Photon beam characterization and modelling for Monte Carlo treatment planning

Characterization of the radiation beam of a tomotherapy equipment with MCNP

This work aims to model and characterize the radiation beam of one Accuray tomotherapy equipment using the Monte Carlo Code MCNP5 (Monte Carlo N-Particle). This tomotherapy equipment is used for delivering high doses of radiation in tumor regions to kill cancer cells and shrink the tumor during radiation therapy of cancer patients, however, the radiation can damage surrounding areas and nearby organs at risk (OAR) if the radiation field is not well delimited. In particular, intensity-modulated radiotherapy treatments (IMRT) with tomotherapy equipment offer great benefits to patients allowing treatment of tumor regions without affecting surrounding areas and OAR. Nowadays, it is well known that a correct simulation of transport of radiation in tomotherapy equipment facilitates considerably the estimation of ideal doses in the tumor, surrounding regions, and OAR. For that reason, in this work, we simulated the geometry of the 6 MV ACCURAY Tomotherapy equipment of the CECAN using the MCNP5. The model includes a TomoLINAC consisting of an electron source that emits Gaussian distribution particles with an average energy of 5.7 MeV and width of 0.3 MeV. The emitted particles impact the tungsten target and pass through primary collimators and jaws that define the irradiation field in the isocenter. To validate the geometry and radiation transport in the TomoLINAC the curves of depth dose percentage (PDD) estimated by simulation and the curves measured experimentally were tuned. In the same way, the simulated transverse and longitudinal profiles were compared with the experimental results. In addition, a comparison between the qualities of the radiation beam characterized with MCNP and measured experimentally in CECAN showed a deviation of 1%. For the simulations, cylindrical detectors located inside a water phantom were considered and it was employed the tally *F8. A good agreement was observed between the PDD's curves obtained from the simulation and those measured experimentally for a field of 5 × 10 cm2 in the isocenter and SSD (distance from the source to the surface) of 85 cm. Also, the comparison between the simulated and experimental transverse profiles obtained at 1.5 cm, 10 cm and 15 cm depth with a radiation field of 5 × 40 cm2 showed very good agreement. The longitudinal profiles were estimated with the same depths as the transverse ones, but for each of them, the openings of the jaws were 5.0 cm, 2.5 cm and 1.0 cm in the longitudinal direction, which corresponds to the direction in which the patient's table moves. The comparison between the simulated and experimental longitudinal profiles showed good concordance too. Once the radiation beam of the ACCURAY tomotherapy equipment had been characterized, experimental dose measurements were made using a Cheese phantom and two A1SL ionization chambers. These results obtained experimentally were compared with those estimated with MCNP for a field of 5 × 40 cm2 at the isocenter and SAD of 85 cm and, it was concluded that both results were similar considering the regions of uncertainty. Finally, we must highlight that the modeling and characterization of the radiation beam of CECAN's ACCURAY tomotherapy equipment can be a key tool for dose estimations in different cancer treatment plans and future research.

Small field output factor measurement and verification for CyberKnife robotic radiotherapy and radiosurgery system using 3D polymer gel, ionization chamber, diode, diamond and scintillator detectors, Gafchromic film and Monte Carlo simulation

The dosimetry of small fields has become tremendously important with the advent of intensity-modulated radiation therapy (IMRT) and stereotactic radiosurgery, where small field segments or very small fields are used to treat tumors. With high dose gradients in the stereotactic radiosurgery or radiotherapy treatment, small field dosimetry becomes challenging due to the lack of lateral electronic equilibrium in the field, x-ray source occlusion, and detector volume averaging. Small volume and tissue-equivalent detectors are recommended to overcome the challenges. With the lack of a perfect radiation detector, studies on available detectors are ongoing with reasonable disagreement and uncertainties. The joint IAEA and AAPM international code of practice (CoP) for small field dosimetry, TRS 483 (Alfonso et al., 2017) provides guidelines and recommendations for the dosimetry of small static fields in external beam radiotherapy. The CoP provides a methodology for field output factor (FOF) measurements and use of field output correction factors for a series of small field detectors and strongly recommends additional measurements, data collection and verification for CyberKnife (CK) robotic stereotactic radiotherapy/radiosurgery system using the listed detectors and more new detectors so that the FOFs can be implemented clinically. The present investigation is focused on using 3D gel along with some other commercially available detectors for the measurement and verification of field output factors (FOFs) for the small fields available in the CK system. The FOF verification was performed through a comparison with published data and Monte Carlo simulation. The results of this study have proved the suitability of an in-house developed 3D polymer gel dosimeter, several commercially available detectors, and Gafchromic films as a part of small field dosimetric measurements for the CK system.

The Study of Dosimetric Characteristics of the XHA600D Medical Linear Accelerator Based on a Monte Carlo Code

By investigating the influence of initial electrons on dosimetric characteristics, reasonable incident electron parameters for the nominal 6 MV photon beam of the XHA600D accelerator are finally established, i.e., a 6 MeV monoenergetic electron beam with a radial intensity FWHM of 2.5 mm and an angular divergency of 0.15°. Based on reasonable initial parameters, Percentage Depth Doses (PDDs), Off-Axis Ratios (OARs), total scatter factors, beam qualities, and penumbra widths of both flatteningfilter (FF) and flattening-filter-free (FFF) beams for fields ranging from 4 × 4 to 30 × 30 cm2 are simulated systematically with EGSnrc codes. Not only the simulated dosimetric properties are in excellent agreement with the measurements, but also the dosimetric discrepancies between FF and FFF beams are consistent with the laws of previous studies on other accelerators. Therefore, reasonable incident electron parameters are able to accurately verify the performance of the XHA600D accelerator and can be used for further dosimetry research.

A polar-coordinate-based pencil beam algorithm for VMAT dose computation with high-resolution gantry angle sampling

PURPOSE

Most commercially available treatment planning systems (TPSs) approximate the continuous delivery of volumetric modulated arc therapy (VMAT) plans with a series of discretized static beams for treatment planning, which can make VMAT dose computation extremely inefficient. In this study, we developed a polar-coordinate-based pencil beam (PB) algorithm for efficient VMAT dose computation with high-resolution gantry angle sampling that can improve the computational efficiency and reduce the dose discrepancy due to the angular under-sampling effect.

METHODS AND MATERIALS

6 MV 1 × 1 mm² pencil beams were simulated on a uniform cylindrical phantom under an EGSnrc Monte Carlo (MC) environment. The MC-generated PB kernels were collected in the polar coordinate system for each bixel on a 40 × 40 cm² fluence map and subsequently fitted via a series of Gaussians. The fluence was calculated using a detectors' eye view with off-axis and MLC transmission factors corrected. Doses of VMAT arc on the phantom were computed by summing the convolution results between the corresponding PB kernels and fluence for each bixel in the polar coordinate system. The convolution was performed using Fast Fourier Transform to expedite the computing speed. The calculated doses were converted to the Cartesian coordinate system and compared with the reference dose computed by a collapsed cone convolution (CCC) algorithm of the TPS. A heterogeneous phantom was created to study the heterogeneity corrections using the proposed algorithm. Ten VMAT arcs were included to evaluate the algorithm performance. Gamma analysis and computation complexity theory were used to measure the dosimetric accuracy and computational efficiency, respectively.

RESULTS

The dosimetric comparisons on the homogeneous phantom between the proposed PB algorithm and the CCC algorithm for ten VMAT arcs demonstrate that the proposed algorithm can achieve a dosimetric accuracy comparable to that of the CCC algorithm with average gamma passing rates of 96% (2%/2mm) and 98% (3%/3mm). In addition, the proposed algorithm can provide better computational efficiency for VMAT dose computation using a PC equipped with a 4-core processor, compared to the CCC algorithm utilizing a dual 10-core server. Moreover, the computation complexity theory reveals that the proposed algorithm has a great advantage with regard to computational efficiency for VMAT dose computation on homogeneous medium, especially when a fine angular sampling rate is applied. This can support a reduction in dose errors from the angular under-sampling effect by using a finer angular sampling rate, while still preserving a practical computing speed. For dose calculation on the heterogeneous phantom, the proposed algorithm with heterogeneity corrections can still offer a reasonable dosimetric accuracy with comparable computational efficiency to that of the CCC algorithm.

CONCLUSIONS

We proposed a novel polar-coordinate-based pencil beam algorithm for VMAT dose computation that enables a better computational efficiency while maintaining clinically acceptable dosimetric accuracy and reducing dose error caused by the angular under-sampling effect. It also provides a flexible VMAT dose computation structure that allows adjustable sampling rates and direct dose computation in regions of interest, which makes the algorithm potentially useful for clinical applications such as independent dose verification for VMAT patient-specific QA. This article is protected by copyright. All rights reserved.

Development of a virtual source model for Monte Carlo-based independent dose calculation for varian linac

Monte Carlo (MC) independent dose calculations are often based on phase-space files (PSF), as they can accurately represent particle characteristics. PSF generally are large and create a bottleneck in computation time. In addition, the number of independent particles is limited by the PSF, preventing further reduction of statistical uncertainty. The purpose of this study is to develop and validate a virtual source model (VSM) to address these limitations. Particles from existing PSF for the Varian TrueBeam medical linear accelerator 6X, 6XFFF, 10X, and 10XFFF beam configurations were tallied, analyzed, and used to generate a dual-source photon VSM that includes electron contamination. The particle density distribution, kinetic energy spectrum, particle direction, and the correlations between characteristics were computed. The VSM models for each beam configuration were validated with water phantom measurements as well as clinical test cases against the original PSF. The new VSM requires 67 MB of disk space for each beam configuration, compared to 50 GB for the PSF from which they are based and effectively remove the bottleneck set by the PSF. At 3% MC uncertainty, the VSM approach reduces the calculation time by a factor of 14 on our server. MC doses obtained using the VSM approach were compared against PSF-generated doses in clinical test cases and measurements in a water phantom using a gamma index analysis. For all tests, the VSMs were in excellent agreement with PSF doses and measurements (>90% passing voxels between doses and measurements). Results of this study indicate the successful derivation and implementation of a VSM model for Varian Linac that significantly saves computation time without sacrificing accuracy for independent dose calculation.

Beam modeling and commissioning for Monte Carlo photon beam on an Elekta Versa HD LINAC

PURPOSE

This study aims at analyzing beam data commissioning along with verifying Monte Carlo-based treatment planning system on the basis of the manufacturer guidelines for Elekta Versa HD Linear Accelerator. Moreover, evaluating the beam match process in terms of quality index, photon profile and multi leaf collimator (MLC) offset is aimed as well.

MATERIALS AND METHODS

The process of collecting beam data for Monaco 5.51 Treatment Planning System commissioning was done based on the instructions provided by the manufacturer as well as AAPM TG-106. Monte Carlo analysis was done for output factors in water, percent depth dose and beam profiles. A set of eight static and intensity modulated radiation therapy fields were used to verify the MLC parameters.

RESULTS

The difference between the measured and modeled penetrative quality (D₁₀) was achieved to be 0.54%. The output factors for 6 MV photon energy were measured and the difference between the measured and Monte Carlo output results was smaller than 1% for all the fields. The average percentage of passing the gamma criteria for commissioning test fields was (95+-4)%, however, the minimum agreement was 87.5% belonging to "7SEGA". Additionally, the agreement between both LINAC is 96%, however, the second LINAC reveals a positive offset in the point of approximately -4 cm on the x-axis at the crossplane.

CONCLUSION

Test commissioning was successfully verified using a homogeneous phantom for point dose measurements, post modelling MLC parameters and patient QA plans. All plan parameters pass the gamma criteria. 6 MV photon beam was successfully commissioned for Elekta VersaHD LINAC and is ready for clinical implementation.

Monte Carlo methods for device simulations in radiation therapy

Monte Carlo (MC) simulations play an important role in radiotherapy, especially as a method to evaluate physical properties that are either impossible or difficult to measure. For example, MC simulations (MCSs) are used to aid in the design of radiotherapy devices or to understand their properties. The aim of this article is to review the MC method for device simulations in radiation therapy. After a brief history of the MC method and popular codes in medical physics, we review applications of the MC method to model treatment heads for neutral and charged particle radiation therapy as well as specific in-room devices for imaging and therapy purposes. We conclude by discussing the impact that MCSs had in this field and the role of MC in future device design.

Beam modeling and beam model commissioning for Monte Carlo dose calculation-based radiation therapy treatment planning: Report of AAPM Task Group 157

Dose calculation plays an important role in the accuracy of radiotherapy treatment planning and beam delivery. The Monte Carlo (MC) method is capable of achieving the highest accuracy in radiotherapy dose calculation and has been implemented in many commercial systems for radiotherapy treatment planning. The objective of this task group was to assist clinical physicists with the potentially complex task of acceptance testing and commissioning MC-based treatment planning systems (TPS) for photon and electron beam dose calculations. This report provides an overview on the general approach of clinical implementation and testing of MC-based TPS with a specific focus on models of clinical photon and electron beams. Different types of beam models are described including those that utilize MC simulation of the treatment head and those that rely on analytical methods and measurements. The trade-off between accuracy and efficiency in the various source-modeling approaches is discussed together with guidelines for acceptance testing of MC-based TPS from the clinical standpoint. Specific recommendations are given on methods and practical procedures to commission clinical beam models for MC-based TPS.

Optimization of Phase Space files from clinical linear accelerators

This work proposes a methodology to produce an optimized phase-space (PhSp) for the Elekta Synergy linac by tuning the energy and direction of particles inside the 6-MV Elekta Precise PhSp, provided by the International Atomic Energy Agency (IAEA), for Monte Carlo (MC) simulations. First, the energies of the particles emerging from the original PhSp were increased by different factors, producing new PhSps. Percentage depth dose (PDD) profiles were simulated and compared to measured data from a Synergy linac for 6-MV photon beam. This process was repeated until a minimum difference was reached. Particles' directions were then manipulated following identified correlations to lateral profiles, resulting in two distinct perturbation factors based on inline and crossline profiles. Both factors were merged into one single optimal factor. For energy optimization, an increase of 0.32 MeV applied to all particles inside the original PhSp, but to 0.511 MeV annihilation photons, provided the best results. The direction optimization factor was the combination of the individual factors for inline (0.605%) and crossline (0.051%). The agreement between measured and simulated profiles, when using the optimized PhSp, improved considerably in comparison to simulations performed with the original IAEA PhSp. For all fields and depths analyzed, the discrepancies for PDD, inline and crossline profiles dropped from 11.2%, 15.7% and 27.5% to under 1.4%, 4.7% and 13.2%, respectively. The optimized PhSp should not replace the full linac modelling, however it offers an alternative for MC dose calculations when neither geometric details nor validated IAEA PhSp are available to the user.

Comparison of gamma index based on dosimetric error and clinically relevant dose-volume index based on three-dimensional dose prediction in breast intensity-modulated radiation therapy

Background

Measurement-guided dose reconstruction has lately attracted significant attention because it can predict the delivered patient dose distribution. Although the treatment planning system (TPS) uses sophisticated algorithm to calculate the dose distribution, the calculation accuracy depends on the particular TPS used. This study aimed to investigate the relationship between the gamma passing rate (GPR) and the clinically relevant dose–volume index based on the predicted 3D patient dose distribution derived from two TPSs (XiO, RayStation).

Methods

Twenty-one breast intensity-modulated radiation therapy plans were inversely optimized using XiO. With the same plans, both TPSs calculated the planned dose distribution. We conducted per-beam measurements on the coronal plane using a 2D array detector and analyzed the difference in 2D GPRs between the measured and planned doses by commercial software. Using in-house software, we calculated the predicted 3D patient dose distribution and derived the predicted 3D GPR, the predicted per-organ 3D GPR, and the predicted clinically relevant dose–volume indices [dose–volume histogram metrics and the value of the tumor-control probability/normal tissue complication probability of the planning target volume and organs at risk]. The results derived from XiO were compared with those from RayStation.

Results

While the mean 2D GPRs derived from both TPSs were 98.1% (XiO) and 100% (RayStation), the mean predicted 3D GPRs of ipsilateral lung (73.3% [XiO] and 85.9% [RayStation]; p < 0.001) had no correlation with 2D GPRs under the 3% global/3 mm criterion. Besides, this significant difference in terms of referenced TPS between XiO and RayStation could be explained by the fact that the error of predicted V_5Gy of ipsilateral lung derived from XiO (29.6%) was significantly larger than that derived from RayStation (− 0.2%; p < 0.001).

Conclusions

GPR is useful as a patient quality assurance to detect dosimetric errors; however, it does not necessarily contain detailed information on errors. Using the predicted clinically relevant dose–volume indices, the clinical interpretation of dosimetric errors can be obtained. We conclude that a clinically relevant dose–volume index based on the predicted 3D patient dose distribution could add to the clinical and biological considerations in the GPR, if we can guarantee the dose calculation accuracy of referenced TPS.

Detectors assessment for stereotactic radiosurgery with cones

The purpose of this work is to assess eight detectors performance for output factor (OF), percent depth dose (PDD), and beam profiles in a 6‐MV Clinac stereotactic radiosurgery mode for cone irradiation using Monte Carlo simulation as reference. Cones with diameters comprised between 30 and 4 mm have been studied. The evaluated detectors were ionization chambers: pinpoint and pinpoint 3D, diodes: SRS, P and E, Edge, MicroDiamond and EBT3 radiochromic films. The results showed that pinpoints underestimate OF up to −2.3% for cone diameters ≥10 mm and down to −12% for smaller cones. Both nonshielded (SRS and E) and shielded diodes (P and Edge) overestimate the OF respectively up to 3.3% and 5.2% for cone diameters ≥10 mm and in both cases more than 7% for smaller cones. MicroDiamond slightly overestimates the OF, 3.7% for all the cones and EBT3 film is the closest to Monte Carlo with maximum difference of ±1% whatever the cone size is. For the profiles and the PDD, particularly for the small cones, the size of the detector predominates. All diodes and EBT3 agree with the simulation within ±0.2 mm for beam profiles determination. For PDD curve all the active detectors response agree with simulation up to 1% for all the cones. EBT3 is the more accurate detector for beam profiles and OF determinations of stereotactic cones but it is restrictive to use. Due to respectively inappropriate size of the sensitive volume and composition, pinpoints and diodes do not seem appropriate without OF corrective factors below 10 mm diameter cone. MicroDiamond appears to be the best detector for OF determination regardless all cones. For off‐axis measurements, the size of the detector predominates and for PDD all detectors give promising results.

Imaging Dose, Cancer Risk and Cost Analysis in Image-guided Radiotherapy of Cancers

The purpose of this retrospective study is to evaluate the cumulative imaging doses, the associated cancer risk and the cost related to the various radiological imaging procedures in image-guided radiotherapy of cancers. Correlations between patients’ size and Monte Carlo simulated organ doses were established and validated for various imaging procedures, and then used for patient-specific organ dose estimation of 4,832 cancer patients. The associated cancer risk was estimated with published models and the cost was calculated based on the standard billing codes. The average (range) cumulative imaging doses to the brain, lungs and red bone marrow were 38.0 (0.5–177.3), 18.8 (0.4–246.5), and 49.1 (0.4–274.4) cGy, respectively. The associated average (range) lifetime attributable risk of cancer incidence per 100,000 persons was 78 (0–2798), 271 (1–8948), and 510 (0–4487) for brain cancer, lung cancer and leukemia, respectively. The median (range) imaging cost was $5256 (4268–15896) for the head scans, $5180 (4268–16274) for the thorax scans, and $7080 (4268–15288) for the pelvic scans, respectively. The image-guidance procedures and the accumulated imaging doses should be incorporated into clinical decision-making to personalize radiotherapy for individual patients.

Hybrid Monte Carlo source model: Advantages and deficiencies

Monte Carlo (MC) simulation is the gold standard for dose calculation. An accurate mathematical source model can be used for the radiation beams. Source models can consist of sub-sources or fewer sources with data that need to be measured. This can speed up treatment plan verification without the need for a full simulation of the radiation treatment machine.

Aims: This study aimed to construct a novel hybrid source model for 6 MV photon beams for an Elekta Synergy accelerator and to commission it against measured beam data and treatments plans.

Methods and Material: The model comprised of a circular photon and planar electron contamination source. The modified Schiff formula provided off-axis variable bremsstrahlung spectra. Collimation and scatter were modelled with error functions. An exponential function modelled the transmitted fluence through the collimators. The source model was commissioned by comparing simulated and measured MC data. Dose data included profiles, depth dose and film measurements in a Rando phantom. Field sizes ranged from 1 × 1 cm2 to 40 × 40 cm2.

Results: Regular, wedged and asymmetrical fields could be modelled within 1.5% or 1.5 mm. More than 95% of all points lie within 3% or 3 mm for the multi-leaf collimators contours data. A gamma criterion of 3% or 3 mm was met for a complex treatment case.

Conclusions: The two sub-source model replicated clinical 6 MV Elekta Synergy photons beams and could calculate the dose accurately for conformal treatments in complex geometries such as a head-and-neck case.

A fast jaw-tracking model for VMAT and IMRT Monte Carlo simulations

Modern radiotherapy techniques involve routine use of volumetric arc therapy (VMAT) and intensity modulated radiotherapy (IMRT) with jaw‐tracking – dynamic motion of the secondary collimators (jaws) in tandem with multi‐leaf collimators (MLCs). These modalities require accurate dose calculations for the purposes of treatment planning and dose verification. Monte Carlo (MC) methods for radiotherapy dose calculation are widely accepted as capable of achieving high accuracy. This paper presents an efficiency‐enhancement method for secondary collimator modeling, presented in the context of a tool for MC‐based dose second checks. The model constitutes an accuracy trade‐off in the source model for the sake of efficiency enhancement, but maintains the advantages of MC transport in patient heterogeneities. The secondary collimator model is called Flat‐Absorbing‐Jaw‐Tracking (FAJT). Transmission through and scatter from the secondary collimators is neglected, and jaws are modeled as perfectly absorbing planes. To couple the motion of secondary collimators with MLCs for jaw‐tracking, the FAJT model was built into the VCU‐MLC model. Gamma‐index analysis of the dose distributions from FAJT against the full BEAMnrc MC simulations showed over 99% pass rate for a range of open fields, two clinical IMRT, and one VMAT treatment plan, for 2%/2 mm criteria above 10%. Using FAJT, the simulation speed of the secondary collimators for open fields increased by a factor of 237, 1489, and 1395 for 4 × 4, 10 × 10, and 30 × 30 cm², respectively. In general, clinically oriented simulation times are reduced from “hours” to “minutes” on identical hardware. Results for nine representative clinical cases (seven with jaw‐tracking) are presented. The average 2%/2 mm γ‐test success rate above the 80% isodose was 96.8% when tested against the EPIDose electronic portal image‐based dose reconstruction method and 97.3% against the Eclipse analytical anisotropic algorithm.

Monte Carlo Investigation of Photon Beam Characteristics and its Variation with Incident Electron Beam Parameters for Indigenous Medical Linear Accelerator

Purpose

A Monte Carlo model of a 6 MV medical linear accelerator (linac) unit built indigenously was developed using the BEAMnrc user code of the EGSnrc code system. The model was benchmarked against the measurements. Monte Carlo simulations were carried out for different incident electron beam parameters in the study.

Materials and Methods

Simulation of indigenously developed linac unit has been carried out using the Monte Carlo based BEAMnrc user-code of the EGSnrc code system. Using the model, percentage depth dose (PDD), and lateral dose profiles were studied using the DOSXYZnrc user code. To identify appropriate electron parameters, three different distributions of electron beam intensity were investigated. For each case, the kinetic energy of the incident electron was varied from 6 to 6.5 MeV (0.1 MeV increment). The calculated dose data were compared against the measurements using the PTW, Germany make RFA dosimetric system (water tank MP3-M and 0.125 cm³ ion chamber).

Results

The best fit of incident electron beam parameter was found for the combination of beam energy of 6.2 MeV and circular Gaussian distributed source in X and Y with FWHM of 1.0 mm. PDD and beam profiles (along both X and Y directions) were calculated for the field sizes from 5 cm × 5 cm to 25 cm × 25 cm. The dose difference between the calculated and measured PDD and profile values were under 1%, except for the penumbra region where the maximum deviation was found to be around 2%.

Conclusions

A Monte Carlo model of indigenous linac (6 MV) has been developed and benchmarked against the measured data.

A single-source photon source model of a linear accelerator for Monte Carlo dose calculation

PURPOSE

To introduce a new method of deriving a virtual source model (VSM) of a linear accelerator photon beam from a phase space file (PSF) for Monte Carlo (MC) dose calculation.

MATERIALS AND METHODS

A PSF of a 6 MV photon beam was generated by simulating the interactions of primary electrons with the relevant geometries of a Synergy linear accelerator (Elekta AB, Stockholm, Sweden) and recording the particles that reach a plane 16 cm downstream the electron source. Probability distribution functions (PDFs) for particle positions and energies were derived from the analysis of the PSF. These PDFs were implemented in the VSM using inverse transform sampling. To model particle directions, the phase space plane was divided into a regular square grid. Each element of the grid corresponds to an area of 1 mm2 in the phase space plane. The average direction cosines, Pearson correlation coefficient (PCC) between photon energies and their direction cosines, as well as the PCC between the direction cosines were calculated for each grid element. Weighted polynomial surfaces were then fitted to these 2D data. The weights are used to correct for heteroscedasticity across the phase space bins. The directions of the particles created by the VSM were calculated from these fitted functions. The VSM was validated against the PSF by comparing the doses calculated by the two methods for different square field sizes. The comparisons were performed with profile and gamma analyses.

RESULTS

The doses calculated with the PSF and VSM agree to within 3% /1 mm (>95% pixel pass rate) for the evaluated fields.

CONCLUSION

A new method of deriving a virtual photon source model of a linear accelerator from a PSF file for MC dose calculation was developed. Validation results show that the doses calculated with the VSM and the PSF agree to within 3% /1 mm.

A measurement-based generalized source model for Monte Carlo dose simulations of CT scans

The goal of this study is to develop a generalized source model for accurate Monte Carlo dose simulations of CT scans based solely on the measurement data without a priori knowledge of scanner specifications. The proposed generalized source model consists of an extended circular source located at x-ray target level with its energy spectrum, source distribution and fluence distribution derived from a set of measurement data conveniently available in the clinic. Specifically, the central axis percent depth dose (PDD) curves measured in water and the cone output factors measured in air were used to derive the energy spectrum and the source distribution respectively with a Levenberg-Marquardt algorithm. The in-air film measurement of fan-beam dose profiles at fixed gantry was back-projected to generate the fluence distribution of the source model. A benchmarked Monte Carlo user code was used to simulate the dose distributions in water with the developed source model as beam input. The feasibility and accuracy of the proposed source model was tested on a GE LightSpeed and a Philips Brilliance Big Bore multi-detector CT (MDCT) scanners available in our clinic. In general, the Monte Carlo simulations of the PDDs in water and dose profiles along lateral and longitudinal directions agreed with the measurements within 4%/1 mm for both CT scanners. The absolute dose comparison using two CTDI phantoms (16 cm and 32 cm in diameters) indicated a better than 5% agreement between the Monte Carlo-simulated and the ion chamber-measured doses at a variety of locations for the two scanners. Overall, this study demonstrated that a generalized source model can be constructed based only on a set of measurement data and used for accurate Monte Carlo dose simulations of patients' CT scans, which would facilitate patient-specific CT organ dose estimation and cancer risk management in the diagnostic and therapeutic radiology.

Efficient independent planar dose calculation for FFF IMRT QA with a bivariate Gaussian source model

The aim of this study is to perform a direct comparison of the source model for photon beams with and without flattening filter (FF) and to develop an efficient independent algorithm for planar dose calculation for FF‐free (FFF) intensity‐modulated radiotherapy (IMRT) quality assurance (QA). The source model consisted of a point source modeling the primary photons and extrafocal bivariate Gaussian functions modeling the head scatter, monitor chamber backscatter, and collimator exchange effect. The model parameters were obtained by minimizing the difference between the calculated and measured in‐air output factors (S_c). The fluence of IMRT beams was calculated from the source model using a backprojection and integration method. The off‐axis ratio in FFF beams were modeled with a fourth degree polynomial. An analytical kernel consisting of the sum of three Gaussian functions was used to describe the dose deposition process. A convolution‐based method was used to account for the ionization chamber volume averaging effect when commissioning the algorithm. The algorithm was validated by comparing the calculated planar dose distributions of FFF head‐and‐neck IMRT plans with measurements performed with a 2D diode array. Good agreement between the measured and calculated S_c was achieved for both FF beams (<0.25%) and FFF beams (<0.10%). The relative contribution of the head‐scattered photons reduced by 34.7% for 6 MV and 49.3% for 10 MV due to the removal of the FF. Superior agreement between the calculated and measured dose distribution was also achieved for FFF IMRT. In the gamma comparison with a 2%/2 mm criterion, the average passing rate was 96.2 ± 1.9% for 6 MV FFF and 95.5 ± 2.6% for 10 MV FFF. The efficient independent planar dose calculation algorithm is easy to implement and can be valuable in FFF IMRT QA.

Modification and validation of an analytical source model for external beam radiotherapy Monte Carlo dose calculations

PURPOSE

A dose calculation tool, which combines the accuracy of the dose planning method (DPM) Monte Carlo code and the versatility of a practical analytical multisource model, which was previously reported has been improved and validated for the Varian 6 and 10 MV linear accelerators (linacs). The calculation tool can be used to calculate doses in advanced clinical application studies. One shortcoming of current clinical trials that report dose from patient plans is the lack of a standardized dose calculation methodology. Because commercial treatment planning systems (TPSs) have their own dose calculation algorithms and the clinical trial participant who uses these systems is responsible for commissioning the beam model, variation exists in the reported calculated dose distributions. Today's modern linac is manufactured to tight specifications so that variability within a linac model is quite low. The expectation is that a single dose calculation tool for a specific linac model can be used to accurately recalculate dose from patient plans that have been submitted to the clinical trial community from any institution. The calculation tool would provide for a more meaningful outcome analysis.

METHODS

The analytical source model was described by a primary point source, a secondary extra-focal source, and a contaminant electron source. Off-axis energy softening and fluence effects were also included. The additions of hyperbolic functions have been incorporated into the model to correct for the changes in output and in electron contamination with field size. A multileaf collimator (MLC) model is included to facilitate phantom and patient dose calculations. An offset to the MLC leaf positions was used to correct for the rudimentary assumed primary point source.

RESULTS

Dose calculations of the depth dose and profiles for field sizes 4 × 4 to 40 × 40 cm agree with measurement within 2% of the maximum dose or 2 mm distance to agreement (DTA) for 95% of the data points tested. The model was capable of predicting the depth of the maximum dose within 1 mm. Anthropomorphic phantom benchmark testing of modulated and patterned MLCs treatment plans showed agreement to measurement within 3% in target regions using thermoluminescent dosimeters (TLD). Using radiochromic film normalized to TLD, a gamma criteria of 3% of maximum dose and 2 mm DTA was applied with a pass rate of least 85% in the high dose, high gradient, and low dose regions. Finally, recalculations of patient plans using DPM showed good agreement relative to a commercial TPS when comparing dose volume histograms and 2D dose distributions.

CONCLUSIONS

A unique analytical source model coupled to the dose planning method Monte Carlo dose calculation code has been modified and validated using basic beam data and anthropomorphic phantom measurement. While this tool can be applied in general use for a particular linac model, specifically it was developed to provide a singular methodology to independently assess treatment plan dose distributions from those clinical institutions participating in National Cancer Institute trials.

Energy Modulated Photon Radiotherapy: A Monte Carlo Feasibility Study

A novel treatment modality termed energy modulated photon radiotherapy (EMXRT) was investigated. The first step of EMXRT was to determine beam energy for each gantry angle/anatomy configuration from a pool of photon energy beams (2 to 10 MV) with a newly developed energy selector. An inverse planning system using gradient search algorithm was then employed to optimize photon beam intensity of various beam energies based on presimulated Monte Carlo pencil beam dose distributions in patient anatomy. Finally, 3D dose distributions in six patients of different tumor sites were simulated with Monte Carlo method and compared between EMXRT plans and clinical IMRT plans. Compared to current IMRT technique, the proposed EMXRT method could offer a better paradigm for the radiotherapy of lung cancers and pediatric brain tumors in terms of normal tissue sparing and integral dose. For prostate, head and neck, spine, and thyroid lesions, the EMXRT plans were generally comparable to the IMRT plans. Our feasibility study indicated that lower energy (<6 MV) photon beams could be considered in modern radiotherapy treatment planning to achieve a more personalized care for individual patient with dosimetric gains.

Intermediate Megavoltage Photon Beams for Improved Lung Cancer Treatments

The goal of this study is to evaluate the effects of intermediate megavoltage (3-MV) photon beams on SBRT lung cancer treatments. To start with, a 3-MV virtual beam was commissioned on a commercial treatment planning system based on Monte Carlo simulations. Three optimized plans (6-MV, 3-MV and dual energy of 3- and 6-MV) were generated for 31 lung cancer patients with identical beam configuration and optimization constraints for each patient. Dosimetric metrics were evaluated and compared among the three plans. Overall, planned dose conformity was comparable among three plans for all 31 patients. For 21 thin patients with average short effective path length (< 10 cm), the 3-MV plans showed better target coverage and homogeneity with dose spillage index R_50% = 4.68±0.83 and homogeneity index = 1.26±0.06, as compared to 4.95±1.01 and 1.31±0.08 in the 6-MV plans (p < 0.001). Correspondingly, the average/maximum reductions of lung volumes receiving 20 Gy (V_20Gy), 5 Gy (V_5Gy), and mean lung dose (MLD) were 7%/20%, 9%/30% and 5%/10%, respectively in the 3-MV plans (p < 0.05). The doses to 5% volumes of the cord, esophagus, trachea and heart were reduced by 9.0%, 10.6%, 11.4% and 7.4%, respectively (p < 0.05). For 10 thick patients, dual energy plans can bring dosimetric benefits with comparable target coverage, integral dose and reduced dose to the critical structures, as compared to the 6-MV plans. In conclusion, our study indicated that 3-MV photon beams have potential dosimetric benefits in treating lung tumors in terms of improved tumor coverage and reduced doses to the adjacent critical structures, in comparison to 6-MV photon beams. Intermediate megavoltage photon beams (< 6-MV) may be considered and added into current treatment approaches to reduce the adjacent normal tissue doses while maintaining sufficient tumor dose coverage in lung cancer radiotherapy.

An analytic linear accelerator source model for GPU-based Monte Carlo dose calculations

Recently, there has been a lot of research interest in developing fast Monte Carlo (MC) dose calculation methods on graphics processing unit (GPU) platforms. A good linear accelerator (linac) source model is critical for both accuracy and efficiency considerations. In principle, an analytical source model should be more preferred for GPU-based MC dose engines than a phase-space file-based model, in that data loading and CPU-GPU data transfer can be avoided. In this paper, we presented an analytical field-independent source model specifically developed for GPU-based MC dose calculations, associated with a GPU-friendly sampling scheme. A key concept called phase-space-ring (PSR) was proposed. Each PSR contained a group of particles that were of the same type, close in energy and reside in a narrow ring on the phase-space plane located just above the upper jaws. The model parameterized the probability densities of particle location, direction and energy for each primary photon PSR, scattered photon PSR and electron PSR. Models of one 2D Gaussian distribution or multiple Gaussian components were employed to represent the particle direction distributions of these PSRs. A method was developed to analyze a reference phase-space file and derive corresponding model parameters. To efficiently use our model in MC dose calculations on GPU, we proposed a GPU-friendly sampling strategy, which ensured that the particles sampled and transported simultaneously are of the same type and close in energy to alleviate GPU thread divergences. To test the accuracy of our model, dose distributions of a set of open fields in a water phantom were calculated using our source model and compared to those calculated using the reference phase-space files. For the high dose gradient regions, the average distance-to-agreement (DTA) was within 1 mm and the maximum DTA within 2 mm. For relatively low dose gradient regions, the root-mean-square (RMS) dose difference was within 1.1% and the maximum dose difference within 1.7%. The maximum relative difference of output factors was within 0.5%. Over 98.5% passing rate was achieved in 3D gamma-index tests with 2%/2 mm criteria in both an IMRT prostate patient case and a head-and-neck case. These results demonstrated the efficacy of our model in terms of accurately representing a reference phase-space file. We have also tested the efficiency gain of our source model over our previously developed phase-space-let file source model. The overall efficiency of dose calculation was found to be improved by ~1.3-2.2 times in water and patient cases using our analytical model.

A deterministic solution of the first order linear Boltzmann transport equation in the presence of external magnetic fields

PURPOSE

Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today's treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann transport equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields.

METHODS

The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf_macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 × 10 cm(2) field as well as a smaller 2 × 2 cm(2) field.

RESULTS

Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm's high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization.

CONCLUSIONS

The feasibility of including magnetic field effects in a deterministic solution to the first order linear Boltzmann transport equation is shown. The results show a high degree of accuracy when compared against Monte Carlo calculations in all magnetic field strengths and orientations tested.

Monte Carlo calculations of an Elekta Precise SL-25 photon beam model

Background

Monte Carlo (MC) simulations have been used extensively for benchmarking photon dose calculations in modern radiotherapy using linear accelerators (linacs). Moreover, a major barrier to widespread clinical implementation of MC dose calculation is the difficulty in characterising the radiation source using data reported from manufacturers.

Purpose

This work aims to develop a generalised full MC histogram source model of an Elekta Precise SL-25 linac (electron exit window, target, flattening filter, monitor chambers and collimators) for 6 MV photon beams used in standard therapies. The inclusion of many different probability processes such as scatter, nuclear reactions, decay, capture cross-sections and more led to more realistic dose calculations in treatment planning and quality assurance.

Materials and methods

Two different codes, MCNPX 2·6 and EGSr-BEAM, were used for the calculation of particle transport, first in the geometry of the internal/external accelerator source, and then followed by tracking the transport and energy deposition in phantom-equivalent tissues. A full phase space file was scored directly above the upper multilayer collimator’s jaws to derive the beam characteristics such as planar fluence, angular distribution and energy spectrum. To check the quality of the generated photon beam, its depth dose curves and cross-beam profiles were calculated and compared with measured data.

Results

In-field dose distributions calculated using the accelerator models were tuned to match measurement data with preliminary calculations performed using the accelerator information provided by the manufacturer. Field sizes of 3×3, 5×5, 10×10, 15×15 and 20×20 cm2were analysed. Local differences between calculated and measured curve doses beneath 2% were obtained for all the studied field sizes. Higher discrepancies were obtained in the air–water interface, where measurements of dose distributions with the ionisation chamber need to be shifted for the effective point of measurement.

Conclusion

The agreements between MC-calculated and measured dose distributions were excellent for both codes, showing the strength and stability of the proposed model. Beam reconstruction methods as direct input to dose-calculation codes using the recorded histograms can be implemented for more accurate patient dose estimation.

Adapted Prescription Dose for Monte Carlo Algorithm in Lung SBRT: Clinical Outcome on 205 Patients

Purpose

SBRT is the standard of care for inoperable patients with early-stage lung cancer without lymph node involvement. Excellent local control rates have been reported in a large number of series. However, prescription doses and calculation algorithms vary to a great extent between studies, even if most teams prescribe to the D95 of the PTV. Type A algorithms are known to produce dosimetric discrepancies in heterogeneous tissues such as lungs. This study was performed to present a Monte Carlo (MC) prescription dose for NSCLC adapted to lesion size and location and compare the clinical outcomes of two cohorts of patients treated with a standard prescription dose calculated by a type A algorithm or the proposed MC protocol.

Patients and Methods

Patients were treated from January 2011 to April 2013 with a type B algorithm (MC) prescription with 54 Gy in three fractions for peripheral lesions with a diameter under 30 mm, 60 Gy in 3 fractions for lesions with a diameter over 30 mm, and 55 Gy in five fractions for central lesions. Clinical outcome was compared to a series of 121 patients treated with a type A algorithm (TA) with three fractions of 20 Gy for peripheral lesions and 60 Gy in five fractions for central lesions prescribed to the PTV D95 until January 2011. All treatment plans were recalculated with both algorithms for this study. Spearman’s rank correlation coefficient was calculated for GTV and PTV. Local control, overall survival and toxicity were compared between the two groups.

Results

205 patients with 214 lesions were included in the study. Among these, 93 lesions were treated with MC and 121 were treated with TA. Overall survival rates were 86% and 94% at one and two years, respectively. Local control rates were 79% and 93% at one and two years respectively. There was no significant difference between the two groups for overall survival (p = 0.785) or local control (p = 0.934). Fifty-six patients (27%) developed grade I lung fibrosis without clinical consequences. GTV size was a prognostic factor for overall survival (HR = 1.026, IC95% [1.01–1.041], p<0.001) and total dose was a prognostic factor for local control (HR = 0.924, IC95% [0.870–0.982], p = 0.011). D50 of the GTV calculated with MC correlated poorly with the D95 of the PTV calculated with TA (r = 0.116) for lesions with a diameter of 20 mm or less. For lesions larger than 20 mm, spearman correlation was higher (r = 0.618), but still insufficient.

Conclusion

No difference in local control or overall survival was found between patients treated with a type A or a type B algorithm in our cohort. A size and location adapted GTV-based prescription method could be used with a type B algorithm. External validation of these results is warranted.

A hybrid phase-space and histogram source model for GPU-based Monte Carlo radiotherapy dose calculation

In GPU-based Monte Carlo simulations for radiotherapy dose calculation, source modelling from a phase-space source can be an efficiency bottleneck. Previously, this has been addressed using phase-space-let (PSL) sources, which provided significant efficiency enhancement. We propose that additional speed-up can be achieved through the use of a hybrid primary photon point source model combined with a secondary PSL source. A novel phase-space derived and histogram-based implementation of this model has been integrated into gDPM v3.0. Additionally, a simple method for approximately deriving target photon source characteristics from a phase-space that does not contain inheritable particle history variables (LATCH) has been demonstrated to succeed in selecting over 99% of the true target photons with only ~0.3% contamination (for a Varian 21EX 18 MV machine). The hybrid source model was tested using an array of open fields for various Varian 21EX and TrueBeam energies, and all cases achieved greater than 97% chi-test agreement (the mean was 99%) above the 2% isodose with 1% / 1 mm criteria. The root mean square deviations (RMSDs) were less than 1%, with a mean of 0.5%, and the source generation time was 4-5 times faster. A seven-field intensity modulated radiation therapy patient treatment achieved 95% chi-test agreement above the 10% isodose with 1% / 1 mm criteria, 99.8% for 2% / 2 mm, a RMSD of 0.8%, and source generation speed-up factor of 2.5.

Development and reproducibility evaluation of a Monte Carlo-based standard LINAC model for quality assurance of multi-institutional clinical trials

Technical developments in radiotherapy (RT) have created a need for systematic quality assurance (QA) to ensure that clinical institutions deliver prescribed radiation doses consistent with the requirements of clinical protocols. For QA, an ideal dose verification system should be independent of the treatment-planning system (TPS). This paper describes the development and reproducibility evaluation of a Monte Carlo (MC)-based standard LINAC model as a preliminary requirement for independent verification of dose distributions. The BEAMnrc MC code is used for characterization of the 6-, 10- and 15-MV photon beams for a wide range of field sizes. The modeling of the LINAC head components is based on the specifications provided by the manufacturer. MC dose distributions are tuned to match Varian Golden Beam Data (GBD). For reproducibility evaluation, calculated beam data is compared with beam data measured at individual institutions. For all energies and field sizes, the MC and GBD agreed to within 1.0% for percentage depth doses (PDDs), 1.5% for beam profiles and 1.2% for total scatter factors (Scps.). Reproducibility evaluation showed that the maximum average local differences were 1.3% and 2.5% for PDDs and beam profiles, respectively. MC and institutions' mean Scps agreed to within 2.0%. An MC-based standard LINAC model developed to independently verify dose distributions for QA of multi-institutional clinical trials and routine clinical practice has proven to be highly accurate and reproducible and can thus help ensure that prescribed doses delivered are consistent with the requirements of clinical protocols.

Automatic commissioning of a GPU-based Monte Carlo radiation dose calculation code for photon radiotherapy

Monte Carlo (MC) simulation is commonly considered as the most accurate method for radiation dose calculations. Commissioning of a beam model in the MC code against a clinical linear accelerator beam is of crucial importance for its clinical implementation. In this paper, we propose an automatic commissioning method for our GPU-based MC dose engine, gDPM. gDPM utilizes a beam model based on a concept of phase-space-let (PSL). A PSL contains a group of particles that are of the same type and close in space and energy. A set of generic PSLs was generated by splitting a reference phase-space file. Each PSL was associated with a weighting factor, and in dose calculations the particle carried a weight corresponding to the PSL where it was from. Dose for each PSL in water was pre-computed, and hence the dose in water for a whole beam under a given set of PSL weighting factors was the weighted sum of the PSL doses. At the commissioning stage, an optimization problem was solved to adjust the PSL weights in order to minimize the difference between the calculated dose and measured one. Symmetry and smoothness regularizations were utilized to uniquely determine the solution. An augmented Lagrangian method was employed to solve the optimization problem. To validate our method, a phase-space file of a Varian TrueBeam 6 MV beam was used to generate the PSLs for 6 MV beams. In a simulation study, we commissioned a Siemens 6 MV beam on which a set of field-dependent phase-space files was available. The dose data of this desired beam for different open fields and a small off-axis open field were obtained by calculating doses using these phase-space files. The 3D γ-index test passing rate within the regions with dose above 10% of dmax dose for those open fields tested was improved averagely from 70.56 to 99.36% for 2%/2 mm criteria and from 32.22 to 89.65% for 1%/1 mm criteria. We also tested our commissioning method on a six-field head-and-neck cancer IMRT plan. The passing rate of the γ-index test within the 10% isodose line of the prescription dose was improved from 92.73 to 99.70% and from 82.16 to 96.73% for 2%/2 mm and 1%/1 mm criteria, respectively. Real clinical data measured from Varian, Siemens, and Elekta linear accelerators were also used to validate our commissioning method and a similar level of accuracy was achieved.

A comprehensive procedure for characterizing arbitrary azimuthally symmetric photon beams

PURPOSE

A new Monte Carlo (MC) source model (SM) has been developed for azimuthally symmetric photon beams.

METHODS

The MC simulation tallied phase space file (PSF) is divided into two categories depending on the relationship of the particle track line to the beam central axis: multiple point source (MPS) and spatial mesh based surface source (SMBSS). To validate this SM, MCNPX2.6 was used to generate two PSFs for a 6 MV photon beam from a Varian 2100C/D linear accelerator.

RESULTS

PDDs and profiles were calculated using the SM and original PSF for different field sizes from 5 × 5 to 40 × 40 cm2. Agreement was within 2% of the maximum dose at 100 cm SSD and 2.5% of the maximum dose at 200 cm SSD for beam profiles at depths of 3.5 cm and 15 cm with respect to the original PSF. Differences between the source model and the PSF in the out-of-field regions were less than 0.5% of the profile maximum value at 100 cm SSD. Differences between measured and calculated points were less than 2% of the maximum dose or 2 mm distance to agreement (DTA) at 100 cm SSD.

CONCLUSIONS

This SM is unique in that it accounts for a higher level of energy dependence on the particle's direction and it is independent from accelerator components, unlike other published SMs. The model can be applied to any arbitrary azimuthally symmetric beam and has source biasing capabilities that significantly increase the simulation speed up to 3300 for certain field sizes.

GPU-based Monte Carlo radiotherapy dose calculation using phase-space sources

A novel phase-space source implementation has been designed for graphics processing unit (GPU)-based Monte Carlo dose calculation engines. Short of full simulation of the linac head, using a phase-space source is the most accurate method to model a clinical radiation beam in dose calculations. However, in GPU-based Monte Carlo dose calculations where the computation efficiency is very high, the time required to read and process a large phase-space file becomes comparable to the particle transport time. Moreover, due to the parallelized nature of GPU hardware, it is essential to simultaneously transport particles of the same type and similar energies but separated spatially to yield a high efficiency. We present three methods for phase-space implementation that have been integrated into the most recent version of the GPU-based Monte Carlo radiotherapy dose calculation package gDPM v3.0. The first method is to sequentially read particles from a patient-dependent phase-space and sort them on-the-fly based on particle type and energy. The second method supplements this with a simple secondary collimator model and fluence map implementation so that patient-independent phase-space sources can be used. Finally, as the third method (called the phase-space-let, or PSL, method) we introduce a novel source implementation utilizing pre-processed patient-independent phase-spaces that are sorted by particle type, energy and position. Position bins located outside a rectangular region of interest enclosing the treatment field are ignored, substantially decreasing simulation time with little effect on the final dose distribution. The three methods were validated in absolute dose against BEAMnrc/DOSXYZnrc and compared using gamma-index tests (2%/2 mm above the 10% isodose). It was found that the PSL method has the optimal balance between accuracy and efficiency and thus is used as the default method in gDPM v3.0. Using the PSL method, open fields of 4 × 4, 10 × 10 and 30 × 30 cm(2) in water resulted in gamma passing rates of 99.96%, 99.92% and 98.66%, respectively. Relative output factors agreed within 1%. An intensity modulated radiation therapy patient plan using the PSL method resulted in a passing rate of 97%, and was calculated in 50 s (per GPU) compared to 8.4 h (per CPU) for BEAMnrc/DOSXYZnrc.

Measurement comparison and Monte Carlo analysis for volumetric-modulated arc therapy (VMAT) delivery verification using the ArcCHECK dosimetry system

The objective of this study is to validate the capabilities of a cylindrical diode array system for volumetric‐modulated arc therapy (VMAT) treatment quality assurance (QA). The VMAT plans were generated by the Eclipse treatment planning system (TPS) with the analytical anisotropic algorithm (AAA) for dose calculation. An in‐house Monte Carlo (MC) code was utilized as a validation tool for the TPS calculations and the ArcCHECK measurements. The megavoltage computed tomography (MVCT) of the ArcCHECK system was adopted for the geometry reconstruction in the TPS and for MC simulations. A 10×10 cm2 open field validation was performed for both the 6 and 10 MV photon beams to validate the absolute dose calibration of the ArcCHECK system and also the TPS dose calculations for this system. The impact of the angular dependency on noncoplanar deliveries was investigated with a series of 10×10 cm2 fields delivered with couch rotation 0° to 40°. The sensitivity of detecting the translational (1 to 10 mm) and the rotational (1° to 3°) misalignments was tested with a breast VMAT case. Ten VMAT plans (six prostate, H&N, pelvis, liver, and breast) were investigated to evaluate the agreement of the target dose and the peripheral dose among ArcCHECK measurements, and TPS and MC dose calculations. A customized acrylic plug holding an ion chamber was used to measure the dose at the center of the ArcCHECK phantom. Both the entrance and the exit doses measured by the ArcCHECK system with and without the plug agreed with the MC simulation to 1.0%. The TPS dose calculation with a 2.5 mm grid overestimated the exit dose by up to 7.2% when the plug was removed. The agreement between the MC and TPS calculations for the ArcCHECK without the plug improved significantly when a 1 mm dose calculation grid was used in the TPS. The noncoplanar delivery test demonstrated that the angular dependency has limited impact on the gamma passing rate (<1.2% drop) for the 2%–3% dose and 2 mm–3 mm DTA criteria. A 1° rotational misalignment introduces 11.3% (3%/3 mm) to 21.3% (1%/1 mm) and 0.2% (3%/3 mm) to 0.8% (1%/1 mm) Gamma passing rate drop for ArcCHECK system and MatriXX system, respectively. Both systems have comparable sensitivity to the AP misalignments. However, a 2 mm RL misalignment introduces gamma passing rate drop ranging from 0.9% (3%/3 mm) to 4.0% (1%/1 mm) and 5.0% (3%/3 mm) to 12.0% (1%/1 mm) for ArcCHECK and MatriXX measurements, respectively. For VMAT plan QA, the gamma analysis passing rates ranged from 96.1% (H&N case) to 99.9% (prostate case), when using the 3%/3 mm DTA criteria for the peripheral dose validation between the TPS and ArcCHCEK measurements. The peripheral dose validation between the MC simulation and ArcCHECK measurements showed at least 97.9% gamma passing rates. The central dose validation also showed an agreement within 2.2% between TPS/MC calculations and ArcCHECK measurements. The worst discrepancy was found in the H&N case, which is the most complex VMAT case. The ArcCHECK system is suitable for VMAT QA evaluation based on the sensitivity to detecting misalignments, the clinical impact of the angular dependency, and the correlation between the dose agreements in the peripheral region and the central region. This work also demonstrated the importance of carrying out a thorough validation of both the TPS and the dosimetry system prior to utilizing it for QA, and the value of having an independent dose calculation tool, such as the MC method, in clinical practice.

PACS number: 87.55.Qr

Investigation of pulsed low dose rate radiotherapy using dynamic arc delivery techniques

There has been no consensus standard of care to treat recurrent cancer patients who have previously been irradiated. Pulsed low dose rate (PLDR) external beam radiotherapy has the potential to reduce normal tissue toxicities while still providing significant tumor control for recurrent cancers. This work investigates the dosimetry feasibility of PLDR treatment using dynamic arc delivery techniques. Five treatment sites were investigated in this study including breast, pancreas, prostate, head and neck, and lung. Dynamic arc plans were generated using the Varian Eclipse system and the RapidArc delivery technique with 6 and 10 MV photon beams. Each RapidArc plan consisted of two full arcs and the plan was delivered five times to achieve a daily dose of 200 cGy. The dosimetry requirement was to deliver approximately 20 cGy/arc with a 3 min interval to achieve an effective dose rate of 6.7 cGy min⁻¹. Monte Carlo simulations were performed to calculate the actual dose delivered to the planning target volume (PTV) per arc taking into account beam attenuation/scattering and intensity modulation. The maximum, minimum and mean doses to the PTV were analyzed together with the dose volume histograms and isodose distributions. The dose delivery for the five plans was validated using solid water phantoms inserted with an ionization chamber and film, and a cylindrical detector array. Two intensity-modulated arcs were used to efficiently deliver the PLDR plans that provided conformal dose distributions for treating complex recurrent cancers. For the five treatment sites, the mean PTV dose ranged from 18.9 to 22.6 cGy/arc. For breast, the minimum and maximum PTV dose was 8.3 and 35.2 cGy/arc, respectively. The PTV dose varied between 12.9 and 27.5 cGy/arc for pancreas, 12.6 and 28.3 cGy/arc for prostate, 12.1 and 30.4 cGy/arc for H&N, and 16.2 and 27.6 cGy/arc for lung. Advanced radiation therapy can provide superior target coverage and normal tissue sparing for PLDR reirradiation of recurrent cancers, which can be delivered using dynamic arc delivery techniques with ten full arcs and an effective dose rate of 6.7 ± 4.0 cGy min⁻¹.