Abstract
Some different types of models of cell proliferation are discussed. The importance of basing the models on experimental data is emphasised, but warnings are given about some of the pitfalls in fitting models of data. The importance of investigating alternative models which might lead to similar experimental findings is stressed. The use of simulation to assess the ability of an analytical method to extract correct information from experimental data is advocated. In this instance, the modelling process takes place in advance of the data collection. Models described relate to cell proliferation in a transplantable tumor, the prostate of the castrate mouse stimulated with testosterone, and stratified squamous epithelium. Experimental techiques include measurment of tumor size, calculation of labelling and mitotic indices over time, and the fraction labelled mitoses method.
Highlights
Some different types of models of cell proliferation are discussed
We look at a model constructed for a quite different purpose: to try to explain the proliferative response of the prostate of the castrate mouse to injections of testosterone (Morley, Wright and Appleton, 1973)
We have tried to show how mathematical and statistical attitudes may be applied to the study of cell proliferation, and have strongly advocated the use of simulation
Summary
Some different types of models of cell proliferation are discussed. The importance of basing the models on experimental data is emphasised, but warnings are given about some of the pitfalls in fitting models to data. Experimental techniques include measurement of tumour size, calculation of labelling and mitotic indices over time, and the fraction labelled mitoses method It is un$sual to begin a mathematical paper with a resum of its author's career, but this is not a typical m$hematical paper. The applied mathematicians I have met, whether or not working in biology, have subscribed to the view of modelling typical of the mathematical physicist They believe in the essential simplicity of natural phenomena and in their own ability to represent them through differential equations. The solution of these equations in particular circumstances may be difficult because of the dimensionality of the problem, its boundary conditions, or its ill-conditioning; but they know that their models are, if not absolutely true, at least entirely adequate representations of the reality they wish to describe. They are obsessed with estimating 'confidence limits' for the parameters of their equations
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