Cell kinetic model of tumour growth and regression for a rhabdomyosarcoma in the rat: Undisturbed growth and radiation response to large single doses

Abstract

A mathematical model of tumour growth and regression has been developed using experimental data on the cellular kinetics and radiation survival of cells of a rhabdomyosarcoma in the WAG/Rij rat. For the undisturbed tumour, the model assumes a time-dependent mean cell cycle time, cell proliferation parameter ( 1 + growth fraction) and cell-loss rate, consistent with available experimental data, to predict the (non-exponential) time variation of the tumour volume. To treat the response to radiation, it is assumed that the irradiated tumour is composed of two components: the “doomed” population, those cells which are incapable of unlimited proliferation but may undergo several divisions before dying, and the “surviving” population, those cells which may have received non-lethal damage but are capable of unlimited proliferation. Time dependence of the proliferating fraction, the cell density, and the reoxygenation rate are introduced to describe the regression and regrowth of the tumour after single massive radiation doses. The results show that reasonable time dependences of the parameters describe the response of the tumour to 2000 and 1000 rads of X-rays. A long delay in tumour regrowth after 600 rads of fast neutrons, however, remains to be adequately explained in terms of the model in its present form.