Mathematical analysis of cancer chemotherapy

Chuang, Shui-Nan; Lloyd, Harris H.

doi:10.1007/bf02470621

Cited by 17 publications

(2 citation statements)

References 12 publications

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“…Some examples of multicompartment models of cell-growth, used in the study of chemotherapy, may be found in [8,26], where the models are structured by age. Some examples of multicompartment models of cell-growth, used in the study of chemotherapy, may be found in [8,26], where the models are structured by age.…”

Section: Introductionmentioning

confidence: 99%

The steady-states of a multi-compartment, age–size distribution model of cell-growth

Begg¹,

Wall²,

Wake³

2008

Eur. J. Appl. Math

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A model of cell-growth, describing the evolution of the age–size distribution of cells in different phases of cell-growth, is studied. The model is based on that used in several papers by Basse et al. and is composed of a system of partial differential equations, each describing the changes in the age–size distribution of cells in a specific phase of cell-growth. Here, the ‘age’ of a cell is considered to be the time spent in its current phase of cell-growth, while ‘size’ is considered to be the DNA content of the cell. The existence of steady age–size distributions (SASDs), where the age–size distributions retain the same shape but are scaled up or down as time increases, is investigated and it is shown that SASDs exist. A speculative discussion of the stability of these SASDs is also included, but their stability is not conclusively proved.

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Section: Introductionmentioning

confidence: 99%

The steady-states of a multi-compartment, age–size distribution model of cell-growth

Begg¹,

Wall²,

Wake³

2008

Eur. J. Appl. Math

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“…There have been numerous attempts to predict mathematically the results of the cytostatic action of various drugs in recent years (see for instance Chuang & Lloyd, 1975;Chuang & Soong, 1978;Swan & Vincent, 1977; and references contained therein). Very recently, Dibrov et al (1983) presented a mathematical theory of optimum scheduling for blocking agents.…”

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confidence: 99%

Kinetic Analysis of Drug‐Induced G₂ Block In Vitro

Kimmel

Traganos

1985

Cell Proliferation

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Generalized Norton‐Simon models of tumour growth

Heitjan

1991

Statistics in Medicine

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This paper considers the analysis of serial data on the growth of tumours in laboratory rodents. I propose a model-a generalization of the tumour growth model of Norton and Simon-that leads to a rich family of growth and decay curves. The model assumes that unperturbed growth follows the generalized logistic form; it accommodates time-varying treatment effects through an effective dose function. I fit two such models to data on a human prostate tumour growing in nude mice and compare the fitted curves and dose functions with a non-parametric curve and dose function estimated from a cubic spline model. All three models account for both random animal effects and autocorrelation. Monte Carlo results suggest that (a) maximum likelihood estimates of growth parameters are biased, although not severely, and (b) standard errors are conservative in small samples but become increasingly accurate in larger samples.

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Mathematical analysis of cancer chemotherapy

Cited by 17 publications

References 12 publications

The steady-states of a multi-compartment, age–size distribution model of cell-growth

The steady-states of a multi-compartment, age–size distribution model of cell-growth

Kinetic Analysis of Drug‐Induced G₂ Block In Vitro

Generalized Norton‐Simon models of tumour growth

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Mathematical analysis of cancer chemotherapy

Cited by 17 publications

References 12 publications

The steady-states of a multi-compartment, age–size distribution model of cell-growth

The steady-states of a multi-compartment, age–size distribution model of cell-growth

Kinetic Analysis of Drug‐Induced G2 Block In Vitro

Generalized Norton‐Simon models of tumour growth

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Product

Resources

About

Kinetic Analysis of Drug‐Induced G₂ Block In Vitro