Josep Sempau

PENELOPE: An algorithm for Monte Carlo simulation of the penetration and energy loss of electrons and positrons in matter

Abstract A mixed algorithm for Monte Carlo simulation of relativistic electron and positron transport in matter is described. Cross sections for the different interaction mechanisms are approximated by expressions that permit the generation of random tracks by using purely analytical methods. Hard elastic collisions, with scattering angle greater than a preselected cutoff value, and hard inelastic collisions and radiative events, with energy loss larger than given cutoff values, are simulated in detail. Soft interactions, with scattering angle or energy loss less than the corresponding cutoffs, are simulated by means of multiple scattering approaches. This algorithm handles lateral displacements correctly and completely avoids difficulties related with interface crossing. The simulation is shown to be stable under variations of the adopted cutoffs; these can be made quite large, thus speeding up the simulation considerably, without altering the results. The reliability of the algorithm is demonstrated through a comparison of simulation results with experimental data. Good agreement is found for electrons and positrons with kinetic energies down to a few keV.

An algorithm for Monte Carlo simulation of coupled electron-photon transport

Abstract An algorithm for Monte Carlo simulation of coupled electron-photon transport is described. Electron and positron tracks are generated by means of PENELOPE, a mixed procedure developed by Baro et al. [Nucl. Instr. and Meth. B 100 (1995) 31]. The simulation of photon transport follows the conventional, detailed method. Photons are assumed to interact via coherent and incoherent scattering, photoelectric absorption and electron-positron pair production. Photon interactions are simulated through analytical differential cross sections, derived from simple physical models and renormalized to reproduce accurate attenuation coefficients available from the literature. The combined algorithm has been implemented in a FORTRAN 77 computer code that generates electron-photon showers in arbitrary materials for the energy range from ∼1 GeV down to 1 keV or the binding energy of the L-shell of the heaviest element in the medium, whichever is the largest. The code is capable of following secondary particles that are generated within this energy range. The reliability of the algorithm and computer code is demonstrated by comparing simulation results with experimental data and with results from other Monte Carlo codes.

Experimental benchmarks of the Monte Carlo code penelope

Abstract The physical algorithms implemented in the latest release of the general-purpose Monte Carlo code penelope for the simulation of coupled electron–photon transport are briefly described. We discuss the mixed (class II) scheme used to transport intermediate- and high-energy electrons and positrons and, in particular, the approximations adopted to account for the energy dependence of the interaction cross-sections. The reliability of the simulation code, i.e. of the adopted interaction models and tracking algorithms, is analyzed by means of a comprehensive comparison of simulation results with experimental data available from the literature. The present analysis demonstrates that penelope yields a consistent description of electron transport processes in the energy range from a few keV up to about 1 GeV.

A PENELOPE-based system for the automated Monte Carlo simulation of clinacs and voxelized geometries - application to far-from-axis fields

PURPOSE Two new codes, PENEASY and PENEASYLINAC, which automate the Monte Carlo simulation of Varian Clinacs of the 600, 1800, 2100, and 2300 series, together with their electron applicators and multileaf collimators, are introduced. The challenging case of a relatively small and far-from-axis field has been studied with these tools. METHODS PENEASY is a modular, general-purpose main program for the PENELOPE Monte Carlo system that includes various source models, tallies and variance-reduction techniques (VRT). The code includes a new geometry model that allows the superposition of voxels and objects limited by quadric surfaces. A variant of the VRT known as particle splitting, called fan splitting, is also introduced. PENEASYLINAC, in turn, automatically generates detailed geometry and configuration files to simulate linacs with PENEASY. These tools are applied to the generation of phase-space files, and of the corresponding absorbed dose distributions in water, for two 6 MV photon beams from a Varian Clinac 2100 C∕D: a 40 × 40 cm(2) centered field; and a 3 × 5 cm(2) field centered at (4.5, -11.5) cm from the beam central axis. This latter configuration implies the largest possible over-traveling values of two of the jaws. Simulation results for the depth dose and lateral profiles at various depths are compared, by using the gamma index, with experimental values obtained with a PTW 31002 ionization chamber. The contribution of several VRTs to the computing speed of the more demanding off-axis case is analyzed. RESULTS For the 40 × 40 cm(2) field, the percentages γ(1) and γ(1.2) of voxels with gamma indices (using 0.2 cm and 2% criteria) larger than unity and larger than 1.2 are 0.2% and 0%, respectively. For the 3 × 5 cm(2) field, γ(1) = 0%. These figures indicate an excellent agreement between simulation and experiment. The dose distribution for the off-axis case with voxels of 2.5 × 2.5 × 2.5 mm(3) and an average standard statistical uncertainty of 2% (1σ) is computed in 3.1 h on a single core of a 2.8 GHz Intel Core 2 Duo processor. This result is obtained with the optimal combination of the tested VRTs. In particular, fan splitting for the off-axis case accelerates execution by a factor of 240 with respect to standard particle splitting. CONCLUSIONS PENEASY and PENEASYLINAC can simulate the considered Varian Clinacs both in an accurate and efficient manner. Fan splitting is crucial to achieve simulation results for the off-axis field in an affordable amount of CPU time. Work to include Elekta linacs and to develop a graphical interface that will facilitate user input is underway.

Development of a GPU-based Monte Carlo dose calculation code for coupled electron?photon transport

Monte Carlo simulation is the most accurate method for absorbed dose calculations in radiotherapy. Its efficiency still requires improvement for routine clinical applications, especially for online adaptive radiotherapy. In this paper, we report our recent development on a GPU-based Monte Carlo dose calculation code for coupled electron-photon transport. We have implemented the dose planning method (DPM) Monte Carlo dose calculation package (Sempau et al 2000 Phys. Med. Biol. 45 2263-91) on the GPU architecture under the CUDA platform. The implementation has been tested with respect to the original sequential DPM code on the CPU in phantoms with water-lung-water or water-bone-water slab geometry. A 20 MeV mono-energetic electron point source or a 6 MV photon point source is used in our validation. The results demonstrate adequate accuracy of our GPU implementation for both electron and photon beams in the radiotherapy energy range. Speed-up factors of about 5.0-6.6 times have been observed, using an NVIDIA Tesla C1060 GPU card against a 2.27 GHz Intel Xeon CPU processor.

Output correction factors for nine small field detectors in 6 MV radiation therapy photon beams: A PENELOPE Monte Carlo study

PURPOSE To determine detector-specific output correction factors,[Formula: see text], in 6 MV small photon beams for air and liquid ionization chambers, silicon diodes, and diamond detectors from two manufacturers. METHODS Field output factors, defined according to the international formalism published byAlfonso et al. [Med. Phys. 35, 5179-5186 (2008)], relate the dosimetry of small photon beams to that of the machine-specific reference field; they include a correction to measured ratios of detector readings, conventionally used as output factors in broad beams. Output correction factors were calculated with the PENELOPE Monte Carlo (MC) system with a statistical uncertainty (type-A) of 0.15% or lower. The geometries of the detectors were coded using blueprints provided by the manufacturers, and phase-space files for field sizes between 0.5 × 0.5 cm(2) and 10 × 10 cm(2) from a Varian Clinac iX 6 MV linac used as sources. The output correction factors were determined scoring the absorbed dose within a detector and to a small water volume in the absence of the detector, both at a depth of 10 cm, for each small field and for the reference beam of 10 × 10 cm(2). RESULTS The Monte Carlo calculated output correction factors for the liquid ionization chamber and the diamond detector were within about ± 1% of unity even for the smallest field sizes. Corrections were found to be significant for small air ionization chambers due to their cavity dimensions, as expected. The correction factors for silicon diodes varied with the detector type (shielded or unshielded), confirming the findings by other authors; different corrections for the detectors from the two manufacturers were obtained. The differences in the calculated factors for the various detectors were analyzed thoroughly and whenever possible the results were compared to published data, often calculated for different accelerators and using the EGSnrc MC system. The differences were used to estimate a type-B uncertainty for the correction factors. Together with the type-A uncertainty from the Monte Carlo calculations, an estimation of the combined standard uncertainty was made, assigned to the mean correction factors from various estimates. CONCLUSIONS The present work provides a consistent and specific set of data for the output correction factors of a broad set of detectors in a Varian Clinac iX 6 MV accelerator and contributes to improving the understanding of the physics of small photon beams. The correction factors cannot in general be neglected for any detector and, as expected, their magnitude increases with decreasing field size. Due to the reduced number of clinical accelerator types currently available, it is suggested that detector output correction factors be given specifically for linac models and field sizes, rather than for a beam quality specifier that necessarily varies with the accelerator type and field size due to the different electron spot dimensions and photon collimation systems used by each accelerator model.

MANTIS: combined x-ray, electron and optical Monte Carlo simulations of indirect radiation imaging systems

We describe MANTIS (Monte carlo x-rAy electroN opTical Imaging Simulation), a tool for simulating imaging systems that tracks x-rays, electrons and optical photons in arbitrary materials and complex geometries. The x-ray and electron transport and involved physics models are from the PENELOPE package, and the optical transport and corresponding physics models are from DETECT-II and include Fresnel refraction and reflection at material boundaries, bulk absorption and scattering. Complex geometries can be handled with the aid of the geometry routines included in PENELOPE. When x-rays or electrons interact and deposit energy in the scintillator, the code generates a number of optical quanta according to a user-selected model for the conversion process. The optical photons are then tracked until they reach an absorption event, which in some cases contributes to the output signal, or escape from the geometry. We demonstrate the capabilities of this new tool with respect to the statistics of the optical signal detected and to the three-dimensional point-response functions corresponding to columnar phosphor screens.

A package of Linux scripts for the parallelization of Monte Carlo simulations

Despite the fact that fast computers are nowadays available at low cost, there are many situations where obtaining a reasonably low statistical uncertainty in a Monte Carlo (MC) simulation involves a prohibitively large amount of time. This limitation can be overcome by having recourse to parallel computing. Most tools designed to facilitate this approach require modification of the source code and the installation of additional software, which may be inconvenient for some users. We present a set of tools, named clonEasy, that implement a parallelization scheme of a MC simulation that is free from these drawbacks. In clonEasy, which is designed to run under Linux, a set of “clone” CPUs is governed by a “master” computer by taking advantage of the capabilities of the Secure Shell (ssh) protocol. Any Linux computer on the Internet that can be ssh-accessed by the user can be used as a clone. A key ingredient for the parallel calculation to be reliable is the availability of an independent string of random numbers for each CPU. Many generators—such as RANLUX, RANECU or the Mersenne Twister—can readily produce these strings by initializing them appropriately and, hence, they are suitable to be used with clonEasy. This work was primarily motivated by the need to find a straightforward way to parallelize PENELOPE, a code for MC simulation of radiation transport that (in its current 2005 version) employs the generator RANECU, which uses a combination of two multiplicative linear congruential generators (MLCGs). Thus, this paper is focused on this class of generators and, in particular, we briefly present an extension of RANECU that increases its period up to ∼ 5 × 10 27 and we introduce seedsMLCG, a tool that provides the information necessary to initialize disjoint sequences of an MLCG to feed different CPUs. This program, in combination with clonEasy, allows to run PENELOPE in parallel easily, without requiring specific libraries or significant alterations of the sequential code. Program summary 1

The accuracy of EGSnrc, Geant4 and PENELOPE Monte Carlo systems for the simulation of electron scatter in external beam radiotherapy

Three widely used Monte Carlo systems were benchmarked against recently published measurements of the angular distribution of 13 MeV and 20 MeV electrons scattered from foils of different atomic numbers and thicknesses. Source and geometry were simulated in detail to calculate electron fluence profiles 118.2 cm from the exit window. Results were compared to the measured fluence profiles and the characteristic angle where the fluence drops to 1/e of its maximum value. EGSnrc and PENELOPE results, on average, agreed with measurement within 1 standard deviation experimental uncertainty, with EGSnrc estimating slightly lower scatter than measurement and PENELOPE slightly higher scatter. Geant4.9.2 overestimated the characteristic angle for the lower atomic number foils by as much as 10%. Retuning of the scatter distributions in Geant4 led to a much better agreement with measurement, close to that achieved with the other codes. The 3% differences from measurement seen with all codes for at least some of the foils would result in clinically significant errors in the fluence profiles (2%/4 mm), given accurate knowledge of the electron source and treatment head geometry used in radiotherapy. Further improvement in simulation accuracy is needed to achieve 1%/1 mm agreement with measurement for the full range of beam energies, foil atomic number and thickness used in radiotherapy. EGSnrc would achieve this accuracy with an increase in thickness of the mylar sheets in the monitor chamber, PENELOPE with a decrease in thickness.

Development and commissioning of a Monte Carlo photon beam model for the forthcoming clinical trials in microbeam radiation therapy

PURPOSE A new radiotherapy technique, named microbeam radiation therapy (MRT), is under development at the ID17 Biomedical Beamline of the European Synchrotron Radiation Facility (ESRF). This innovative method is based on the fact that normal tissue can withstand high radiation doses in small volumes without any significant damage. The promising results obtained in the preclinical studies have paved the way to forthcoming clinical trials, which are currently in preparation. Highly accurate dose calculations at the treatment planning stage are required in this context. The aims of this study are the development and experimental benchmarking of a photon beam source model, which will be the core of the future MRT treatment planning system (TPS). METHODS The ID17 x-ray source was modeled by the synchrotron ray tracing code SHADOW. The Monte Carlo (MC) simulation code PENELOPE/PENEASY was employed to transport the photon beam from the source to the patient position through all the beamline components. The phase-space state variables of the particles reaching the patient position were used as an input to generate a photon beam model. Computed dose distributions in a homogeneous media were experimentally verified by using Gafchromic(®) films in a solid-water phantom. Benchmarking was split into two phases. First, the lateral dose profiles and the percentage depth-dose (PDD) curves in the broad beam configuration were considered. The acceptability criteria for radiotherapy dose computations recommended by international protocols such as the Technical Reports Series 430 (TRS 430) of the International Atomic Energy Agency (IAEA) were used. Second, the analogous dosimetric magnitudes in MRT irradiations, i.e., PDD of the central microbeam and the corresponding peak-to-valley dose ratios (PVDR) were evaluated and compared with MC calculations. RESULTS A full characterization of the ID17 Biomedical Beamline (ESRF) synchrotron x-ray source and the development of an accurate photon beam model were achieved in this work. Calculated and experimental dose distributions agreed to within the recommended acceptability criteria described in international codes of practice (TRS 430) for broad beam irradiations. The overall deviation in low gradient areas amounted to 2%-3%. The maximum distance-to-agreement in high gradient regions was lower than 0.7 mm. MC calculations also reproduced MRT experimental results within uncertainty bars. These results validate the photon beam model for its use in MRT radiation therapy calculations. CONCLUSIONS The first MC synchrotron photon beam model for MRT irradiations that reproduces experimental dose distributions in homogeneous media has been developed. This beam model will constitute an essential component of the TPS calculation engine for patient dose computation in forthcoming MRT clinical trials.