Considerations on IMRT for quasi-isotropic non-coplanar irradiation.

The purpose of this study was the mathematical analysis of IMRT with many non-coplanar fields for planning target volumes (PTV) surrounding nearly spherical organs at risk (OAR). Our approach is partially analogous to the well known inverse planning for a cylindrically symmetric (CS) case (Brahme et al 1982 Phys. Med. Biol. 27 1221-9) and leads to a spherically symmetric (SS) solution. For the planning study we approximated isotropic 4 Pi irradiation by a quasi-isotropic non-coplanar IMRT technique with 16 fields which we compared to a coplanar IMRT technique with 15 equidistant fields. A virtual spherical phantom contained a spherical central organ at risk which was surrounded by a PTV shaped like a spherical shell with a gap towards the spherical OAR. We compared three types of plans: (1) non-segmented inversely planned fluence distributions prior to sequencing, (2) plans obtained by direct machine parameter optimization (DMPO) with up to 120 segments (good approximation of non-segmented fluence) and (3) more practical DMPO plans with up to 64 segments. In this study we sought an analytical SS solution for the non-segmented fluence distribution in 4 Pi-geometry. For the CS case Brahme et al found that a special narrow fluence peak ('Brahme peak') has to be applied to improve dose uniformity in PTV areas adjacent to the OAR. We showed that in the SS case the peak was steeper but the area under the peak was smaller. The relevance of the peak decreased for increasing gap between the OAR and the PTV. The plan quality of the non-segmented SS plans was higher albeit the fluence distributions were less uniform. The plan quality of the segmented plans degraded if the allowed number of segments was reduced; the degradation was quicker for the SS beam arrangement than for the CS beam arrangement. For 64 segments, the SS plans delivered less uniform and more conformal dose distributions than the CS plans, ensuring better sparing of the healthy tissue. Also, the SS plans always needed less monitor units than the CS plans. In conclusion, due to substructures or steeper fluence gradients, the improved potential of quasi-isotropic SS-plan quality can only be exploited, if many segments are allowed. SS plans seem to spare normal tissue better. Further analysis of non-coplanar beam arrangements with less degree of symmetry is planned, followed by a study on non-coplanar intensity modulated arc techniques.