Ideal spatial radiotherapy dose distributions subject to positional uncertainties

In radiotherapy a common method used to compensate for patient setup error and organ motion is to enlarge the clinical target volume (CTV) by a 'margin' to produce a 'planning target volume' (PTV). Using weighted power loss functions as a measure of performance for a treatment plan, a simple method can be developed to calculate the ideal spatial dose distribution (one that minimizes expected loss) when there is uncertainty. The spatial dose distribution is assumed to be invariant to the displacement of the internal structures and the whole patient. The results provide qualitative insights into the suitability of using a margin at all, and (if one is to be used) how to select a 'good' margin size. The common practice of raising the power parameters in the treatment loss function, in order to enforce target dose requirements, is shown to be potentially counter-productive. These results offer insights into desirable dose distributions and could be used, in conjunction with well-established inverse radiotherapy planning techniques, to produce dose distributions that are robust against uncertainties.