Integration of the M6 Cyberknife in the Moderato Monte Carlo platform and prediction of beam parameters using machine learning

PurposeThis work describes the integration of the M6 Cyberknife in the Moderato Monte Carlo platform, and introduces a machine learning method to accelerate the modelling of a linac.MethodsThe MLC-equipped M6 Cyberknife was modelled and integrated in Moderato, our in-house platform offering independent verification of radiotherapy dose distributions. The model was validated by comparing TPS dose distributions with Moderato and by film measurements. Using this model, a machine learning algorithm was trained to find electron beam parameters for other M6 devices, by simulating dose curves with varying spot size and energy. The algorithm was optimized using cross-validation and tested with measurements from other institutions equipped with a M6 Cyberknife.ResultsOptimal agreement in the Monte Carlo model was reached for a monoenergetic electron beam of 6.75 MeV with Gaussian spatial distribution of 2.4 mm FWHM. Clinical plan dose distributions from Moderato agreed within 2% with the TPS, and film measurements confirmed the accuracy of the model. Cross-validation of the prediction algorithm produced mean absolute errors of 0.1 MeV and 0.3 mm for beam energy and spot size respectively. Prediction-based simulated dose curves for other centres agreed within 3% with measurements, except for one device where differences up to 6% were detected.ConclusionsThe M6 Cyberknife was integrated in Moderato and validated through dose re-calculations and film measurements. The prediction algorithm was successfully applied to obtain electron beam parameters for other M6 devices. This method would prove useful to speed up modelling of new machines in Monte Carlo systems.     

Calculation of the proximity function of electrons

A new semianalytical method to calculate the proximity function for electrons is proposed. An integral equation for the proximity function that can be solved by using information on the spatial dose distributions is obtained. The proximity function for electrons in the energy range from 10 eV to 10 keV is calculated by solving the equation numerically, using a set of electron collision cross sections for water vapor. The results are in good agreement with those obtained using the Monte Carlo method. The proposed method can be used for electrons of high energies much more efficiently than the Monte Carlo method.     

Model of total skin electron treatment using the 'six-dual-field' technique

During implementation of the total skin electron treatment, using six-dual-field technique, at radiotherapy department a large number of measurements are needed. To assess depth dose curve required by clinicians and dose uniformity over a whole treatment plane, combinations of different irradiation parameters are used (electron energy, beam angle, scatterers). Measurements for each combination must be performed. One possible way to reduce number of measurements is to model the treatment using the Monte Carlo simulation of electron transport. We made a simplified multiple-source Monte Carlo model of electron beam and tested it by comparing calculations and experimental results. Calculated data differs less than 5 percent from measurements in the treatment plane. During the treatment patient can be approximated using cylinders with different diameters and orientations. We tried to model the depth dose variations in the total skin electron treatment not just around the body cross-section (simplified to cylinders of different diameters), but also along the body to account for the variations in body curvature longitudinally. This effect comes down to the problem of modeling distribution in different cylinders, but varying the longitudinal orientation of those cylinders. We compared Monte Carlo calculations and film measurements of depth dose curves for two orientations of the cylindrical phantom, which were the simplest for experimental arrangement. Comparison of the results proved accuracy of the model and we used it to calculate depth dose curves for a number of other cylinder orientations.     

Radial secondary electron dose profiles and biological effects in light-ion beams based on analytical and Monte Carlo calculations using distorted wave cross sections

To speed up dose calculation, an analytical pencil-beam method has been developed to calculate the mean radial dose distributions due to secondary electrons that are set in motion by light ions in water. For comparison, radial dose profiles calculated using a Monte Carlo technique have also been determined. An accurate comparison of the resulting radial dose profiles of the Bragg peak for (1)H(+), (4)He(2+) and (6)Li(3+) ions has been performed. The double differential cross sections for secondary electron production were calculated using the continuous distorted wave-eikonal initial state method (CDW-EIS). For the secondary electrons that are generated, the radial dose distribution for the analytical case is based on the generalized Gaussian pencil-beam method and the central axis depth-dose distributions are calculated using the Monte Carlo code PENELOPE. In the Monte Carlo case, the PENELOPE code was used to calculate the whole radial dose profile based on CDW data. The present pencil-beam and Monte Carlo calculations agree well at all radii. A radial dose profile that is shallower at small radii and steeper at large radii than the conventional 1/r(2) is clearly seen with both the Monte Carlo and pencil-beam methods. As expected, since the projectile velocities are the same, the dose profiles of Bragg-peak ions of 0.5 MeV (1)H(+), 2 MeV (4)He(2+) and 3 MeV (6)Li(3+) are almost the same, with about 30% more delta electrons in the sub keV range from (4)He(2+)and (6)Li(3+) compared to (1)H(+). A similar behavior is also seen for 1 MeV (1)H(+), 4 MeV (4)He(2+) and 6 MeV (6)Li(3+), all classically expected to have the same secondary electron cross sections. The results are promising and indicate a fast and accurate way of calculating the mean radial dose profile.     

Model for radial dependence of frequency distributions for energy imparted in nanometer volumes from HZE particles

This paper develops a deterministic model of frequency distributions for energy imparted (total energy deposition) in small volumes similar to DNA molecules from high-energy ions of interest for space radiation protection and cancer therapy. Frequency distributions for energy imparted are useful for considering radiation quality and for modeling biological damage produced by ionizing radiation. For high-energy ions, secondary electron (delta-ray) tracks originating from a primary ion track make dominant contributions to energy deposition events in small volumes. Our method uses the distribution of electrons produced about an ion's path and incorporates results from Monte Carlo simulation of electron tracks to predict frequency distributions for ions, including their dependence on radial distance. The contribution from primary ion events is treated using an impact parameter formalism of spatially restricted linear energy transfer (LET) and energy-transfer straggling. We validate our model by comparing it directly to results from Monte Carlo simulations for proton and alpha-particle tracks. We show for the first time frequency distributions of energy imparted in DNA structures by several high-energy ions such as cosmic-ray iron ions. Our comparison with results from Monte Carlo simulations at low energies indicates the accuracy of the method.     

Multiple-source models for electron beams of a medical linear accelerator using BEAMDP computer code

AimThe aim of this work was to develop multiple-source models for electron beams of the NEPTUN 10PC medical linear accelerator using the BEAMDP computer code.BackgroundOne of the most accurate techniques of radiotherapy dose calculation is the Monte Carlo (MC) simulation of radiation transport, which requires detailed information of the beam in the form of a phase-space file. The computing time required to simulate the beam data and obtain phase-space files from a clinical accelerator is significant. Calculation of dose distributions using multiple-source models is an alternative method to phase-space data as direct input to the dose calculation system.Materials and methodsMonte Carlo simulation of accelerator head was done in which a record was kept of the particle phase-space regarding the details of the particle history. Multiple-source models were built from the phase-space files of Monte Carlo simulations. These simplified beam models were used to generate Monte Carlo dose calculations and to compare those calculations with phase-space data for electron beams.ResultsComparison of the measured and calculated dose distributions using the phase-space files and multiple-source models for three electron beam energies showed that the measured and calculated values match well each other throughout the curves.ConclusionIt was found that dose distributions calculated using both the multiple-source models and the phase-space data agree within 1.3%, demonstrating that the models can be used for dosimetry research purposes and dose calculations in radiotherapy.     

Two-step validation of a Monte Carlo dosimetry framework for general radiology

The Monte Carlo technique is considered gold standard when it comes to patient-specific dosimetry. Any newly developed Monte Carlo simulation framework, however, has to be carefully calibrated and validated prior to its use. For many researchers this is a tedious work. We propose a two-step validation procedure for our newly built Monte Carlo framework and provide all input data to make it feasible for future related application by the wider community. The validation was at first performed by benchmarking against simulation data available in literature. The American Association of Physicists in Medicine (AAPM) report of task group 195 (case 2) was considered most appropriate for our application. Secondly, the framework was calibrated and validated against experimental measurements for trunk X-ray imaging protocols using a water phantom. The dose results obtained from all simulations and measurements were compared. Our Monte Carlo framework proved to agree with literature data, by showing a maximal difference below 4% to the AAPM report. The mean difference with the water phantom measurements was around 7%. The statistical uncertainty for clinical applications of the dosimetry model is expected to be within 10%. This makes it reliable for clinical dose calculations in general radiology. Input data and the described procedure allow for the validation of other Monte Carlo frameworks.     

Towards MR-guided electron therapy: Measurement and simulation of clinical electron beams in magnetic fields

PurposeIn the current era of MRI-linac radiotherapy, dose optimization with arbitrary dose distributions is a reality. For the first time, we present new and targeted experiments and modeling to aid in evaluating the potential dose improvements offered with an electron beam mode during MRI-linac radiotherapy.MethodsSmall collimated (1 cm diameter and 1.5 × 1.5 cm² square) electron beams (6, 12 and 20 MeV) from a clinical linear accelerator (Varian Clinac 2100C) are incident perpendicular and parallel to the strong and localized magnetic fields (0–0.7 T) generated by a permanent magnet device. Gafchromic EBT3 film is placed inside a slab phantom to measure two-dimensional dose distributions. A benchmarked and comprehensive Monte Carlo model (Geant4) is established to directly compare with experiments.ResultsWith perpendicular fields a 5% narrowing of the beam FWHM and a 10 mm reduction in the 15% isodose penetration is seen for the 20 MeV beam. In the inline setup the penumbral width is reduced by up to 20%, and a local central dose enhancement of 100% is observed. Monte Carlo simulations are in agreement with the measured dose distributions (2% or 2 mm).ConclusionA new range of experiments have been performed to offer insight into how an electron beam mode could offer additional choices in MRI-linac radiotherapy. The work extends on historic studies to bring a successful unified experimental and Monte Carlo modeling approach for studying small field electron beam dosimetry inside magnetic fields. The results suggest further work, particularly on the inline magnetic field scenario.     

蒙特卡罗方法和三维数字人体模型在放疗计划质量保证中的应用

放射治疗的质量保证是保证放射治疗成功的有力方法。对于放疗计划的验证和评估有CT模拟机、仿体等方法,这些方法各有优缺点。文章提出了一种用人体图像数据构造仿真模型的方法,并用蒙特卡罗软件和美国“可视人项目”的数据集计算该模型在接受放射治疗时体内剂量的三维分布。由于采用人体的真实图像数据,以及蒙特卡罗方法计算粒子输运时的准确性,该方法能够得到真实的三维剂量分布。     

Determination of initial electron parameters by means of Monte Carlo simulations for the Siemens Artiste Linac 6 MV photon beam

AimIn this study, we investigated initial electron parameters of Siemens Artiste Linac with 6 MV photon beam using the Monte Carlo method.BackgroundIt is essential to define all the characteristics of initial electrons hitting the target, i.e. mean energy and full width of half maximum (FWHM) of the spatial distribution intensity, which is needed to run Monte Carlo simulations. The Monte Carlo is the most accurate method for simulation of radiotherapy treatments.Materials and methodsLinac head geometry was modeled using the BEAMnrc code. The phase space files were used as input file to DOSXYZnrc simulation to determine the dose distribution in a water phantom. We obtained percent depth dose curves and the lateral dose profile. All the results were obtained at 100 cm of SSD and for a 10 × 10 cm² field.ResultsWe concluded that there existed a good conformity between Monte Carlo simulation and measurement data when we used electron mean energy of 6.3 MeV and 0.30 cm FWHM value as initial parameters. We observed that FWHM values had very little effect on PDD and we found that the electron mean energy and FWHM values affected the lateral dose profile. However, these effects are between tolerance values.ConclusionsThe initial parameters especially depend on components of a linac head. The phase space file which was obtained from Monte Carlo Simulation for a linac can be used as calculation of scattering, MLC leakage, to compare dose distribution on patients and in various studies.     

An MCNP-based model for the evaluation of the photoneutron dose in high energy medical electron accelerators

The development of a computational model for the treatment head of a medical electron accelerator (Elekta/Philips SL-18) by the Monte Carlo code mcnp-4C2 is discussed. The model includes the major components of the accelerator head and a pmma phantom representing the patient body. Calculations were performed for a 14 MeV electron beam impinging on the accelerator target and a 10 cm×10 cm beam area at the isocentre. The model was used in order to predict the neutron ambient dose equivalent at the isocentre level and moreover the neutron absorbed dose distribution within the phantom. Calculations were validated against experimental measurements performed by gold foil activation detectors. The results of this study indicated that the equivalent dose at tissues or organs adjacent to the treatment field due to photoneutrons could be up to 10% of the total peripheral dose, for the specific accelerator characteristics examined. Therefore, photoneutrons should be taken into account when accurate dose calculations are required to sensitive tissues that are adjacent to the therapeutic X-ray beam. The method described can be extended to other accelerators and collimation configurations as well, upon specification of treatment head component dimensions, composition and nominal accelerating potential.     

Dosimetric characterization of an 192Ir brachytherapy source with the Monte Carlo code PENELOPE

Monte Carlo calculations are highly spread and settled practice to calculate brachytherapy sources dosimetric parameters. In this study, recommendations of the AAPM TG-43U1 report have been followed to characterize the Varisource VS2000 ¹⁹²Ir high dose rate source, provided by Varian Oncology Systems.In order to obtain dosimetric parameters for this source, Monte Carlo calculations with PENELOPE code have been carried out. TG-43 formalism parameters have been presented, i.e., air kerma strength, dose rate constant, radial dose function and anisotropy function. Besides, a 2D Cartesian coordinates dose rate in water table has been calculated. These quantities are compared to this source reference data, finding results in good agreement with them.The data in the present study complement published data in the next aspects: (i) TG-43U1 recommendations are followed regarding to phantom ambient conditions and to uncertainty analysis, including statistical (type A) and systematic (type B) contributions; (ii) PENELOPE code is benchmarked for this source; (iii) Monte Carlo calculation methodology differs from that usually published in the way to estimate absorbed dose, leaving out the track-length estimator; (iv) the results of the present work comply with the most recent AAPM and ESTRO physics committee recommendations about Monte Carlo techniques, in regards to dose rate uncertainty values and established differences between our results and reference data.The results stated in this paper provide a complete parameter collection, which can be used for dosimetric calculations as well as a means of comparison with other datasets from this source.     

一维响应变量时最高无毒副作用剂量水平的识别

在毒性试验中,将暴露在某一剂量水平下的处理组与接受相当于零剂量处理的对照组相比,随着药物剂量的增加,感兴趣的变量通常会呈现一种递增的趋势。考虑不会导致风险显著增加的最高剂量,本文使用AIC(Akaike information criterion)方法得到该剂量水平的强相合估计,并且通过两组数据及模拟的结果来说明AIC方法的优良性.     

A method for calculating the dose absorbed by terrestrial animals to assess the environmental impact of radioactive contamination

A method for calculating the exposures of terrestrial animals in areas contaminated with radionuclides using a point source dose function is presented. To take into account scattered γ-radiation, the Berger formula for dose buildup factor in an infinite air medium has been parameterized. In the dosimetric model proposed, an animal phantom is presented as a parallelepiped to estimate external exposures and as a tissue-quivalent sphere to estimate internal doses. Using analytical expressions, dose rate conversion coefficients for external and internal exposures of animals have been estimated for individual radionuclides. For energies of γ-rays above 50 keV, the results are in good agreement with those estimated by the Monte Carlo method for ellipsoidal phantoms of animals.     

Low-dose-rate extrapolation using the multistage model

The distribution of the maximum likelihood estimates of virtually safe levels of exposure to environmental chemicals is derived by using large-sample theory and Monte Carlo simulation according to the Armitage-Doll multistage model. Using historical dose-response we develop a set of 33 two-stage models upon which we base our conclusions. The large-sample distributions of the virtually safe dose are normal for cases in which the multistage-model parameters have nonzero expectation, and are skewed in other cases. The large-sample theory does not provide a good approximation of the distribution observed for small bioassays when Monte Carlo simulation is used. The constrained nature of the multistage-model parameters leads to bimodal distributions for small bioassays. The two modes are the direct result of estimating the linear parameter in the multistage model; the lower mode results from estimating this parameter to be nonzero, and the upper mode from estimating it to be zero. The results of this research emphasize the need for incorporation of the biological theory in the model-selection process.     

A Monte Carlo maximum likelihood method for estimating uncertainty arising from shared errors in exposures in epidemiological studies of nuclear workers

Errors in the estimation of exposures or doses are a major source of uncertainty in epidemiological studies of cancer among nuclear workers. This paper presents a Monte Carlo maximum likelihood method that can be used for estimating a confidence interval that reflects both statistical sampling error and uncertainty in the measurement of exposures. The method is illustrated by application to an analysis of all cancer (excluding leukemia) mortality in a study of nuclear workers at the Oak Ridge National Laboratory (ORNL). Monte Carlo methods were used to generate 10,000 data sets with a simulated corrected dose estimate for each member of the cohort based on the estimated distribution of errors in doses. A Cox proportional hazards model was applied to each of these simulated data sets. A partial likelihood, averaged over all of the simulations, was generated; the central risk estimate and confidence interval were estimated from this partial likelihood. The conventional unsimulated analysis of the ORNL study yielded an excess relative risk (ERR) of 5.38 per Sv (90% confidence interval 0.54-12.58). The Monte Carlo maximum likelihood method yielded a slightly lower ERR (4.82 per Sv) and wider confidence interval (0.41-13.31).     

Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract

The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.     

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.      

An EGS4 based Monte Carlo code for the calculation of organ equivalent dose to a modified Yale voxel phantom.

Organ or tissue equivalent dose, the most important quantity in radiation protection, cannot be measured directly. Therefore it became common practice to calculate the quantity of interest with Monte Carlo methods applied to so-called human phantoms, which are virtual representations of the human body. The Monte Carlo computer code determines conversion coefficients, which are ratios between organ or tissue equivalent dose and measurable quantities. Conversion coefficients have been published by the ICRP (Report No. 74) for various types of radiation, energies and fields, which have been calculated, among others, with the mathematical phantoms ADAM and EVA. Since then progress of image processing, and of clock speed and memory capacity of computers made it possible to create so-called voxel phantoms, which are a far more realistic representation of the human body. Voxel (Volume pixel) phantoms are built from segmented CT and/or MRI images of real persons. A complete set of such images can be joined to a 3-dimensional representation of the human body, which can be linked to a Monte Carlo code allowing for particle transport calculations. A modified version of the VOX_TISS8 human voxel phantom (Yale University) has been connected to the EGS4 Monte Carlo code. The paper explains the modifications, which have been made, the method of coupling the voxel phantom with the code, and presents results as conversion coefficients between organ equivalent dose and kerma in air for external photon radiation. A comparison of the results with published data shows good agreement.     

Microdosimetry of electron microbeams

Track structures of 25, 50 and 80 keV primary electrons, simulated by the detailed-history Monte Carlo method, were analyzed for the frequency distributions of energy deposited in spheres with a diameter of 1 microm, placed in a cylindrically symmetrical array around the projected initial direction of the primary electron. The frequency mean of specific energy, the dose mean of lineal energy, and the parameters of lognormal functions fit to the dose distributions were calculated as a function of beam penetration and radial distance from the projected beam axis. Given these data, the stochastics of dose and radiation quality for micrometer-scale sites targeted by a medium-energy electron microbeam can be predicted as a function of the site's location relative to the beam entry point.