Positron emission tomography (PET) has been extensively studied and clinically investigated for dose verification in proton therapy. However, the production distributions of positron emitters are not proportional to the dose distribution. Thus, direct dose evaluation is limited when using the conventional PET-based approach. We propose a method for estimating the dose distribution from the positron emitter distributions using the maximum likelihood (ML) expectation maximization (EM) algorithm combined with filtering. In experiments to verify the effectiveness of the proposed method, mono-energetic and spread-out Bragg-peak proton beams were delivered by a synchrotron, and a water target was irradiated at clinical dose levels. Planar PET measurements were performed during beam pauses and after irradiation over a total period of 200 s. In addition, we conducted a Monte Carlo simulation to obtain the required filter functions and analyze the influence of the number of algorithm iterations on estimation. We successfully estimated the 2D dose distributions even under statistical noise in the PET images. The accuracy of the 2D dose estimation was about 10% for both beams at the 1-σ values of relative error. This value is comparable to the deviations in the measured PET activity distributions. For the laterally integrated profile along the beam direction, a low error within 5% was obtained per irradiation value. Moreover, the difference of estimated proton ranges was within 1 mm, and 2D estimation from the PET images was completed in 21 ms. Hence, the proposed algorithm may be applied to real-time dose monitoring. Although this is the first attempt to use the ML-EM algorithm for dose estimation, the proposed method showed high accuracy and speed in the estimation of proton dose distribution from PET data. The proposed method is thus a step forward to exploit the full potential of PET for in vivo dose verification.
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