LONG-RANGE PREDICTABILITY IN MODELS OF CELL POPULATIONS SUBJECTED TO PHASE-SPECIFIC DRUGS: GROWTH-RATE APPROXIMATION USING PROPERTIES OF POSITIVE COMPACT OPERATORS

Abstract

The aim of the present work is twofold: to develop numerical procedures for a priori determining whether a given cell population, having a distributed cell-cycle duration, will grow or decay when subjected to prescribed chemotherapy; to evaluate the cumulative error in the long-term predictions for such populations. We show that cell population dynamics under drug treatment can be modelled by iterative application of a compact operator on the initial cell age-distribution. We further show that this model can be approximated by iterative application of matrices on some finite-dimensional vector, containing initial conditions. Moreover, we develop a method for estimating the growth rate of cell population and show that in fully periodic treatments the estimated error does not grow as time tends to infinity. From the biomedical viewpoint this means that only fully periodic (strictly periodic) schedules can be considered for successfully predicting the long-term effect of chemotherapy. Thus, cyclic drug treatment is shown to be advantageous, not only in increasing selectivity of chemotherapy, as has been previously demonstrated, but also in increasing long-term predictability of specific treatment schedules.