A general tumour control probability model for non-uniform dose distributions

Perfectly uniform dose distributions over target volumes are almost impossible to achieve in clinical practice, due to surrounding normal tissues dose constraints that are commonly imposed to treatment plans. This article introduces a new approach to compute tumour control probabilities (TCPs) under inhomogeneous dose conditions. The equivalent subvolume model presented here does not assume independence between cell responses and can be derived from any homogeneous dose TCP model. To check the consistency of this model, some natural properties are shown to hold, including the so-called uniform dose theorem. In the spirit of the equivalent uniform dose (EUD) concept introduced by Niemierko (1997, Med. Phys., 24, 103-110), the probability-EUD is defined. This concept together with the methodology introduced to compute TCPs for inhomogeneous doses is applied to different uniform dose TCP models. As expected, the TCP takes into account the whole dose distribution over the target volume, but it is influenced more strongly by the low-dose regions. Finally, the proposed methodology and other approaches to the inhomogeneous dose scenario are compared.