Objective: This paper presents a new method for fast reconstruction (compatible with in-beam use) of deposited dose during proton therapy using data acquired from a PET scanner. The most innovative feature of this novel method is the production of noiseless reconstructed dose distributions from which proton range can be derived with high precision. Approach: A new MLEM $\&$ Simulated Annealing (MSA) algorithm, developed especially in this work, reconstructs the deposited dose distribution from a realistic pre-calculated activity-dose dictionary. This dictionary contains the contribution of each beam in the plan to the 3D activity and dose maps, as calculated by a Monte Carlo (MC) simulation. The MSA algorithm, using a priori information of the treatment plan, seeks for the linear combination of activities of the precomputed beams that best fits the observed PET data, obtaining at the same time the deposited dose. Main results: the method has been tested using simulated data to determine its performance under 4 different test cases: 1) dependency of range detection accuracy with delivered dose, 2) in-beam vs offline verification, 3) ability to detect anatomical changes and 4) reconstruction of a realistic spread-out Bragg peak. The results show the ability of the method to accurately reconstruct doses from PET data corresponding to 1-Gy irradiations, both in intra-fraction and inter-fraction verification scenarios. For this dose level (1 Gy) the method was able to spot range variations as small as 0.6 mm. Significance: out method is able to reconstruct dose maps with remarkable accuracy from clinically relevant dose levels down to 1 Gy. Furthermore, due to the noiseless nature of reconstructed dose maps, an accuracy better than one millimeter was obtained in proton range estimates. These features make of this method a realistic option for range verification in proton therapy.

Real-time positron emission tomography (PET) may provide information from first-shot images, enable PET-guided biopsies, and allow awake animal studies. Fully-3D iterative reconstructions yield the best images in PET, but they are too slow for real-time imaging. Analytical methods such as Fourier back projection (FBP) are very fast, but yield images of poor quality with artifacts due to noise or data incompleteness. In this work, an image reconstruction based on the pseudoinverse of the system response matrix (SRM) is presented. w. To implement the pseudoinverse method, the reconstruction problem is separated into two stages. First, the axial part of the SRM is pseudo-inverted (PINV) to rebin the 3D data into 2D datasets. Then, the resulting 2D slices can be reconstructed with analytical methods or by applying the pseudoinverse algorithm again. The proposed two-step PINV reconstruction yielded good-quality images at a rate of several frames per second, compatible with real time applications. Furthermore, extremely fast direct PINV reconstruction of projections of the 3D image collapsed along specific directions can be implemented.

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