A fast and accurate dose calculation engine for hadrontherapy is critical for both routine clinical and advanced research applications. FRoG is a graphics processing unit (GPU)-based forward calculation tool developed at CNAO (Centro Nazionale di Adroterapia Oncologica) and at HIT (Heidelberg Ion Beam Therapy Center) for fast and accurate calculation of both physical and biological dose. FRoG calculation engine adopts a triple Gaussian parameterization for the description of the lateral dose distribution. FRoG provides dose, dose-averaged linear energy transfer, and biological dose-maps, -profiles, and -volume-histograms. For the benchmark of the FRoG calculation engine, using the clinical settings available at CNAO, spread-out Bragg peaks (SOBPs) and patient cases for both proton and carbon ion beams have been calculated and compared against FLUKA Monte Carlo (MC) predictions. In addition, FRoG patient-specific quality assurance (QA) has been performed for twenty-five proton and carbon ion fields. As a result, for protons, biological dose values, using a relative biological effectiveness (RBE) of 1.1, agree on average with MC within ~1% for both SOBPs and patient plans. For carbon ions, RBE-weighted dose (D_RBE) agreement against FLUKA is within ~2.5% for the studied SOBPs and patient plans. Both MKM (Microdosimetric Kinetic Model) and LEM (Local Effect Model) D_RBE are implemented and tested in FRoG to support the NIRS (National Institute of Radiological Sciences)-based to LEM-based biological dose conversion. FRoG matched the measured QA dosimetric data within ~2.0% for both particle species. The typical calculation times for patients ranged from roughly 1 to 4 min for proton beams and 3 to 6 min for carbon ions on a NVIDIA^® GeForce^® GTX 1080 Ti. This works demonstrates FRoG’s potential to bolster clinical activity with proton and carbon ion beams at CNAO.

The clinical application of different relative biological effectiveness (RBE) models for carbon ion RBE-weighted dose calculation hinders a global consensus in defining normal tissue constraints. This work aims to update the local effect model (LEM)-based constraints for the rectum using microdosimetric kinetic model (mMKM)-defined values, relying on RBE translation and the analysis of long-term clinical outcomes. LEM-optimized plans of treated patients, having suffered from prostate adenocarcinoma (n = 22) and sacral chordoma (n = 41), were recalculated with the mMKM using an in-house developed tool. The relation between rectum dose-volume points in the two RBE systems (D_LEM|v and D_MKM|v) was fitted to translate new LEM-based constraints. Normal tissue complication probability (NTCP) values, predicting late rectal toxicity, were obtained by applying published parameters. No late rectal toxicity events were reported within the patient cohort. The rectal toxicity outcome was confirmed using dosimetric analysis: D_MKMVHs lay largely below original constraints; the translated D_LEM|v values were 4.5%, 8.3%, 18.5%, and 35.4% higher than the nominal D_MKM|v of the rectum volume, v—1%, 5%, 10% and 20%. The average NTCP value ranged from 5% for the prostate adenocarcinoma, to 0% for the sacral chordoma group. The redefined constraints, to be confirmed prospectively with clinical data, are D_LEM|5cc ≤ 61 Gy(RBE) and D_LEM|1cc ≤ 66 Gy(RBE).