A photon source model for alpha-emitter radionuclides.

Objective.A Monte Carlo virtual source model named PHID (photon from Ion decay) that generates photons emitted in the complex decay chain process of alpha-emitter radionuclides is proposed, typically for use during the simulation of SPECT image acquisition.Approach.Given an alpha-emitter radionuclide, the PHID model extracts from Geant4 databases the photon emission lines from all decaying daughters for both isometric transition and atomic relaxation processes. According to a given time range, abundances and activities in the decay chain are considered thanks to the Bateman equations, taking into account the decay rates and the initial abundances.Main results.PHID is evaluated by comparison with analog Monte Carlo simulation. It generates photons with the correct energy and temporal distribution, avoiding the costly simulation of the complete decay chain thus decreasing the computation time. The exact time gain depends on the simulation setup. As an example, it is 30× faster for simulating 1 MBq of225Ac in water for 1 section Moreover, for225Ac, PHID was also compared to a simplified source model with the two main photon emission lines (218 and 440 keV). PHID shows that 2 times more particles are simulated and 60% more counts are detected in the images.Significance.PHID can simulate any alpha-emitter radionuclide available in the Geant4 database. As a limitation, photons emitted from Bremsstrahlung are ignored, but they represent only 0.7% of the photons above 30 keV and are not significant for SPECT imaging. PHID is open-source, available in GATE 10, and eases the investigation of imaging photon emission from alpha emitters.

Annihilation photon GAN source model for PET Monte Carlo simulation.

Objective.Following previous works on virtual sources model with Generative Adversarial Network (GAN), we extend the proof of concept for generating back-to-back pairs of gammas with timing information, typically for Monte Carlo simulation of Positron Emission Tomography(PET) imaging.Approach.A conditional GAN is trained once from a low statistic simulation in a given attenuation phantom and enables the generation of various activity source distributions. GAN training input is a set of gammas exiting a phantom, tracked from a source of positron emitters, described by position, direction and energy. A new parameterization that improves the training is also proposed. An ideal PET reconstruction algorithm is used to evaluate the quality of the GAN.Main results.The proposed method is evaluated on National Electrical Manufacturers Association (NEMA) International Electrotechnical Commission (IEC) phantoms and with CT patient image showing good agreement with reference simulations. The proportions of 2-gammas, 1-gammas and absorbed-gammas are respected to within one percent, image profiles matched and recovery coefficients were close with less than 5% difference. GAN tends to blur gamma energy peak, e.g. 511 keV.Significance.Once trained, the GAN generator can be used as input source for Monte Carlo simulations of PET imaging systems, decreasing the computational time with speedups up to ×400 according to the configurations.

Analytical modeling and Monte Carlo simulations of multi-parallel slit and knife-edge slit prompt gamma cameras.

Purpose.Present and validate an analytical model (AM) to calculate efficiency and spatial resolution of multi-parallel slit (MPS) and knife-edge slit (KES) cameras in the context of prompt gamma (PG) imaging in proton therapy, as well as perform a fair comparison between two prototypes of these cameras with their design specifications.Materials and methods.Monte Carlo (MC) simulations with perfect (ideal) conditions were performed to validate the proposed AM, as well as simulations in realistic conditions for the comparison of both prototypes. The spatial resolution obtained from simulations was derived from reconstructed PG profiles. The falloff retrieval precision (FRP) was quantified based on the variability of PG profiles from 50 different realizations.Results.The AM shows that KES and MPS designs fulfilling 'MPS-KES similar conditions' should have very close actual performances if the KES slit width corresponds to the half of the MPS slit width. Reconstructed PG profiles from simulated data with both cameras were used to compute the efficiency and spatial resolutions to compare against the model predictions. The FRP of both cameras was calculated with realistic detection conditions for beams with 107, 108and 109incident protons. A good agreement was found between the values predicted by the AM and those obtained from MC simulations (relative deviations of the order of 5%).Conclusion.The MPS camera outperforms the KES camera with their design specifications in realistic conditions and both systems can reach millimetric precision in the determination of the falloff position with 108or more initial protons.

Evaluation of simulators for x-ray speckle-based phase contrast imaging.

X-ray phase contrast imaging (PCI) denotes a group of highly sensitive imaging techniques that permits imaging at scales ranging from nanoscopic to the medical. Recently introduced, speckle-based imaging has seen a rapid development because of its experimental simplicity and its capability to retrieve the refraction, the scattering and the absorption of a sample using a conventional x-ray set-up. Precise simulation would permit to optimise the imaging setups for different applications, but until now works on simulation of x-ray speckle-based PCI have been very few. In this work we evaluate different simulation codes, based on Monte-Carlo, analytical ray-tracing and wave-optics Fresnel propagation. The simulation results are compared to both synchrotron and conventional imaging experiments to permits their validation. We obtain a strong similarity between simulated and experimental data. We discuss the validity and applicability of each approach.

Modeling complex particles phase space with GAN for Monte Carlo SPECT simulations: a proof of concept.

A method is proposed to model by a generative adversarial network the distribution of particles exiting a patient during Monte Carlo simulation of emission tomography imaging devices. The resulting compact neural network is then able to generate particles exiting the patient, going towards the detectors, avoiding costly particle tracking within the patient. As a proof of concept, the method is evaluated for single photon emission computed tomography (SPECT) imaging and combined with another neural network modeling the detector response function (ARF-nn). A complete rotating SPECT acquisition can be simulated with reduced computation time compared to conventional Monte Carlo simulation. It also allows the user to perform simulations with several imaging systems or parameters, which is useful for imaging system design.

Scattering proton CT.

Proton computed tomography (CT) is an imaging modality investigated mainly in the context of proton therapy as a complement to x-ray CT. It uses protons with high enough energy to fully traverse the imaged object. Common prototype systems measure each proton's position and direction upstream and downstream of the object as well as the energy loss which can be converted into the water equivalent thickness. A reconstruction algorithm then produces a map of the relative stopping power in the object. As an alternative to energy-loss proton CT, it has been proposed to reconstruct a map of the object's scattering power based on the protons' angular dispersion which can be estimated from the measured directions. As in energy-loss proton CT, reconstruction should best be performed considering the non-linear shape of proton trajectories due to multiple Coulomb scattering (MCS), but no algorithm to achieve this is so far available in the literature. In this work, we propose a filtered backprojection algorithm with distance-driven binning to account for the protons' most likely path. Furthermore, we present a systematic study of scattering proton CT in terms of inherent noise and spatial resolution and study the artefacts which arise from the physics of MCS. Our analysis is partly based on analytical models and partly on Monte Carlo simulations. Our results show that the proposed algorithm performs well in reconstructing relative scattering power maps, i.e. scattering power relative to that of water. Spatial resolution is improved by almost a factor of three compared to straight line projection and is comparable to energy-loss proton CT. Image noise, on the other hand, is inherently much higher. For example, in a water cylinder of 20 cm diameter, representative of a human head, noise in the central image pixel is about 40 times higher in scattering proton CT than in energy-loss proton CT. Relative scattering power in dense regions such as bone inserts is systematically underestimated by a few percent, depending on beam energy and phantom geometry.

Ultra-fast prompt gamma detection in single proton counting regime for range monitoring in particle therapy.

In order to fully exploit the ballistic potential of particle therapy, we propose an online range monitoring concept based on time-of-flight (TOF)-resolved prompt gamma (PG) detection in a single proton counting regime. In a proof of principle experiment, different types of monolithic scintillating gamma detectors are read in time coincidence with a diamond-based beam hodoscope, in order to build TOF spectra of PG generated in a target presenting an air cavity of variable thickness. Since the measurement was carried out at low beam currents (< 1 proton/bunch) it was possible to reach excellent coincidence time resolutions, of the order of 100 ps (σ). Our goal is to detect possible deviations of the proton range with respect to treatment planning within a few intense irradiation spots at the beginning of the session and then carry on the treatment at standard beam currents. The measurements were limited to 10 mm proton range shift. A Monte Carlo simulation study reproducing the experiment has shown that a 3 mm shift can be detected at 2σ by a single detector of ∼1.4 × 10-3 absolute detection efficiency within a single irradiation spot (∼108 protons) and an optimised experimental set-up.

2D directional ramp filter.

Usual tomographic reconstruction methods start by filtering projections before backprojecting the data. In some cases, inverting the filtering and the backprojection steps can be useful to preserve spatial information. In this paper, an intermediate between a filter-backproject and a backproject-filter approach is proposed, based on the extension of the usual ramp filter to two dimensions. To this end, an expression for a band-limited 2D version of the ramp filter is derived. We have tested this filter on simulated x-ray CT projections of a Shepp-Logan phantom and on proton CT list-mode data. We accurately reconstructed the x-ray CT and the proton CT data, although the reconstruction can be slightly noisier than a standard filtered backprojection in some cases. A slight improvement of the spatial resolution of proton CT images reconstructed with this 2D filter has been observed.

CCMod: a GATE module for Compton camera imaging simulation.

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°. Moreover, with the aim of demonstrating the versatility of such a tool the performance of two different Compton camera designs was evaluated and compared.

Generative adversarial networks (GAN) for compact beam source modelling in Monte Carlo simulations.

A method is proposed and evaluated to model large and inconvenient phase space files used in Monte Carlo simulations by a compact generative adversarial network (GAN). The GAN is trained based on a phase space dataset to create a neural network, called Generator (G), allowing G to mimic the multidimensional data distribution of the phase space. At the end of the training process, G is stored with about 0.5 million weights, around 10 MB, instead of a few GB of the initial file. Particles are then generated with G to replace the phase space dataset. This concept is applied to beam models from linear accelerators (linacs) and from brachytherapy seed models. Simulations using particles from the reference phase space on one hand and those generated by the GAN on the other hand were compared. 3D distributions of deposited energy obtained from source distributions generated by the GAN were close to the reference ones, with less than 1% of voxel-by-voxel relative difference. Sharp parts such as the brachytherapy emission lines in the energy spectra were not perfectly modeled by the GAN. Detailed statistical properties and limitations of the GAN-generated particles still require further investigation, but the proposed exploratory approach is already promising and paves the way for a wide range of applications.

Polynomial modelling of proton trajectories in homogeneous media for fast most likely path estimation and trajectory simulation.

Protons undergo many small angle deflections when traversing a medium, such as a patient. This effect, known as multiple Coulomb scattering (MCS), leads to degraded image resolution in proton radiography and computed tomography (CT) and to lateral spreading of the dose distribution in proton therapy. To optimally account for MCS in proton imaging, the most likely path (MLP) of a proton is estimated based on its position and propagation angle measured in front of and behind the object. In this work, we propose a functional which quantifies the likelihood of a proton trajectory and study how it can be used to model proton trajectories in a homogeneous medium. We focus on two aspects: first, we present an analytical method to quickly generate proton trajectories in a homogeneous medium based on the likelihood functional and validate it through Monte Carlo simulations. It could be used for fast generation of proton CT images without a full Monte Carlo simulation, or potentially to complement the components in a treatment planning Monte Carlo which simulate MCS. Second, by maximising the likelihood functional, we derive an expression for the MLP which is equivalent to the conventional ones reported in the literature yet computationally more convenient. Moreover, we show that the MLP is strictly a polynomial function if the protons' energy loss in the medium is approximated as a polynomial and that the orders of both are linked. We validate our MLP through Monte Carlo simulations and compare proton CT images reconstructed with our expression and with the conventional one. We find that an MLP polynomial of orders larger than five do not lead to increased spatial resolution compared to lower order expressions.

Learning SPECT detector angular response function with neural network for accelerating Monte-Carlo simulations.

A method to speed up [Formula: see text] simulations of single photon emission computed tomography (SPECT) imaging is proposed. It uses an artificial neural network (ANN) to learn the angular response function (ARF) of a collimator-detector system. The ANN is trained once from a complete simulation including the complete detector head with collimator, crystal, and digitization process. In the simulation, particle tracking inside the SPECT head is replaced by a plane. Photons are stopped at the plane and the energy and direction are used as input to the ANN, which provides detection probabilities in each energy window. Compared to histogram-based ARF, the proposed method is less dependent on the statistics of the training data, provides similar simulation efficiency, and requires less training data. The implementation is available within the GATE platform.

A comprehensive theoretical comparison of proton imaging set-ups in terms of spatial resolution.

We present a comprehensive analytical comparison of four types of proton imaging set-ups and, to this end, develop a mathematical framework to calculate the width of the uncertainty envelope around the most likely proton path depending on set-up geometry, detector properties, and proton beam parameters. As a figure of merit for the spatial resolution achievable with each set-up, we use the frequency [Formula: see text] at which the modular transfer function of a density step decreases below 10%. We verify the analytical results with Monte Carlo simulations. We find that set-ups which track the angle and position of individual protons in front of and behind the phantom would yield an average spatial resolution of 0.3-0.35 lp mm-1 assuming realistic geometric parameters (i.e. 30-40 cm distance between detector and phantom, 15-20 cm phantom thickness). For set-ups combining pencil beam scanning with either a position sensitive detector, e.g. an x-ray flat panel, or with a position insensitive detector, e.g. a range telescope, we find an average spatial resolution of about 0.1 lp mm-1 for an 8 mm FWHM beam spot size. The pixel information improves the spatial resolution by less than 10%. In both set-up types, performance can be significantly improved by reducing the pencil beam size down to 2 mm FWHM. In this case, the achievable spatial resolution reaches about 0.25 lp mm-1. Our results show that imaging set-ups combining double scattering with a pixel detector can provide sufficient spatial resolution only under very stringent conditions and are not ideally suited for computed tomography applications. We further propose a region-of-interest method for set-ups with a pixel detector to filter out protons which have undergone nuclear reactions and discuss the impact of tracker detector uncertainties on the most likely path.

Neutron track length estimator for GATE Monte Carlo dose calculation in radiotherapy.

The out-of-field dose in radiation therapy is a growing concern in regards to the late side-effects and secondary cancer induction. In high-energy x-ray therapy, the secondary neutrons generated through photonuclear reactions in the accelerator are part of this secondary dose. The neutron dose is currently not estimated by the treatment planning system while it appears to be preponderant for distances greater than 50 cm from the isocenter. Monte Carlo simulation has become the gold standard for accurately calculating the neutron dose under specific treatment conditions but the method is also known for having a slow statistical convergence, which makes it difficult to be used on a clinical basis. The neutron track length estimator, a neutron variance reduction technique inspired by the track length estimator method has thus been developped for the first time in the Monte Carlo code GATE to allow a fast computation of the neutron dose in radiotherapy. The details of its implementation, as well as the comparison of its performances against the analog MC method, are presented here. A gain of time from 15 to 400 can be obtained by our method, with a mean difference in the dose calculation of about 1% in comparison with the analog MC method.

Fixed forced detection for fast SPECT Monte-Carlo simulation.

Monte-Carlo simulations of SPECT images are notoriously slow to converge due to the large ratio between the number of photons emitted and detected in the collimator. This work proposes a method to accelerate the simulations based on fixed forced detection (FFD) combined with an analytical response of the detector. FFD is based on a Monte-Carlo simulation but forces the detection of a photon in each detector pixel weighted by the probability of emission (or scattering) and transmission to this pixel. The method was evaluated with numerical phantoms and on patient images. We obtained differences with analog Monte Carlo lower than the statistical uncertainty. The overall computing time gain can reach up to five orders of magnitude. Source code and examples are available in the Gate V8.0 release.

Compton camera study for high efficiency SPECT and benchmark with Anger system.

Single photon emission computed tomography (SPECT) is at present one of the major techniques for non-invasive diagnostics in nuclear medicine. The clinical routine is mostly based on collimated cameras, originally proposed by Hal Anger. Due to the presence of mechanical collimation, detection efficiency and energy acceptance are limited and fixed by the system's geometrical features. In order to overcome these limitations, the application of Compton cameras for SPECT has been investigated for several years. In this study we compare a commercial SPECT-Anger device, the General Electric HealthCare Infinia system with a High Energy General Purpose (HEGP) collimator, and the Compton camera prototype under development by the French collaboration CLaRyS, through Monte Carlo simulations (GATE-GEANT4 Application for Tomographic Emission-version 7.1 and GEANT4 version 9.6, respectively). Given the possible introduction of new radio-emitters at higher energies intrinsically allowed by the Compton camera detection principle, the two detectors are exposed to point-like sources at increasing primary gamma energies, from actual isotopes already suggested for nuclear medicine applications. The Compton camera prototype is first characterized for SPECT application by studying the main parameters affecting its imaging performance: detector energy resolution and random coincidence rate. The two detector performances are then compared in terms of radial event distribution, detection efficiency and final image, obtained by gamma transmission analysis for the Anger system, and with an iterative List Mode-Maximum Likelihood Expectation Maximization (LM-MLEM) algorithm for the Compton reconstruction. The results show for the Compton camera a detection efficiency increased by a factor larger than an order of magnitude with respect to the Anger camera, associated with an enhanced spatial resolution for energies beyond 500 keV. We discuss the advantages of Compton camera application for SPECT if compared to present commercial Anger systems, with particular focus on dose delivered to the patient, examination time, and spatial uncertainties.

Experimental validation of a multi-energy x-ray adapted scatter separation method.

Both in radiography and computed tomography (CT), recently emerged energy-resolved x-ray photon counting detectors enable the identification and quantification of individual materials comprising the inspected object. However, the approaches used for these operations require highly accurate x-ray images. The accuracy of the images is severely compromised by the presence of scattered radiation, which leads to a loss of spatial contrast and, more importantly, a bias in radiographic material imaging and artefacts in CT. The aim of the present study was to experimentally evaluate a recently introduced partial attenuation spectral scatter separation approach (PASSSA) adapted for multi-energy imaging. For this purpose, a prototype x-ray system was used. Several radiographic acquisitions of an anthropomorphic thorax phantom were performed. Reference primary images were obtained via the beam-stop (BS) approach. The attenuation images acquired from PASSSA-corrected data showed a substantial increase in local contrast and internal structure contour visibility when compared to uncorrected images. A substantial reduction of scatter induced bias was also achieved. Quantitatively, the developed method proved to be in relatively good agreement with the BS data. The application of the proposed scatter correction technique lowered the initial normalized root-mean-square error (NRMSE) of 45% between the uncorrected total and the reference primary spectral images by a factor of 9, thus reducing it to around 5%.

Accelerated prompt gamma estimation for clinical proton therapy simulations.

There is interest in the particle therapy community in using prompt gammas (PGs), a natural byproduct of particle treatment, for range verification and eventually dose control. However, PG production is a rare process and therefore estimation of PGs exiting a patient during a proton treatment plan executed by a Monte Carlo (MC) simulation converges slowly. Recently, different approaches to accelerating the estimation of PG yield have been presented. Sterpin et al (2015 Phys. Med. Biol. 60 4915-46) described a fast analytic method, which is still sensitive to heterogeneities. El Kanawati et al (2015 Phys. Med. Biol. 60 8067-86) described a variance reduction method (pgTLE) that accelerates the PG estimation by precomputing PG production probabilities as a function of energy and target materials, but has as a drawback that the proposed method is limited to analytical phantoms. We present a two-stage variance reduction method, named voxelized pgTLE (vpgTLE), that extends pgTLE to voxelized volumes. As a preliminary step, PG production probabilities are precomputed once and stored in a database. In stage 1, we simulate the interactions between the treatment plan and the patient CT with low statistic MC to obtain the spatial and spectral distribution of the PGs. As primary particles are propagated throughout the patient CT, the PG yields are computed in each voxel from the initial database, as a function of the current energy of the primary, the material in the voxel and the step length. The result is a voxelized image of PG yield, normalized to a single primary. The second stage uses this intermediate PG image as a source to generate and propagate the number of PGs throughout the rest of the scene geometry, e.g. into a detection device, corresponding to the number of primaries desired. We achieved a gain of around 103 for both a geometrical heterogeneous phantom and a complete patient CT treatment plan with respect to analog MC, at a convergence level of 2% relative uncertainty in the 90% yield region. The method agrees with reference analog MC simulations to within 10-4, with negligible bias. Gains per voxel range from 102 to 104. The presented generic PG yield estimator is drop-in usable with any geometry and beam configuration. We showed a gain of three orders of magnitude compared to analog MC. With a large number of voxels and materials, memory consumption may be a concern and we discuss the consequences and possible tradeoffs. The method is available as part of Gate 7.2.

A novel scatter separation method for multi-energy x-ray imaging.

X-ray imaging coupled with recently emerged energy-resolved photon counting detectors provides the ability to differentiate material components and to estimate their respective thicknesses. However, such techniques require highly accurate images. The presence of scattered radiation leads to a loss of spatial contrast and, more importantly, a bias in radiographic material imaging and artefacts in computed tomography (CT). The aim of the present study was to introduce and evaluate a partial attenuation spectral scatter separation approach (PASSSA) adapted for multi-energy imaging. This evaluation was carried out with the aid of numerical simulations provided by an internal simulation tool, Sindbad-SFFD. A simplified numerical thorax phantom placed in a CT geometry was used. The attenuation images and CT slices obtained from corrected data showed a remarkable increase in local contrast and internal structure detectability when compared to uncorrected images. Scatter induced bias was also substantially decreased. In terms of quantitative performance, the developed approach proved to be quite accurate as well. The average normalized root-mean-square error between the uncorrected projections and the reference primary projections was around 23%. The application of PASSSA reduced this error to around 5%. Finally, in terms of voxel value accuracy, an increase by a factor >10 was observed for most inspected volumes-of-interest, when comparing the corrected and uncorrected total volumes.