Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel

Basse, Britta; Baguley, Bruce C.; Marshall, Elaine S.; Joseph, Wayne R.; Brunt, Bruce van; Wake, G. C.; Wall, David J. N.

doi:10.1007/s00285-003-0254-2

Cited by 59 publications

(55 citation statements)

References 9 publications

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“…The second is to base the calculation on a theoretical model for the cell cycle, and we have previously developed such a model, on the basis of the assumption that the transition from G 1 phase to S phase is controlled by a probability function (Basse et al, 2003). Such a model fits experimental data for a number of cell lines treated with paclitaxel and analysed using flow cytometry (Basse et al, 2004a, b). The theoretical model provides an equation T ¼ Àx/(log 10 P), where x tends upwards towards 4.8, as the G 1 -phase proportion increases towards 100%.…”

Section: Discussionmentioning

confidence: 99%

Cell cycle times of short-term cultures of brain cancers as predictors of survival

et al. 2008

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Tumour cytokinetics estimated in vivo as potential doubling times (T pot values) have been found to range in a variety of human cancers from 2 days to several weeks and are often related to clinical outcome. We have previously developed a method to estimate culture cycle times of short-term cultures of surgical material for several tumour types and found, surprisingly, that their range was similar to that reported for T pot values. As T pot is recognised as important prognostic variable in cancer, we wished to determine whether culture cycle times had clinical significance. Brain tumour material obtained at surgery from 70 patients with glioblastoma, medulloblastoma, astrocytoma, oligodendroglioma and metastatic melanoma was cultured for 7 days on 96-well plates, coated with agarose to prevent proliferation of fibroblasts. Culture cycle times were estimated from relative 3 H-thymidine incorporation in the presence and absence of cell division. Patients were divided into two groups on the basis of culture cycle times of p10 days and 410 days and patient survival was compared. For patients with brain cancers of all types, median survival for the p10-day and 410-day groups were 5.1 and 12.5 months, respectively (P ¼ 0.0009). For 42 patients with glioblastoma, the corresponding values were 6.5 and 9.0 months, respectively (P ¼ 0.03). Lower grade gliomas had longer median culture cycle times (16 days) than those of medulloblastomas (9.9 days), glioblastomas (9.8 days) or melanomas (6.7 days). We conclude that culture cycle times determined using short-term cultures of surgical material from brain tumours correlate with patient survival. Tumour cells thus appear to preserve important cytokinetic characteristics when transferred to culture.

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Section: Discussionmentioning

confidence: 99%

Cell cycle times of short-term cultures of brain cancers as predictors of survival

et al. 2008

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“…The cell division problem has been generalized to include dispersion [17,18] and this led to the study of second-order pantograph equations [19]. The problem has also been studied for certain non-constant coefficients [20,21], and a multi-compartment model has been developed for an application to the treatment of cancer [22].…”

Section: Introductionmentioning

confidence: 99%

Solutions to an advanced functional partial differential equation of the pantograph type

2015

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A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

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“…The observations are always radiological or MRI. But in cell cultures and in animals, such experimental observations are of course much easier and may allow comparing parameters of interest evaluated by using any of the methods mentioned above in different situations: cell cultures, fresh blood samples from patients, tumour growth curves [11,18,19,20,35,117] and it is then possible to propose optimised treatments based on these estimations [10,15,35].…”

Section: Measurement Of Pharmacodynamic Effectsmentioning

confidence: 99%

“…They are linked to cell population samples, either with observation on a global population, such as given by flow cytometry (or FACS, for fluorescence activated cell sorting) [16,17,18,19,20,95,135], or by observations on individual cells and statistics performed on the sampled population of individual cells marked with fluorescent proteins, such as FUCCI [125] in [25,26]. These methods require previous cell staining, e.g.…”

Section: Parameters In Cell and Molecular-based Models Of Tissue Growthmentioning

confidence: 99%

“…Basse et al [17,18,19] developed a phase-and size-structured model of a cell population submitted to paclitaxel, a cancer agent that induces mitotic arrest of the cell cycle and cell death. The size of the cell was considered as determined by its DNA content and some of the model parameters were determined by fitting experimental flow cytometry data.…”

Section: Physiologically Structured Pde Models For the Cell Cycle Andmentioning

confidence: 99%

See 1 more Smart Citation

Optimisation of Cancer Drug Treatments Using Cell Population Dynamics

Billy

Clairambault

Fercoq

2012

Lecture Notes on Mathematical Modelling in the Life Sciences

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Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel

Cited by 59 publications

References 9 publications

Cell cycle times of short-term cultures of brain cancers as predictors of survival

Cell cycle times of short-term cultures of brain cancers as predictors of survival

Solutions to an advanced functional partial differential equation of the pantograph type

Optimisation of Cancer Drug Treatments Using Cell Population Dynamics

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