Extension of the ML-EM algorithm for dose estimation using PET in proton therapy: application to an inhomogeneous target

Positron emission tomography (PET) has been used for in vivo treatment verification, mainly for range verification, in proton therapy. Evaluating the direct dose from PET measurements remains challenging; however, it is highly desirable from a clinical perspective. In this study, a method for estimating the dose distribution from the positron emitter distributions was developed using the maximum likelihood expectation maximization algorithm. The 1D spatial relationship between positron emitter distributions and a dose distribution in an inhomogeneous target was inputted into the system matrix based on a filter framework. In contrast, spatial resolution of the PET system and total variation regularization (as prior knowledge for dose distribution) were considered in the 3D image-space. The dose estimation was demonstrated using Monte Carlo simulated PET activity distributions with substantial noise in a head and neck phantom. This mimicked the single field irradiation of the spread-out Bragg peak beams at clinical dose levels. Besides the simple implementation of the algorithm, this strategy achieved a high-speed calculation (30 s for a 3D dose estimation) and accurate dose and range estimations (less than 10% and 2 mm errors at 1-σ values, respectively). The proposed method could be key for using PET for in vivo dose monitoring.