[en] 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. (paper)

[en] 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. (paper)

[en] This work investigates the attenuation of a proton beam to reconstruct the map of the linear attenuation coefficient of a material which is mainly caused by the inelastic interactions of protons with matter. Attenuation proton computed tomography (pCT) suffers from a poor spatial resolution due to multiple Coulomb scattering (MCS) of protons in matter, similarly to the conventional energy-loss pCT. We therefore adapted a recent filtered back-projection algorithm along the most likely path (MLP) of protons for energy-loss pCT (Rit et al 2013) to attenuation pCT assuming a pCT scanner that can track the position and the direction of protons before and after the scanned object. Monte Carlo simulations of pCT acquisitions of density and spatial resolution phantoms were performed to characterize the new algorithm using Geant4 (via Gate). Attenuation pCT assumes an energy-independent inelastic cross-section, and the impact of the energy dependence of the inelastic cross-section below 100 MeV showed a capping artifact when the residual energy was below 100 MeV behind the object. The statistical limitation has been determined analytically and it was found that the noise in attenuation pCT images is 411 times and 278 times higher than the noise in energy-loss pCT images for the same imaging dose at 200 MeV and 300 MeV, respectively. Comparison of the spatial resolution of attenuation pCT images with a conventional straight-line path binning showed that incorporating the MLP estimates during reconstruction improves the spatial resolution of attenuation pCT. Moreover, regardless of the significant noise in attenuation pCT images, the spatial resolution of attenuation pCT was better than that of conventional energy-loss pCT in some studied situations thanks to the interplay of MCS and attenuation known as the West–Sherwood effect. (paper)

[en] 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. (note)

[en] 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. (paper)

[en] Sliding motion is a challenge for deformable image registration because it leads to discontinuities in the sought deformation. In this paper, we present a method to handle sliding motion using multiple B-spline transforms. The proposed method decomposes the sought deformation into sliding regions to allow discontinuities at their interfaces, but prevents unrealistic solutions by forcing those interfaces to match. The method was evaluated on 16 lung cancer patients against a single B-spline transform approach and a multi B-spline transforms approach without the sliding constraint at the interface. The target registration error (TRE) was significantly lower with the proposed method (TRE = 1.5 mm) than with the single B-spline approach (TRE = 3.7 mm) and was comparable to the multi B-spline approach without the sliding constraint (TRE = 1.4 mm). The proposed method was also more accurate along region interfaces, with 37% less gaps and overlaps when compared to the multi B-spline transforms without the sliding constraint. (paper)

[en] Motion artifacts appear in four-dimensional computed tomography (4DCT) images because of suboptimal acquisition parameters or patient breathing irregularities. Frequency of motion artifacts is high and they may introduce errors in radiation therapy treatment planning. Motion artifact detection can be useful for image quality assessment and 4D reconstruction improvement but manual detection in many images is a tedious process. We propose a novel method to evaluate the quality of 4DCT images by automatic detection of motion artifacts. The method was used to evaluate the impact of the optimization of acquisition parameters on image quality at our institute. 4DCT images of 114 lung cancer patients were analyzed. Acquisitions were performed with a rotation period of 0.5 seconds and a pitch of 0.1 (74 patients) or 0.081 (40 patients). A sensitivity of 0.70 and a specificity of 0.97 were observed. End-exhale phases were less prone to motion artifacts. In phases where motion speed is high, the number of detected artifacts was systematically reduced with a pitch of 0.081 instead of 0.1 and the mean reduction was 0.79. The increase of the number of patients with no artifact detected was statistically significant for the 10%, 70% and 80% respiratory phases, indicating a substantial image quality improvement.

[en] 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 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. (paper)

[en] Purpose: Proton CT (pCT) is a promising imaging modality for reducing range uncertainty in image-guided proton therapy. Range uncertainties partially originate from X-ray CT number conversion to stopping power ratio (SPR) and are limiting the exploitation of the full potential of proton therapy. In this study we explore the concept of spatially dependent fluence modulated proton CT (FMpCT), for achieving optimal image quality in a clinical region of interest (ROI), while reducing significantly the imaging dose to the patient. Methods: The study was based on simulated ideal pCT using pencil beam (PB) scanning. A set of 250 MeV protons PBs was used to create 360 projections of a cylindrical water phantom and a head and neck cancer patient. The tomographic images were reconstructed using a filtered backprojection (FBP) as well as an iterative algorithm (ITR). Different fluence modulation levels were investigated and their impact on the image was quantified in terms of SPR accuracy as well as noise within and outside selected ROIs, as a function of imaging dose. The unmodulated image served as reference. Results: Both FBP reconstruction and ITR without total variation (TV) yielded image quality in the ROIs similar to the reference images, for modulation down to 0.1 of the full proton fluence. The average dose was reduced by 75% for the water phantom and by 40% for the patient. FMpCT does not improve the noise for ITR with TV and modulation 0.1. Conclusion: This is the first work proposing and investigating FMpCT for producing optimal image quality for treatment planning and image guidance, while simultaneously reducing imaging dose. Future work will address spatial resolution effects and the impact of FMpCT on the quality of proton treatment plans for a prototype pCT scanner capable of list mode data acquisition. Acknowledgement: DFG-MAP DFG - Munich-Centre for Advanced Photonics (MAP)

[en] Purpose: The quantification of the intrinsic performances of proton computed tomography (pCT) as a modality for treatment planning in proton therapy. The performance of an ideal pCT scanner is studied as a function of various parameters. Methods: Using GATE/Geant4, we simulated an ideal pCT scanner and scans of several cylindrical phantoms with various tissue equivalent inserts of different sizes. Insert materials were selected in order to be of clinical relevance. Tomographic images were reconstructed using a filtered backprojection algorithm taking into account the scattering of protons into the phantom. To quantify the performance of the ideal pCT scanner, we study the precision and the accuracy with respect to the theoretical relative stopping power ratios (RSP) values for different beam energies, imaging doses, insert sizes and detector positions. The planning range uncertainty resulting from the reconstructed RSP is also assessed by comparison with the range of the protons in the analytically simulated phantoms. Results: The results indicate that pCT can intrinsically achieve RSP resolution below 1%, for most examined tissues at beam energies below 300 MeV and for imaging doses around 1 mGy. RSP maps accuracy of less than 0.5 % is observed for most tissue types within the studied dose range (0.2–1.5 mGy). Finally, the uncertainty in the proton range due to the accuracy of the reconstructed RSP map is well below 1%. Conclusion: This work explores the intrinsic performance of pCT as an imaging modality for proton treatment planning. The obtained results show that under ideal conditions, 3D RSP maps can be reconstructed with an accuracy better than 1%. Hence, pCT is a promising candidate for reducing the range uncertainties introduced by the use of X-ray CT alongside with a semiempirical calibration to RSP.Supported by the DFG Cluster of Excellence Munich-Centre for Advanced Photonics (MAP)