Radiation treatment dose optimisation using Poisson tumour control probability parameters

Abstract

This study examines the Poisson tumour control probability (TCP) γ37 and D37 parameters of a uniformly irradiated numerical tumour model using changes in tumour burden as a surrogate for treatment response information. An optimum dose Di for a tumour sub-volume element Vi is described that maximizes TCP as a function of fixed tumour integral dose ξ. TCP was calculated for spatially-varying clonogen density for a total 108 cells and radiosensitivity α with mean radiosensitivity in the range 0.4 – 1.0 Gy−1. A bivariate normal distribution is used to describe the radiosensitivity α and the linear term of the linear-quadratic (LQ) cell kill governed the changes in the regional tumour burden within sub-volumes Vi. The optimum dose distribution, Di, for Vi is obtained as a function of fixed tumour integral dose ξ. For a uniform dose delivery and for TCP = 37%, γ37 and D37 are described by the effective radiosensitivity αeff and the effective clonogen number N0,eff, respectively. αeff is equivalent to differential dose changes in the number of clonogenic cells (tumour burden). The γ37 values were found to be inversely correlated with variance of the probability density function of the α distribution. For the biologically optimum dose distribution, γ37 was found to converge to the theoretical maximum limit and D37 was found to reduce relative to that obtained for the uniform dose case. The TCP parameters γ37 and D37 could thus be useful in optimising individual radiation treatment doses even when tumour heterogeneity is taken into account.