An analytical approach to predict 3D positron emitter distribution in carbon ion therapy

Objective.Carbon ion therapy could benefit from range verification due to its sensitivity to range uncertainties. Positron emission tomography (PET) aids in this and comparing PET signals to a predicted positron emitter distribution (PED) is one viable approach. Monte Carlo (MC) simulations are one way to predict PED but are computationally intensive and time-consuming. To address this, an analytical approach was previously suggested to predict 1D PED from depth dose profiles. Here we aim to develop a computational framework for 3D PED prediction in carbon ion therapy, building on the 1D approach to provide a faster method than MC simulations, with potential for integration into treatment planning systems (TPS).Approach.The 1D approach was revised by considering more PEs channels and introducing new modeling functions. A mapping process for handling longitudinal heterogeneity effects in projectile PED was developed. Then, a dedicated framework for 3D PED generation based on a pencil beam algorithm (PBA) and the updated 1D method was proposed. Validation was performed throughin-silicostudies against MC calculations for several phantoms as well as realistic computed tomography scans from patient data.Main results.For range assessment, the differences between distal fall-off positions of predicted and simulated 1D PED profiles were calculated to be below 0.8 mm for all validation cases. The comparison of predicted 3D PED with simulated results was performed by global gamma index analysis using the 2%/2 mm and 1%/1 mm criteria. For patient cases, the passing rates for 1%/1 mm criteria were above 95%.Significance.These results demonstrated the capability of our approach to predict 3D PED with good accuracy in terms of range and magnitude, paving the way to future implementation in a TPS, which commonly relies on PBA for¹²C ions. Moreover, a significant speed-up compared to MC simulations was achieved, with future speed-optimized implementations.