Monte Carlo techniques in medical radiation physics

Use of Monte Carlo computation in benchmarking radiotherapy treatment planning system algorithms

Radiotherapy treatments are becoming more complex, often requiring the dose to be calculated in three dimensions and sometimes involving the application of non-coplanar beams. The ability of treatment planning systems to accurately calculate dose under a range of these and other irradiation conditions requires evaluation. Practical assessment of such arrangements can be problematical, especially when a heterogeneous medium is used. This work describes the use of Monte Carlo computation as a benchmarking tool to assess the dose distribution of external photon beam plans obtained in a simple heterogeneous phantom by several commercially available 3D and 2D treatment planning system algorithms. For comparison, practical measurements were undertaken using film dosimetry. The dose distributions were calculated for a variety of irradiation conditions designed to show the effects of surface obliquity, inhomogeneities and missing tissue above tangential beams. The results show maximum dose differences of 47% between some planning algorithms and film at a point 1 mm below a tangentially irradiated surface. Overall, the dose distribution obtained from film was most faithfully reproduced by the Monte Carlo N-Particle results illustrating the potential of Monte Carlo computation in evaluating treatment planning system algorithms.

Analytical versus voxelized phantom representation for Monte Carlo simulation in radiological imaging

Monte Carlo simulations in nuclear medicine, with accurately modeled photon transport and high-quality random number generators, require precisely defined and often detailed phantoms as an important component in the simulation process. Contemporary simulation models predominantly employ voxel-driven algorithms, but analytical models offer important advantages. We discuss the implementation of ray-solid intersection algorithms in analytical superquadric-based complex phantoms with additional speed-up rejection testing for use in nuclear medicine imaging simulations, and we make comparisons with voxelized counterparts. Comparisons are made with well-known cold rod:sphere and anthropomorphic phantoms. For these complex phantoms, the analytical phantom representations are nominally several orders of magnitude smaller in memory requirements than are voxelized versions. Analytical phantoms facilitate constant distribution parameters. As a consequence of discretizing a continuous surface into finite bins, for example, time-dependent voxelized phantoms can have difficulties preserving accurate volumes of a beating heart. Although virtually no inaccuracy is associated with path calculations in analytical phantoms, the discretization can negatively impact the simulation process and results. Discretization errors are apparent in reconstructed images of cold rod:sphere voxel-based phantoms because of a redistribution of the count densities in the simulated objects. These problems are entirely avoided in analytical phantoms. Voxelized phantoms can accurately model detailed human shapes based on segmented computed tomography (CT) or magnetic resonance imaging (MRI) images, but analytical phantoms offer advantages in time and accuracy for evaluation and investigation of imaging physics and reconstruction algorithms in a straightforward and efficient manner.

Comparative dosimetry in narrow high-energy photon beams

A comparison of the response of different dosimeters in narrow photon beams (phi > or = 4 mm) of 6 and 18 MV bremsstrahlung has been performed. The detectors used were a natural diamond detector, a liquid ionization chamber, a plastic scintillator and two dedicated silicon diodes. The diodes had a very small detection volume and one was a specially designed double diode using two parallel opposed active volumes with compensating interface perturbations. The characteristics of the detectors were investigated both for dose distribution measurements, such as depth-dose curves and lateral beam profiles, and for output factors. The dose rate and angular dependence of the diamond and the two diodes were also studied separately. The depth-dose distributions for small fields agree well for the diamond, the scintillator and the single diode, while the measured dose maximum for the double diode is about 1% higher and for the liquid chamber about 1% lower than the mean of the others when normalized at a depth of 10 cm. The plastic scintillator and the liquid ionization chamber detect a penumbra width that is slightly broadened due to the influence of their finite size, while the double diode may even underestimate the penumbra width due to its small size and high density. When corrected for the extension of the detector volume a good agreement with Monte Carlo calculated beam profiles was obtained for the plastic scintillator and the liquid ionization chamber. Profiles measured with the diamond show an asymmetry when positioned with the smallest dimension facing the beam, while the double diode, the scintillator and the liquid chamber measure symmetric profiles irrespective of positioning. Significant differences in the output factors were obtained with the different detectors. The natural diamond detector measures output factors close to those with an ionization chamber (less than 1% difference) for field sizes between 3 x 3 and 15 x 15 cm2, but overestimates the output factors for large fields and underestimates the output factors for the smallest field sizes. The single and double diodes overestimated the output factor for large field sizes by up to 7 and 12% respectively due to the high content of low-energy photons. The double diode, and to some extent the single diode, also showed a relative increase in response compared with the more water equivalent liquid chamber and plastic scintillator at the smallest fields where there is a lack of lateral electron equilibrium. Both the plastic scintillator and the liquid chamber also show responses that deviate from the ionization chamber for larger field sizes. The major deviations can be explained based on the characteristics of the sensitive materials and the construction of the detectors.

Photon beam characterization and modelling for Monte Carlo treatment planning

Photon beams of 4, 6 and 15 MV from Varian Clinac 2100C and 2300C/D accelerators were simulated using the EGS4/BEAM code system. The accelerators were modelled as a combination of component modules (CMs) consisting of a target, primary collimator, exit window, flattening filter, monitor chamber, secondary collimator, ring collimator, photon jaws and protection window. A full phase space file was scored directly above the upper photon jaws and analysed using beam data processing software, BEAMDP, to derive the beam characteristics, such as planar fluence, angular distribution, energy spectrum and the fractional contributions of each individual CM. A multiple-source model has been further developed to reconstruct the original phase space. Separate sources were created with accurate source intensity, energy, fluence and angular distributions for the target, primary collimator and flattening filter. Good agreement (within 2%) between the Monte Carlo calculations with the source model and those with the original phase space was achieved in the dose distributions for field sizes of 4 cm x 4 cm to 40 cm x 40 cm at source surface distances (SSDs) of 80-120 cm. The dose distributions in lung and bone heterogeneous phantoms have also been found to be in good agreement (within 2%) for 4, 6 and 15 MV photon beams for various field sizes between the Monte Carlo calculations with the source model and those with the original phase space.

Electron beam modeling and commissioning for Monte Carlo treatment planning

A hybrid approach for commissioning electron beam Monte Carlo treatment planning systems has been studied. The approach is based on the assumption that accelerators of the same type have very similar electron beam characteristics and the major difference comes from the on-site tuning of the electron incident energy at the exit window. For one type of accelerator, a reference machine can be selected and simulated with the Monte Carlo method. A multiple source model can be built on the full Monte Carlo simulation of the reference beam. When commissioning electron beams from other accelerators of the same type, the energy spectra in the source model are tuned to match the measured dose distributions. A Varian Clinac 2100C accelerator was chosen as the reference machine and a four-source beam model was established based on the Monte Carlo simulations. This simplified beam model can be used to generate Monte Carlo dose distributions accurately (within 2%/2 mm compared to those calculated with full phase space data) for electron beams from the reference machine with various nominal energies, applicator sizes, and SSDs. Three electron beams were commissioned by adjusting the energy spectra in the source model. The dose distributions calculated with the adjusted source model were compared with the dose distributions calculated using the phase space data for these beams. The agreement is within 1% in most of cases and 2% in all situations. This preliminary study has shown the capability of the commissioning approach for handling large variation in the electron incident energy. The possibility of making the approach more versatile is also discussed.

Radial dose distribution, dose to water and dose rate constant for monoenergetic photon point sources from 10 keV to 2 MeV:EGS4 Monte Carlo model calculation

A comprehensive set of dose distributions from monoenergetic photon-emitting isotropic point sources in a medium can be used as a reference database for the dosimetry of photon emitter sources in that medium. Data of this type for water over the photon energy range from 15 keV to 2 MeV have been published based on calculations using a one-dimensional photon transport model. The present work, based on a previously published EGS4 Monte Carlo code, updates the classic data set of Berger and provides more extensive calculations than previously available. Air kerma strength per unit photon emission rate from an isotropic point emitter is obtained as a function of energy using published data for mass energy absorption coefficients. The TG-43 dose rate constant for water as a function of energy is calculated for monoenergetic photon emitters as the ratio of dose rate to water at 1 cm to air kerma strength for unit photon emission rate. Results for the radial dose distribution agree well with the data of Berger between 40 and 400 keV. For energies > or =500 keV, a previously undescribed buildup region for the radial dose function is identified. Thickness of the buildup region ranges from 1 mm at 500 keV to 8 mm at 2 MeV. Between 15 and 30 keV, the radial dose function within a few millimeters of the emitter is calculated to be 4%-5% higher than values derived from Berger's data. The maximum dose rate constant for monoenergetic photon emitters occurs at an energy of 60 keV, and has the value 1.355 cGy h(-1)U(-1), where U is the unit of air kerma strength, 1 microGy m2 h(-1). This would correspond to the maximum hypothetical dose rate constant for a brachytherapy photon source emitting photons of energy < or =2 MeV.

Monte Carlo modelling of electron beams from medical accelerators

Monte Carlo simulation of radiation transport is considered to be one of the most accurate methods of radiation therapy dose calculation. With the rapid development of computer technology, Monte Carlo based treatment planning for radiation therapy is becoming practical. A basic requirement for Monte Carlo treatment planning is a detailed knowledge of the radiation beams from medical accelerators. A practical approach to obtain the above is to perform Monte Carlo simulation of radiation transport in the medical accelerator. Additionally, Monte Carlo modelling of the treatment machine head can also improve our understanding of clinical beam characteristics, help accelerator design and improve the accuracy of clinical dosimetry by providing more realistic beam data. This paper summarizes work over the past two decades on Monte Carlo simulation of clinical electron beams from medical accelerators.

Dose calculations for external photon beams in radiotherapy

Dose calculation methods for photon beams are reviewed in the context of radiation therapy treatment planning. Following introductory summaries on photon beam characteristics and clinical requirements on dose calculations, calculation methods are described in order of increasing explicitness of particle transport. The simplest are dose ratio factorizations limited to point dose estimates useful for checking other more general, but also more complex, approaches. Some methods incorporate detailed modelling of scatter dose through differentiation of measured data combined with various integration techniques. State-of-the-art methods based on point or pencil kernels, which are derived through Monte Carlo simulations, to characterize secondary particle transport are presented in some detail. Explicit particle transport methods, such as Monte Carlo, are briefly summarized. The extensive literature on beam characterization and handling of treatment head scatter is reviewed in the context of providing phase space data for kernel based and/or direct Monte Carlo dose calculations. Finally, a brief overview of inverse methods for optimization and dose reconstruction is provided.

Use of a slit camera for MTF measurements

The slit camera was analyzed in order to establish its utility and limitations as an MTF measurement tool for characterizing radiographic imaging systems. Commercial slit cameras are attractive for MTF measurements because the beveled edges significantly reduce their alignment sensitivity as compared to the conventional parallel jaw slit. Radiation passing through the beveled edges increases the effective width of the slit camera so that a correction based on the nominal slit width would leave residual error in the MTF measurement. Experimental and Monte Carlo simulated MTF measurements were made on a slit camera (10 microm nominal slit width) in order to estimate its sensitivity in alignment, quantify the error in MTF due to transmission through the beveled jaws, and provide a correction factor. The alignment tolerances of the slit camera were found to be about 12 times larger than for the parallel jaw slit at small HVLs (approximately 1.3 mm Al) of the incident beam and 9 times larger at higher HVLs (approximately 7 mm Al). The magnitude of the residual error in MTF was dependent on the quality of the incident spectrum. For incident spectra with high kVp and HVL (> or = 120 kVp, > or =5 mm Al HVL), transmission through the beveled edges produced errors in MTF up to 15% at 5 cycles/mm and 30% at 10 cycles/mm. By assuming a rectangular slit profile with an effective width based on the kVp, HVL, and filtration material of the incident beam, an MTF correction factor was determined. Application of this correction factor reduced the errors to less than 4% up to 10 cycles/mm. At low beam energies and spatial frequencies, the correction is less critical. Ease of alignment and greater availability make a commercial slit camera useful for MTF measurements. Accurate MTF measurements can be made if appropriate correction factors are applied.

Clinical implementation of a Monte Carlo treatment planning system

The purpose of this study was to implement the Monte Carlo method for clinical radiotherapy dose calculations. We used the EGS4/BEAM code to obtain the phase-space data for 6-20 MeV electron beams and 4, 6, and 15 MV photon beams for Varian Clinac 1800, 2100C, and 2300CD accelerators. A multiple-source model was used to reconstruct the phase-space data for both electron and photon beams, which retained the accuracy of the Monte Carlo beam data. The multiple-source model reduced the phase-space data storage requirement by a factor of 1000 and the accelerator simulation time by a factor of 10 or more. Agreement within 2% was achieved between the Monte Carlo calculations and measurements of the dose distributions in homogeneous and heterogeneous phantoms for various field sizes, source-surface distances, and beam modulations. The Monte Carlo calculated electron output factors were within 2% of the measured values for various treatment fields while the heterogeneity correction factors for various lung and bone phantoms were within 1% for photon beams and within 2% for electron beams. The EGS4/DOSXYZ Monte Carlo code was used for phantom and patient dose calculations. The results were compared to the dose distributions produced by a conventional treatment planning system and an intensity-modulated radiotherapy inverse-planning system. Significant differences (>5% in dose and >5 mm shift in isodose lines) were found between Monte Carlo calculations and the analytical calculations implemented in the commercial systems. Treatment sites showing the largest dose differences were for head and neck, lung, and breast cases.

Calculation of absorbed dose and biological effectiveness from photonuclear reactions in a bremsstrahlung beam of end point 50 MeV

The absorbed dose due to photonuclear reactions in soft tissue, lung, breast, adipose tissue and cortical bone has been evaluated for a scanned bremsstrahlung beam of end point 50 MeV from a racetrack accelerator. The Monte Carlo code MCNP4B was used to determine the photon source spectrum from the bremsstrahlung target and to simulate the transport of photons through the treatment head and the patient. Photonuclear particle production in tissue was calculated numerically using the energy distributions of photons derived from the Monte Carlo simulations. The transport of photoneutrons in the patient and the photoneutron absorbed dose to tissue were determined using MCNP4B; the absorbed dose due to charged photonuclear particles was calculated numerically assuming total energy absorption in tissue voxels of 1 cm3. The photonuclear absorbed dose to soft tissue, lung, breast and adipose tissue is about (0.11-0.12)+/-0.05% of the maximum photon dose at a depth of 5.5 cm. The absorbed dose to cortical bone is about 45% larger than that to soft tissue. If the contributions from all photoparticles (n, p, 3He and 4He particles and recoils of the residual nuclei) produced in the soft tissue and the accelerator, and from positron radiation and gammas due to induced radioactivity and excited states of the nuclei, are taken into account the total photonuclear absorbed dose delivered to soft tissue is about 0.15+/-0.08% of the maximum photon dose. It has been estimated that the RBE of the photon beam of 50 MV acceleration potential is approximately 2% higher than that of conventional 60Co radiation.

An MCNP-based model of a linear accelerator x-ray beam

The Monte Carlo N-Particle radiation transport computer code (MCNP) has been employed on a personal computer to develop a simple model simulating the major components within the beam path of a linear accelerator radiation head, namely the electron target, primary conical collimator, beam flattening filter, wedge filter and the secondary collimators. The model was initially used to calculate the energy spectra and angular distributions of the x-ray beam for the Philips SL 75/5 linear accelerator, in a plane immediately beneath the flattening filter. These data were subsequently used as a 'source' of x-rays at the target position, to assess the emergent beam from the secondary collimators. The depth dose distributions and dose profiles at constant depth for various field sizes have been calculated for a nominal operating potential of 4 MV and found to be within acceptable limits. It is concluded that the technique may be used to calculate the energy spectra of any linear accelerator upon specification of the component dimensions, materials and nominal accelerating potential. It is anticipated that this work will serve as the basis of a quality control tool for linear accelerators and treatment planning systems.

Relevance of accurate Monte Carlo modeling in nuclear medical imaging

Monte Carlo techniques have become popular in different areas of medical physics with advantage of powerful computing systems. In particular, they have been extensively applied to simulate processes involving random behavior and to quantify physical parameters that are difficult or even impossible to calculate by experimental measurements. Recent nuclear medical imaging innovations such as single-photon emission computed tomography (SPECT), positron emission tomography (PET), and multiple emission tomography (MET) are ideal for Monte Carlo modeling techniques because of the stochastic nature of radiation emission, transport and detection processes. Factors which have contributed to the wider use include improved models of radiation transport processes, the practicality of application with the development of acceleration schemes and the improved speed of computers. In this paper we present a derivation and methodological basis for this approach and critically review their areas of application in nuclear imaging. An overview of existing simulation programs is provided and illustrated with examples of some useful features of such sophisticated tools in connection with common computing facilities and more powerful multiple-processor parallel processing systems. Current and future trends in the field are also discussed.

Comparisons between MCNP, EGS4 and experiment for clinical electron beams

Understanding the limitations of Monte Carlo codes is essential in order to avoid systematic errors in simulations, and to suggest further improvement of the codes. MCNP and EGS4, Monte Carlo codes commonly used in medical physics, were compared and evaluated against electron depth dose data and experimental backscatter results obtained using clinical radiotherapy beams. Different physical models and algorithms used in the codes give significantly different depth dose curves and electron backscattering factors. The default version of MCNP calculates electron depth dose curves which are too penetrating. The MCNP results agree better with experiment if the ITS-style energy-indexing algorithm is used. EGS4 underpredicts electron backscattering for high-Z materials. The results slightly improve if optimal PRESTA-I parameters are used. MCNP simulates backscattering well even for high-Z materials. To conclude the comparison, a timing study was performed. EGS4 is generally faster than MCNP and use of a large number of scoring voxels dramatically slows down the MCNP calculation. However, use of a large number of geometry voxels in MCNP only slightly affects the speed of the calculation.

An object-oriented Monte Carlo simulator for 3D cylindrical positron tomographs

Monte Carlo simulation is a very powerful tool in understanding performances of positron tomographs as well as in assessing image reconstruction algorithms and their implementations. We present an object-oriented Monte Carlo simulator developed for 3D positron tomography. Results from phantom simulation studies including absorption and scattering of the photons in the field-of-view are presented. Scatter fractions determined from these studies are in good agreement with measured scatter fractions published in the literature. Limitations and future prospects are discussed.

The X-ray and electron benchmarking of the Monte Carlo codes MCNP-4A and 4B on different computers

MCNP (Monte Carlo N-Particle) is a Monte Carlo transport code which has been of widespread use in modelling the dosimetry of ionizing radiations. The most recent version (4B) features improved electron transport compared with the previous version 4A. The processing time required by a number of computing systems to carry out X-ray and electron transport calculations using both versions of the code was compared. Version 4A was installed onto a Dec Alpha Server 8200, a personal computer (Pentium 90 MHz), and a Sun Sparc20, 10, 4 and 1+. MCNP-4B was also installed onto the Sun Sparc20. The benchmark tests consisted of determining the transmission of 2 MeV X-rays and 30 MeV electrons through lead. It was found that the Dec Alpha Server 8200 was the fastest computing platform, and the Sun Sparc1+ was the slowest for both tests. The difference in computational speed between different platforms was not matched by the corresponding differences in price. The time required by version 4B to complete the X-ray and electron benchmark tests was found to be 1.4 and 2.3 times greater than version 4A, respectively, without any difference in the results of the calculation for each type of radiation. This suggests that in cases where computing time is important, it may be preferable to use version 4A instead of 4B.

Off-axis x-ray spectra: a comparison of Monte Carlo simulated and computed x-ray spectra with measured spectra

The off-axis x-ray spectra from a constant potential x-ray generator were measured with a high purity germanium spectrometer cooled to liquid nitrogen temperature. The measured spectra were compared with off-axis x-ray spectra calculated using a code based on the semiempirical model developed by Tucker et al. and Monte Carlo simulated x-ray spectra using the EGS4 code system. In this study, both the Tucker model, and the EGS4 code system, were found to produce off-axis bremsstrahlung x-ray spectra which agreed well with the spectra measured at three emerging angles. In the measured and the EGS4 generated spectra the total K-characteristic peaks were in increasing order, as observed in the anode to cathode direction, whereas the Tucker model produced maximum total K-characteristic peaks at the 6 degrees anode side, and lesser amounts at the central axis and the 6 degrees cathode side. Large differences in the total K-characteristic lines is seen among the three different methods. The EGS4 code system was able to produce x-ray spectra for a combination of target materials.

Simulation of dose distribution irradiation by the Leksell Gamma Unit

The dose distributions in a spherical phantom irradiated by a Leksell Gamma Unit have been calculated using the EGS4 Monte Carlo code. In the simulation, the photon beams are considered to emanate from point sources, ignoring the scattering from source and collimating systems. The calculated results are in good agreement with results obtained with semiconductor diodes.

Radiation dosimetry in nuclear medicine

Radionuclides are used in nuclear medicine in a variety of diagnostic and therapeutic procedures. A knowledge of the radiation dose received by different organs in the body is essential to an evaluation of the risks and benefits of any procedure. In this paper, current methods for internal dosimetry are reviewed, as they are applied in nuclear medicine. Particularly, the Medical Internal Radiation Dose (MIRD) system for dosimetry is explained, and many of its published resources discussed. Available models representing individuals of different age and gender, including those representing the pregnant woman are described; current trends in establishing models for individual patients are also evaluated. The proper design of kinetic studies for establishing radiation doses for radiopharmaceuticals is discussed. An overview of how to use information obtained in a dosimetry study, including that of the effective dose equivalent (ICRP 30) and effective dose (ICRP 60), is given. Current trends and issues in internal dosimetry, including the calculation of patient-specific doses and in the use of small scale and microdosimetry techniques, are also reviewed.

A Monte Carlo study of grid performance in diagnostic radiology: task-dependent optimization for digital imaging

A Monte Carlo computational model has been used to optimize grid design in digital radiography. The optimization strategy involved finding grid designs that, for a constant signal-to-noise ratio, resulted in the lowest mean absorbed dose in the patient. Different examinations were simulated to explore the dependence of the optimal scatter-rejection technique on the imaging situation. A large range of grid designs was studied, including grids with both aluminium and fibre interspaces and covers, and compared to a 20 cm air gap. The results show that the optimal tube potential in each examination does not depend strongly on the scatter-rejection technique. There is a significant dose reduction associated with the use of fibre-interspaced grids, particularly in paediatric radiography. The optimal grid ratio and strip width increase with increasing scattering volume. With increasing strip density, the optimal strip width decreases, and the optimal grid ratio increases. Optimal grid ratios are higher than those used today, particularly for grids with large strip density. It is, however, possible to identify grids of good performance for a range of strip densities and grid ratios provided the strip width is selected accordingly. The computational method has been validated by comparison with measurements with a caesium iodide image receptor.

Photon backscattering tissue characterization by energy dispersive spectroscopy evaluations

Techniques for in vivo tissue characterization based on scattered photons have usually been confined to evaluating coherent and Compton peaks. However, information can also be obtained from the energy analysis of the Compton scattered distribution. This paper looks at the extension of a technique validated by the authors for characterizing tissues composed of low-atomic-number elements. To this end, an EDXRS (energy dispersive x-ray spectrometry) computer simulation procedure was performed and applied to test the validity of a figure of merit able to characterize binary compounds. This figure of merit is based on the photon fluence values in a restricted energy interval of the measured distribution of incoherently scattered photons. After careful experimental tests with 59.54 keV incident photons at scattering angles down to 60degrees, the simulation procedure was applied to quasi-monochromatic and polychromatic high-radiance sources. The results show that the characterization by the figure of merit, which operates satisfactorily with monochromatic sources, is unsatisfactory in the latter cases, which seem to favour a different parameter for compound characterization.

The Monte Carlo modelling of in vivo X-ray fluorescence measurement of lead in tissue

A Monte Carlo model has been developed, using the EGS4 code, to model the in vivo x-ray fluorescence (XRF) measurement of Pb in non-superficial bone/tissue. Unlike previous work in this field the current model incorporates a correction for Doppler broadening of the Compton scatter peak due to the electron momentum distribution of the medium (tissue/water) in which the photons are Compton scattered by convolving the Compton peak of the Monte Carlo generated spectrum with a modified Compton profile for water. This correction improves the agreement between the measured spectral shape obtained using an experimental in vivo x-ray fluorescence Pb analyser with a 109Cd/180 degrees source/geometry combination, measuring a bone phantom at depth in water and the generated spectral shape obtained from the equivalent Monte Carlo model. The model enables improved estimates to be made of the spectral background beneath the Pb Kalpha1 and Kalpha2 x-ray peaks compared with estimates based on simpler models that assume that Compton interactions are with 'free' electrons and hence permits better optimization of in vivo analyser system design.

Monte Carlo calculations of electron beam output factors for a medical linear accelerator

The purpose of this study was to investigate the application of the Monte Carlo technique to the calculation and analysis of output factors for electron beams used in radiotherapy. The code EGS4/BEAM was used to obtain phase-space files for 6, 12 and 20 MeV clinical electron beams from a scattering-foil linac (Varian Clinac 2100C) for a clinically representative range of applicator and square or rectangular insert combinations. The source-to-surface distance used was 100 cm. The field sizes ranged from 1 x 1 cm2 to 20 x 20 cm2. These phase-space files were analysed to study the intrinsic beam characteristics and used as source input for relative dose and output factor computations in homogeneous water phantoms using the code EGS4/DOSXYZ. The calculated relative central-axis depth-dose and transverse dose profiles at various depths of clinical interest agreed with the corresponding measured dose profiles to within 2% of the maximum dose. Calculated output factors for the fields studied agreed with measured output factors to about 2%. This demonstrated that for the Varian Clinac 2100C linear accelerator, electron beam dose calculations in homogeneous water phantoms can be performed accurately at the 2% level using Monte Carlo simulations.

Monte Carlo calculation of the dose distributions of two 106Ru eye applicators

BACKGROUND AND PURPOSE

Beta emitting 106Ru applicators are widely used to treat choroidal melanoma. In view of the importance of clinical applications of this radioisotope and the relative lack of knowledge of the dose distributions, three-dimensional dose maps of two concave applicators were calculated by means of Monte Carlo simulation.

MATERIALS AND METHODS

Simulations of small CCA and CCB concave applicators manufactured by Bebig were performed using the Monte Carlo code PENELOPE, which allows the description of the structure (geometry and materials) of the applicator in detail. Electrons are emitted from the 106Ru nuclei isotropically, with initial energy randomly sampled from the corresponding Fermi spectra and with initial positions uniformly distributed on the radioactive layer. Primary electrons, as well as the produced delta-rays, are assumed to be absorbed in the medium when they slow down to an energy of 70 keV. Bremsstrahlung photons with energies larger than 7 keV are also simulated. The simulation code has been run on a 166 MHz PENTIUM PC.

RESULTS

Three-dimensional dose distributions produced by the CCA and CCB applicators in a water sphere, concentric with the applicator, were evaluated. To minimize the magnitude of statistical uncertainties, advantage has been taken of the cylindrical symmetry of the problem. The relative depth-dose (along the symmetry axis of the applicator) was also evaluated from the applicator surface up to distances larger than I cm, with statistical uncertainties of a few percent. Results compare well with data supplied by the manufacturer.

CONCLUSIONS

We have performed accurate Monte Carlo calculations of three-dimensional dose distributions from CCA and CCB 106Ru applicators. The results, presented in the form of two-dimensional maps, depth-dose distributions along the symmetry axis and lateral dose profiles, provide a detailed description of the dose delivered in treatments of choroidal melanoma.

Monte Carlo generated mammograms: development and validation

We have developed a model using Monte Carlo methods to simulate x-ray mammography. All possible physical processes of interaction of x-rays with matter have been taken into account. A simplified geometry of the mammographic apparatus has been considered along with a software phantom of compressed breast. The phantom may contain inhomogeneities of various compositions and sizes. We have used this model to produce Monte Carlo mammograms under realistic conditions. The validation of the simulation includes both the modelling of physical processes and the production of Monte Carlo mammograms. The first part is accomplished by the demonstration of the coincidence between Monte Carlo and theoretical data, whereas the second is accomplished by the comparison of real mammograms, taken from irradiation of a simplified breast phantom that we have constructed, and Monte Carlo mammograms taken from simulation of the above phantom under the corresponding exposure conditions. The limitations of the model as well as the future use of Monte Carlo mammograms are discussed.

A patient-specific Monte Carlo dose-calculation method for photon beams

A patient-specific, CT-based, Monte Carlo dose-calculation method for photon beams has been developed to correctly account for inhomogeneity in the patient. The method employs the EGS4 system to sample the interaction of radiation in the medium. CT images are used to describe the patient geometry and to determine the density and atomic number in each voxel. The user code (MCPAT) provides the data describing the incident beams, and performs geometry checking and energy scoring in patient CT images. Several variance reduction techniques have been implemented to improve the computation efficiency. The method was verified with measured data and other calculations, both in homogeneous and inhomogeneous media. The method was also applied to a lung treatment, where significant differences in dose distributions, especially in the low-density region, were observed when compared with the results using an equivalent pathlength method. Comparison of the DVHs showed that the Monte Carlo calculated plan predicted an underdose of nearly 20% to the target, while the maximum doses to the cord and the heart were increased by 25% and 33%, respectively. These results suggested that the Monte Carlo method may have an impact on treatment designs, and also that it can be used as a benchmark to assess the accuracy of other dose calculation algorithms. The computation time for the lung case employing five 15-MV wedged beams, with an approximate field size of 13 X 13 cm and the dose grid size of 0.375 cm, was less than 14 h on a 175-MHz computer with a standard deviation of 1.5% in the high-dose region.

Combined use of FLUKA and MCNP-4A for the Monte Carlo simulation of the dosimetry of 10B neutron capture enhancement of fast neutron irradiations

Boron neutron capture enhancement (BNCE) of the fast neutron irradiations use thermal neutrons produced in depth of the tissues to generate neutron capture reactions on 10B within tumor cells. The dose enhancement is correlated to the 10B concentration and to thermal neutron flux measured in the depth of the tissues, and in this paper we demonstrate the feasibility of Monte Carlo simulation to study the dosimetry of BNCE. The charged particle FLUKA code has been used to calculate the primary neutron yield from the beryllium target, while MCNP-4A has been used for the transport of these neutrons in the geometry of the Biomedical Cyclotron of Nice. The fast neutron spectrum and dose deposition, the thermal flux and thermal neutron spectrum in depth of a Plexiglas phantom has been calculated. The thermal neutron flux has been compared with experimental results determined with calibrated thermoluminescent dosimeters (TLD-600 and TLD-700, respectively, doped with 6Li or 7Li). The theoretical results were in good agreement with the experimental results: the thermal neutron flux was calculated at 10.3 X 10(6) n/cm2 s1 and measured at 9.42 X 10(6) n/cm2 s1 at 4 cm depth of the phantom and with a 10 cm X 10 cm irradiation field. For fast neutron dose deposition the calculated and experimental curves have the same slope but different shape: only the experimental curve shows a maximum at 2.27 cm depth corresponding to the build-up. The difference is due to the Monte Carlo simulation which does not follow the secondary particles. Finally, a dose enhancement of, respectively, 4.6% and 10.4% are found for 10 cm X 10 cm or 20 cm X 20 cm fields, provided that 100 micrograms/g of 10B is loaded in the tissues. It is anticipated that this calculation method may be used to improve BNCE of fast neutron irradiations through collimation modifications.

Comparison of EGS4 and MCNP Monte Carlo codes when calculating radiotherapy depth doses

The Monte Carlo codes EGS4 and MCNP have been compared when calculating radiotherapy depth doses in water. The aims of the work were to study (i) the differences between calculated depth doses in water for a range of monoenergetic photon energies and (ii) the relative efficiency of the two codes for different electron transport energy cut-offs. The depth doses from the two codes agree with each other within the statistical uncertainties of the calculations (1-2%). The relative depth doses also agree with data tabulated in the British Journal of Radiology Supplement 25. A discrepancy in the dose build-up region may by attributed to the different electron transport algorithims used by EGS4 and MCNP. This discrepancy is considerably reduced when the improved electron transport routines are used in the latest (4B) version of MCNP. Timing calculations show that EGS4 is at least 50% faster than MCNP for the geometries used in the simulations.

Calculation of photon energy and dose distributions in a 50 MV scanned photon beam for different target configurations and scan patterns

A method to characterize the energy distribution in the whole photon field is valuable when designing an accelerator for choosing target and flattening filter or scan pattern. Another field of application is beam characterization for treatment planning systems or other dosimetric purposes. This work is focused on the energy distribution in different 50 MV bremsstrahlung beams with different scanning of electrons on three different targets. Fluence differential in energy and angle at the exit of each target has been determined by Monte Carlo calculations for a narrow beam. Data for broad beams were obtained by convolution of the narrow beams with different scan patterns. Photon energy fluence differential in energy at SSD 100 were thus found to be rather different for the targets studied. The results are presented as mean energy profiles and narrow beam half-value layer (HVL) in water. Two different experimental setups were used to measure HVL at the central axis and at off-axis positions. The two methods gave results which differ by 5%-6% and the calculated data where within these experimental results. In conclusion, the presented method for characterization of the photon field energy distribution is well within the experimental results and can thus be used to improve accelerator design or dosimetric calculations, e.g., for treatment planning.

Parallel operation of Monte Carlo simulations on a diverse network of computers

Monte Carlo simulation methods are frequently used to determine light propagation in tissue and x-ray propagation as well as for solving other non-medically related problems. Such techniques are computationally slow, with the signal to noise ratio improving only as the square root of computation time. We present a method for the design of a Monte Carlo program that is capable of running on up to 24 computers simultaneously, with there being very few restrictions on the computer types as long as they run on a common network. This parallel operation is useful when the run time is expected to be long. A mixture of PCs and Sun workstations have been successfully used. The program as described was designed for the simulation of light transport in tissue, but the technique of achieving simple simultaneous execution on a number of different computers could be used wherever Monte Carlo techniques are used.

Monte Carlo and analytical calculation of proton pencil beams for computerized treatment plan optimization

Proton pencil beams in water, in a format suitable for treatment planning algorithms and covering the radiotherapy energy range (50-250 MeV), have been calculated using a modified version of the Monte Carlo code PTRAN. A simple analytical model has also been developed for calculating proton broad-beam dose distributions which is in excellent agreement with the Monte Carlo calculations. Radial dose distributions are also calculated analytically and narrow proton pencil-beam dose distributions derived. The physical approximations in the Monte Carlo code and in the analytical model together with their limitations are discussed. Examples showing the use of the calculated set of proton pencil beams as input to an existing photon treatment planning algorithm based on biological optimization are given for fully 3D scanned proton pencil beams; these include intensity modulated beams with range shift and scanning in the transversal plane.

Improved modeling of multiple scattering in the Voxel Monte Carlo model

The implementation of an improved model for multiple scattering into the-Voxel Monte Carlo (VMC) algorithm for fast electron dose calculation in radiation therapy is presented. The model takes into account path-length corrections (PLC) and lateral displacement in the individual electron steps. The extraction of the scattering power from the available computed-tomography images is discussed. It is shown that with the improved modeling of multiple electron scattering, the VMC algorithm is comparable in accuracy with PRESTA, the electron transport algorithm of EGS4. The problem of double counting of contributions from atomic electrons to the scattering power is considered and a simple solution is found.

Accurate characterization of Monte Carlo calculated electron beams for radiotherapy

Monte Carlo studies of dose distributions in patients treated with radiotherapy electron beams would benefit from generalized models of clinical beams if such models introduce little error into the dose calculations. Methodology is presented for the design of beam models, including their evaluation in terms of how well they preserve the character of the clinical beam, and the effect of the beam models on the accuracy of dose distributions calculated with Monte Carlo. This methodology has been used to design beam models for electron beams from two linear accelerators, with either a scanned beam or a scattered beam. Monte Carlo simulations of the accelerator heads are done in which a record is kept of the particle phase-space, including the charge, energy, direction, and position of every particle that emerges from the treatment head, along with a tag regarding the details of the particle history. The character of the simulated beams are studied in detail and used to design various beam models from a simple point source to a sophisticated multiple-source model which treats particles from different parts of a linear accelerator as from different sub-sources. Dose distributions calculated using both the phase-space data and the multiple-source model agree within 2%, demonstrating that the model is adequate for the purpose of Monte Carlo treatment planning for the beams studied. Benefits of the beam models over phase-space data for dose calculation are shown to include shorter computation time in the treatment head simulation and a smaller disk space requirement, both of which impact on the clinical utility of Monte Carlo treatment planning.

Monte Carlo calculated stopping-power ratios, water/air, for clinical proton dosimetry (50-250 MeV)

Calculations of stopping power ratios, water to air, for the determination of absorbed dose to water in clinical proton beams using ionization chamber measurements have been undertaken using the Monte Carlo method. A computer code to simulate the transport of protons in water (PETRA) has been used to calculate sw.air-data under different degrees of complexity, ranging from values based on primary protons only to data including secondary electrons and high-energy secondary protons produced in nonelastic nuclear collisions. All numerical data are based on ICRU 49 proton stopping powers. Calculations using primary protons have been compared to the simple continuous slowing-down approximation (c.s.d.a.) analytical technique used in proton dosimetry protocols, not finding significant differences that justify elaborate Monte Carlo simulations except beyond the mean range of the protons (the far side of the Bragg peak). The influence of nuclear nonelastic processes, through the detailed generation and transport of secondary protons, on the calculated stopping-power ratios has been found to be negligible. The effect of alpha particles has also been analysed, finding differences smaller than 0.1% from the results excluding them. Discrepancies of up to 0.6% in the plateau region have been found, however, when the production and transport of secondary electrons are taken into account. The large influence of nonelastic nuclear interactions on proton depth-dose distributions shows that the removal of primary protons from the incident beam decreases the peak-to-plateau ratio by a large factor, up to 40% at 250 MeV. It is therefore emphasized that nonelastic nuclear reactions should be included in Monte Carlo simulations of proton beam depth-dose distributions.

Theoretical and experimental determination of phantom scatter factors for photon fields with different radial energy variation

The output factor used for monitor unit determination in radiotherapy can be divided into two factors: the head scatter factor and the phantom scatter factor. Theoretical and experimental phantom scatter factors have been compared for different beam qualities between 4 MV and 50 MV and field sizes from 5 cm x 5 cm to 30 cm x 30 cm. The theoretical data were obtained through a convolution method based on Monte Carlo calculated energy spectra and dose kernels. The calculations have been performed both for accelerators with a rather large energy variation within the field and for accelerators with a constant energy distribution in the field. Deviations between theoretical and experimental data were found to be less than 1%.

Microdosimetry and radiocurability: modelling targeted therapy with beta-emitters

Tumour control probability (TCP) is a more relevant quantity than the dose distribution in the target volume for estimating the likely efficacy of any type of radiation therapy, be it external beam or targeted using radionuclides. This paper concentrates on a TCP modelling study, for tumour spheres of different radii assuming a uniform uptake of six different beta emitters (ranging from 67Cu to 90Y or 0.58 to 2.3 MeV in endpoint energy). The dose at varying radii, expressed as a fraction of the equilibrium dose, D beta (R)/Deq, was computed by numerical integration of the point-dose kernel over the sphere volume, and shows clearly the effect of electron disequilibrium for small radii and also at the edges of the spheres. These D beta(R)/Deq were converted into volume-dose distribution V(D) and thence into clonogenic cell numbers, n(D), from which the TCPs for spheres of different radii were computed, for different cumulated activities per unit mass, in megabecquerel hours per gram assuming a clonogenic cell density of 10(8) cm-3 and a tumour-cell radiosensitivity alpha of 1.0 Gy-1. Using V(D) rather than simply the mean dose decreases the TCP at both large and small tumour radii for a given number of megabecquerel hour per gram. Curves of iso-TCP go through a shallow minimum in megabecquerel hour per gram at a tumour radius approximately equal to the maximum beta-particle range. The fall in dose at small radii outweighs the reduction in cell number, making it improbable that micrometastases can be eliminated solely by beta-emitters targeted to the tumour cells. An explicit comparison with external-beam therapy for a fixed number of tumour cells divided into different numbers of spheres further emphasizes the difficulties caused by small tumours in beta-particle targeted therapy. Alternative strategies to overcome these limitations are briefly discussed.

Perturbation effects in dosimetry: Part I. Kilovoltage x-rays and electrons

Perturbation effects are defined as departures from ideal large-detector or Bragg-Gray cavity behaviour. Such effects are central to the use of practical dosimeters for accurate dose determination, as is required in external-beam radiotherapy. A theoretical framework for treating perturbation effects is established. In this first part of the review, perturbation in kilovoltage x-ray and megavoltage electron beams are treated in detail, with the emphasis on ionization chambers. The displacement factor for ion chambers in kilovoltage x-ray beams is discussed, starting with the early, pioneering work of Lamerton and Lidén. The evidence for the large values of the perturbation factor in medium-energy x-ray beams (between 100 and 300 kV) recommended in the 1987 IAEA dosimetry code is critically examined and revised, smaller values are given. In electron beams the theoretical approaches to the correction for the in-scattering correction in gas-filled cavities is discussed in detail. The evidence for negligible perturbation in low-energy electron beams in plane-parallel chambers with adequate guardring widths is critically reviewed, including the suggested correction for perturbation due to backscattering differences between the chamber-wall material and the medium. The various models for the response of thermoluminescent dosimeters in electron beams are discussed. It is concluded that Monte Carlo simulation of dosimeter response is likely to play an even bigger role in the future.

Detour factors in water and plastic phantoms and their use for range and depth scaling in electron-beam dosimetry

Average penetration depths and detour factors of 1-50 MeV electrons in water and plastic materials have been computed by means of analytical calculation, within the continuous-slowing-down approximation and including multiple scattering, and using the Monte Carlo codes ITS and PENELOPE. Results are compared to detour factors from alternative definitions previously proposed in the literature. Different procedures used in low-energy electron-beam dosimetry to convert ranges and depths measured in plastic phantoms into water-equivalent ranges and depths are analysed. A new simple and accurate scaling method, based on Monte Carlo-derived ratios of average electron penetration depths and thus incorporating the effect of multiple scattering, is presented. Data are given for most plastics used in electron-beam dosimetry together with a fit which extends the method to any other low-Z plastic material. A study of scaled depth-dose curves and mean energies as a function of depth for some plastics of common usage shows that the method improves the consistency and results of other scaling procedures in dosimetry with electron beams at therapeutic energies.

Wall effects in plane-parallel ionization chambers

All dosimetry protocols recommend the use of plane-parallel chambers for dose determination in electron beams with energies below 10-15 MeV. The protocols have assumed chamber perturbation effects to be negligible. The new AAPM Protocol (TG39) includes a cavity replacement factor prepl that differs from unity for some chambers, but assumes that the wall perturbation factor, pwall, may be taken as unity. In this paper the perturbation of the wall has been determined, using a large plane-parallel ionization chamber with exchangeable front and back walls. The results show that in many commercial chambers there is an energy dependent pwall factor, mainly due to differences in backscatter from the often thick chamber body as compared to the phantom material. Backscatter in common phantom and chamber materials may differ by as much as 2% at low electron energies (Plastic Water as compared to polystyrene). The front walls are often thin, resulting in negligible perturbation, but the 0.5 mm front wall of graphite in the NACP chamber was found to increase the response by 0.7% in a PMMA phantom. The experimental results have been compared with EGS4 Monte Carlo calculations using the DOSRZ code. There is an agreement within statistical and experimental uncertainties (0.5%) indicating that it is possible to use Monte Carlo calculations to calculate perturbation factors with good accuracy.

A comparison of speeds of personal computers using an x-ray scattering Monte Carlo benchmark

In recent years personal computers, PCs, have become more popular and competitive with other computers, in terms of price and memory, to run Monte Carlo (MC) programmes. A few years ago some work was performed to test computer speed, mainly other than PCs, using the MC code EGS4. In the present work a Monte Carlo neutron and photon code, MCNP version 4.2 and 4A, was used to test the speed of various PCs. A benchmark was written, with previously checked results, to test the PCs' speed. PCs used in the test were based on the Intel 486 (33, 66 and 100 MHz) and pentium 90. The benchmark was also used on an upgraded SunSparcstation 4/360. The pentium speed was found ot be about 3.5, 2 and 1.5 times faster than that of the 33, 66 and 100 MHz, respectively. The 33 MHz speed was comparable to that of the SunSparcstation. It is concluded that the application of MC code, the cost of the PC and the required speed of results may influence the choice of the PC.

A Monte-Carlo program converting activity distributions to absorbed dose distributions in a radionuclide treatment planning system

In systemic radiation therapy, the absorbed dose distribution must be calculated from the individual activity distribution. A computer code has been developed for the conversion of an arbitrary activity distribution to a 3-D absorbed dose distribution. The activity distribution can be described either analytically or as a voxel based distribution, which comes from a SPECT acquisition. Decay points are sampled according to the activity map, and particles (photons and electrons) from the decay are followed through the tissue until they either escape the patient or drop below a cut off energy. To verify the calculated results, the mathematically defined MIRD phantom and unity density spheres have been included in the code. Also other published dosimetry data were used for verification. Absorbed fractions and S-values were calculated. A comparison with simulated data from the code with MIRD data shows good agreement. The S values are within 10-20% of published MIRD S values for most organs. Absorbed fractions for photons and electrons in spheres (masses between 1 g and 200 kg) are within 10-15% of those published. Radial absorbed dose distributions in a necrotic tumor show good agreement with published data. The application of the code in a radionuclide therapy dose planning system, based on quantitative SPECT, is discussed.

Limitations of a pencil beam approach to photon dose calculations in lung tissue

A common limitation in treatment planning systems for photon dose calculation is to ignore the impact on electron transport and photon scatter from patient heterogeneities. The heterogeneity correlation is often based on scaling operations along beam rays as for the method according to Batho or the more novel approach of 1D convolutions along beam paths applied in pencil-beam-based systems. The effects of the limitation have been studied in a mediastinum geometry for a wide range of beam qualities by comparing the results from a pencil-beam-based treatment planning system with the results from Monte Carlo calculations. As expected, the deviations within unit-density volumes are small while deviations in low-density volumes increase with increasing beam energy from approximately 3% for 4 MV to 14% for 18 MV x-rays as a result of increased electron disequilibrium.