Modelling and analysis of time-lags in some basic patterns of cell proliferation |
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Authors: | C T H Baker G A Bocharov C A H Paul F A Rihan |
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Institution: | (1) Mathematics Department, The Victoria University of Manchester, Manchester M13 9PL, England, GB;(2) Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia, RU |
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Abstract: | In this paper, we present a systematic approach for obtaining qualitatively and quantitatively correct mathematical models
of some biological phenomena with time-lags. Features of our approach are the development of a hierarchy of related models
and the estimation of parameter values, along with their non-linear biases and standard deviations, for sets of experimental
data.
We demonstrate our method of solving parameter estimation problems for neutral delay differential equations by analyzing some
models of cell growth that incorporate a time-lag in the cell division phase. We show that these models are more consistent
with certain reported data than the classic exponential growth model. Although the exponential growth model provides estimates
of some of the growth characteristics, such as the population-doubling time, the time-lag growth models can additionally provide
estimates of: (i) the fraction of cells that are dividing, (ii) the rate of commitment of cells to cell division, (iii) the
initial distribution of cells in the cell cycle, and (iv) the degree of synchronization of cells in the (initial) cell population.
Received: 15 September 1997/Revised version: 1 April 1998 |
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Keywords: | : Cell proliferation Mathematical modelling Time-lag Neutral delay differential equation Sensitivity analysis |
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