Including Volume Effects in Biological Treatment Plan Optimization for Carbon Ion Therapy: Generalized Equivalent Uniform Dose-Based Objective in TRiP98

We describe a way to include biologically based objectives in plan optimization specific for carbon ion therapy, beyond the standard voxel-dose-based criteria already implemented in TRiP98, research planning software for ion beams. The aim is to account for volume effects-tissue architecture-dependent response to damage-in the optimization procedure, using the concept of generalized equivalent uniform dose (gEUD), which is an expression to convert a heterogeneous dose distribution (e.g., in an organ at risk (OAR)) into a uniform dose associated with the same biological effect. Moreover, gEUD is closely related to normal tissue complication probability (NTCP). The multi-field optimization problem here takes also into account the relative biological effectiveness (RBE), which in the case of ion beams is not factorizable and introduces strong non-linearity. We implemented the gEUD-based optimization in TRiP98, allowing us to control the whole dose-volume histogram (DVH) shape of OAR with a single objective by adjusting the prescribed gEUD(0) and the volume effect parameter a, reducing the volume receiving dose levels close to mean dose when a = 1 (large volume effect) while close to maximum dose for a >> 1 (small volume effect), depending on the organ type considered. We studied the role of gEUD(0) and a in the optimization, and we compared voxel-dose-based and gEUD-based optimization in chordoma cases with different anatomies. In particular, for a plan containing multiple OARs, we obtained the same target coverage and similar DVHs for OARs with a small volume effect while decreasing the mean dose received by the proximal parotid, thus reducing its NTCP by a factor of 2.5. Further investigations are done for this plan, considering also the distal parotid gland, obtaining a NTCP reduction by a factor of 1.9 for the proximal and 2.9 for the distal one. In conclusion, this novel optimization method can be applied to different OARs, but it achieves the largest improvement for organs whose volume effect is larger. This allows TRiP98 to perform a double level of biologically driven optimization for ion beams, including at the same time RBE-weighted dose and volume effects in inverse planning. An outlook is presented on the possible extension of this method to the target.