Monte Carlo simulation of RapidArc radiotherapy delivery

RapidArc radiotherapy technology from Varian Medical Systems is one of the most complex delivery systems currently available, and achieves an entire intensity-modulated radiation therapy (IMRT) treatment in a single gantry rotation about the patient. Three dynamic parameters can be continuously varied to create IMRT dose distributions-the speed of rotation, beam shaping aperture and delivery dose rate. Modeling of RapidArc technology was incorporated within the existing Vancouver Island Monte Carlo (VIMC) system (Zavgorodni et al 2007 Radiother. Oncol. 84 S49, 2008 Proc. 16th Int. Conf. on Medical Physics). This process was named VIMC-Arc and has become an efficient framework for the verification of RapidArc treatment plans. VIMC-Arc is a fully automated system that constructs the Monte Carlo (MC) beam and patient models from a standard RapidArc DICOM dataset, simulates radiation transport, collects the resulting dose and converts the dose into DICOM format for import back into the treatment planning system (TPS). VIMC-Arc accommodates multiple arc IMRT deliveries and models gantry rotation as a series of segments with dynamic MLC motion within each segment. Several verification RapidArc plans were generated by the Eclipse TPS on a water-equivalent cylindrical phantom and re-calculated using VIMC-Arc. This includes one 'typical' RapidArc plan, one plan for dual arc treatment and one plan with 'avoidance' sectors. One RapidArc plan was also calculated on a DICOM patient CT dataset. Statistical uncertainty of MC simulations was kept within 1%. VIMC-Arc produced dose distributions that matched very closely to those calculated by the anisotropic analytical algorithm (AAA) that is used in Eclipse. All plans also demonstrated better than 1% agreement of the dose at the isocenter. This demonstrates the capabilities of our new MC system to model all dosimetric features required for RapidArc dose calculations.     

瓦里安加速器IGRT过程中患者吸收剂量的研究

目的：测量不同图像引导方式下患者的吸收剂量。方法：采用0°和270°两个正交野,分别使用MV和kV级X线获取二维图像,测量模体中不同点的吸收剂量;采用CBCT获取三维图像,测量模体中不同点的吸收剂量。结果：MV/MV成像,模体内5个点的吸收剂量在82.08 mGy～100.99 mGy之间,中心吸收剂量为89.76 mGy;kV/kV成像,模体吸收剂量在0.461 mGy～1.044 mGy之间,中心为0.737 mGy;CBCT成像,吸收剂量在2.998 mGy～6.426 mGy之间,中心为4.676mGy,低剂量模式为标准模式的50%。结论：OBI系统比EPID系统成像剂量更低,图像质量更好。CBCT日常摆位验证是安全的。治疗过程中应选择合适的图像引导方式和扫描参数,确保患者的治疗准确和安全。     

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.     

Development of a Monte Carlo model for the Brainlab microMLC

Stereotactic radiosurgery with several static conformal beams shaped by a micro multileaf collimator (microMLC) is used to treat small irregularly shaped brain lesions. Our goal is to perform Monte Carlo calculations of dose distributions for certain treatment plans as a verification tool. A dedicated microMLC component module for the BEAMnrc code was developed as part of this project and was incorporated in a model of the Varian CL2300 linear accelerator 6 MV photon beam. As an initial validation of the code, the leaf geometry was visualized by tracing particles through the component module and recording their position each time a leaf boundary was crossed. The leaf dimensions were measured and the leaf material density and interleaf air gap were chosen to match the simulated leaf leakage profiles with film measurements in a solid water phantom. A comparison between Monte Carlo calculations and measurements (diode, radiographic film) was performed for square and irregularly shaped fields incident on flat and homogeneous water phantoms. Results show that Monte Carlo calculations agree with measured dose distributions to within 2% and/or 1 mm except for field size smaller than 1.2 cm diameter where agreement is within 5% due to uncertainties in measured output factors.     

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.     

Development and validation of a BEAMnrc component module for accurate Monte Carlo modelling of the Varian dynamic Millennium multileaf collimator

A new component module (CM), designated DYNVMLC, was developed to fully model the geometry of the Varian Millennium 120 leaf collimator using the BEAMnrc Monte Carlo code. The model includes details such as the leaf driving screw hole, support railing groove and leaf tips. Further modifications also allow sampling of leaf sequence files to simulate the movement of the multileaf collimator (MLC) leaves during an intensity modulated radiation therapy (IMRT) delivery. As an initial validation of the code, the individual leaf geometries were visualized by tracing particles through the component module and recording their position each time a leaf boundary was crossed. A model of the Varian CL21EX linear accelerator 6 MV photon beam incorporating the new CM was built with the BEAMnrc user code. The leaf material density and abutting leaf air gap were chosen to match simulated leaf leakage profiles with film measurements in a solid water phantom. Simulated depth dose and off-axis profiles for a variety of MLC defined static fields agreed to within 2% with ion chamber and diode measurements in a water phantom. Simulated dose distributions for IMRT intensity patterns delivered using both static and dynamic techniques were found to agree with film measurements to within 4%. A comparison of interleaf leakage profiles for the new CM and an equivalent leaf model using the existing VARMLC CM demonstrated that the simplified geometry of VARMLC is not able to accurately predict the details of the MLC leakage for the 120 leaf collimator.     

A Monte Carlo model for the absorption and flux distributions of light in tissue

A Monte Carlo computer model has been developed to study the propagation of light in tissues. Light attenuation is assumed to result from absorption and isotropic scattering. The model has been used to predict the distribution of absorbed dose in homogeneous tissues of different absorption/scattering ratios, for illumination both by external light beams and via implanted optical fibers. The photon flux into optical fibers placed in the tissue as detectors has also been investigated. The results are interpreted in relation to the use of visible light irradiation for photo radiation therapy.     

A Monte Carlo model for out-of-field dose calculation from high-energy photon therapy

As cancer therapy becomes more efficacious and patients survive longer, the potential for late effects increases, including effects induced by radiation dose delivered away from the treatment site. This out-of-field radiation is of particular concern with high-energy radiotherapy, as neutrons are produced in the accelerator head. We recently developed an accurate Monte Carlo model of a Varian 2100 accelerator using MCNPX for calculating the dose away from the treatment field resulting from low-energy therapy. In this study, we expanded and validated our Monte Carlo model for high-energy (18 MV) photon therapy, including both photons and neutrons. Simulated out-of-field photon doses were compared with measurements made with thermoluminescent dosimeters in an acrylic phantom up to 55 cm from the central axis. Simulated neutron fluences and energy spectra were compared with measurements using moderated gold foil activation in moderators and data from the literature. The average local difference between the calculated and measured photon dose was 17%, including doses as low as 0.01% of the central axis dose. The out-of-field photon dose varied substantially with field size and distance from the edge of the field but varied little with depth in the phantom, except at depths shallower than 3 cm, where the dose sharply increased. On average, the difference between the simulated and measured neutron fluences was 19% and good agreement was observed with the neutron spectra. The neutron dose equivalent varied little with field size or distance from the central axis but decreased with depth in the phantom. Neutrons were the dominant component of the out-of-field dose equivalent for shallow depths and large distances from the edge of the treatment field. This Monte Carlo model is useful to both physicists and clinicians when evaluating out-of-field doses and associated potential risks.     

An image-based rat model for Monte Carlo organ dose calculations

An anatomically realistic rat model was developed from color images of successive cryosections of a mature Sprague-Dawley rat. Images were obtained, by digital scanning, of 9475 slices with thickness of 0.02 mm. A total of 13 major organs and tissues were selected, and models of these organs and tissues constructed from the images were used for calculations of absorbed dose from external photon sources. A detailed set of conversion coefficients from kerma free-in-air to organ absorbed dose have been calculated for external monoenergetic photon beams with energies ranging from 10 keV to 10 MeV under five idealized irradiation conditions (left lateral, right lateral, dorsal-ventral, ventral-dorsal, and isotropic) using the Monte Carlo code MCNPX. Dose results are presented in form of tables as supplemental data for practical use and comparison. The influence of anatomical characteristics, including organ volume, shape, location, and orientation, on dose distributions were evaluated. It would also be possible to make internal dose assessments using the computational rat model.     

Monte Carlo simulation of a planar shoulder model

Although variability of anthropometric measures within a population is a well established phenomenon, most biomechanical models are based on average parameter values. For example, optimisation models for predicting muscle forces from net joint reaction moments typically use average muscle moment arms. However, understanding the distribution of musculoskeletal morbidity within a population requires information about the variation of tissue loads within the population. This study investigated the use of Monte Carlo simulation techniques to predict the statistical distribution of deltoid and rotator cuff muscle forces during static arm elevation. Muscle moment arms were modelled either as independent random variables or jointly distributed random variables. Moment arm data was collected on 22 cadaver specimens. The results demonstrated the use of Monte Carlo techniques to describe the statistical distribution of muscle forces. Although assuming statistically independent moment arms did affect the statistical distribution shape, that assumption did not affect the median predicted forces. The standard deviations of muscle forces predicted using Monte Carlo techniques were similar to the standard deviation of muscle force predictions using the whole sample of specimens. It is concluded that Monte Carlo simulation techniques are a useful tool to analyse the interindividual variability of rotator cuff muscle forces.     

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.     

A Monte Carlo model for calculating out-of-field dose from a varian 6 MV beam

Dose to the patient outside of the treatment field is important when evaluating the outcome of radiotherapy treatments. However, determining out-of-field doses for any particular treatment plan currently requires either time-consuming measurements or calculated estimations that may be highly uncertain. A Monte Carlo model may allow these doses to be determined quickly, accurately, and with a great degree of flexibility. MCNPX was used to create a Monte Carlo model of a Varian Clinac 2100 accelerator head operated at 6 MV. Simulations of the dose out-of-field were made and measurements were taken with thermoluminescent dosimeters in an acrylic phantom and with an ion chamber in a water tank to validate the Monte Carlo model. Although local differences between the out-of-field doses calculated by the model and those measured did exceed 50% at some points far from the treatment field, the average local difference was only 16%. This included a range of doses as low as 0.01% of the central axis dose, and at distances in excess of 50 cm from the central axis of the treatment field. The out-of-field dose was found to vary with field size and distance from the central axis, but was almost independent of the depth in the phantom except where the dose increased substantially at depths less than dmax. The relationship between dose and kerma was also investigated, and kerma was found to be a good estimate of dose (within 3% on average) except near the surface and in the field penumbra. Our Monte Carlo model was found to well represent typical Varian 2100 accelerators operated at 6 MV.     

A multiple model approach to respiratory motion prediction for real-time IGRT

Respiration induces significant movement of tumours in the vicinity of thoracic and abdominal structures. Real-time image-guided radiotherapy (IGRT) aims to adapt radiation delivery to tumour motion during irradiation. One of the main problems for achieving this objective is the presence of time lag between the acquisition of tumour position and the radiation delivery. Such time lag causes significant beam positioning errors and affects the dose coverage. A method to solve this problem is to employ an algorithm that is able to predict future tumour positions from available tumour position measurements. This paper presents a multiple model approach to respiratory-induced tumour motion prediction using the interacting multiple model (IMM) filter. A combination of two models, constant velocity (CV) and constant acceleration (CA), is used to capture respiratory-induced tumour motion. A Kalman filter is designed for each of the local models and the IMM filter is applied to combine the predictions of these Kalman filters for obtaining the predicted tumour position. The IMM filter, likewise the Kalman filter, is a recursive algorithm that is suitable for real-time applications. In addition, this paper proposes a confidence interval (CI) criterion to evaluate the performance of tumour motion prediction algorithms for IGRT. The proposed CI criterion provides a relevant measure for the prediction performance in terms of clinical applications and can be used to specify the margin to accommodate prediction errors. The prediction performance of the IMM filter has been evaluated using 110 traces of 4-minute free-breathing motion collected from 24 lung-cancer patients. The simulation study was carried out for prediction time 0.1-0.6 s with sampling rates 3, 5 and 10 Hz. It was found that the prediction of the IMM filter was consistently better than the prediction of the Kalman filter with the CV or CA model. There was no significant difference of prediction errors for the sampling rates 5 and 10 Hz. For these sampling rates, the errors of the IMM filter for 0.4 s prediction time were less than 2.1 mm in terms of the 95% CI criterion or 1.1 mm in terms of the standard deviation (SD) or root mean squared errors (RMSE) criterion. For the prediction time of 0.6 s the errors were less than 3.6 mm in terms of the 95% CI criterion or 1.8 mm in terms of the SD/RMSE criterion. The prediction error analysis showed that the average percentage of the target lies outside the 95% CI margin was 5.2% and outside the SD/RMSE margin was 24.3%. This indicates the effectiveness of the 95% CI criterion as a margining strategy to accommodate prediction errors.     

Comparison of EGS4 and MCNP4b Monte Carlo codes for generation of photon phase space distributions for a Varian 2100C

Monte Carlo based dose calculation algorithms require input data or distributions describing the phase space of the photons and secondary electrons prior to the patient-dependent part of the beam-line geometry. The accuracy of the treatment plan itself is dependent upon the accuracy of this distribution. The purpose of this work is to compare phase space distributions (PSDs) generated with the MCNP4b and EGS4 Monte Carlo codes for the 6 and 18 MV photon modes of the Varian 2100C and determine if differences relevant to Monte Carlo based patient dose calculations exist. Calculations are performed with the same energy transport cut-off values. At 6 MV, target bremsstrahlung production for MCNP4b is approximately 10% less than for EGS4, while at 18 MV the difference is about 5%. These differences are due to the different bremsstrahlung cross sections used in the codes. Although the absolute bremsstrahlung production differs between MCNP4b and EGS4, normalized PSDs agree at the end of the patient-independent geometry (prior to the jaws), resulting in similar dose distributions in a homogeneous phantom. EGS4 and MCNP4b are equally suitable for the generation of PSDs for Monte Carlo based dose computations.     

A Monte Carlo multiple source model applied to radiosurgery narrow photon beams

Monte Carlo (MC) methods are nowadays often used in the field of radiotherapy. Through successive steps, radiation fields are simulated, producing source Phase Space Data (PSD) that enable a dose calculation with good accuracy. Narrow photon beams used in radiosurgery can also be simulated by MC codes. However, the poor efficiency in simulating these narrow photon beams produces PSD whose quality prevents calculating dose with the required accuracy. To overcome this difficulty, a multiple source model was developed that enhances the quality of the reconstructed PSD, reducing also the time and storage capacities. This multiple source model was based on the full MC simulation, performed with the MC code MCNP4C, of the Siemens Mevatron KD2 (6 MV mode) linear accelerator head and additional collimators. The full simulation allowed the characterization of the particles coming from the accelerator head and from the additional collimators that shape the narrow photon beams used in radiosurgery treatments. Eight relevant photon virtual sources were identified from the full characterization analysis. Spatial and energy distributions were stored in histograms for the virtual sources representing the accelerator head components and the additional collimators. The photon directions were calculated for virtual sources representing the accelerator head components whereas, for the virtual sources representing the additional collimators, they were recorded into histograms. All these histograms were included in the MC code, DPM code and using a sampling procedure that reconstructed the PSDs, dose distributions were calculated in a water phantom divided in 20000 voxels of 1 x 1 x 5 mm3. The model accurately calculates dose distributions in the water phantom for all the additional collimators; for depth dose curves, associated errors at 2sigma were lower than 2.5% until a depth of 202.5 mm for all the additional collimators and for profiles at various depths, deviations between measured and calculated values were less than 2.5% or 1 mm.     

A new analytical model for Varian enhanced dynamic wedge factors

Dynamic and physical (hard) wedges are used in 3D conformal radiotherapy in order to improve dose distribution in patients. Unlike wedge factors for physical wedges that depend on wedge material and thickness, wedge factors for Varian dynamic wedges depend on the relationship between the position of the moving jaw and the number of delivered monitor units. In this study, we describe a new analytical model for dynamic wedge factors. We also review the existing analytical models and compare calculated and measured wedge factors. The comparison is performed for different wedge angles, symmetric and asymmetric fields and two different photon energies. The obtained results indicate that the new dynamic wedge model provides the best overall agreement (within 1%) with the measured wedge factors.     

A Monte Carlo dose calculation algorithm for proton therapy

A Monte Carlo (MC) code (VMCpro) for treatment planning in proton beam therapy of cancer is introduced. It is based on ideas of the Voxel Monte Carlo algorithm for photons and electrons and is applicable to human tissue for clinical proton energies. In the present paper the implementation of electromagnetic and nuclear interactions is described. They are modeled by a Class II condensed history algorithm with continuous energy loss, ionization, multiple scattering, range straggling, delta-electron transport, nuclear elastic proton nucleus scattering and inelastic proton nucleus reactions. VMCpro is faster than the general purpose MC codes FLUKA by a factor of 13 and GEANT4 by a factor of 35 for simulations in a phantom with inhomogeneities. For dose calculations in patients the speed improvement is larger, because VMCpro has only a weak dependency on the heterogeneity of the calculation grid. Dose distributions produced with VMCpro are in agreement with GEANT4 results. Integrated or broad beam depth dose curves show maximum deviations not larger than 1% or 0.5 mm in regions with large dose gradients for the examples presented here.     

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.     

Dosimetric verification of a Monte Carlo electron beam model for an add-on eMLC

Dosimetric verification of a new Monte Carlo beam model for multi-leaf collimated electrons was performed using experimental data from an add-on electron multi-leaf collimator (eMLC) prototype. The measurements were compared against calculations using an electron phase space sampled from a parameterized electron beam model and the voxel Monte Carlo++ (VMC++) code for in-phantom energy deposition. Verification of the calculations was performed in a water phantom with the developed eMLC attached to a Varian 2100 C/D radiotherapy accelerator with nominal energies 6 MeV, 9 MeV, 12 MeV, 16 MeV and 20 MeV. The eMLC prototype consisting of 2 cm thick and 5 mm wide steel leaves is fixed under the 20 x 20 cm(2) electron applicator with a source-to-leaf distance 97.2 cm. The eMLC prototype has non-motorized leaves with straight leaf edges and a maximum field size of 20 x 20 cm(2) at SSD 100 cm. The beam model is a coupled multi-source model with parameters derived from detailed beam characterization measurements and a kernel model for the indirect leaf-scattered electrons. Typical calculation times with a 2% mean statistical uncertainty was under 5 min. In extensive set of in-water measurements 88% of the voxels were within 2% /2 mm acceptance criterion. Although at SSD 100 cm the dose near the phantom surface is slightly pronounced due to the short collimator-to-surface distance, the new beam model was suitable for dose calculation of the add-on type eMLC.