Microdosimetric properties of ionizing electrons in water: a test of the PENELOPE code system

The ability to simulate the tortuous path of very low-energy electrons in condensed matter is important for a variety of applications in radiobiology. Event-by-event Monte Carlo codes such as OREC, MOCA and PITS represent the preferred method of computing distributions of microdosimetric quantities. However, event-by-event Monte Carlo is computationally expensive, and the cross sections needed to transport simulations to this level of detail are usually only available for water. In the recently developed PENELOPE code system, 'hard' electron and positron interactions are simulated in a detailed way while soft' interactions are treated using multiple scattering theory. Using this mixed simulation algorithm, electrons and positrons can be transported down to energies as low as 100 eV. To our knowledge, PENELOPE is the first widely available, general purpose Monte Carlo code system capable of transporting electrons and positrons in arbitrary media down to such low energies. The ability to transport electrons and positrons to such low energies opens up the possibility of using a general purpose Monte Carlo code system for microdosimetry. This paper presents the results of a code intercomparison study designed to test the applicability of the PENELOPE code system for microdosimetry applications. For sites comparable in size to a mammalian cell or cell nucleus, single-event distributions, site-hit probabilities and the frequency-mean specific energy per event are in reasonable agreement with those predicted using event-by-event Monte Carlo. Site-hit probabilities and the mean specific energy per event can be estimated to within about 1-10% of those predicted using event-by-event Monte Carlo. However, for some combinations of site size and source-target geometry, site-hit probabilities and the mean specific energy per event may only agree to within 25-60%. The most problematic source-target geometry is one in which the emitted electrons are very close to the tally site (e.g., a point source on the surface of a cell). Although event-by-event Monte Carlo will continue to be the method of choice for microdosimetry, PENELOPE is a useful, computationally efficient tool for some classes of microdosimetry problem. PENELOPE may prove particularly useful for applications that involve radiation transport through materials other than water or for applications that are too computationally intensive for event-by-event Monte Carlo, such as in vivo microdosimetry of spatially complex distributions of radioisotopes inside the human body.     

A particle track-repeating algorithm for proton beam dose calculation

A particle track-repeating algorithm has been developed for proton beam dose calculation for radiotherapy. Monoenergetic protons with 250 MeV kinetic energy were simulated in an infinite water phantom using the GEANT3 Monte Carlo code. The changes in location, angle and energy for every transport step and the energy deposition along the track were recorded for the primary protons and all secondary particles. When calculating dose for a patient with a realistic proton beam, the pre-generated particle tracks were repeated in the patient geometry consisting of air, soft tissue and bone. The medium and density for each dose scoring voxel in the patient geometry were derived from patient CT data. The starting point, at which a proton track was repeated, was determined according to the incident proton energy. Thus, any protons with kinetic energy less than 250 MeV can be simulated. Based on the direction of the incident proton, the tracks were first rotated and for the subsequent steps, the scattering angles were simply repeated for air and soft tissue but adjusted properly based on the scattering power for bone. The particle step lengths were adjusted based on the density for air and soft tissue and also on the stopping powers for bone while keeping the energy deposition unchanged in each step. The difference in nuclear interactions and secondary particle generation between water and these materials was ignored. The algorithm has been validated by comparing the dose distributions in uniform water and layered heterogeneous phantoms with those calculated using the GEANT3 code for 120, 150, 180 and 250 MeV proton beams. The differences between them were within 2%. The new algorithm was about 13 times faster than the GEANT3 Monte Carlo code for a uniform phantom geometry and over 700 times faster for a heterogeneous phantom geometry.     

The Monte Carlo SRNA-VOX code for 3D proton dose distribution in voxelized geometry using CT data

This paper describes the application of the SRNA Monte Carlo package for proton transport simulations in complex geometry and different material compositions. The SRNA package was developed for 3D dose distribution calculation in proton therapy and dosimetry and it was based on the theory of multiple scattering. The decay of proton induced compound nuclei was simulated by the Russian MSDM model and our own using ICRU 63 data. The developed package consists of two codes: the SRNA-2KG, which simulates proton transport in combinatorial geometry and the SRNA-VOX, which uses the voxelized geometry using the CT data and conversion of the Hounsfield's data to tissue elemental composition. Transition probabilities for both codes are prepared by the SRNADAT code. The simulation of the proton beam characterization by multi-layer Faraday cup, spatial distribution of positron emitters obtained by the SRNA-2KG code and intercomparison of computational codes in radiation dosimetry, indicate immediate application of the Monte Carlo techniques in clinical practice. In this paper, we briefly present the physical model implemented in the SRNA package, the ISTAR proton dose planning software, as well as the results of the numerical experiments with proton beams to obtain 3D dose distribution in the eye and breast tumour.     

Monte Carlo microdosimetry of 188Re- and 131I-labelled anti-CD20

The radiolabelled monoclonal antibody anti-CD20 has the property of binding to the CD20 antigen expressed on the cell surface of B-lymphocytes, thus making it a useful tool in the treatment of non-Hodgkin's lymphoma. In this work, the event-by-event Monte Carlo code NOREC is used to calculate the single-event distribution function f(1)(z) in the cell nucleus using the beta spectra of the (188)Re and (131)I radionuclides. The simulated geometry consists of two concentric spheres representing the nucleus and the cell surface embedded in a semi-infinite water medium. An isotropic point source was placed on the cell surface to simulate the binding of the anti-CD20 labelled with either (188)Re or (131)I. The simulations were carried out for two combinations of cell surface and nucleus radii. A method was devised that allows one to calculate the contribution of betas of energy greater than 1 MeV, which cannot be simulated by the NOREC code, to the single-event distribution function. It is shown that disregarding this contribution leads to an overestimation of the frequency-mean specific energy of the order of 9-12%. In general, the antibody radiolabelled with (131)I produces single-event distribution functions that yield higher frequency-mean specific energies.     

An analytic model of neutron ambient dose equivalent and equivalent dose for proton radiotherapy

Stray neutrons generated in passively scattered proton therapy are of concern because they increase the risk that a patient will develop a second cancer. Several investigations characterized stray neutrons in proton therapy using experimental measurements and Monte Carlo simulations, but capabilities of analytical methods to predict neutron exposures are less well developed. The goal of this study was to develop a new analytical model to calculate neutron ambient dose equivalent in air and equivalent dose in phantom based on Monte Carlo modeling of a passively scattered proton therapy unit. The accuracy of the new analytical model is superior to a previous analytical model and comparable to the accuracy of typical Monte Carlo simulations and measurements. Predictions from the new analytical model agreed reasonably well with corresponding values predicted by a Monte Carlo code using an anthropomorphic phantom.     

The significance of electron binding corrections in Monte Carlo photon transport calculations

Many Monte Carlo simulations ignore coherent scattering events and utilise the Klein-Nishina free electron distribution, rather than the incoherent differential cross-section, for choosing the trajectories of incoherently scattered photons. We assess the accuracy of this model by comparing its results with those of the complete bound electron model (form factor approach), which simulates coherent scattering events, and uses the appropriate bound electron angular scattering distributions. Both analytic and Monte Carlo calculations demonstrate that use of the free electron scattering distributions significantly underestimates the angular distribution of scattered photon energy resulting from low and medium energy photons incident upon carbon, iron, and platinum barriers. In using the free electron approximations to calculate barrier transmission, significant errors occur only for primary photon energies below 100 keV. Implementation of the complete bound electron model reduces the computational efficiency of our Monte Carlo code by only 10-25%.     

A convolution algorithm for brachytherapy dose computations in heterogeneous geometries.

Currently-available brachytherapy dose computation algorithms ignore heterogeneities such as tissue-air interfaces, shielded gynecological colpostats, and tissue-composition variations in 125I implants despite dose computation errors as large as 40%. To calculate dose in the presence of tissue and applicator heterogeneities, a computer code has been developed that describes scatter dose as a 3-D spatial integral which convolves primary photon fluence with a dose-spread array. The dose-spread array describes the distribution of dose due to multiple scattering about a single primary interaction site and is precomputed by the Monte Carlo method. To correct for heterogeneities traversed by the primary photons, the dose-spread array is renormalized to reflect the density and composition of the element, and the distance to the point of interest is scaled by the path-length of the intervening medium. Convolution calculations for 125I and 137Cs point sources in the presence of finite phantoms, air voids and high-density shields have been compared to the corresponding Monte Carlo calculations. The convolution code absolute and relative dose rate predictions are shown to agree with Monte Carlo calculations within 3%. Direct evaluation of the 3-D spatial convolution integral using 1-D adaptive integration reveals efficiency gains of 20-50 relative to Monte Carlo photon-transport calculations.     

A standard timing benchmark for EGS4 Monte Carlo calculations.

A Fortran 77 Monte Carlo source code built from the EGS4 Monte Carlo code system has been used for timing benchmark purposes on 29 different computers. This code simulates the deposition of energy from an incident electron beam in a 3-D rectilinear geometry such as one would employ to model electron and photon transport through a series of CT slices. The benchmark forms a standalone system and does not require that the EGS4 system be installed. The Fortran source code may be ported to different architectures by modifying a few lines and only a moderate amount of CPU time is required ranging from about 5 h on PC/386/387 to a few seconds on a massively parallel supercomputer (a BBN TC2000 with 512 processors).     

Simulation of organ-specific patient effective dose due to secondary neutrons in proton radiation treatment

Cancer patients undergoing radiation treatment are exposed to high doses to the target (tumour), intermediate doses to adjacent tissues and low doses from scattered radiation to all parts of the body. In the case of proton therapy, secondary neutrons generated in the accelerator head and inside the patient reach many areas in the patient body. Due to the improved efficacy of management of cancer patients, the number of long term survivors post-radiation treatment is increasing substantially. This results in concern about the risk of radiation-induced cancer appearing at late post-treatment times. This paper presents a case study to determine the effective dose from secondary neutrons in patients undergoing proton treatment. A whole-body patient model, VIP-Man, was employed as the patient model. The geometry dataset generated from studies made on VIP-Man was implemented into the GEANT4 Monte Carlo code. Two proton treatment plans for tumours in the lung and paranasal sinus were simulated. The organ doses and ICRP-60 radiation and tissue weighting factors were used to calculate the effective dose. Results show whole body effective doses for the two proton plans of 0.162 Sv and 0.0266 Sv, respectively, to which the major contributor is due to neutrons from the proton treatment nozzle. There is a substantial difference among organs depending on the treatment site.     

A combined approach of variance-reduction techniques for the efficient Monte Carlo simulation of linacs

A method based on a combination of the variance-reduction techniques of particle splitting and Russian roulette is presented. This method improves the efficiency of radiation transport through linear accelerator geometries simulated with the Monte Carlo method. The method named as 'splitting-roulette' was implemented on the Monte Carlo code [Formula: see text] and tested on an Elekta linac, although it is general enough to be implemented on any other general-purpose Monte Carlo radiation transport code and linac geometry. Splitting-roulette uses any of the following two modes of splitting: simple splitting and 'selective splitting'. Selective splitting is a new splitting mode based on the angular distribution of bremsstrahlung photons implemented in the Monte Carlo code [Formula: see text]. Splitting-roulette improves the simulation efficiency of an Elekta SL25 linac by a factor of 45.     

Monte Carlo dose calculations for spot scanned proton therapy

Density heterogeneities can have a profound effect on dose distributions for proton therapy. Although analytical calculations in homogeneous media are relatively straightforward, the modelling of the propagation of the beam through density heterogeneities can be more problematical. At the Paul Scherrer Institute, an in-house dedicated Monte Carlo (MC) code has been used for over a decade to assess the possible deficiencies of the analytical calculations in patient geometries. The MC code has been optimized for speed, and as such traces primary protons only through the treatment nozzle and patient's CT. Contributions from nuclear interactions are modelled analytically with no tracing of secondary particles. The MC code has been verified against measured data in water and experimental proton radiographs through a heterogeneous anthropomorphic phantom. In comparison to the analytical calculation, the MC code has been applied to both spot scanned and intensity modulated proton therapy plans, and to a number of cases containing titanium metal implants. In summary, MC-based dose calculations could provide an invaluable tool for independently verifying the calculated dose distribution within a patient geometry as part of a comprehensive quality assurance protocol for proton treatment plans.     

Monte Carlo calculations and measurements of absorbed dose per monitor unit for the treatment of uveal melanoma with proton therapy

The treatment of uveal melanoma with proton radiotherapy has provided excellent clinical outcomes. However, contemporary treatment planning systems use simplistic dose algorithms that limit the accuracy of relative dose distributions. Further, absolute predictions of absorbed dose per monitor unit are not yet available in these systems. The purpose of this study was to determine if Monte Carlo methods could predict dose per monitor unit (D/MU) value at the center of a proton spread-out Bragg peak (SOBP) to within 1% on measured values for a variety of treatment fields relevant to ocular proton therapy. The MCNPX Monte Carlo transport code, in combination with realistic models for the ocular beam delivery apparatus and a water phantom, was used to calculate dose distributions and D/MU values, which were verified by the measurements. Measured proton beam data included central-axis depth dose profiles, relative cross-field profiles and absolute D/MU measurements under several combinations of beam penetration ranges and range-modulation widths. The Monte Carlo method predicted D/MU values that agreed with measurement to within 1% and dose profiles that agreed with measurement to within 3% of peak dose or within 0.5 mm distance-to-agreement. Lastly, a demonstration of the clinical utility of this technique included calculations of dose distributions and D/MU values in a realistic model of the human eye. It is possible to predict D/MU values accurately for clinical relevant range-modulated proton beams for ocular therapy using the Monte Carlo method. It is thus feasible to use the Monte Carlo method as a routine absolute dose algorithm for ocular proton therapy.     

Clinical implementation of full Monte Carlo dose calculation in proton beam therapy

The goal of this work was to facilitate the clinical use of Monte Carlo proton dose calculation to support routine treatment planning and delivery. The Monte Carlo code Geant4 was used to simulate the treatment head setup, including a time-dependent simulation of modulator wheels (for broad beam modulation) and magnetic field settings (for beam scanning). Any patient-field-specific setup can be modeled according to the treatment control system of the facility. The code was benchmarked against phantom measurements. Using a simulation of the ionization chamber reading in the treatment head allows the Monte Carlo dose to be specified in absolute units (Gy per ionization chamber reading). Next, the capability of reading CT data information was implemented into the Monte Carlo code to model patient anatomy. To allow time-efficient dose calculation, the standard Geant4 tracking algorithm was modified. Finally, a software link of the Monte Carlo dose engine to the patient database and the commercial planning system was established to allow data exchange, thus completing the implementation of the proton Monte Carlo dose calculation engine ('DoC++'). Monte Carlo re-calculated plans are a valuable tool to revisit decisions in the planning process. Identification of clinically significant differences between Monte Carlo and pencil-beam-based dose calculations may also drive improvements of current pencil-beam methods. As an example, four patients (29 fields in total) with tumors in the head and neck regions were analyzed. Differences between the pencil-beam algorithm and Monte Carlo were identified in particular near the end of range, both due to dose degradation and overall differences in range prediction due to bony anatomy in the beam path. Further, the Monte Carlo reports dose-to-tissue as compared to dose-to-water by the planning system. Our implementation is tailored to a specific Monte Carlo code and the treatment planning system XiO (Computerized Medical Systems Inc.). However, this work describes the general challenges and considerations when implementing proton Monte Carlo dose calculation in a clinical environment. The presented solutions can be easily adopted for other planning systems or other Monte Carlo codes.     

Particle in cell simulation of laser-accelerated proton beams for radiation therapy

In this article we present the results of particle in cell (PIC) simulations of laser plasma interaction for proton acceleration for radiation therapy treatments. We show that under optimal interaction conditions protons can be accelerated up to relativistic energies of 300 MeV by a petawatt laser field. The proton acceleration is due to the dragging Coulomb force arising from charge separation induced by the ponderomotive pressure (light pressure) of high-intensity laser. The proton energy and phase space distribution functions obtained from the PIC simulations are used in the calculations of dose distributions using the GEANT Monte Carlo simulation code. Because of the broad energy and angular spectra of the protons, a compact particle selection and beam collimation system will be needed to generate small beams of polyenergetic protons for intensity modulated proton therapy.     

A practical Monte Carlo MU verification tool for IMRT quality assurance

Quality assurance (QA) for intensity-modulated radiation therapy (IMRT) treatment planning and beam delivery, using ionization chamber measurements and film dosimetry in a phantom, is time consuming. The Monte Carlo method is the most accurate method for radiotherapy dose calculation. However, a major drawback of Monte Carlo dose calculation as currently implemented is its slow speed. The goal of this work is to bring the efficiency of Monte Carlo into a practical range by developing a fast Monte Carlo monitor unit (MU) verification tool for IMRT. A special estimator for dose at a point called the point detector has been used in this research. The point detector uses the next event estimation (NEE) method to calculate the photon energy fluence at a point of interest and then converts it to collision kerma by the mass energy absorption coefficient assuming the presence of transient charged particle equilibrium. The MU verification tool has been validated by comparing the calculation results with measurements. It can be used for both patient dose verification and phantom QA calculation. The dynamic leaf-sequence log file is used to rebuild the actual MLC leaf sequence in order to predict the dose actually received by the patient. Dose calculations for 20 patient plans have been performed using the point detector method. Results were compared with direct Monte Carlo simulations using EGS4/MCSIM, which is a well-benchmarked Monte Carlo code. The results between the point detector and MCSIM agreed to within 2%. A factor of 20 speedup can be achieved with the point detector method compared with direct Monte Carlo simulations.     

Investigation of an efficient source design for Cobalt-60-based tomotherapy using EGSnrc Monte Carlo simulations

Recent investigations demonstrate a strong potential for Cobalt-60 (Co-60)-based tomotherapy. Reported work suggests that Co-60-based tomotherapy offers a clinically and commercially viable alternative to megavoltage x-ray-based tomotherapy. Tomotherapy applications use a combination of intensity-modulated fan beams to deliver highly conformal radiotherapy. However, conventional Co-60 units are designed to give large uniform rectangular fields using an isotropic radioactive source in a cylindrical geometry. Such cylindrical source geometry likely provides a sub-optimal use of the radioactivity within the source volume for tomotherapy applications due to a significant loss of radiated energy outside the fan beam collimation system. To investigate a more efficient source geometry suitable for Co-60 tomotherapy applications, a computer code was written to model an isotropic source in a 6-faced polyhedron geometry such as cube, parallelepiped, prism and truncated pyramid. This code was integrated with the existing EGSnrc/BEAMnrc Monte Carlo (MC) code. The integrated source code was thoroughly tested, validated and used to investigate the energy spectra, radiation output and self-shielding properties of various rectangular-shaped (RS) Co-60 sources. Fan beam dose profiles were calculated for various cylindrical and RS Co-60 sources for a range of source-to-axis distances (SAD), multi-leaf collimator-to-isocentre distances (CID) and modified collimator systems. Fringe and penumbra distances were analysed for the simulated dose profiles. Our results demonstrate that clinically acceptable fringe and penumbra distances can be achieved by a careful selection of SAD, CID, source shape and dimensions and modified collimator system. Significant overall gain in radiation output of the 20 x 1 cm(2) fan beams can be achieved by an optimal selection of the source geometry for a given active volume of Co-60. The overall gain includes the effects of change in packing density (accounting for self-absorption) and change in source shape.     

A theoretical model for event statistics in microdosimetry. II: Nonuniform distribution of heavy ion tracks.

A microdosimetry model, described in Part I, applies to the case of a convex site immersed in a uniform distribution of heavy particle tracks, and assumes no restrictions in site geometry or the kind of randomness. In Part II, this model is extended to include nonuniform distributions of particle tracks. This situation is relevant to the study of microdosimetry, for example, in boron neutron capture, in irradiation experiments using heavy ion particle beams, where the sources of particle tracks are external to the cell, or in irradiation from internally incorporated particle-emitting radionuclides, such as environmental radon or occupational exposure to radioactive materials. The formalism developed permits the calculation of statistical properties, track length distributions, and microdosimetric spectra for convex sites where the "inner" and "outer" concentrations of sources may be different, or for tracks originating on the surface of a convex site. Expressions applicable to the case of surface-distributed sources of tracks are presented that may represent situations such as boron compounds bound to the membrane of a cellular nucleus in boron neutron capture. A series of Monte Carlo calculations and analytical solutions, illustrating the case of spherical site geometry, are presented and compared. Finally, microdosimetric spectra and specific energy averages are calculated for alpha and lithium particles originating from thermal neutron capture in 10B, showing their dependence on 10B localization (extra-site, uniform, intra-site, or surface-distributed).     

Dose distributions in regions containing beta sources: plane interface in a homogeneous medium

An analytic model to calculate dose distributions in regions containing beta sources is developed along with a solution for the dose distribution in an infinite, homogeneous medium in which there is a uniform, monenergetic, isotropic source distribution on only one side of a plane. Comparisons with published Monte Carlo calculations are made.     

A Monte Carlo track structure code for electrons (approximately 10 eV-10 keV) and protons (approximately 0.3-10 MeV) in water: partitioning of energy and collision events

An event-by-event Monte Carlo simulation code for track structure studies is described. In the present form the code transports protons (approximately 0.3-10 MeV) and electrons (approximately 10 eV-10 keV) in a water medium in the gas phase approximation. For the type of particles and energy range considered, ionization, electronic excitation and electron elastic scattering are the most important collision events accounted for in the transport simulation. Efforts were made to ensure that the analytic representation of the various interaction cross sections rests on well established experimental data and theory. For example, the secondary-electron spectrum as well as partial and total ionization cross sections are represented by a semitheoretical formulation combining Bethe's asymptotic expansion and binary-encounter theory. Binding effects for five levels of ionization and eight levels of electronic excitation of the water molecule are explicitly considered. The validity of the model cross sections is examined against available experimental data and theoretical predictions from other similar studies. Results pertaining to the partitioning of energy loss and interaction events for the first-collision probability and nanometre-size track segments are presented.