Investigating the robustness of ion beam therapy treatment plans to uncertainties in biological treatment parameters

Uncertainties in determining clinically used relative biological effectiveness (RBE) values for ion beam therapy carry the risk of absolute and relative misestimations of RBE-weighted doses for clinical scenarios. This study assesses the consequences of hypothetical misestimations of input parameters to the RBE modelling for carbon ion treatment plans by a variational approach. The impact of the variations on resulting cell survival and RBE values is evaluated as a function of the remaining ion range. In addition, the sensitivity to misestimations in RBE modelling is compared for single fields and two opposed fields using differing optimization criteria. It is demonstrated for single treatment fields that moderate variations (up to ±50%) of representative nominal input parameters for four tumours result mainly in a misestimation of the RBE-weighted dose in the planning target volume (PTV) by a constant factor and only smaller RBE-weighted dose gradients. Ensuring a more uniform radiation quality in the PTV eases the clinical importance of uncertainties in the radiobiological treatment parameters, as for such a condition uncertainties tend to result only in a systematic misestimation of RBE-weighted dose in the PTV by a constant factor. Two opposed carbon ion fields with a constant RBE in the PTV are found to result in rather robust conditions. Treatments using two ion species may be used to achieve a constant RBE in the PTV irrespective of the size and depth of the spread-out Bragg peak.