Monte Carlo source model for photon beam radiotherapy: photon source characteristics

A major barrier to widespread clinical implementation of Monte Carlo dose calculation is the difficulty in characterizing the radiation source within a generalized source model. This work aims to develop a generalized three-component source model (target, primary collimator, flattening filter) for 6- and 18-MV photon beams that match full phase-space data (PSD). Subsource by subsource comparison of dose distributions, using either source PSD or the source model as input, allows accurate source characterization and has the potential to ease the commissioning procedure, since it is possible to obtain information about which subsource needs to be tuned. This source model is unique in that, compared to previous source models, it retains additional correlations among PS variables, which improves accuracy at nonstandard source-to-surface distances (SSDs). In our study, three-dimensional (3D) dose calculations were performed for SSDs ranging from 50 to 200 cm and for field sizes from 1 x 1 to 30 x 30 cm2 as well as a 10 x 10 cm2 field 5 cm off axis in each direction. The 3D dose distributions, using either full PSD or the source model as input, were compared in terms of dose-difference and distance-to-agreement. With this model, over 99% of the voxels agreed within +/-1% or 1 mm for the target, within 2% or 2 mm for the primary collimator, and within +/-2.5% or 2 mm for the flattening filter in all cases studied. For the dose distributions, 99% of the dose voxels agreed within 1% or 1 mm when the combined source model-including a charged particle source and the full PSD as input-was used. The accurate and general characterization of each photon source and knowledge of the subsource dose distributions should facilitate source model commissioning procedures by allowing scaling the histogram distributions representing the subsources to be tuned.     

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.     

Monte Carlo calculation of nine megavoltage photon beam spectra using the BEAM code

A recent paper analyzed the sensitivity to various simulation parameters of the Monte Carlo simulations of nine beams from three major manufacturers of commercial medical linear accelerators, ranging in energy from 4-25 MV. In this work the nine models are used: to calculate photon energy spectra and average energy distributions and compare them to those published by Mohan et al. [Med. Phys. 12, 592-597 (1985)]; to separate the spectra into primary and scatter components from the primary collimator, the flattening filter and the adjustable collimators; and to calculate the contaminant-electron fluence spectra and the electron contribution to the depth-dose curves. Notwithstanding the better precision of the calculated spectra, they are similar to those calculated by Mohan et al. The three photon spectra at 6 MV from the machines of three different manufacturers show differences in their shapes as well as in the efficiency of bremsstrahlung production in the corresponding target and filter combinations. The contribution of direct photons to the photon energy fluence in a 10 x 10 field varies between 92% and 97%, where the primary collimator contributes between 0.6% and 3.4% and the flattening filter contributes between 0.6% and 4.5% to the head-scatter energy fluence. The fluence of the contaminant electrons at 100 cm varies between 5 x 10(-9) and 2.4 x 10(-7) cm(-2) per incident electron on target, and the corresponding spectrum for each beam is relatively invariant inside a 10 x 10 cm2 field. On the surface the dose from electron contamination varies between 5.7% and 11% of maximum dose and, at the depth of maximum dose, between 0.16% and 2.5% of maximum dose. The photon component of the percentage depth-dose at 10 cm depth is compared with the general formula provided by AAPM's task group 51 and confirms the claimed accuracy of 2%.     

Monte Carlo study of photon fields from a flattening filter-free clinical accelerator

In conventional clinical linear accelerators, the flattening filter scatters and absorbs a large fraction of primary photons. Increasing the beam-on time, which also increases the out-of-field exposure to patients, compensates for the reduction in photon fluence. In recent years, intensity modulated radiation therapy has been introduced, yielding better dose distributions than conventional three-dimensional conformal therapy. The drawback of this method is the further increase in beam-on time. An accelerator with the flattening filter removed, which would increase photon fluence greatly, could deliver considerably higher dose rates. The objective of the present study is to investigate the dosimetric properties of 6 and 18 MV photon beams from an accelerator without a flattening filter. The dosimetric data were generated using the Monte Carlo programs BEAMnrc and DOSXYZnrc. The accelerator model was based on the Varian Clinac 2100 design. We compared depth doses, dose rates, lateral profiles, doses outside collimation, total and collimator scatter factors for an accelerator with and without a flatteneing filter. The study showed that removing the filter increased the dose rate on the central axis by a factor of 2.31 (6 MV) and 5.45 (18 MV) at a given target current. Because the flattening filter is a major source of head scatter photons, its removal from the beam line could reduce the out-of-field dose.     

The flatness of Siemens linear accelerator x-ray fields

The primary definer for Siemens MXE and MDX linear accelerators projects a circular opening with a radius of 25 cm at 100 cm from the target. Our measurements of photon beam profiles, however, indicate that the photon fluence drops to 95% of the central axis value at a radius of 18 cm. The flattening filter for these machines projects a flattened field size that is much smaller than the primary definer would allow. The clinical implications of this mismatch for large rectangular fields and for fields defined by asymmetric jaws are discussed and solutions are considered. A large field flattener was designed for our Siemens MXE 6 MV beam using Monte Carlo simulation of the treatment head and water phantom. The accuracy required of source and geometry details for dose distributions calculation is presented. The key parameters are the mean energy and focal spot size of the electron beam incident on the exit window, the material composition, and thickness profile of the exit window, target, flattener, and primary collimator, and the position of the primary collimator relative to the target. Profiles were more sensitive than central axis depth doses to simulation details. The beam energy and primary collimator position were selected to achieve good agreement between measured and calculated dose distributions. The flattener we designed with Monte Carlo was machined from brass and mounted on our MXE treatment unit. Measurements demonstrate that the large field flattener extends the useful radius of the field out to 22 cm, right into the penumbra cast by the primary collimator.     

Sensitivity of megavoltage photon beam Monte Carlo simulations to electron beam and other parameters

The BEAM code is used to simulate nine photon beams from three major manufacturers of medical linear accelerators (Varian, Elekta, and Siemens), to derive and evaluate estimates for the parameters of the electron beam incident on the target, and to study the effects of some mechanical parameters like target width, primary collimator opening, flattening filter material and density. The mean energy and the FWHM of the incident electron beam intensity distributions (assumed Gaussian and cylindrically symmetric) are derived by matching calculated percentage depth-dose curves past the depth of maximum dose (within 1% of maximum dose) and off-axis factors (within 2sigma at 1% statistics or less) with measured data from the AAPM RTC TG-46 compilation. The off-axis factors are found to be very sensitive to the mean energy of the electron beam, the FWHM of its intensity distribution, its angle of incidence, the dimensions of the upper opening of the primary collimator, the material of the flattening filter and its density. The off-axis factors are relatively insensitive to the FWHM of the electron beam energy distribution, its divergence and the lateral dimensions of the target. The depth-dose curves are sensitive to the electron beam energy, and to its energy distribution, but they show no sensitivity to the FWHM of the electron beam intensity distribution. The electron beam incident energy can be estimated within 0.2 MeV when matching either the measured off-axis factors or the central-axis depth-dose curves when the calculated uncertainties are about 0.7% at the 1 sigma level. The derived FWHM (+/-0.1 mm) of the electron beam intensity distributions all fall within 1 mm of the manufacturer specifications except in one case where the difference is 1.2 mm.     

A virtual photon energy fluence model for Monte Carlo dose calculation

The presented virtual energy fluence (VEF) model of the patient-independent part of the medical linear accelerator heads, consists of two Gaussian-shaped photon sources and one uniform electron source. The planar photon sources are located close to the bremsstrahlung target (primary source) and to the flattening filter (secondary source), respectively. The electron contamination source is located in the plane defining the lower end of the filter. The standard deviations or widths and the relative weights of each source are free parameters. Five other parameters correct for fluence variations, i.e., the horn or central depression effect. If these parameters and the field widths in the X and Y directions are given, the corresponding energy fluence distribution can be calculated analytically and compared to measured dose distributions in air. This provides a method of fitting the free parameters using the measurements for various square and rectangular fields and a fixed number of monitor units. The next step in generating the whole set of base data is to calculate monoenergetic central axis depth dose distributions in water which are used to derive the energy spectrum by deconvolving the measured depth dose curves. This spectrum is also corrected to take the off-axis softening into account. The VEF model is implemented together with geometry modules for the patient specific part of the treatment head (jaws, multileaf collimator) into the XVMC dose calculation engine. The implementation into other Monte Carlo codes is possible based on the information in this paper. Experiments are performed to verify the model by comparing measured and calculated dose distributions and output factors in water. It is demonstrated that open photon beams of linear accelerators from two different vendors are accurately simulated using the VEF model. The commissioning procedure of the VEF model is clinically feasible because it is based on standard measurements in air and water. It is also useful for IMRT applications because a full Monte Carlo simulation of the treatment head would be too time-consuming for many small fields.     

Decoupling initial electron beam parameters for Monte Carlo photon beam modelling by removing beam-modifying filters from the beam path

A new method is presented to decouple the parameters of the incident e(-) beam hitting the target of the linear accelerator, which consists essentially in optimizing the agreement between measurements and calculations when the difference filter, which is an additional filter inserted in the linac head to obtain uniform lateral dose-profile curves for the high energy photon beam, and flattening filter are removed from the beam path. This leads to lateral dose-profile curves, which depend only on the mean energy of the incident electron beam, since the effect of the radial intensity distribution of the incident e- beam is negligible when both filters are absent. The location of the primary collimator and the thickness and density of the target are not considered as adjustable parameters, since a satisfactory working Monte Carlo model is obtained for the low energy photon beam (6 MV) of the linac using the same target and primary collimator. This method was applied to conclude that the mean energy of the incident e- beam for the high energy photon beam (18 MV) of our Elekta SLi Plus linac is equal to 14.9 MeV. After optimizing the mean energy, the modelling of the filters, in accordance with the information provided by the manufacturer, can be verified by positioning only one filter in the linac head while the other is removed. It is also demonstrated that the parameter setting for Bremsstrahlung angular sampling in BEAMnrc ('Simple' using the leading term of the Koch and Motz equation or 'KM' using the full equation) leads to different dose-profile curves for the same incident electron energy for the studied 18 MV beam. It is therefore important to perform the calculations in 'KM' mode. Note that both filters are not physically removed from the linac head. All filters remain present in the linac head and are only rotated out of the beam. This makes the described method applicable for practical usage since no recommissioning process is required.     

A three-source model for the calculation of head scatter factors

Accurate determination of the head scatter factor Sc is an important issue, especially for intensity modulated radiation therapy, where the segmented fields are often very irregular and much less than the collimator jaw settings. In this work, we report an Sc calculation algorithm for symmetric, asymmetric, and irregular open fields shaped by the tertiary collimator (a multileaf collimator or blocks) at different source-to-chamber distance. The algorithm was based on a three-source model, in which the photon radiation to the point of calculation was treated as if it originated from three effective sources: one source for the primary photons from the target and two extra-focal photon sources for the scattered photons from the primary collimator and the flattening filter, respectively. The field mapping method proposed by Kim et al. [Phys. Med. Biol. 43, 1593-1604 (1998)] was extended to two extra-focal source planes and the scatter contributions were integrated over the projected areas (determined by the detector's eye view) in the three source planes considering the source intensity distributions. The algorithm was implemented using Microsoft Visual C/C++ in the MS Windows environment. The only input data required were head scatter factors for symmetric square fields, which are normally acquired during machine commissioning. A large number of different fields were used to evaluate the algorithm and the results were compared with measurements. We found that most of the calculated Sc's agreed with the measured values to within 0.4%. The algorithm can also be easily applied to deal with irregular fields shaped by a multileaf collimator that replaces the upper or lower collimator jaws.     

A virtual source model for Monte Carlo modeling of arbitrary intensity distributions

A photon virtual source model was developed for simulating arbitrary, external beam, intensity distributions using the Monte Carlo method. The source model consists of a photon fluence grid composed of a matrix of square elements, located 25-cm downstream from the linear accelerator target. Each particle originating from the fluence map is characterized by the seven phase space parameters, position (x, y, z), direction (u, v, w), and energy. The map was reconstructed from fluence and energy spectra acquired by modeling components of the linear accelerator treatment head using the Monte Carlo code MCNP4B. The effect of contaminant electrons is accounted for by the use of a sub-source derived from a phase-space simulation of a 25-MV linac treatment head using the code BEAM. The BEAM sub-source was incorporated into the MCNP4B phase-space model and is sampled using a field-size dependent sampling ratio. A Gaussian blurring kernel is convolved with the photon fluence map to account for the finite focal spot size and scattering effects from structures such as the flattening filter and MLC leaves. Depth dose and profile source calculations for 6-MV and 25-MV photon beams, for 5 x 5 cm2, 10 x 10 cm2, and 15 x 15 cm2 field sizes, are in good agreement with measurement and are well within acceptability criteria suggested by the AAPM Task Group Report No. 53. Irregular field calculations compared with film measurement and with a 3-D pencil beam algorithm show that the source model is capable of accurately simulating arbitrary MLC fields.     

A virtual photon source model of an Elekta linear accelerator with integrated mini MLC for Monte Carlo based IMRT dose calculation

A dedicated, efficient Monte Carlo (MC) accelerator head model for intensity modulated stereotactic radiosurgery treatment planning is needed to afford a highly accurate simulation of tiny IMRT fields. A virtual source model (VSM) of a mini multi-leaf collimator (MLC) (the Elekta Beam Modulator (EBM)) is presented, allowing efficient generation of particles even for small fields. The VSM of the EBM is based on a previously published virtual photon energy fluence model (VEF) (Fippel et al 2003 Med. Phys. 30 301) commissioned with large field measurements in air and in water. The original commissioning procedure of the VEF, based on large field measurements only, leads to inaccuracies for small fields. In order to improve the VSM, it was necessary to change the VEF model by developing (1) a method to determine the primary photon source diameter, relevant for output factor calculations, (2) a model of the influence of the flattening filter on the secondary photon spectrum and (3) a more realistic primary photon spectrum. The VSM model is used to generate the source phase space data above the mini-MLC. Later the particles are transmitted through the mini-MLC by a passive filter function which significantly speeds up the time of generation of the phase space data after the mini-MLC, used for calculation of the dose distribution in the patient. The improved VSM model was commissioned for 6 and 15 MV beams. The results of MC simulation are in very good agreement with measurements. Less than 2% of local difference between the MC simulation and the diamond detector measurement of the output factors in water was achieved. The X, Y and Z profiles measured in water with an ion chamber (V = 0.125 cm(3)) and a diamond detector were used to validate the models. An overall agreement of 2%/2 mm for high dose regions and 3%/2 mm in low dose regions between measurement and MC simulation for field sizes from 0.8 x 0.8 cm(2) to 16 x 21 cm(2) was achieved. An IMRT plan film verification was performed for two cases: 6 MV head&neck and 15 MV prostate. The simulation is in agreement with film measurements within 2%/2 mm in the high dose regions (> or = 0.1 Gy = 5% D(max)) and 5%/2 mm in low dose regions (<0.1 Gy).     

Analysing collimator structure effects in head-scatter calculations for IMRT class fields using scatter raytracing

The frequent blocking of the irradiated volume in intensity modulated radiation therapy (IMRT) makes the head-scatter fraction of the incident photon fluence more significant than that in conventional therapy with open fields. On the other hand. certain collimator configurations block scatter photons directed to a given observation point while allowing primary photons to be transmitted. The 'anomalous blocking' makes the primary field a poor indicator of the scatter fluence. Since large MU-to-cGy ratios in IMRT can magnify head-scatter uncertainties, it becomes necessary to accurately model both the effective scatter source and the collimator structure that limits the scatter reaching the irradiated volume. First we obtain a dual-source model, using a Taylor series expansion to derive the effective scatter source distribution from the data measured for the Elekta SL20 linac equipped with a multi-leaf collimator (MLC). Then, using a raytracing algorithm, we calculate the transmission of scatter rays from the effective scatter source plane to points in the patient plane. The method can account for the anomalous blocking of scatter by the MLC leaves and the backup diaphragms. For a variety of collimator settings tested, the calculations agree with measurements to an accuracy of 0.002psi10 x 10, where psi10 x 10 is the total (primary + scatter) photon fluence of an open 10 x 10 cm2 field for the same MU delivered. Although the significance of collimator structure in IMRT depends strongly on fields shapes employed for the delivery, potential cumulative errors on the order of a few per cent can be avoided in fluence calculations if the proposed method is used.     

Using a photon phase-space source for convolution/superposition dose calculations in radiation therapy

For a given linac design, the dosimetric characteristics of a photon beam are determined uniquely by the energy and radial distributions of the electron beam striking the x-ray target. However, in the usual commissioning of a beam from measured data, a large number of variables can be independently tuned, making it difficult to derive a unique and self-consistent beam model. For example, the measured dosimetric penumbra in water may be attributed in various proportions to the lateral secondary electron range, the focal spot size and the transmission through the tips of a non-divergent collimator; the head-scatter component in the tails of the transverse profiles may not be easy to resolve from phantom scatter and head leakage; and the head-scatter tails corresponding to a certain extra-focal source model may not agree self-consistently with in-air output factors measured on the central axis. To reduce the number of adjustable variables in beam modelling, we replace the focal and extra-focal sources with a single phase-space plane scored just above the highest adjustable collimator in a EGS/BEAM simulation of the linac. The phase-space plane is then used as photon source in a stochastic convolution/superposition dose engine. A photon sampled from the uncollimated phase-space plane is first propagated through an arbitrary collimator arrangement and then interacted in the simulation phantom. Energy deposition kernel rays are then randomly issued from the interaction points and dose is deposited along these rays. The electrons in the phase-space file are used to account for electron contamination. 6 MV and 18 MV photon beams from an Elekta SL linac are used as representative examples. Except for small corrections for monitor backscatter and collimator forward scatter for large field sizes (<0.5% with <20 x 20 cm2 field size), we found that the use of a single phase-space photon source provides accurate and self-consistent results for both relative and absolute dose calculations.     

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.     

Mixing intensity modulated electron and photon beams: combining a steep dose fall-off at depth with sharp and depth-independent penumbras and flat beam profiles.

For application in radiotherapy, intensity modulated high-energy electron and photon beams were mixed to create dose distributions that feature: (a) a steep dose fall-off at larger depths, similar to pure electron beams, (b) flat beam profiles and sharp and depth-independent beam penumbras, as in photon beams, and (c) a selectable skin dose that is lower than for pure electron beams. To determine the required electron and photon beam fluence profiles, an inverse treatment planning algorithm was used. Mixed beams were realized at a MM50 racetrack microtron (Scanditronix Medical AB, Sweden), and evaluated by the dose distributions measured in a water phantom. The multileaf collimator of the MM50 was used in a static mode to shape overlapping electron beam segments, and the dynamic multileaf collimation mode was used to realize the intensity modulated photon beam profiles. Examples of mixed beams were generated at electron energies of up to 40 MeV. The intensity modulated electron beam component consists of two overlapping concentric fields with optimized field sizes, yielding broad, fairly depth-independent overall beam penumbras. The matched intensity modulated photon beam component has high fluence peaks at the field edges to sharpen this penumbra. The combination of the electron and the photon beams yields dose distributions with the characteristics (a)-(c) mentioned above.     

On the field-size dependence of relative output from a linear accelerator.

The radiation output in air on the central axis of a linac photon beam has been modeled as the sum of two components. These are a point source representing radiation direct from the target and a distributed source representing scatter in the flattening filter and primary collimator. By fitting only two parameters, the ratio of the two components for a 20 x 20 field and a width parameter for the distributed source this semi-empirical model describes the relative outputs of square, symmetric rectangular, and asymmetric rectangular fields with an average error of 0.25% for the field sizes studied.     

A flattening filter free photon treatment concept evaluation with Monte Carlo

In principle, the concept of flat initial radiation-dose distribution across the beam is unnecessary for intensity modulated radiation therapy. Dynamic leaf positioning during irradiation could appropriately adjust the fluence distribution of an unflattened beam that is peaked in the center and deliver the desired uniform or nonuniform dose distribution. Removing the flattening filter could lead to reduced treatment time through higher dose rates and reduced scatter, because there would be substantially less material in the beam; and possibly other dosimetric and clinical advantages. This work aims to evaluate the properties of a flattening filter free clinical accelerator and to investigate its possible advantages in clinical intensity modulated radiation therapy applications by simulating a Varian 2100-based treatment delivery system with Monte Carlo techniques. Several depth-dose curves and lateral dose distribution profiles have been created for various field sizes, with and without the flattening filter. Data computed with this model were used to evaluate the overall quality of such a system in terms of changes in dose rate, photon and electron fluence, and reduction in out-of-field stray dose from the scattered components and were compared to the corresponding data for a standard treatment head with a flattening filter. The results of the simulations of the flattening filter free system show that a substantial increase in dose rate can be achieved, which would reduce the beam on time and decrease the out-of-field dose for patients due to reduced head-leakage dose. Also close to the treatment field edge, a significant improvement in out-of-field dose could be observed for small fields, which can be attributed to the change in the photon spectra, when the flattening filter is removed from the beamline.     

Dose delivery error detection by a computer-controlled linear accelerator

A commercial dual photon energy, computer-controlled linear accelerator has a complex collimation and beam delivery system. For accurate dose delivery, six separate motorized elements must be properly positioned for a given beam selection. Experimentally instituted misalignments of the primary electron scattering foils, the primary collimator, the flattening filter, the scattering foil carousel, and the backscatter shield or shutter produced significant dose delivery errors. The ability of the Mylar window monitor chamber to detect these errors was examined for x-ray beams. The fault detection system failed to interrupt dose delivery in a number of situations where the error in dose per monitor unit delivered ranged from -6% to +270% of the calibrated value.     

Correlated histogram representation of Monte Carlo derived medical accelerator photon-output phase space.

We present a method for condensing the photon energy and angular distributions obtained from Monte Carlo simulations of medical accelerators. This method represents the output as a series of correlated histograms and as such is well-suited for inclusion as the photon-source package for Monte Carlo codes used to determine the dose distributions in photon teletherapy. The method accounts for the isocenter-plane variations of the photon energy spectral distributions with increasing distance from the beam central axis for radiation produced in the bremsstrahlung target as well as for radiation scattered by the various treatment machine components within the accelerator head. Comparison of the isocenter energy fluence computed by this algorithm with that of the underlying full-physics Monte Carlo photon phase space indicates that energy fluence errors are less than 1% of the maximum energy fluence for a range of open-field sizes. Comparison of jaw-edge penumbrae shows that the angular distributions of the photons are accurately reproduced. The Monte Carlo sampling efficiency (the fraction of generated photons which clear the collimator jaws) of the algorithm is approximately 83% for an open 10x10 field, rising to approximately 96% for an open 40x40 field. Data file sizes for a typical medical accelerator, at a given energy, are approximately 150 kB, compared to the 1 GB size of the underlying full-physics phase space file.     

Assessing the effect of electron density in photon dose calculations

Photon dose calculation algorithms (such as the pencil beam and collapsed cone, CC) model the attenuation of a primary photon beam in media other than water, by using pathlength scaling based on the relative mass density of the media to water. In this study, we assess if differences in the electron density between the water and media, with different atomic composition, can influence the accuracy of conventional photon dose calculations algorithms. A comparison is performed between an electron-density scaling method and the standard mass-density scaling method for (i) tissues present in the human body (such as bone, muscle, etc.), and for (ii) water-equivalent plastics, used in radiotherapy dosimetry and quality assurance. We demonstrate that the important material property that should be taken into account by photon dose algorithms is the electron density, and not the mass density. The mass-density scaling method is shown to overestimate, relative to electrondensity predictions, the primary photon fluence for tissues in the human body and water-equivalent plastics, where 6%-7% and 10% differences were observed respectively for bone and air. However, in the case of patients, differences are expected to be smaller due to the large complexity of a treatment plan and of the patient anatomy and atomic composition and of the smaller thickness of bone/air that incident photon beams of a treatment plan may have to traverse. Differences have also been observed for conventional dose algorithms, such as CC, where an overestimate of the lung dose occurs, when irradiating lung tumors. The incorrect lung dose can be attributed to the.incorrect modeling of the photon beam attenuation through the rib cage (thickness of 2-3 cm in bone upstream of the lung tumor) and through the lung and the oversimplified modeling of electron transport in convolution algorithms. In the present study, the overestimation of the primary photon fluence, using the mass-density scaling method, was shown to be a consequence of the differences in the hydrogen content between the various media studied and water. On the other hand, the electron-density scaling method was shown to predict primary photon fluence in media other than water to within 1%-2% for all the materials studied and for energies up to 5 MeV. For energies above 5 MeV, the accuracy of the electron-density scaling method was shown to depend on the photon energy, where for materials with a high content of calcium (such as bone, cortical bone) or for primary photon energies above 10 MeV, the pair-production process could no longer be neglected. The electron-density scaling method was extended to account for pair-production attenuation of the primary photons. Therefore the scaling of the dose distributions in media other than water became dependent on the photon energy. The extended electron-scaling method was shown to estimate the photon range to within 1% for all materials studied and for energies from 100 keV to 20 MeV, allowing it to be used to scale dose distributions to media other than water and generated by clinical radiotherapy photon beams with accelerator energies from 4 to 20 MV.