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.
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
R2
equal to 0.998, 0.995 and 0.986 for each one of the particles considered. Fits for the Gaussian lateral functions yield average
R2
of 0.997, 0.982 and 0.993, respectively. Similarly, the Gaussian functions fitted to the computed spectra lead to average
R2
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.
Purpose
This work introduces the concept of segment‐averaged linear energy transfer (LET) as a new approach to average distributions of LET of proton beams based on a revisiting of microdosimetry ...theory. The concept of segment‐averaged LET is then used to generate an analytical model from Monte Carlo simulations data to perform fast and accurate calculations of LET distributions for proton beams.
Methods and material
The distribution of energy imparted by a proton beam into a representative biological structure or site is influenced by the distributions of (a) LET, (b) segment length, which is the section of the proton track in the site, and (c) energy straggling of the proton beam. The distribution of LET is thus generated by the LET of each component of the beam in the site. However, the situation when the LET of each single proton varies appreciably along its path in the site is not defined. Therefore, a new distribution can be obtained if the particle track segment is decomposed into smaller portions in which LET is roughly constant. We have called “segment distribution” of LET the one generated by the contribution of each portion. The average of that distribution is called segment‐averaged LET. This quantity is obtained in the microdosimetry theory from the average and standard deviation of the distributions of energy imparted to the site, segment length, and energy imparted per collision. All this information is calculated for protons of clinically relevant energies by means of Geant4‐DNA microdosimetric simulations. Finally, a set of analytical functions is proposed for each one of the previous quantities. The presented model functions are fitted to data from Geant4‐DNA simulations for monoenergetic beams from 100 keV to 100 MeV and for spherical sites of 1, 5, and 10 μm in diameter.
Results
The average differences along the considered energy range between calculations based on our analytical models and MC for segment‐averaged dose‐averaged restricted LET are −0.2 ± 0.7 keV/μm for the 1 μm case, 0.0 ± 0.9 keV/μm for the 5 μm case, and −0.3 ± 1.1 keV/μm for the 10 μm case, respectively. All average differences are below the average standard deviation (1σ) of the MC calculations.
Conclusions
A new way of averaging LET for a proton beam is performed to incorporate the effects produced by the variation of stopping power of each individual proton along microscopic biological structures. An analytical model based on MC simulations allows for fast and accurate calculations of segment‐averaged dose‐averaged restricted LET for proton beams, which otherwise would need to be calculated from exhaustive MC simulations of clinical plans.
Background
Geant4 is a Monte Carlo code extensively used in medical physics for a wide range of applications, such as dosimetry, micro‐ and nanodosimetry, imaging, radiation protection, and nuclear ...medicine. Geant4 is continuously evolving, so it is crucial to have a system that benchmarks this Monte Carlo code for medical physics against reference data and to perform regression testing.
Aims
To respond to these needs, we developed G4‐Med, a benchmarking and regression testing system of Geant4 for medical physics.
Materials and Methods
G4‐Med currently includes 18 tests. They range from the benchmarking of fundamental physics quantities to the testing of Monte Carlo simulation setups typical of medical physics applications. Both electromagnetic and hadronic physics processes and models within the prebuilt Geant4 physics lists are tested. The tests included in G4‐Med are executed on the CERN computing infrastructure via the use of the geant‐val web application, developed at CERN for Geant4 testing. The physical observables can be compared to reference data for benchmarking and to results of previous Geant4 versions for regression testing purposes.
Results
This paper describes the tests included in G4‐Med and shows the results derived from the benchmarking of Geant4 10.5 against reference data.
Discussion
Our results indicate that the Geant4 electromagnetic physics constructor G4EmStandardPhysics_option4 gives a good agreement with the reference data for all the tests. The QGSP_BIC_HP physics list provided an overall adequate description of the physics involved in hadron therapy, including proton and carbon ion therapy. New tests should be included in the next stage of the project to extend the benchmarking to other physical quantities and application scenarios of interest for medical physics.
Conclusion
The results presented and discussed in this paper will aid users in tailoring physics lists to their particular application.
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.
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.
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.
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.
•Validation of analytical microdosimetric models for protons of low energy.•Silicon-based microdosimeter is calibrated and employed for experimental data.•Distributions and averages of lineal energy are compared.•We found agreement among experiments, Geant4-DNA and analytical results.
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 δ2 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.
To calculate 3D distributions of microdosimetric-based restricted dose-averaged LET (LETd) and dose-mean lineal energy () in order to explore their similarities and differences between each other and ...with the traditional unrestricted LETd. Additionally, a new expression for optimum restricted LETd calculation is derived, allowing for disregarding straggling-associated functions in the classical microdosimetric theory. Restricted LETd and for polyenergetic beams can be obtained by integrating previously developed energy-dependent microdosimetric functions over the energetic spectrum of these beams. This calculation is extended to the entire calculation volume using an algorithm to determine spectral fluence. Equivalently, unrestricted LETd can be obtained integrating the stopping power curve on the spectrum. A new expression to calculate restricted LETd is also derived. Results for traditional and new formulas are compared for a clinical 100 MeV proton beam. Distributions of unrestricted LETd, restricted LETd and are analyzed for a prostate case, for microscopic spherical sites of 1 µm and 10 µm in diameter. Traditional and new expressions for restricted LETd remarkably agree, being the mean differences 0.05 ± 0.04 keV µm−1 for the 1 µm site and 0.05 ± 0.02 keV µm−1 for the 10 µm site. In the prostate case, the ratio between the maximum and the central value for central axis (CAX) profiles is around 2 for all the quantities, being the highest for restricted LETd for 1 µm (2.17) and the lowest for for 1 µm (1.78). Unrestricted LETd, restricted LETd and can be analytically computed and compared for clinical plans. Two important consequences of the calculation of are: (1) its distribution can be verified by directly measuring it in clinical beams; and (2), optimization of proton treatments based on these quantities is enabled as well as future developments of RBE models based on them.
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.
Recent developments in Geant4 Allison, J.; Amako, K.; Apostolakis, J. ...
Nuclear instruments & methods in physics research. Section A, Accelerators, spectrometers, detectors and associated equipment,
11/2016, Letnik:
835, Številka:
C
Journal Article
Recenzirano
Odprti dostop
Geant4 is a software toolkit for the simulation of the passage of particles through matter. It is used by a large number of experiments and projects in a variety of application domains, including ...high energy physics, astrophysics and space science, medical physics and radiation protection. Over the past several years, major changes have been made to the toolkit in order to accommodate the needs of these user communities, and to efficiently exploit the growth of computing power made available by advances in technology. The adaptation of Geant4 to multithreading, advances in physics, detector modeling and visualization, extensions to the toolkit, including biasing and reverse Monte Carlo, and tools for physics and release validation are discussed here.
•Multithreading resulted in a smaller memory footprint and nearly linear speed-up.•Scoring options, faster geometry primitives, more versatile visualization were added.•Improved electromagnetic and hadronic models and cross sections were developed.•Reverse Monte Carlo and general biasing methods were added.•Physics validation efforts were expanded and new validation tools were added.
In this work, we present a methodology to analytically determine microdosimetric quantities in radioimmunotherapy and targeted radiotherapy with alpha particles. Monte Carlo simulations using the ...Geant4-DNA toolkit, which provides interaction models at the microscopic level, are performed for monoenergetic alpha particles traversing spherical sites with diameters of 1, 5 and 10 µm. An analytical function is fitted against the data in each case to model the energy imparted by monoenergetic particles to the site, as well as the variance of the distribution of energy imparted. Those models allow us to obtain the mean and dose-mean values of specific energy (z) and lineal energy (y) for polyenergetic arrangements of alpha particles. The energetic spectrum is estimated by considering the distance that each particle needs to travel to reach the sensitive target. We apply this methodology to a simple case in radioimmunotherapy: a spherical cell that has its membrane uniformly covered by 211At, an alpha emitter, with a spherical target representing the nucleus, placed at the center of the cell. We compare the results of our analytical method with calculations using Geant4-DNA of this specific setup for three nucleus sizes corresponding to our three functions. For nuclei with diameter of 1 µm and 5 µm, all mean and dose-mean quantities for y and z were in an agreement within 4% to Geant4-DNA calculations. This agreement improves to approximately 1% for dose-mean lineal energy and dose-mean specific energy. For the 10-µm-diameter case, discrepancies scale to approximately 9% for mean values and 3% for dose-mean values. Dose-mean values are within Geant4-DNA uncertainties in all cases. Our method provides accurate analytical calculations of dose-mean quantities that may be further employed to characterize radiobiological effectiveness of targeted radiotherapy. The spatial distributions of sources and targets are required to calculate microdosimetric-relevant quantities.
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