Estimation of respiratory phases during proton radiotherapy from a 4D-CT and Prompt gamma detection profiles

Proton radiotherapy has a potential to provide an effective cancer treatment while sparing greater volume of healthy tissue than the conventional X-ray based radiotherapy. However, in lungs this potential is hindered by motion due to breathing. An important quantity in treatment verification is the correlation between the respiratory phases (RP) and the timing of pencil beam scanning (PBS). In this note, we demonstrate how the RP can be estimated using Prompt gamma (PG) detection profiles collected during a treatment. We utilized a 4D-CT of a patient with lung cancer, a treatment plan and a PG simulator. The treatment plan consisted of ten layers corresponding to ten proton energies. The RPs of the 4D-CT were interpolated using a deformable registration algorithm, so as to have fifty RPs in total. Deviations from regular breathing were introduced via time dependent frequency modulation. Fifty unique breathing patterns were generated, for which PG profiles were simulated for each pencil beam. Poisson noise was added to each PG profile to account for photon statistics. The RPs were estimated by comparing the PG profiles with and without Poisson noise via three different methods: the RP associated with each layer was estimated 1) independently of the other layers, 2) using a linear correlation between the layers, and 3) using a quadratic correlation between the layers. The best model, the quadratic model, yielded an average error in RP estimation relative to the breathing period of 5% of the breathing period or less with a 90% confidence interval.