Section: Exploiting Structural Differences Between Healthy and Cancermentioning

confidence: 99%

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

Chisholm

Lorenzi

Clairambault

2016

Biochimica et Biophysica Acta (BBA) - General Subjects

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BACKGROUND. Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. SCOPE OF REVIEW.We focus on intra-tumour heterogeneity, namely betweencell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies.MAJOR CONCLUSIONS. Plasticity in cancer cells, i.e., partial reversal to a stemlike status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies.GENERAL SIGNIFICANCE. Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics.

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Section: Exploiting Structural Differences Between Healthy and Cancermentioning

confidence: 99%

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

Chisholm

Lorenzi

Clairambault

2016

Biochimica et Biophysica Acta (BBA) - General Subjects

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“…4.3, where the healthy cell population number Fig. 4 Results of the optimization method, from [17]. Contrary to the model presented in Sect.…”

Section: Another Optimization Problem Under Toxicity Constraintsmentioning

confidence: 70%

“…The dashed curve common to both panels represents the corrected (by treatment) gating function OE1 g.t/: 2 .t /, where g is the output of the algorithm, solution to the optimization problem, prescribing to deliver a cancer drug (by the general circulation to both tissues simultaneously) so as to result locally (at the tumor and at the healthy tissue site) in the pharmacodynamic function g. See text and Ref. [17,18] for details that are well synchronized when the gating is sharp (gate, open during a brief interval of time), and poorly synchronized when it is loose. This modelling choice relies on the intuitive, not proven, but likely assumption (private conversation with F. Lévi) that healthy cell populations are more synchronized than cancer cell populations with respect to cell cycle timing, and that such synchronization is due to the central circadian clock, i.e., the circadian pacemaker makes healthy cells pass in a "disciplined" and orderly way from one phase to the next, while cancer cells, less "obedient" to messages of the clock, pass in a disorderly way.…”

Section: Another Optimization Problem Under Toxicity Constraintsmentioning

confidence: 99%

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Deterministic Mathematical Modelling for Cancer Chronotherapeutics: Cell Population Dynamics and Treatment Optimization

Clairambault¹

2014

Mathematical Oncology 2013

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In this short review paper, I will present the mathematical models that have been designed in the frame of continuous deterministic cell population dynamics that aim at optimization of cancer treatments using chronotherapeutics. Many authors have dealt with chronobiology of cancer, less with continuous mathematical models and even less with the declared aim to optimize chronotherapeutics. The biological and theoretical bases for these models are sketched, started from a historical viewpoint, and the main theoretical results are presented, with biological suggestions to account for them. Chronotherapeutics that leads to therapeutic optimization with the constraint of limiting unwanted toxicity of anticancer drugs towards healthy cell populations is put in a medical perspective together with the other main pitfall of cancer therapeutics, for which optimization procedures should have little to do with circadian biology, i.e., emergence of drug resistance in cancer cell populations, which is amenable to the use of other sorts of models, that are briefly mentioned.

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“…Moreover, the timing of daily administration can also affect the tolerance and the efficacy of anti-cancer agents. Theory suggests ways to optimize treatment schedules to adapt to the circadian clock, a strategy termed chronotherapy [6,7,22,34,35], and also shows that the effect of periodic entrainment of the cell cycle leads to unexpected results.…”

Section: Discussionmentioning

confidence: 99%

Modeling Biological Rhythms in Cell Populations

Cheikh

Lepoutre

Bernard

2012

Math. Model. Nat. Phenom.

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Abstract. Biological rhythms occur at different levels in the organism. In single cells, the cell division cycle shows rhythmicity in the way its molecular regulators, the cyclin dependant kinases (CDKs), modulate their activity periodically to ensure a healthy progression. In tissues, cell proliferation is driven by the circadian clock, which modulates the progression through the cell cycle along the day. The circadian clock shows endogenous rhythmicity through a robust network of transcription-translation feedback loops that create sustained oscillations. Rhythmicity is preserved in cell populations by the coordination of the clocks among cells, through rhythmic synchronization signals. Here we discuss mechanisms for generating rhythmic activities in cell populations by reviewing some of the mathematical models that deal with them. We discuss the implication of biological rhythms for tissue growth and the possible application to chronomodulated cancer treatments.

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Optimisation of Cancer Drug Treatments Using Cell Population Dynamics

Cited by 24 publications

References 128 publications

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

Deterministic Mathematical Modelling for Cancer Chronotherapeutics: Cell Population Dynamics and Treatment Optimization

Modeling Biological Rhythms in Cell Populations

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