Development and commissioning of a multileaf collimator model in monte carlo dose calculations for intensity-modulated radiation therapy

A multileaf collimator (MLC) model, "MATMLC," was developed to simulate MLCs for Monte Carlo (MC) dose calculations of intensity-modulated radiation therapy (IMRT). This model describes MLCs using matrices of regions, each of which can be independently defined for its material and geometry, allowing flexibility in simulating MLCs from various manufacturers. The free parameters relevant to the dose calculations with this MLC model included MLC leaf density, interleaf air gap, and leaf geometry. To commission the MLC model and its free parameters for the Varian Millennium MLC-120 (Varian Oncology Systems, Palo Alto, CA), we used the following leaf patterns: (1) MLC-blocked fields to test the effects of leaf transmission and leakage; (2) picket-fence fields to test the effects of the interleaf air gap and tongue-groove design; and (3) abutting-gap fields to test the effects of rounded leaf ends. Transmission ratios and intensity maps for these leaf patterns were calculated with various sets of modeling parameters to determine their dosimetric effects, sensitivities, and their optimal combinations to give the closest agreement with measured results. Upon commissioning the MLC model, we computed dose distributions for clinical IMRT plans using the MC system and verified the results with those from ion chamber and thermoluminescent dosimeter measurements in water phantoms and anthropomorphic phantoms. This study showed that the MLC transmission ratios were strongly dependent on both leaf density and the interleaf air gap. The effect of interleaf air gap and tongue-groove geometry can be determined most effectively through fence-type MLC patterns. Using the commissioned MLC model, we found that the calculated dose from the MC system agreed with the measured data within clinically acceptable criteria from low- to high-dose regions, showing that the model is acceptable for clinical applications.     

Electron beam dose calculations

Electron beam dose distributions in the presence of inhomogeneous tissue are calculated by an algorithm that sums the dose distribution of individual pencil beams. The off-axis dependence of the pencil beam dose distribution is described by the Fermi-Eyges theory of thick-target multiple Coulomb scattering. Measured square-field depth-dose data serve as input for the calculations. Air gap corrections are incorporated and use data from'in-air' measurements in the penumbra of the beam. The effective depth, used to evaluate depth-dose, and the sigma of the off-axis Gaussian spread against depth are calculated by recursion relations from a CT data matrix for the material underlying individual pencil beams. The correlation of CT number with relative linear stopping power and relative linear scattering power for various tissues is shown. The results of calculations are verified by comparison with measurements in a 17 MeV electron beam from the Therac 20 linear accelerator. Calculated isodose lines agree nominally to within 2 mm of measurements in a water phantom. Similar agreement is observed in cork slabs simulating lung. Calculations beneath a bone substitute illustrate a weakness in the calculation. Finally a case of carcinoma in the maxillary antrum is studied. The theory suggests an alternative method for the calculation of depth-dose of rectangular fields.     

Quantifying tumor-selective radiation dose enhancements using gold nanoparticles: a monte carlo simulation study

Gold nanoparticles can enhance the biological effective dose of radiation delivered to tumors, but few data exist to quantify this effect. The purpose of this project was to build a Monte Carlo simulation model to study the degree of dose enhancement achievable with gold nanoparticles. A Monte Carlo simulation model was first built using Geant4 code. An Ir-192 brachytherapy source in a water phantom was simulated and the calculation model was first validated against previously published data. We then introduced up to 10¹³ gold nanospheres per cm³ into the water phantom and examined their dose enhancement effect. We compared this enhancement against a gold-water mixture model that has been previously used to attempt to quantify nanoparticle dose enhancement. In our benchmark test, dose-rate constant, radial dose function, and two-dimensional anisotropy function calculated with our model were within 2% of those reported previously. Using our simulation model we found that the radiation dose was enhanced up to 60% with 10¹³ gold nanospheres per cm³ (9.6% by weight) in a water phantom selectively around the nanospheres. The comparison study indicated that our model more accurately calculated the dose enhancement effect and that previous methodologies overestimated the dose enhancement up to 16%. Monte Carlo calculations demonstrate that biologically-relevant radiation dose enhancement can be achieved with the use of gold nanospheres. Selective tumor labeling with gold nanospheres may be a strategy for clinically enhancing radiation effects. This study was partially funded by a grant from the U. S. Department of Defense Breast Cancer Research Program (W81XWH-06-1-0672) and by the institutional core grant (CA 16672). The authors also wish to acknowledge the Department of Scientific Publications at The University of Texas M. D. Anderson Cancer Center for its editorial assistance during the preparation of this article.     

Efficient photon beam dose calculations using DOSXYZnrc with BEAMnrc

This study examines the efficiencies of doses calculated using DOSXYZnrc for 18 MV (10 X 10 cm2 field size) and 6 MV (10 X 10 cm2 and 20 X 20 cm2 field sizes) photon beams simulated using BEAMnrc. Both phase-space sources and full BEAMnrc simulation sources are used in the DOSXYZnrc calculations. BEAMnrc simulation sources consist of a BEAMnrc accelerator simulation compiled as a shared library and run by the user code (DOSXYZnrc in this case) to generate source particles. Their main advantage is in eliminating the need to store intermediate phase-space files. In addition, the efficiency improvements due to photon splitting and particle recycling in the DOSXYZnrc simulation are examined. It is found that photon splitting increases dose calculation efficiency by a factor of up to 6.5, depending on beam energy, field size, voxel size, and the type of secondary collimation used in the BEAMnrc simulation (multileaf collimator vs photon jaws). The optimum efficiency with photon splitting is approximately 55% higher than that with particle recycling, indicating that, while most of the gain is due to time saved by reusing source particle data, there is significant gain due to the uniform distribution of interaction sites and faster DOSXYZnrc simulation time when photon splitting is employed. Use of optimized directional bremsstrahlung splitting in the BEAMnrc simulation sources increases the efficiency of photon beam simulations sufficiently that the peak efficiencies (i.e., with optimum setting of the photon splitting number) of DOSXYZnrc simulations using these sources are only 3-13% lower than those with phase-space file sources. This points towards eliminating the need for storing intermediate phase-space files.     

Multiple-estimate monte carlo calculation of the dose rate constant for a cesium-131 interstitial brachytherapy seed

The purpose of this study was to calculate a more accurate dose rate constant for the 131Cs (model CS-1, IsoRay Medical, Inc., Richland, WA) interstitial brachytherapy seed. Previous measurements of the dose rate constant for this seed have been reported by others with incongruity. Recent direct measurements by thermoluminescence dosimetry and by gamma-ray spectroscopy were about 15% greater than earlier thermoluminescence dosimetry measurements. Therefore, we set about to calculate independent values by a Monte Carlo approach that combined three estimates as a consistency check, and to quantify the computational uncertainty. The calculated dose rate constant for the 131Cs seed was 1.040 cGy h(-1) U(-1) for an ionization chamber model and 1.032 cGy h(-1) U(-1) for a circular ring model. A formal value of 2.2% uncertainty was calculated for both values. The range of our multiestimate values were from 1.032 to 1.061 cGy h(-1) U(-1). We also modeled three 125I seeds with known dose rate constants to test the accuracy of this study's approach.     

Proton loss model for therapeutic beam dose calculations

A transport algorithm called the proton loss (PL) model is developed for proton pencil beams of therapeutic energies. The PL model takes into account inelastic nuclear reactions, pathlength straggling, and energy-loss straggling and predicts the 3D dose distribution from a proton pencil beam. In proton beams, the multiple scattering and ionizational energy loss processes approach their diffusional limit where scattering and energy loss probability densities become Gaussian. Therefore we chose to derive the PL model from the Fermi-Eyges diffusional multiple scattering theory and the Gaussian theory of energy straggling. We first introduce a generalization of the Fermi-Eyges equation for proton pencil beams, labeled the proton loss (PL) transport equation. This new equation includes terms that model inelastic nuclear reactions as a depth-dependent absorption and pathlength straggling as a quasi-absorption. Then energy straggling is taken into account by using a weighted superposition of a discrete number of elementary pencil beams. These elementary pencil beams have different initial energies and lose energy according to the CSDA, thus they have different ranges of penetration. A final solution for the proton beam transport is obtained as a linear combination of elementary pencil beam solutions with weights defined by the Gaussian evolution of the proton energy spectrum with depth. A numerical comparison of the dose distribution predictions of the PL model with measurements and PTRAN Monte Carlo simulations indicates the model is both computational fast and accurate.     

A monte carlo study of dose rate distribution around the specially asymmetric CSM3-a 137Cs source

The CSM3 137Cs type stainless-steel encapsulated source is widely used in manually afterloaded low dose rate brachytherapy. A specially asymmetric source, CSM3-a, has been designed by CIS Bio International (France) substituting the eyelet side seed with an inactive material in the CSM3 source. This modification has been done in order to allow a uniform dose level over the upper vaginal surface when this 'linear' source is inserted at the top of the dome vaginal applicators. In this study the Monte Carlo GEANT3 simulation code, incorporating the source geometry in detail, was used to investigate the dosimetric characteristics of this special CSM3-a 137Cs brachytherapy source. The absolute dose rate distribution in water around this source was calculated and is presented in the form of an along-away table. Comparison of Sievert integral type calculations with Monte Carlo results are discussed.     

Inclusion of compensator-induced scatter and beam filtration in pencil beam dose calculations

Compensators can be used as beam intensity modulation devices for intensity-modulated radiation therapy applications. In contrast with multileaf collimators, compensators introduce scatter and beam hardening into the therapeutic x-ray beam. The degree of scatter and beam filtering depends on the compensator material and beam energy. Pencil beam dose calculation models can be used to derive the shape of the compensator. In this study a novel way of incorporating the effect of compensator-induced scatter and beam filtration is presented. The study was conducted using 6, 8, and 15 MV polyenergetic pencil beams (PBs). The compensator materials that were studied included wax, brass, copper, and lead. The perturbation effects of the compensators on the PB dose profiles were built in the PB dose profiles and tested for regular fields containing a step compensator and benchmarked against DOSXYZnrc Monte Carlo calculated dose profiles. These effects include compensator beam filtration and Compton-scattered photons generated in the compensator materials that influence the resulting PB dose profiles. These data were obtained from DOSXYZnrc simulations. A Gaussian function was used to model off-axis scatter and an exponential function was used to model beam hardening at any radius, r. Dose profiles were calculated under a step compensator using the method that can model beam hardening and off-axis scatter, as well as a conventional method where the PB profiles are not adjusted, but a single effective attenuation coefficient is used instead to best match the dose profiles. Both sets of data were compared to the DOSXYZnrc data. Depth and profile dose data for 10 x 10 cm2 and 20 x 20 cm2 fields indicated that at 2 cm depth in water the method that takes compensator scatter into account agrees more closely with the DOSXYZnrc data compared to the data using only an effective attenuation coefficient. Further, it was found that the effective attenuation method can only replicate the DOSXYZnrc data at 10 cm depth where it was chosen to do so. At shallower depths the effective attenuation method overestimates the dose and beyond 10 cm depth it causes an underestimation in the dose. The scatter and beam hardening inclusion method does not exhibit such properties. The exclusion of scatter can lead to dose errors of up to 4 percent with a copper compensator at 5 cm depth for a 10 X 10 cm2 field under a thickness of 5 cm at 6 MV. For materials such as lead this discrepancy could be as high as 7 to 8 percent at 6 MV. For larger fields (20 X 20 cm2) the effect of in-phantom scatter reduces the differences between the dose profiles calculated with the mentioned methods.     

Simple beam models for Monte Carlo photon beam dose calculations in radiotherapy

Monte Carlo (code GEANT) produced 6 and 15 MV phase space (PS) data were used to define several simple photon beam models. For creating the PS data the energy of starting electrons hitting the target was tuned to get correct depth dose data compared to measurements. The modeling process used the full PS information within the geometrical boundaries of the beam including all scattered radiation of the accelerator head. Scattered radiation outside the boundaries was neglected. Photons and electrons were assumed to be radiated from point sources. Four different models were investigated which involved different ways to determine the energies and locations of beam particles in the output plane. Depth dose curves, profiles, and relative output factors were calculated with these models for six field sizes from 5x5 to 40x40cm2 and compared to measurements. Model 1 uses a photon energy spectrum independent of location in the PS plane and a constant photon fluence in this plane. Model 2 takes into account the spatial particle fluence distribution in the PS plane. A constant fluence is used again in model 3, but the photon energy spectrum depends upon the off axis position. Model 4, finally uses the spatial particle fluence distribution and off axis dependent photon energy spectra in the PS plane. Depth dose curves and profiles for field sizes up to 10x10cm2 were not model sensitive. Good agreement between measured and calculated depth dose curves and profiles for all field sizes was reached for model 4. However, increasing deviations were found for increasing field sizes for models 1-3. Large deviations resulted for the profiles of models 2 and 3. This is due to the fact that these models overestimate and underestimate the energy fluence at large off axis distances. Relative output factors consistent with measurements resulted only for model 4.     

Converting absorbed dose to medium to absorbed dose to water for Monte Carlo based photon beam dose calculations

Current clinical experience in radiation therapy is based upon dose computations that report the absorbed dose to water, even though the patient is not made of water but of many different types of tissue. While Monte Carlo dose calculation algorithms have the potential for higher dose accuracy, they usually transport particles in and compute the absorbed dose to the patient media such as soft tissue, lung or bone. Therefore, for dose calculation algorithm comparisons, or to report dose to water or tissue contained within a bone matrix for example, a method to convert dose to the medium to dose to water is required. This conversion has been developed here by applying Bragg-Gray cavity theory. The dose ratio for 6 and 18 MV photon beams was determined by computing the average stopping power ratio for the primary electron spectrum in the transport media. For soft tissue, the difference between dose to medium and dose to water is approximately 1.0%, while for cortical bone the dose difference exceeds 10%. The variation in the dose ratio as a function of depth and position in the field indicates that for photon beams a single correction factor can be used for each particular material throughout the field for a given photon beam energy. The only exception to this would be for the clinically non-relevant dose to air. Pre-computed energy spectra for 60Co to 24 MV are used to compute the dose ratios for these photon beams and to determine an effective energy for evaluation of the dose ratio.     

Electron dose distributions in experimental phantoms: a comparison with 2D pencil beam calculations

Dose distributions were measured and computed within inhomogeneous phantoms irradiated with beams of electrons having initial energies of 10 and 18 MeV. The measurements were made with a small p-type silicon diode and the calculations were performed using the pencil beam algorithm developed originally at the M D Anderson Hospital (MDAH). This algorithm, which is available commercially on many radiotherapy planning computers, is based on the Fermi-Eyges theory of electron transport. The phantoms used in this work were composed of water into which two- and three-dimensional inhomogeneities of aluminum and air (embedded in wax) were introduced. This was done in order to simulate the small bones and the air cavities encountered clinically in radiation therapy of the chest wall or neck. Our intent was to test the adequacy of the two-dimensional implementation of the pencil beam approach. The agreement between measured and computed doses is very good for inhomogeneities which are essentially two-dimensional but discrepancies as large as 40% were observed for more complex three-dimensional inhomogeneities. We can only trace the discrepancies to the complex interplay of numerous approximations in the Fermi-Eyges theory of multiple scattering and its adaptation for practical computer-aided radiotherapy planning.     

An analysis of equivalent fields for electron beam central-axis dose calculations.

The concepts of the equivalent square or circular field have long been used in dose calculations for photon beams. These concepts allow data measured for square or circular fields to be extended to calculate, for example, the percentage depth doses or output factors of rectangular or irregular fields. It has been pointed out in the past that an electron beam equivalent field dimension varies with depth and, thus, will have questionable utility. As the equivalent square and circle have proven to be useful in photon beam dose calculations, the work described in this paper has sought to analyze conditions under which equivalent fields may be useful for electron beam dose calculations. Equivalent square field dimensions and circular field radii are derived using the Fermi-Eyges theory and are compared to a number of approximate equivalent fields that have been applied to electron dose calculations. Calculations are also compared with measurements presented in the literature. It is shown that the accuracy of an electron dose calculation using these approximate equivalent fields diminishes with a decreasing degree of lateral scatter equilibrium at the central axis and only becomes accurate once equilibrium is established. As the central-axis dose under this latter condition is in any event independent of field shape or size, the equivalent field approach becomes unnecessary. Because of this and other restrictions discussed, it is concluded that the equivalent fields analyzed here should not be used for electron beam dose calculations.     

Modelling lateral beam quality variations in pencil kernel based photon dose calculations

Standard treatment machines for external radiotherapy are designed to yield flat dose distributions at a representative treatment depth. The common method to reach this goal is to use a flattening filter to decrease the fluence in the centre of the beam. A side effect of this filtering is that the average energy of the beam is generally lower at a distance from the central axis, a phenomenon commonly referred to as off-axis softening. The off-axis softening results in a relative change in beam quality that is almost independent of machine brand and model. Central axis dose calculations using pencil beam kernels show no drastic loss in accuracy when the off-axis beam quality variations are neglected. However, for dose calculated at off-axis positions the effect should be considered, otherwise errors of several per cent can be introduced. This work proposes a method to explicitly include the effect of off-axis softening in pencil kernel based photon dose calculations for arbitrary positions in a radiation field. Variations of pencil kernel values are modelled through a generic relation between half value layer (HVL) thickness and off-axis position for standard treatment machines. The pencil kernel integration for dose calculation is performed through sampling of energy fluence and beam quality in sectors of concentric circles around the calculation point. The method is fully based on generic data and therefore does not require any specific measurements for characterization of the off-axis softening effect, provided that the machine performance is in agreement with the assumed HVL variations. The model is verified versus profile measurements at different depths and through a model self-consistency check, using the dose calculation model to estimate HVL values at off-axis positions. A comparison between calculated and measured profiles at different depths showed a maximum relative error of 4% without explicit modelling of off-axis softening. The maximum relative error was reduced to 1% when the off-axis softening was accounted for in the calculations.     

Point dose calculations using an analytical pencil beam kernel for IMRT plan checking

A method to verify the monitor units for a treatment plan is to calculate point doses, possibly at the isocentre, by using a simple calculation method. This verification is recommended to find mistakes in the treatment plan. Treatment plans for intensity modulated radiation therapy are no exception. The method should employ a simple physical model and a dose calculation algorithm, which is different from the method used for the treatment plan. Our approach uses a convolution algorithm and an analytical pencil beam kernel with eight parameters. The model is intuitive and simple. At the same time, the method is so general that it can be applied to both step-and-shoot and sliding-window techniques. The results of applications to actual treatment plans show that the calculated total isocentre doses are accurate within +/-2% of planned doses for six-field prostate plans when calculation points are in a uniform dose region. Head and neck cases show a slightly larger difference than prostate cases. When calculation points are located in a region of high dose gradient, however, the difference could be greater than 5%.     

A finite-size pencil beam model for photon dose calculations in three dimensions.

A three-dimensional dose computation model employing a finite-size, diverging, pencil beam has been developed and is demonstrated for Cobalt-60 gamma rays. The square cross-section pencil beam is simulated in a semi-infinite water phantom by convolving the pencil beam photon fluence with the Monte Carlo point dose kernel for Cobalt-60. This finite-size pencil beam is calculated one time and becomes a new data base with which to build larger beams by two-dimensional superposition. The pencil beam fluence profile, angle correction for beam divergence, the Mayneord inverse square correction, radial and angular sampling rates, error propagation, and computation time have been investigated and are reported. Radial and angular sampling rates have a great effect on accuracy and their appropriate selection is important. Percent depth doses calculated by finite-size pencil beam superposition are within 1% of values calculated by full convolution and the agreement with values from the literature is within 6%. The latter disagreement is shown to be due to a low-energy photon component which is not modeled in other calculations. Computation time measurements show the pencil beam method to be faster than full convolution and one implementation of the differential-scatter-air-ratio (dSAR) method.     

A multiple source model for 6 MV photon beam dose calculations using Monte Carlo

A multiple source model (MSM) for the 6 MV beam of a Varian Clinac 2300 C/D was developed by simulating radiation transport through the accelerator head for a set of square fields using the GEANT Monte Carlo (MC) code. The corresponding phase space (PS) data enabled the characterization of 12 sources representing the main components of the beam defining system. By parametrizing the source characteristics and by evaluating the dependence of the parameters on field size, it was possible to extend the validity of the model to arbitrary rectangular fields which include the central 3 x 3 cm2 field without additional precalculated PS data. Finally, a sampling procedure was developed in order to reproduce the PS data. To validate the MSM, the fluence, energy fluence and mean energy distributions determined from the original and the reproduced PS data were compared and showed very good agreement. In addition, the MC calculated primary energy spectrum was verified by an energy spectrum derived from transmission measurements. Comparisons of MC calculated depth dose curves and profiles, using original and PS data reproduced by the MSM, agree within 1% and 1 mm. Deviations from measured dose distributions are within 1.5% and 1 mm. However, the real beam leads to some larger deviations outside the geometrical beam area for large fields. Calculated output factors in 10 cm water depth agree within 1.5% with experimentally determined data. In conclusion, the MSM produces accurate PS data for MC photon dose calculations for the rectangular fields specified.     

Selecting beam weight and wedge filter on the basis of dose gradient analysis

This study proposes an algorithm for selecting beam weight, wedge angle, and wedge orientation for three-dimensional radiation therapy treatment planning. According to dose gradient analysis, the necessary and sufficient condition for achieving a homogeneous dose over the target volume is that the total vector sum of the dose gradients of all beams be zero everywhere in the target volume. This study presents equations for calculating the beam weight, wedge angle, and collimator angle (because the collimator angle determines wedge orientation when beam direction is known) for treatment plans using two angled beams or three coplanar or noncoplanar beams. It also provides suggestions for calculations of treatment plans using more than three beams, for which many feasible solutions will be available. When tested using two clinical cases, this algorithm achieved homogeneous dose distributions over target volumes. With this algorithm, repeated manual adjustments are reduced, and the quality and efficiency of treatment planning are improved.