Experimental validation of an analytical microdosimetric model based on Geant4-DNA simulations by using a silicon-based microdosimeter.

PURPOSE: To study the agreement between proton microdosimetric distributions measured with a silicon-based cylindrical microdosimeter and a previously published analytical microdosimetric model based on Geant4-DNA in-water Monte Carlo simulations for low energy proton beams. METHODS AND MATERIAL: Distributions for lineal energy (y) are measured for four proton monoenergetic beams with nominal energies from 2.0 MeV to 4.5 MeV, with a tissue equivalent proportional counter (TEPC) and a silicon-based microdosimeter. The actual energy for protons traversing the silicon-based microdosimeter is simulated with SRIM. Monoenergetic beams with these energies are simulated with Geant4-DNA code by simulating a water cylinder site of dimensions equal to those of the microdosimeter. The microdosimeter response is calibrated by using the distribution peaks obtained from the TEPC. Analytical calculations for y ¯ F and y ¯ D using our methodology based on spherical sites are also performed choosing the equivalent sphere to be checked against experimental results. RESULTS: Distributions for y at silicon are converted into tissue equivalent and compared to the Geant4-DNA simulated, yielding maximum deviations of 1.03% for y ¯ F and 1.17% for y ¯ D . Our analytical method generates maximum deviations of 1.29% and 3.33%, respectively, with respect to experimental results. CONCLUSION: Simulations in Geant4-DNA with ideal cylindrical sites in liquid water produce similar results to the measurements in an actual silicon-based cylindrical microdosimeter properly calibrated. The found agreement suggests the possibility to experimentally verify the calculated clinical y ¯ D with our analytical method.

Proton monoenergetic arc therapy (PMAT) to enhance LETd within the target.

We show the performance and feasibility of a proton arc technique so-called proton monoenergetic arc therapy (PMAT). Monoenergetic partial arcs are selected to place spots at the middle of a target and its potential to enhance the dose-averaged linear energy transfer (LETd) distribution within the target. Single-energy partial arcs in a single 360 degree gantry rotation are selected to deposit Bragg's peaks at the central part of the target to increase LETd values. An in-house inverse planning optimizer seeks for homogeneous doses at the target while keeping the dose to organs at risk (OARs) within constraints. The optimization consists of balancing the weights of spots coming out of selected partial arcs. A simple case of a cylindrical target in a phantom is shown to illustrate the method. Three different brain cancer cases are then considered to produce actual clinical plans, compared to those clinically used with pencil beam scanning (PBS). The relative biological effectiveness (RBE) is calculated according to the microdosimetric kinetic model (MKM). For the ideal case of a cylindrical target placed in a cylindrical phantom, the mean LETd in the target increases from 2.8 keV µm-1 to 4.0 keV µm-1 when comparing a three-field PBS plan with PMAT. This is replicated for clinical plans, increasing the mean RBE-weighted doses to the CTV by 3.1%, 1.7% and 2.5%, respectively, assuming an [Formula: see text] ratio equal to 10 Gy in the CTV. In parallel, LETd to OARs near the distal edge of the tumor decrease for all cases and metrics (mean LETd, LD,2% and LD,98%). The PMAT technique increases the LETd within the target, being feasible for the production of clinical plans meeting physical dosimetric requirements for both target and OARs. Thus, PMAT increases the RBE within the target, which may lead to a widening of the therapeutic index in proton radiotherapy that would be highlighted for low [Formula: see text] ratios and hyperfractionated schedules.

A kernel-based algorithm for the spectral fluence of clinical proton beams to calculate dose-averaged LET and other dosimetric quantities of interest.

PURPOSE: To introduce a new analytical methodology to calculate quantities of interest in particle radiotherapy inside the treatment planning system. Models are proposed to calculate dose-averaged LET (LETd) in proton radiotherapy. MATERIAL AND METHODS: A kernel-based approach for the spectral fluence of particles is developed by means of analytical functions depending on depth and lateral position. These functions are obtained by fitting them to data calculated with Monte Carlo (MC) simulations using Geant4 in liquid water for energies from 50 to 250 MeV. Contributions of primary, secondary protons and alpha particles are modeled separately. Lateral profiles and spectra are modeled as Gaussian functions to be convolved with the fluence coming from the nozzle. LETd is obtained by integrating the stopping power curves from the PSTAR and ASTAR databases weighted by the spectrum at each position. The fast MC code MCsquare is employed to benchmark the results. RESULTS: Considering the nine energies simulated, fits for the functions modeling the fluence in-depth provide an average R 2 equal to 0.998, 0.995 and 0.986 for each one of the particles considered. Fits for the Gaussian lateral functions yield average R 2 of 0.997, 0.982 and 0.993, respectively. Similarly, the Gaussian functions fitted to the computed spectra lead to average R 2 of 0.995, 0.938 and 0.902. LETd calculation in water shows mean differences of -0.007 ± 0.008 keV/µm with respect to MCsquare if only protons are considered and 0.022 ± 0.007 keV/µm including alpha particles. In a prostate case, mean difference for all voxels with dose >5% of prescribed dose is 0.28 ± 0.23 keV/µm. CONCLUSION: This new spectral fluence-based methodology allows for simultaneous calculations of quantities of interest in proton radiotherapy such as dose, LETd or microdosimetric quantities. The method also enables the inclusion of more particles by following an analogous process.

Dose-averaged LET calculation for proton track segments using microdosimetric Monte Carlo simulations.

PURPOSE: There is an increasing interest in calculating linear energy transfer (LET) distributions for proton therapy treatments in order to assess the influence of this quantity in biological terms. Microdosimetric Monte Carlo (MC) simulations are useful tools to calculate dose-averaged LET, as this has been broadly proposed as the most adequate quantity to characterize these biological effects. However, a straightforward uniform sampling of the scoring site turns out to be computationally unaffordable. In contrast, some issues have been pointed out with the more efficient weighted sampling approach, frequently used in literature. Here, we address the issues associated with the latter method and propose adequate corrections to achieve reliable calculations of dose-averaged LET values from microdosimetry. METHODS AND MATERIALS: Proton track structures have been simulated with Geant4-DNA considering two different approaches. One version employs a uniform sampling for placing the spherical site and is used as the reference. The other one uses a weighted sampling by considering the spatial distribution of transfer points. Some corrections are proposed for calculating a dose-averaged LET comparable to the reference case. An additional MC approach is proposed to obtain the weighted mean of the energy imparted per electronic collision of the proton within the site, the δ 2 function, related to the straggling distribution, as an intermediate step in the LET calculation. RESULTS: Energy imparted per event distributions are different when employing either sampling methods, due to the different geometrical randomness. We have found an agreement below (0.15 ± 0.05) keV/µm in the worst case for uniform and weighted methods in dose-averaged LET values when the weighted sampling results are corrected according to our proposal. Our analysis is restricted to spherical sites of 1 and 10 µm diameter and monoenergetic beams in the range from 2 to 90 MeV. CONCLUSIONS: This work shows a reliable and computational-efficient method to perform calculations of track segment dose-averaged LET using MC simulations for proton therapy beams, including the necessary considerations for obtaining the straggling distribution characteristics. The validity of this approach remains as long as the stopping power of the proton can be considered as constant along its track within the site.

Analytical calculation of proton linear energy transfer in voxelized geometries including secondary protons.

In order to integrate radiobiological modelling with clinical treatment planning for proton radiotherapy, we extended our in-house treatment planning system FoCa with a 3D analytical algorithm to calculate linear energy transfer (LET) in voxelized patient geometries. Both active scanning and passive scattering delivery modalities are supported. The analytical calculation is much faster than the Monte-Carlo (MC) method and it can be implemented in the inverse treatment planning optimization suite, allowing us to create LET-based objectives in inverse planning. The LET was calculated by combining a 1D analytical approach including a novel correction for secondary protons with pencil-beam type LET-kernels. Then, these LET kernels were inserted into the proton-convolution-superposition algorithm in FoCa. The analytical LET distributions were benchmarked against MC simulations carried out in Geant4. A cohort of simple phantom and patient plans representing a wide variety of sites (prostate, lung, brain, head and neck) was selected. The calculation algorithm was able to reproduce the MC LET to within 6% (1 standard deviation) for low-LET areas (under 1.7 keV µm(-1)) and within 22% for the high-LET areas above that threshold. The dose and LET distributions can be further extended, using radiobiological models, to include radiobiological effectiveness (RBE) calculations in the treatment planning system. This implementation also allows for radiobiological optimization of treatments by including RBE-weighted dose constraints in the inverse treatment planning process.

A critical study of different Monte Carlo scoring methods of dose average linear-energy-transfer maps calculated in voxelized geometries irradiated with clinical proton beams.

We compare unrestricted dose average linear energy transfer (LET) maps calculated with three different Monte Carlo scoring methods in voxelized geometries irradiated with proton therapy beams with three different Monte Carlo scoring methods. Simulations were done with the Geant4 (Geometry ANd Tracking) toolkit. The first method corresponds to a step-by-step computation of LET which has been reported previously in the literature. We found that this scoring strategy is influenced by spurious high LET components, which relative contribution in the dose average LET calculations significantly increases as the voxel size becomes smaller. Dose average LET values calculated for primary protons in water with voxel size of 0.2 mm were a factor ~1.8 higher than those obtained with a size of 2.0 mm at the plateau region for a 160 MeV beam. Such high LET components are a consequence of proton steps in which the condensed-history algorithm determines an energy transfer to an electron of the material close to the maximum value, while the step length remains limited due to voxel boundary crossing. Two alternative methods were derived to overcome this problem. The second scores LET along the entire path described by each proton within the voxel. The third followed the same approach of the first method, but the LET was evaluated at each step from stopping power tables according to the proton kinetic energy value. We carried out microdosimetry calculations with the aim of deriving reference dose average LET values from microdosimetric quantities. Significant differences between the methods were reported either with pristine or spread-out Bragg peaks (SOBPs). The first method reported values systematically higher than the other two at depths proximal to SOBP by about 15% for a 5.9 cm wide SOBP and about 30% for a 11.0 cm one. At distal SOBP, the second method gave values about 15% lower than the others. Overall, we found that the third method gave the most consistent performance since it returned stable dose average LET values against simulation parameter changes and gave the best agreement with dose average LET estimations from microdosimetry calculations.

FoCa: a modular treatment planning system for proton radiotherapy with research and educational purposes.

FoCa is an in-house modular treatment planning system, developed entirely in MATLAB, which includes forward dose calculation of proton radiotherapy plans in both active and passive modalities as well as a generic optimization suite for inverse treatment planning. The software has a dual education and research purpose. From the educational point of view, it can be an invaluable teaching tool for educating medical physicists, showing the insights of a treatment planning system from a well-known and widely accessible software platform. From the research point of view, its current and potential uses range from the fast calculation of any physical, radiobiological or clinical quantity in a patient CT geometry, to the development of new treatment modalities not yet available in commercial treatment planning systems. The physical models in FoCa were compared with the commissioning data from our institution and show an excellent agreement in depth dose distributions and longitudinal and transversal fluence profiles for both passive scattering and active scanning modalities. 3D dose distributions in phantom and patient geometries were compared with a commercial treatment planning system, yielding a gamma-index pass rate of above 94% (using FoCa's most accurate algorithm) for all cases considered. Finally, the inverse treatment planning suite was used to produce the first prototype of intensity-modulated, passive-scattered proton therapy, using 13 passive scattering proton fields and multi-leaf modulation to produce a concave dose distribution on a cylindrical solid water phantom without any field-specific compensator.

Fast range switching of passively scattered proton beams using a modulation wheel and dynamic beam current modulation.

In proton radiotherapy, the range of particles in the patient body is determined by the energy of the protons. For most systems, the energy selection time is on the order of a few seconds, which becomes a serious obstacle for continuous dose delivery techniques requiring adaptive range modulation. This work analyses the feasibility of using the range modulation wheel, an element in the beamline used to form the spread-out Bragg peak (SOBP), to produce near-instantaneous changes not only in the modulation, but also in the range of the beam. While delivering proton beams in double scattering mode, the beam current can be synchronized with the range modulation wheel rotation by defining a current modulation pattern. Different current modulation patterns were computed from Monte Carlo simulations of our double scattering nozzle to range shift an SOBP of initial range 15 cm by varying degrees of up to ∼9 cm. These patterns were passed to the treatment control system at our institution and the resulting measured depth-dose distributions were analysed in terms of flatness, distal penumbra and relative irradiation time per unit mid-SOBP dose. Suitable SOBPs were obtained in all cases, with the maximum range shift being limited only by the maximum thickness of the wheel. The distal dose fall-off (80% to 20%) of the shifted peaks was broadened to about 1 cm, from the original 0.5 cm, and the predicted overhead in delivery time showed a linear increase with the amount of the shift. By modulating the beam current in clinical scattered proton beams equipped with a modulation wheel, it is possible to dynamically modify the in-patient range of the SOBP without adding any specific hardware or compensators to the beamline. A compromise between sharper distal dose fall-off and lower delivery time can be achieved and is subject to optimization.