Modelling the effect of spread in radiosensitivity parameters and repopulation rate on the probability of tumour control

Abstract

Purpose: To investigate the impact of a variable inter-individual spread in the tumour cell radiosensitivity and repopulation rate on the tumour control probability (TCP).

Methods: The radiosensitivity parameters and the repopulation rate are presumed to be log-normally distributed among the population. Corresponding distributions of TCP across the population are built using a Monte-Carlo simulation algorithm. An analytical formula for the TCP distribution is derived for the case of variability in radiosensitivity only and found to be in excellent agreement with the corresponding Monte-Carlo simulations.

Results and conclusions: It is found that a large variation in individual-patient radiosensitivity results in a dichotomous TCP distribution over the population. In general, the form and width of the TCP distribution depend on the variation in the radiosensitivity. Accounting for tumour repopulation and its variability leads to lower TCP values as expected. It is shown that for a standard fractionation regimen resulting in a population TCP of almost zero, a simple change of the regimen to a hypofractionated one (i.e. typical of SBRT), a decrease in the physical dose is possible such that a beneficial tumour treatment outcome can be still achieved. The reduction in dose will in turn reduce eventual adverse effects caused in the surrounding healthy tissues. This theoretical finding is supported by the increasing amount of clinical evidence for the efficacy of SBRT. The desirability of a pre-clinical independent estimation of the individual radiosensitivity is emphasised.

Keywords: Probability distribution; TCP.