Prediction of positron emitter distributions for range monitoring in carbon ion therapy: an analytical approach

Range verification is one of the most relevant tasks in ion beam therapy. In the case of carbon ion therapy, positron emission tomography (PET) is the most widely used method for this purpose, which images the [Formula: see text]-activation following nuclear interactions of the ions with the tissue nuclei. Since the positron emitter activity profile is not directly proportional to the dose distribution, until today only its comparison to a prediction of the PET profile allows for treatment verification. Usually, this prediction is obtained from time-consuming Monte Carlo simulations of high computational effort, which impacts the clinical workflow. To solve this issue in proton therapy, a convolution approach was suggested to predict positron emitter activity profiles from depth dose distributions analytically. In this work, we introduce an approach to predict positron emitter distributions from depth dose profiles in carbon ion therapy. While the distal fall-off position of the positron emitter profile is predicted from a convolution approach similar to the one suggested for protons, additional analytical functions are introduced to describe the characteristics of the positron emitter distribution in tissue. The feasibility of this approach is demonstrated with monoenergetic depth dose profiles and spread out Bragg peaks in homogeneous and heterogeneous phantoms. In all cases, the positron emitter profile is predicted with high precision and the distal fall-off position is reproduced with millimeter accuracy.