Impact of secondary particles on the magnetic field generated by a proton pencil beam: a finite-element analysis based on Geant4-DNA simulations.

PURPOSE: To investigate the static magnetic field generated by a proton pencil beam as a candidate for range verification by means of Monte Carlo simulations, thereby improving upon existing analytical calculations. We focus on the impact of statistical current fluctuations and secondary protons and electrons. METHODS: We considered a pulsed beam (10 µ ${\umu}$ s pulse duration) during the duty cycle with a peak beam current of 0.2 µ $\umu$ A and an initial energy of 100 MeV. We ran Geant4-DNA Monte Carlo simulations of a proton pencil beam in water and extracted independent particle phase spaces. We calculated longitudinal and radial current density of protons and electrons, serving as an input for a magnetic field estimation based on a finite element analysis in a cylindrical geometry. We made sure to allow for non-solenoidal current densities as is the case of a stopping proton beam. RESULTS: The rising proton charge density toward the range is not perturbed by energy straggling and only lowered through nuclear reactions by up to 15%, leading to an approximately constant longitudinal current. Their relative low density however (at most 0.37 protons/mm3 for the 0.2  µ ${\umu}$ A current and a beam cross-section of 2.5 mm), gives rise to considerable current density fluctuations. The radial proton current resulting from lateral scattering and being two orders of magnitude weaker than the longitudinal current is subject to even stronger fluctuations. Secondary electrons with energies above 10 eV, that far outnumber the primary protons, reduce the primary proton current by only 10% due to their largely isotropic flow. A small fraction of electrons (<1%), undergoing head-on collisions, constitutes the relevant electron current. In the far-field, both contributions to the magnetic field strength (longitudinal and lateral) are independent of the beam spot size. We also find that the nuclear reaction-related losses cause a shift of 1.3 mm to the magnetic field profile relative to the actual range, which is further enlarged to 2.4 mm by the electron current (at a distance of ρ = 50 $\rho =50$  mm away from the central beam axis). For ρ > 45 $\rho >45$  mm, the shift increases linearly. While the current density variations cause significant magnetic field uncertainty close to the central beam axis with a relative standard deviation (RSD) close to 100%, they average out at a distance of 10 cm, where the RSD of the total magnetic field drops below 2%. CONCLUSIONS: With the small influence of the secondary electrons together with the low RSD, our analysis encourages an experimental detection of the magnetic field through sensitive instrumentation, such as optical magnetometry or SQUIDs.

Patient-specific CT calibration based on ion radiography for different detector configurations in 1H, 4He and 12C ion pencil beam scanning.

The empirical conversion of the treatment planning x-ray computed tomography (CT) image to ion stopping power relative to water causes dose calculation inaccuracies in ion beam therapy. A patient-specific calibration of the CT image is enabled by the combination of an ion radiography (iRad) with the forward-projection of the empirically converted CT image along the estimated ion trajectories. This work investigated the patient-specific CT calibration for list-mode and integration-mode detector configurations, with reference to a ground truth ion CT (iCT) image. Analytical simulations of idealized carbon ion and proton trajectories in a numerical anthropomorphic phantom and realistic Monte Carlo simulations of proton, helium and carbon ion pencil beam scanning in a clinical CT image of a head-and-neck patient were considered. Controlled inaccuracy and noise levels were applied to the calibration curve and to the iRad, respectively. The impact of the selection of slices and angles of the iRads, as well as the choice of the optimization algorithm, were investigated. Accurate and robust CT calibration was obtained in analytical simulations of straight carbon ion trajectories. Analytical simulations of non-straight proton trajectories due to scattering suggested limitations for integration-mode but not for list-mode. To make the most of integration-mode, a dedicated objective function was proposed, demonstrating the desired accuracy for sufficiently high proton statistics in analytical simulations. In clinical data the inconsistencies between the iRad and the forward-projection of the ground truth iCT image were in the same order of magnitude as the applied inaccuracies (up to 5%). The accuracy of the CT calibration were within 2%-5% for integration-mode and 1%-3% for list-mode. The feasibility of successful patient-specific CT calibration depends on detector technologies and is primarily limited by these above mentioned inconsistencies that slightly penalize protons over helium and carbon ions due to larger scattering and beam spot size.

Two-dimensional noise reconstruction in proton computed tomography using distance-driven filtered back-projection of simulated projections.

We present a formalism for two-dimensional (2D) noise reconstruction in proton computed tomography (pCT). This is necessary for the application of fluence modulated pCT (FMpCT) since it permits image noise prescription and the corresponding proton fuence optimization. We aimed at extending previously published formalisms to account for the impact of multiple Coulomb scattering (MCS) on projection noise, and the use of filtered back projection (FBP) reconstruction along curved paths with distance driven binning (DDB). 2D noise reconstruction for a beam of protons with parallel initial momentum vectors, and for projections binned both at the rear tracker and with DDB, was established. Monte Carlo (MC) simulations of pCT scans of a water cylinder were employed to generate pCT projections and to calculate their noise for use in 2D noise reconstruction. These were compared to results from an analytical model accounting for MCS for rear tracker binning as well as against the previously published central pixel model which ignores MCS. Image noise reconstructed with the formalism for rear tracker binning and DDB were compared to MC results using annular regions of interest (ROIs). Agreement better than 8% was obtained between the noise of projections calculated with MC simulation and our model. Noise from annular ROIs agreed with our noise reconstructions for rear tracker binning and DDB. The central pixel model ignoring MCS underestimated projection and thus image noise by up to 40% towards the object's edge. The use of DDB decreased the image noise towards the object's edge when compared to rear tracker binning and yielded more uniform noise throughout the image. MCS should not be neglected when predicting image noise for pixels away from the center of an object in a pCT scan due to the increasing influence of the gradient of the object's hull closer to the edges.