4D ML reconstruction as a tool for volumetric PET-based treatment verification in ion beam radiotherapy

Purpose: An innovative strategy to improve the sensitivity of positron emission tomography (PET)- based treatment verification in ion beam radiotherapy is proposed. Methods: Low counting statistics PET images acquired during or shortly after the treatment (Measured PET) and a Monte Carlo estimate of the same PET images derived from the treatment plan (Expected PET) are considered as two frames of a 4D dataset. A 4D maximum likelihood reconstruction strategy was adapted to iteratively estimate the annihilation events distribution in a reference frame and the deformation motion fields that map it in the Expected PET and Measured PET frames. The outputs generated by the proposed strategy are as follows: (1) an estimate of the Measured PET with an image quality comparable to the Expected PET and (2) an estimate of the motion field mapping Expected PET to Measured PET. The details of the algorithm are presented and the strategy is preliminarily tested on analytically simulated datasets. Results: The algorithm demonstrates (1) robustness against noise, even in the worst conditions where 1.5-104 true coincidences and a random fraction of 73% are simulated; (2) a proper sensitivity to different kind and grade of mismatches ranging between 1 and 10 mm; (3) robustness against bias due to incorrect washout modeling in the Monte Carlo simulation up to 1/3 of the original signal amplitude; and (4) an ability to describe the mismatch even in presence of complex annihilation distributions such as those induced by two perpendicular superimposed ion fields. Conclusions: The promising results obtained in this work suggest the applicability of the method as a quantification tool for PET-based treatment verification in ion beam radiotherapy. An extensive assessment of the proposed strategy on real treatment verification data is planned.