A theoretical investigation of adequate range uncertainty margins in proton treatment planning to preserve tumor control probability.

Proton dose distributions are sensitive to range uncertainties, resulting in margins added to ensure adequate tumor control probability (TCP). We investigated the required margin and dose shape needed to ensure adequate TCP, for representative tumor cell distributions in the clinical target volume (CTV). A mechanistic tumor response model, validated for lung tumors, was used to estimate TCP. The tumor cell distribution ( ) was assumed to decrease exponentially in the CTV with decay parameter toward the outer border ( ). It was investigated if a gradual dose fall-off could reduce the dose to normal tissues outside the CTV, while achieving adequate TCP. For various values of and we derived adequate uniform dose margins ( ), coupled to linear dose fall-off regions ( cm), that ensured while delivering the least mean dose outside the CTV. To account for variabilities in patients and tumor types, variable probabilities ( ) of finding tumor cells in the non-GTV part of the CTV for a given patient were also tested. Dose from a single beam or two opposing beams was simulated under the influence of a typical stopping power ratio uncertainty of 3.5%. For large and a dose distribution with a shallower dose fall-off ( ) was advantageous, and could be smaller than In the case of small values, however, a conventional dose distribution ( ) would generally perform better. For no CTV, cm in the case of two opposing beams, while it was 0.7 cm for a single beam, however, for two opposing beams cm ( cm), while it was zero for a single beam. The details of the underlying cancer cell distribution characteristics do impact the adequate dose arrangements, and for opposing beams a non-conventional dose distribution shape is often advantageous.