Potential pitfalls of the PTV concept in dose-to-medium planning optimization

In typical treatment planning of 3D IMRT, the incident energy fluence is optimized to achieve a homogeneous dose distribution to the PTV. The PTV includes the tumour but also healthy tissues that may have a different dose response for the same incident energy fluence, like bony structures included in the PTV (mandibles in head and neck tumours or femoral bones in sarcomas). Dose to medium optimization compensates for this heterogeneous response, leading to a non-homogeneous energy fluence in the PTV and a non-homogeneous dose in the CTV in the presence of geometric errors. We illustrate qualitatively this statement in a cylindrical geometry where the PTV includes a CTV (7cm diameter) made of water surrounded by ICRU compact bone (1.2cm thickness); such configuration was chosen to exaggerate the aforementioned effect. Optimization was performed assuming dose equals photon energy fluence times mass energy absorption coefficient. Bone has a 4% lower dose response in a 6 MV flattening filter free spectrum. After optimization either in medium or assuming everything as water composition, the geometry was shifted by 1.2cm and dose recomputed. As expected, compensating for the under-response of the bone material during optimization in medium leads to an overdosage of the CTV when patient geometric errors are taken into account. Optimization in dose assuming everything as water composition leads to a uniform coverage. Robust optimization or forcing a uniform atomic composition in the PTV margin may resolve this incompatibility between the PTV concept and dose to medium optimization.