On the scattering power of radiotherapy protons.

PURPOSE: First, to show that accurate formulas for scattering power T must take into account the competition between the Gaussian core and the single scattering tail of the angular distribution, which affects the rate of change in the Gaussian width and leads to the single scattering correction (SSC). Second, to show that the SSC requires that T(x) be nonlocal: Besides material properties and energy at the point of interest, it must depend in some fashion on how much multiple scattering has already taken place. Third, after reviewing five previous formulas (three local and two nonlocal), to derive an improved "differential Molière" formula T(dM). Last, to investigate, by studying some practical cases, when an accurate formula for T is actually needed. METHODS: We first take the numerical derivative of the Molière/Fano/Hanson (theta2) in order to find the true SSC. We simplify the formula for T(IC) (ICRU Report 35) for protons, introducing a new material dependent property, the "scattering length" X(s), analogous to radiation length X(0). We then use T(IC) as a basis for T(dM) by including a nonlocal correction factor fdM which, by virtue of the Øverås approximation, parametrizes the single scattering correction. RESULTS: The improved scattering power is T(dM)[triple band]f(dM)(pv,p1v1) x (E(s)/pv)(2)1/X(s) where fdM 0.5244+0.1975 lg(1-(pv/p1v1)2)+0.2320 lg(pv)-0.0098 lg(pv)lg(1-(pv/p1v1)2), P1v1 (MeV) is the initial product of proton momentum and speed, pv is the same at the point of interest, and E(s) = 15.0 MeV. T(dM) is easily computed and generalizes readily to mixed slabs because fdM is not material dependent. CONCLUSIONS: Whether an accurate formula for T is required depends very much on the problem at hand. For beam spreading in water, five of the six formulas for T give almost identical results, suggesting that patient dose calculations are insensitive to T. That is not true, however, of beam spreading in Pb. At the opposite extreme, the projected rms beam width at the end of a Pb/Lexan/air stack, analogous to the upstream modulator in a passive beam spreading system, is sensitive to T. In this case a simple experiment would discriminate between all but two of the six formulas discussed. Scattering power applies as much to Monte Carlo as to deterministic transport calculations. Using T in any of its forms will avoid step size dependence. Using the best available T could be important in general purpose Monte Carlo codes, which are expected to give the correct answer to many different problems.

FLASH Investigations Using Protons: Design of Delivery System, Preclinical Setup and Confirmation of FLASH Effect with Protons in Animal Systems.

Extremely high-dose-rate irradiation, referred to as FLASH, has been shown to be less damaging to normal tissues than the same dose administrated at conventional dose rates. These results, typically seen at dose rates exceeding 40 Gy/s (or 2,400 Gy/min), have been widely reported in studies utilizing photon or electron radiation as well as in some proton radiation studies. Here, we report the development of a proton irradiation platform in a clinical proton facility and the dosimetry methods developed. The target is placed in the entry plateau region of a proton beam with a specifically designed double-scattering system. The energy after the double-scattering system is 227.5 MeV for protons that pass through only the first scatterer, and 225.5 MeV for those that also pass through the second scatterer. The double-scattering system was optimized to deliver a homogeneous dose distribution to a field size as large as possible while keeping the dose rate >100 Gy/s and not exceeding a cyclotron current of 300 nA. We were able to obtain a collimated pencil beam (1.6 × 1.2 cm2 ellipse) at a dose rate of ∼120 Gy/s. This beam was used for dose-response studies of partial abdominal irradiation of mice. First results indicate a potential tissue-sparing effect of FLASH.

Comparison of Geant4 multiple Coulomb scattering models with theory for radiotherapy protons.

Usually, Monte Carlo models are validated against experimental data. However, models of multiple Coulomb scattering (MCS) in the Gaussian approximation are exceptional in that we have theories which are probably more accurate than the experiments which have, so far, been done to test them. In problems directly sensitive to the distribution of angles leaving the target, the relevant theory is the Molière/Fano/Hanson variant of Molière theory (Gottschalk et al 1993 Nucl. Instrum. Methods Phys. Res. B 74 467-90). For transverse spreading of the beam in the target itself, the theory of Preston and Koehler (Gottschalk (2012 arXiv:1204.4470)) holds. Therefore, in this paper we compare Geant4 simulations, using the Urban and Wentzel models of MCS, with theory rather than experiment, revealing trends which would otherwise be obscured by experimental scatter. For medium-energy (radiotherapy) protons, and low-Z (water-like) target materials, Wentzel appears to be better than Urban in simulating the distribution of outgoing angles. For beam spreading in the target itself, the two models are essentially equal.

Validation of nuclear models in Geant4 using the dose distribution of a 177 MeV proton pencil beam.

A proton pencil beam is associated with a surrounding low-dose envelope, originating from nuclear interactions. It is important for treatment planning systems to accurately model this envelope when performing dose calculations for pencil beam scanning treatments, and Monte Carlo (MC) codes are commonly used for this purpose. This work aims to validate the nuclear models employed by the Geant4 MC code, by comparing the simulated absolute dose distribution to a recent experiment of a 177 MeV proton pencil beam stopping in water. Striking agreement is observed over five orders of magnitude, with both the shape and normalisation well modelled. The normalisations of two depth dose curves are lower than experiment, though this could be explained by an experimental positioning error. The Geant4 neutron production model is also verified in the distal region. The entrance dose is poorly modelled, suggesting an unaccounted upstream source of low-energy protons. Recommendations are given for a follow-up experiment which could resolve these issues.

On the nuclear halo of a proton pencil beam stopping in water.

The dose distribution of a proton beam stopping in water has components due to basic physics and may have others from beam contamination. We propose the concise terms core for the primary beam, halo (see Pedroni et al 2005 Phys. Med. Biol. 50 541-61) for the low dose region from charged secondaries, aura for the low dose region from neutrals, and spray for beam contamination. We have measured the dose distribution in a water tank at 177 MeV under conditions where spray, therefore radial asymmetry, is negligible. We used an ADCL calibrated thimble chamber and a Faraday cup calibrated integral beam monitor so as to obtain immediately the absolute dose per proton. We took depth scans at fixed distances from the beam centroid rather than radial scans at fixed depths. That minimizes the signal range for each scan and better reveals the structure of the core and halo. Transitions from core to halo to aura are already discernible in the raw data. The halo has components attributable to coherent and incoherent nuclear reactions. Due to elastic and inelastic scattering by the nuclear force, the Bragg peak persists to radii larger than can be accounted for by Molière single scattering. The radius of the incoherent component, a dose bump around midrange, agrees with the kinematics of knockout reactions. We have fitted the data in two ways. The first is algebraic or model dependent (MD) as far as possible, and has 25 parameters. The second, using 2D cubic spline regression, is model independent. Optimal parameterization for treatment planning will probably be a hybrid of the two, and will of course require measurements at several incident energies. The MD fit to the core term resembles that of the PSI group (Pedroni et al 2005), which has been widely emulated. However, we replace their T(w), a mass stopping power which mixes electromagnetic (EM) and nuclear effects, with one that is purely EM, arguing that protons that do not undergo hard single scatters continue to lose energy according to the Beth-Bloch formula. If that is correct, it is no longer necessary to measure T(w), and the dominant role played by the 'Bragg peak chamber' vanishes. For mathematical and other details we will refer to Gottschalk et al (2014, arXiv: 1409.1938v1), a long technical report of this project.

Validation of an in-vivo proton beam range check method in an anthropomorphic pelvic phantom using dose measurements.

PURPOSE: In-vivo dosimetry and beam range verification in proton therapy could play significant role in proton treatment validation and improvements. In-vivo beam range verification, in particular, could enable new treatment techniques one of which could be the use of anterior fields for prostate treatment instead of opposed lateral fields as in current practice. This paper reports validation study of an in-vivo range verification method which can reduce the range uncertainty to submillimeter levels and potentially allow for in-vivo dosimetry. METHODS: An anthropomorphic pelvic phantom is used to validate the clinical potential of the time-resolved dose method for range verification in the case of prostrate treatment using range modulated anterior proton beams. The method uses a 3 × 4 matrix of 1 mm diodes mounted in water balloon which are read by an ADC system at 100 kHz. The method is first validated against beam range measurements by dose extinction measurements. The validation is first completed in water phantom and then in pelvic phantom for both open field and treatment field configurations. Later, the beam range results are compared with the water equivalent path length (WEPL) values computed from the treatment planning system XIO. RESULTS: Beam range measurements from both time-resolved dose method and the dose extinction method agree with submillimeter precision in water phantom. For the pelvic phantom, when discarding two of the diodes that show sign of significant range mixing, the two methods agree with ±1 mm. Only a dose of 7 mGy is sufficient to achieve this result. The comparison to the computed WEPL by the treatment planning system (XIO) shows that XIO underestimates the protons beam range. Quantifying the exact XIO range underestimation depends on the strategy used to evaluate the WEPL results. To our best evaluation, XIO underestimates the treatment beam range between a minimum of 1.7% and maximum of 4.1%. CONCLUSIONS: Time-resolved dose measurement method satisfies the two basic requirements, WEPL accuracy and minimum dose, necessary for clinical use, thus, its potential for in-vivo protons range verification. Further development is needed, namely, devising a workflow that takes into account the limits imposed by proton range mixing and the susceptibility of the comparison of measured and expected WEPLs to errors on the detector positions. The methods may also be used for in-vivo dosimetry and could benefit various proton therapy treatments.

Comments on 'Calculation of water equivalent thickness of materials of arbitrary density, elemental composition and thickness in proton beam irradiation'.

We comment on a previous article by Zhang and Newhauser (2009 Phys. Med. Biol. 54 1383-95) which presents several approximate ways of computing the water equivalent of an arbitrary degrader. First, we present a simple exact method which depends only on the range-energy relation of water and of the degrader material. Second, we point out that any theoretical method, approximate or exact, ultimately depends on the range-energy relation, that is to say, the correct value of the mean excitation energy I for the materials in question. Unfortunately I is particularly problematic for water. Therefore, at the present state of knowledge, we should measure water equivalent, rather than computing it, whenever an accurate value is needed.