Mathematical analysis of cancer chemotherapy

Chuang, Shui-Nan; Lloyd, Harris H.

doi:10.1016/s0092-8240(75)80022-x

Cited by 10 publications

(1 citation statement)

References 8 publications

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“…Denoting by a (a 0) the cell age and by n(a, t) the cell density with respect to age, that is, n(a, t) da is the number of cells with age between a and a + da at time t, the basic model is given by where β(a) is the age-dependent division rate coefficient, which is related to the distribution of cell cycle duration, and µ(a) represents cell loss. More complex models, involving age-structured subpopulations, are required to take into account the different cell cycle phases [5]. Another approach to represent the kinetic heterogeneity was proposed by Lebowitz and Rubinow [9], considering the cell population as composed by a continuous spectrum of subpopulations each characterized by a given cell cycle transit time τ .…”

Section: Introductionmentioning

confidence: 99%

The asynchronous exponential growth property in a model for the kinetic heterogeneity of tumour cell populations

Arino¹,

Bertuzzi

Gandolfi

et al. 2005

Journal of Mathematical Analysis and Applications

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A continuous cell population model, which represents both the cell cycle phase structure and the kinetic heterogeneity of the population following Shackney's ideas [J. Theor. Biol. 38 (1973) 305-333], is studied. The asynchronous exponential growth property is proved in the framework of the theory of strongly continuous semigroups of bounded linear operators.  2004 Elsevier Inc. All rights reserved.

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Section: Introductionmentioning

confidence: 99%