Abstract: The AAPM TG-43 brachytherapy dosimetry formalism, introduced in 1995, has become a standard for brachytherapy dosimetry worldwide; it implicitly assumes that charged-particle equilibrium (CPE) exists for the determination of absorbed dose to water at different locations, except in the vicinity of the source capsule. Subsequent dosimetry developments, based on Monte Carlo calculations or analytical solutions of transport equations, do not rely on the CPE assumption and determine directly the dose to different tissues. At the time of relating dose to tissue and dose to water, or vice versa, it is usually assumed that the photon fluence in water and in tissues are practically identical, so that the absorbed dose in the two media can be related by their ratio of mass energy-absorption coefficients. In this work, an efficient way to correlate absorbed dose to water and absorbed dose to tissue in brachytherapy calculations at clinically relevant distances for low-energy photon emitting seeds is proposed. A correction is introduced that is based on the ratio of the water-to-tissue photon energy-fluences. State-of-the art Monte Carlo calculations are used to score photon fluence differential in energy in water and in various human tissues (muscle, adipose and bone), which in all cases include a realistic modelling of low-energy brachytherapy sources in order to benchmark the formalism proposed. The energy-fluence based corrections given in this work are able to correlate absorbed dose to tissue and absorbed dose to water with an accuracy better than 0.5% in the most critical cases (e.g. bone tissue).

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 gamma-ray imaging systems which have been proposed for a wide variety of applications such as medical imaging, nuclear decommissioning or homeland security. In the design and optimization of such a system Monte Carlo simulations play an essential role. In this work, we propose a generic module to perform Monte Carlo simulations and analyses of Compton Camera imaging which is included in the open-source GATE/Geant4 platform. Several digitization stages have been implemented within the module to mimic the performance of the most commonly employed detectors (e.g. monolithic blocks, pixelated scintillator crystals, strip detectors...). Time coincidence sorter and sequence coincidence reconstruction are also available in order to aim at providing modules to facilitate the comparison and reproduction of the data taken with different prototypes. All processing steps may be performed during the simulation (on-the-fly mode) or as a post-process of the output files (offline mode). The predictions of the module have been compared with experimental data in terms of energy spectra, angular resolution, efficiency and back-projection image reconstruction. Consistent results within a 3-sigma interval were obtained for the energy spectra except for low energies where small differences arise. The angular resolution measure for incident photons of 1275 keV was also in good agreement between both data sets with a value close to 13 degrees. Moreover, with the aim of demonstrating the versatility of such a tool the performance of two different Compton camera designs was evaluated and compared.

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: Purpose. To estimate Type B uncertainties in absorbed-dose calculations arising from the different implementations in current state-of-the-art Monte Carlo (MC) codes of low-energy photon cross-sections (<200 keV). Methods. MC simulations are carried out using three codes widely used in the low-energy domain: PENELOPE-2018, EGSnrc, and MCNP. Three dosimetry-relevant quantities are considered: mass energy-absorption coefficients for water, air, graphite, and their respective ratios; absorbed dose; and photon-fluence spectra. The absorbed dose and the photon-fluence spectra are scored in a spherical water phantom of 15 cm radius. Benchmark simulations using similar cross-sections have been performed. The differences observed between these quantities when different cross-sections are considered are taken to be a good estimator for the corresponding Type B uncertainties. Results. A conservative Type B uncertainty for the absorbed dose (k = 2) of 1.2%-1.7% (<50 keV), 0.6%-1.2% (50-100 keV), and 0.3% (100-200 keV) is estimated. The photon-fluence spectrum does not present clinically relevant differences that merit considering additional Type B uncertainties except for energies below 25 keV, where a Type B uncertainty of 0.5% is obtained. Below 30 keV, mass energy-absorption coefficients show Type B uncertainties (k = 2) of about 1.5% (water and air), and 2% (graphite), diminishing in all materials for larger energies and reaching values about 1% (40-50 keV) and 0.5% (50-75 keV). With respect to their ratios, the only significant Type B uncertainties are observed in the case of the water-to-graphite ratio for energies below 30 keV, being about 0.7% (k = 2). Conclusions. In contrast with the intermediate (about 500 keV) or high (about 1 MeV) energy domains, Type B uncertainties due to the different cross-sections implementation cannot be considered subdominant with respect to Type A uncertainties or even to other sources of Type B uncertainties (tally volume averaging, manufacturing tolerances, etc). Therefore, the values reported here should be accommodated within the uncertainty budget in low-energy photon dosimetry studies.