Mathematical models for optimizing tumour radiotherapy. I: A simple two compartment cell-kinetic model for the unperturbed growth of transplantable tumours.
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Date
1987-06
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Abstract
Tumour growth kinetics has been analysed on the basis of interactions between
two compartments comprising the proliferating and non-proliferating cells. Starting from
the differential equations of growth of the cell-populations in the two compartments and
assuming the process of intercompartmental cell transfers to be linear, an analytic expression
on the variation of growth-fraction with the age of the tumour is obtained. The restricted
conditions on the cell-cycle time and cell-loss-rate, under which these differential
equations lead to a Gompertzian growth of the tumour, are critically analysed. The formalism
permits the estimation of some important cell-kinetic parameters, like growth-fraction
or cell-loss-factor, from a knowledge of the tumour-growth curve, cell-cycle-time and a
single measurement of the cell-loss-rate of the matured tumour, provided the tumour
follows a Gompertzian growth. The validity of the model has been verified with the experimental
data on 4 different transplantable murine tumour systems. Usefulness of the model
has been demonstrated by making some interesting predictions regarding the radiation
response of the tumours from the cell-kinetic parameters.
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Keywords
Cell-kinetics, growth-fraction, cell-loss-factor, transplantable tumours, mathematical model, radiotherapy
Citation
Bhaumik K, Jain V K. Mathematical models for optimizing tumour radiotherapy. I: A simple two compartment cell-kinetic model for the unperturbed growth of transplantable tumours. Journal of Biosciences. 1987 Jun; 12(2): 153-164.