Abstract: Random coincidences ('randoms') are one of the main sources of image degradation in PET imaging. In order to correct for this effect, an accurate method to estimate the contribution of random events is necessary. This aspect becomes especially relevant for high-resolution PET scanners where the highest image quality is sought and accurate quantitative analysis is undertaken. One common approach to estimate randoms is the so-called singles rate method (SR) widely used because of its good statistical properties. SR is based on the measurement of the singles rate in each detector element. However, recent studies suggest that SR systematically overestimates the correct random rate. This overestimation can be particularly marked for low energy thresholds, below 250 keV used in some applications and could entail a significant image degradation. In this work, we investigate the performance of SR as a function of the activity, geometry of the source and energy acceptance window used. We also investigate the performance of an alternative method, which we call 'singles trues' (ST) that improves SR by properly modeling the presence of true coincidences in the sample. Nevertheless, in any real data acquisition the knowledge of which singles are members of a true coincidence is lost. Therefore, we propose an iterative method, STi, that provides an estimation based on ST but which only requires the knowledge of measurable quantities: prompts and singles. Due to inter-crystal scatter, for wide energy windows ST only partially corrects SR overestimations. While SR deviations are in the range 86-300% (depending on the source geometry), the ST deviations are systematically smaller and contained in the range 4-60%. STi fails to reproduce the ST results, although for not too high activities the deviation with respect to ST is only a few percent. For conventional energy windows, i.e. those without inter-crystal scatter, the ST method corrects the SR overestimations, and deviations from the true random rate are of the order of 1% or less. In addition, in the case of conventional energy window STi results reproduce ST results and therefore the former can be used to obtain the true random rate.

Abstract: In the development of prototype systems for positron emission tomography a valid and robust image reconstruction algorithm is required. However, prototypes often employ novel detector and system geometries which may change rapidly under optimization. In addition, developing systems generally produce highly granular, or possibly continuous detection domains which require some level of on-the-fly calculation for retention of measurement precision. In this investigation a new method of on-the-fly system matrix calculation is proposed that provides advantages in application to such list-mode systems in terms of flexibility in system modeling. The new method is easily adaptable to complicated system geometries and available computational resources. Detection uncertainty models are used as random number generators to produce ensembles of possible photon trajectories at image reconstruction time for each datum in the measurement list. However, the result of this approach is that the system matrix elements change at each iteration in a non-repetitive manner. The resulting algorithm is considered the simulation of a one-pass list (SOPL) which is generated and the list traversed during image reconstruction. SOPL alters the system matrix in use at each iteration and so behavior within the maximum likelihood-expectation maximization algorithm was investigated. A two-pixel system and a small two dimensional imaging model are used to illustrate the process and quantify aspects of the algorithm. The two-dimensional imaging system showed that, while incurring a penalty in image resolution, in comparison to a non-random equal-computation counterpart, SOPL provides much enhanced noise properties. In addition, enhancement in system matrix quality is straightforward (by increasing the number of samples in the ensemble) so that the resolution penalty can be recovered when desired while retaining improvement in noise properties. Finally the approach is tested and validated against a standard (highly accurate) system matrix using experimental data from a prototype system-the AX-PET.

Abstract: Given the strong variations in the sensitivity of Compton cameras for the detection of events originating from different points in the field of view (FoV), sensitivity correction is often necessary in Compton image reconstruction. Several approaches for the calculation of the sensitivity matrix have been proposed in the literature. While most of these models are easily implemented and can be useful in many cases, they usually assume high angular coverage over the scattered photon, which is not the case for our prototype. In this work, we have derived an analytical model that allows us to calculate a detailed sensitivity matrix, which has been compared to other sensitivity models in the literature. Specifically, the proposed model describes the probability of measuring a useful event in a two-plane Compton camera, including the most relevant physical processes involved. The model has been used to obtain an expression for the system and sensitivity matrices for iterative image reconstruction. These matrices have been validated taking Monte Carlo simulations as a reference. In order to study the impact of the sensitivity, images reconstructed with our sensitivity model and with other models have been compared. Images have been reconstructed from several simulated sources, including point-like sources and extended distributions of activity, and also from experimental data measured with Na-22 sources. Results show that our sensitivity model is the best suited for our prototype. Although other models in the literature perform successfully in many scenarios, they are not applicable in all the geometrical configurations of interest for our system. In general, our model allows to effectively recover the intensity of point-like sources at different positions in the FoV and to reconstruct regions of homogeneous activity with minimal variance. Moreover, it can be employed for all Compton camera configurations, including those with low angular coverage over the scatterer.

Abstract: Compton Cameras are electronically collimated photon imagers suitable for sub-MeV to few MeV gamma-ray detection. Such features are desirable to enablein vivorange verification in hadron therapy, through the detection of secondary Prompt Gammas. A major concern with this technique is the poor image quality obtained when the incoming gamma-ray energy is unknown. Compton Cameras with more than two detector planes (multi-layer Compton Cameras) have been proposed as a solution, given that these devices incorporate more signal sequences of interactions to the conventional two interaction events. In particular, three interaction events convey more spectral information as they allow inferring directly the incident gamma-ray energy. A three-layer Compton Telescope based on continuous Lanthanum (III) Bromide crystals coupled to Silicon Photomultipliers is being developed at the IRIS group of IFIC-Valencia. In a previous work we proposed a spectral reconstruction algorithm for two interaction events based on an analytical model for the formation of the signal. To fully exploit the capabilities of our prototype, we present here an extension of the model for three interaction events. Analytical expressions of the sensitivity and the System Matrix are derived and validated against Monte Carlo simulations. Implemented in a List Mode Maximum Likelihood Expectation Maximization algorithm, the proposed model allows us to obtain four-dimensional (energy and position) images by using exclusively three interaction events. We are able to recover the correct spectrum and spatial distribution of gamma-ray sources when ideal data are employed. However, the uncertainties associated to experimental measurements result in a degradation when real data from complex structures are employed. Incorrect estimation of the incident gamma-ray interaction positions, and missing deposited energy associated with escaping secondaries, have been identified as the causes of such degradation by means of a detailed Monte Carlo study. As expected, our current experimental resolution and efficiency to three interaction events prevents us from correctly recovering complex structures of radioactive sources. However, given the better spectral information conveyed by three interaction events, we expect an improvement of the image quality of conventional Compton imaging when including such events. In this regard, future development includes the incorporation of the model assessed in this work to the two interaction events model in order to allow using simultaneously two and three interaction events in the image reconstruction.

Abstract: The IRIS group at IFIC Valencia is developing a three-layer Compton camera for treatment monitoring in proton therapy. The system is composed of three detector planes, each made of a LaBr3<i monolithic crystal coupled to a SiPM array. Having obtained successful results with the first prototype (MACACO) that demonstrated the feasibility of the proposed technology, a second prototype (MACACO II) with improved performance has been developed, and is the subject of this work. The new system has an enhanced detector energy resolution which translates into a higher spatial resolution of the telescope. The image reconstruction method has also been improved with an accurate model of the sensitivity matrix. The device has been tested with high energy photons at the National Accelerator Centre (CNA, Seville). The tests involved a proton beam of 18 MeV impinging on a graphite target, to produce 4.4 MeV photons. Data were taken at different system positions of the telescope with the first detector at 65 and 160 mm from the target, and at different beam intensities. The measurements allowed successful reconstruction of the photon emission distribution at two target positions separated by 5 mm in different telescope configurations. This result was obtained both with data recorded in the first and second telescope planes (two interaction events) and, for the first time in beam experiments, with data recorded in the three planes (three interaction events).