Radiation treatment dose optimisation using Poisson tumour control probability parameters

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 D_i for a tumour sub-volume element V_i 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 V_i. The optimum dose distribution, D_i, for V_i 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 α_eff and the effective clonogen number N_0,eff, respectively. α_eff 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.