Optimum parameters in a model for tumour control probability including interpatient heterogeneity

A model for computing tumour control probability (TCP) is studied which embodies a dependence on the size of the irradiated volume, the density of clonogenic cells and the dose received, together with the alpha and beta parameters of the linear quadratic model of cell kill. The model can be used to describe situations where both the dose and the clonogenic cell densities are inhomogeneously distributed; however there is still uncertainty about its radiobiological parameters and the author aims to establish parameters for four types of tumour. In its simplest form, when the volumes are spherical, the clonogenic cell density is considered constant throughout the volume and the dose is uniform, the model has been used (by D.J. Brenner, 1993) to predict the radiobiological parameter alpha which allows the model to best fit the observed clinical data for four types of tumour. Here a new set of fits to the data presented by Brenner is constructed using a model which includes the distribution of radiosensitivity across a heterogeneous patient population. It is shown that this leads to a different set of optimum radiobiological parameters when the clonogenic cell density is of the order of 107 cells cm-3.