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.

A Monte Carlo feasibility study on quantitative laser-driven proton radiography.

Laser-accelerated proton bunches with kinetic energies up to several tens of MeV and at repetition rates in the order of Hz are nowadays achievable at several research centres housing high-power laser system. The unique features of such ultra-short bunches are also arousing interest in the field of radiological and biomedical applications. For many of these applications, accurate positioning of the biological target is crucial, raising the need for on-site imaging. One convenient option is proton radiography, which can exploit the polyenergetic spectrum of laser-accelerated proton bunches. We present a Monte Carlo (MC) feasibility study to assess the applicability and potential of laser-driven proton radiography of millimetre to centimetre sized objects. Our radiography setup consists of a thin time-of-flight spectrometer operated in transmission prior to the object and a pixelated silicon detector for imaging. Proton bunches with kinetic energies up to 20MeV and up to 100MeV were investigated. The water equivalent thickness (WET) of the traversed material is calculated from the energy deposition inside an imaging detector, using an online generated calibration curve that is based on a MC generated look-up table and the reconstructed proton energy distribution. With a dose of 43mGy for a 1mm thin object imaged with protons up to 20MeV, the reconstructed WET of defined regions-of-interest was within 1.5% of the ground truth values. The spatial resolution, which strongly depends on the gap between object and imaging detector, was 2.5lpmm-1 for a realistic distance of 5mm. Due to this relatively high imaging dose, our proposed setup for laser-driven proton radiography is currently limited to objects with low radio-sensitivity, but possibilities for further dose reduction are presented and discussed.

The impact of path estimates in iterative ion CT reconstructions for clinical-like cases.

Ion computed tomography (CT) promises to mitigate range uncertainties inherent in the conversion of x-ray Hounsfield units into ion relative stopping power (RSP) for ion beam therapy treatment planning. To improve accuracy and spatial resolution of ion CT by accounting for statistical multiple Coulomb scattering deflection of the ion trajectories from a straight line path (SLP), the most likely path (MLP) and the cubic spline path (CSP) have been proposed. In this work, we use FLUKA Monte Carlo simulations to investigate the impact of these path estimates in iterative tomographic reconstruction algorithms for proton, helium and carbon ions. To this end the ordered subset simultaneous algebraic reconstruction technique was used and coupled with a total variation superiorization (TVS). We evaluate the image quality and dose calculation accuracy in proton therapy treatment planning of cranial patient anatomies. CSP and MLP generally yielded nearly equal image quality with an average RSP relative error improvement over the SLP of 0.6%, 0.3% and 0.3% for proton, helium and carbon ion CT, respectively. Bone and low density materials have been identified as regions of largest enhancement in RSP accuracy. Nevertheless, only minor differences in dose calculation results were observed between the different models and relative range errors of better than 0.5% were obtained in all cases. Largest improvements were found for proton CT in complex scenarios with strong heterogeneities along the beam path. The additional TVS provided substantially reduced image noise, resulting in improved image quality in particular for soft tissue regions. Employing the CSP and MLP for iterative ion CT reconstructions enabled improved image quality over the SLP even in realistic and heterogeneous patient anatomy. However, only limited benefit in dose calculation accuracy was obtained even though an ideal detector system was simulated.

Deformable image registration of the treatment planning CT with proton radiographies in perspective of adaptive proton therapy.

The purpose of this work is to investigate the potentiality of using a limited number of in-room proton radiographies to compensate anatomical changes in adaptive proton therapy. The treatment planning CT is adapted to the treatment delivery scenario relying on 2D-3D deformable image registration (DIR). The proton radiographies, expressed in water equivalent thickness (WET) are simulated for both list-mode and integration-mode detector configurations in pencil beam scanning. Geometrical and analytical simulations of an anthropomorphic phantom in the presence of anatomical changes due to breathing are adopted. A Monte Carlo simulation of proton radiographies based on a clinical CT image in the presence of artificial anatomical changes is also considered. The accuracy of the 2D-3D DIR, calculated as root mean square error, strongly depends on the considered anatomical changes and is considered adequate for promising adaptive proton therapy when comparable to the accuracy of conventional 3D-3D DIR. In geometrical simulation, this is achieved with a minimum of eight/nine radiographies (more than 90% accuracy). Negligible improvement (sim1%) is obtained with the use of 180 radiographies. Comparing different detector configurations, superior accuracy is obtained with list-mode than integration-mode max (WET with maximum occurrence) and mean (average WET weighted by occurrences). Moreover, integration-mode max performs better than integration-mode mean. Results are minimally affected by proton statistics. In analytical simulation, the anatomical changes are approximately compensated (about 60%-70% accuracy) with two proton radiographies and minor improvement is observed with nine proton radiographies. In clinical data, two proton radiographies from list-mode have demonstrated better performance than nine from integration-mode (more than 100% and about 50%-70% accuracy, respectively), even avoiding the finer grid spacing of the last numerical optimization stage. In conclusion, the choice of detector configuration as well as the amount and complexity of the considered anatomical changes determine the minimum number of radiographies to be used.

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.

Experimental comparison of clinically used ion beams for imaging applications using a range telescope.

In particle therapy, the x-ray based treatment planning converting photon attenuation values to relative stopping power ratio (RSP) introduces clinically relevant range uncertainties. Recently, novel imaging technologies using transmission ion beams have been investigated to directly assess the water equivalent thickness (WET) of tissue, showing improved accuracy in RSP reconstruction, while potentially reducing the imaging dose. Due to their greater availability, protons have been mostly used for ion imaging. To this end, in this work, the influence of three ion species (protons, helium and carbon ions) on the image quality of radiographic WET retrieval has been explored with a dedicated experimental setup and compared to Monte Carlo (MC) simulations. Three phantom setups with different tissue interfaces and features have been irradiated with clinically validated proton, helium and carbon ion pencil beams under comparable imaging dose and beam settings at the Heidelberg Ion-Beam Therapy Center. Ion radiographies (iRADs) were acquired with an integration mode detector, that functions as a range telescope with 61 parallel plate ionization chambers. For comparison, experiments were reproduced in-silico with FLUKA MC simulations. Carbon ions provide iRADs with highest image quality in terms of normalized root mean square error, followed by helium ions and protons. All ions show similar capabilities of resolving WET for the considered phantoms, as shown by the similar average relative error < 3%. Besides for the slab phantom, MC simulations yielded better results than the experiment, indicating potential improvement of the experimental setup. Our results showed that the ability to resolve the WET is similar for all particles, intrinsically limited by the granularity of the detector system. While carbon ions are best suited for acquiring iRADs with the investigated integration mode detector, helium ions are put forward as a less technical challenging alternative.

Dosimetric accuracy and radiobiological implications of ion computed tomography for proton therapy treatment planning.

Ion computed tomography (iCT) represents a potential replacement for x-ray CT (xCT) in ion therapy treatment planning to reduce range uncertainties, inherent in the semi-empirical conversion of xCT information into relative stopping power (RSP). In this work, we aim to quantify the increase in dosimetric accuracy associated with using proton-, helium- and carbon-CT compared to conventional xCT for clinical scenarios in proton therapy. Three cases imaged with active beam-delivery using an ideal single-particle-tracking detector were investigated using FLUKA Monte-Carlo (MC) simulations. The RSP accuracy of the iCTs was evaluated against the ground truth at similar physical dose. Next, the resulting dosimetric accuracy was investigated by using the RSP images as a patient model in proton therapy treatment planning, in comparison to common uncertainties associated with xCT. Finally, changes in relative biological effectiveness (RBE) with iCT particle type/spectrum were investigated by incorporating the repair-misrepair-fixation (RMF) model into FLUKA, to enable first insights on the associated biological imaging dose. Helium-CT provided the lowest overall RSP error, whereas carbon-CT offered the highest accuracy for bone and proton-CT for soft tissue. For a single field, the average relative proton beam-range variation was -1.00%, +0.09%, -0.08% and -0.35% for xCT, proton-, helium- and carbon-CT, respectively. Using a 0.5%/0.5mm gamma-evaluation, all iCTs offered comparable accuracy with a better than 99% passing rate, compared to 83% for xCT. The RMF model predictions for RBE for cell death relative to a diagnostic xCT spectrum were 0.82-0.85, 0.85-0.89 and 0.97-1.03 for proton-, helium-, and carbon-CT, respectively. The corresponding RBE for DNA double-strand break induction was generally below one. iCT offers great clinical potential for proton therapy treatment planning by providing superior dose calculation accuracy as well as lower physical and potentially biological dose exposure compared to xCT. For the investigated dose level and ideal detector, proton-CT and helium-CT yielded the best performance.

Comparative Monte Carlo study on the performance of integration- and list-mode detector configurations for carbon ion computed tomography.

Ion beam therapy offers the possibility of a highly conformal tumor-dose distribution; however, this technique is extremely sensitive to inaccuracies in the treatment procedures. Ambiguities in the conversion of Hounsfield units of the treatment planning x-ray CT to relative stopping power (RSP) can cause uncertainties in the estimated ion range of up to several millimeters. Ion CT (iCT) represents a favorable solution allowing to directly assess the RSP. In this simulation study we investigate the performance of the integration-mode configuration for carbon iCT, in comparison with a single-particle approach under the same set-up. The experimental detector consists of a stack of 61 air-filled parallel-plate ionization chambers, interleaved with 3 mm thick PMMA absorbers. By means of Monte Carlo simulations, this design was applied to acquire iCTs of phantoms of tissue-equivalent materials. An optimization of the acquisition parameters was performed to reduce the dose exposure, and the implications of a reduced absorber thickness were assessed. In order to overcome limitations of integration-mode detection in the presence of lateral tissue heterogeneities a dedicated post-processing method using a linear decomposition of the detector signal was developed and its performance was compared to the list-mode acquisition. For the current set-up, the phantom dose could be reduced to below 30 mGy with only minor image quality degradation. By using the decomposition method a correct identification of the components and a RSP accuracy improvement of around 2.0% was obtained. The comparison of integration- and list-mode indicated a slightly better image quality of the latter, with an average median RSP error below 1.8% and 1.0%, respectively. With a decreased absorber thickness a reduced RSP error was observed. Overall, these findings support the potential of iCT for low dose RSP estimation, showing that integration-mode detectors with dedicated post-processing strategies can provide a RSP accuracy comparable to list-mode configurations.