A simplified model of the source channel of the Leksell GammaKnife® tested with PENELOPE

Comparison of penumbra regions produced by ancient Gamma knife model C and Gamma ART 6000 using Monte Carlo MCNP6 simulation

The accuracy of penumbral measurements in radiotherapy is pivotal because dose planning computers require accurate data to adequately modeling the beams, which in turn are used to calculate patient dose distributions. Gamma knife is a non-invasive intracranial technique based on principles of the Leksell stereotactic system for open deep brain surgeries, invented and developed by Professor Lars Leksell. The aim of this study is to compare the penumbra widths of Leksell Gamma Knife model C and Gamma ART 6000. Initially, the structure of both systems were simulated by using Monte Carlo MCNP6 code and after validating the accuracy of simulation, beam profiles of different collimators were plotted. MCNP6 beam profile calculations showed that the penumbra values of Leksell Gamma knife model C and Gamma ART 6000 for 18, 14, 8 and 4 mm collimators are 9.7, 7.9, 4.3, 2.6 and 8.2, 6.9, 3.6, 2.4, respectively. The results of this study showed that since Gamma ART 6000 has larger solid angle in comparison with Gamma Knife model C, it produces better beam profile penumbras than Gamma Knife model C in the direct plane.

A Monte Carlo model and its commissioning for the Leksell Gamma Knife Perfexion radiosurgery system

PURPOSE

To develop and commission a Monte Carlo (MC) simulation model for the Leksell Gamma Knife (LGK) Perfexion (PFX) radiosurgery system.

METHOD

We previously established a source model for MC simulations of the LGK PFX for the purpose of the treatment planning system (TPS) dose verification and plan evaluation. To make practical and effective use of the model in clinic, several issues need to be addressed. First, thorough commissioning procedures are needed to ensure the validity of the model parameters, such as the source-to-focus (STF) distance, the source solid angle. Second, an efficient source particle sampling method is required to facilitate dose calculations for multitarget and multishot configurations in patient treatment plans. Third, inseparably, it is interesting to know the dose difference between the two GK TPS algorithms (TMR and convolution) and the MC method in extreme heterogeneous cases resulting from the inhomogeneous effect. We report our recent development in addressing these issues. Phantoms with the frame fiducials were manually created in the format of DICOM CT image to eliminate the uncertainties associated with scanner artifacts and image registration. The created homogeneous phantom was used to calibrate the model parameters to match the output factors with the manufacturer provided data, and the heterogeneous phantom with multilayer materials was used to study the inhomogeneous effect.

RESULTS

The agreement between the MC calculation and TPS was very good for the homogeneous spherical phantom. The difference of the full width at half maximum (FWHM) of the profiles was less than 1 mm except for the profile for 16 mm collimator along z-axis (less than 2 mm). For the extreme heterogeneous test case, it was shown that the TMR algorithm can overestimate the target dose by up to 22% using the measure of dose volume parameter D95. The agreement between the MC method and the TPS convolution method was better (within 3.6%) for the target near the center of phantom, however, discrepancy (up to 10.7%) existed for the target close to the skull. The difference between the two TPS dose algorithms was about 11%.

CONCLUSIONS

Considerable dose difference may result from the effect of heterogeneity, such as in the regions of the air cavities and bones. As the MC method has been extensively used in conventional external beams, it is worthwhile for further investigation in applying the MC method to accurate dose planning in the new GK PFX radiosurgery platform.

Development of a Monte Carlo model for treatment planning dose verification of the Leksell Gamma Knife Perfexion radiosurgery system

Detailed Monte Carlo (MC) modeling of the Leksell Gamma Knife (GK) Perfexion (PFX) collimator system is the only accurate ab initio approach appearing in the literature. As a different approach, in this work, we present a MC model based on film measurement. By adjusting the model parameters and fine-tuning the derived fluence map for each individual source to match the manufacturer's ring output factors, we created a reasonable virtual source model for MC simulations to verify treatment planning dose for the GK PFX radiosurgery system. The MC simulation model was commissioned by simple single shots. Dose profiles and both ring and collimator output factors were compared with the treatment planning system (TPS). Good agreement was achieved for dose profiles especially for the region of plateau (< 2%), while larger difference (< 5%) came from the penumbra region. The maximum difference of the calculated output factor was within 0.7%. The model was further validated by a clinical test case. Good agreement was obtained. The DVHs for brainstem and the skull were almost identical and, for the target, the volume covered by the prescription (12.5 Gy to 50% isodose line) was 95.6% from MC calculation versus 100% from the TPS.

On the development of a comprehensive MC simulation model for the Gamma Knife Perfexion radiosurgery unit

This work presents a comprehensive Monte Carlo (MC) simulation model for the Gamma Knife Perfexion (PFX) radiosurgery unit. Model-based dosimetry calculations were benchmarked in terms of relative dose profiles (RDPs) and output factors (OFs), against corresponding EBT2 measurements. To reduce the rather prolonged computational time associated with the comprehensive PFX model MC simulations, two approximations were explored and evaluated on the grounds of dosimetric accuracy. The first consists in directional biasing of the (60)Co photon emission while the second refers to the implementation of simplified source geometric models. The effect of the dose scoring volume dimensions in OF calculations accuracy was also explored. RDP calculations for the comprehensive PFX model were found to be in agreement with corresponding EBT2 measurements. Output factors of 0.819  ±  0.004 and 0.8941  ±  0.0013 were calculated for the 4 mm and 8 mm collimator, respectively, which agree, within uncertainties, with corresponding EBT2 measurements and published experimental data. Volume averaging was found to affect OF results by more than 0.3% for scoring volume radii greater than 0.5 mm and 1.4 mm for the 4 mm and 8 mm collimators, respectively. Directional biasing of photon emission resulted in a time efficiency gain factor of up to 210 with respect to the isotropic photon emission. Although no considerable effect on relative dose profiles was detected, directional biasing led to OF overestimations which were more pronounced for the 4 mm collimator and increased with decreasing emission cone half-angle, reaching up to 6% for a 5° angle. Implementation of simplified source models revealed that omitting the sources' stainless steel capsule significantly affects both OF results and relative dose profiles, while the aluminum-based bushing did not exhibit considerable dosimetric effect. In conclusion, the results of this work suggest that any PFX simulation model should be benchmarked in terms of both RDP and OF results.

A simple method to prolong the service life of radioactive sources for external radiotherapy

A radioactive source is usually replaced and disposed after being used for a certain amount of time (usually a half‐life). In this study, a simple method is proposed to prolong its service life. Instead of replacing the used source with a new source of full activity, a new source of less activity is added in the source holder in front of the used one, so that the total activity of two sources is equal to the initial activity of the used source or even higher. Similarly, more sources can be added to the previous ones. Attenuation of front source(s) to the back source(s) was evaluated with exponential attenuation equation, and variation of source‐focus distance (SFD) with inverse square law for Leksell 4C Gamma Knife, which served as an example of external radiotherapy units. When the number of front sources increased from 1 to 3, the relative air kerma decreased from 36.5% to 5.0%. Both the attenuation effect and SFD variation contributed to the decrease in air kerma, with the former being the major factor. If the height of the source can be decreased in some way, such as increasing the specific activity of sources, the sources can be used more efficiently. The method prolongs the service life of sources by several factors, and reduces the expense of source exchange and reclamation.

PACS number: 87.56.bg

Study of a spherical phantom for Gamma knife dosimetry

Four 16 cm diameter spherical phantoms were modeled in this study: a homogenous water phantom, and three water phantoms with 1 cm thick shell each made of different materials (PMMA, Plastic Water™ and polystyrene). The PENELOPE Monte Carlo code was utilized to simulate photon beams from the Leksell Gamma Knife (LGK) unit and to determine absorbed dose to water (Dw) from a single 18 mm beam delivered to each phantom. A score spherical volume of 0.007 cm³ was used to simulate the dimensions of the sensitive volume of the Exradin A‐16 ionization chamber, in the center of the phantom. In conclusion, the PMMA shell filled with water required a small correction for the determination of the absorbed dose, while remaining within the statistical uncertainty of the calculations (±0.71). Plastic Water™ and polystyrene shells can be used without correction. There is a potential advantage to measuring the 4 mm helmet output using these spherical water phantoms.

PACS numbers: 87.10.Rt, 87.50.cm

Differential dose volume histograms of Gamma knife in the presence of inhomogeneities using MRI-polymer gel dosimetry and MC simulation

Polymer gel dosimeters offer a practical solution to 3D dose verification for conventional radiotherapy as well as intensity-modulated and stereotactic radiotherapy. In this study, EGSnrc calculated and PAGAT polymer gel dosimeter measured dose volume histograms (DVHs) for single-shot irradiations of the Gamma Knife (GK) unit were used to investigate the effects of the presence of inhomogeneities on 3D dose distribution. The head phantom was a custom-built 16 cm diameter Plexiglas sphere. Inside the phantom, there is a cubic cutout for inserting the gel vials and another cutout for inserting the inhomogeneities. Following irradiation with the GK unit, the polymer gel phantoms were scanned with a 1.5 T MRI scanner. Comparing the results of measurement in homogeneous and heterogeneous phantoms revealed that inserting inhomogeneities inside the homogeneous phantom did not cause considerable disturbances on dose distribution in irradiation with 8 mm collimator within low isodose levels (< 50%), which is essential for the dose sparing of sensitive structures. The results of simulation for homogeneous and inhomogeneous phantoms in irradiation with 18 mm collimator of the GK unit showed 23.24% difference in DVH within 90%-100% relative isodose level and also revealed that a significant part of the target (28.56%) received relative doses higher than the maximum dose, which exceeds the acceptance criterion (5%). Based on these results it is concluded that the presence of inhomogeneities inside the phantom can cause considerable errors in dose calculation within high isodose levels with respect to LGP prediction which assumes that the target is a homogeneous material. Moreover, it is demonstrated that the applied MC code is an accurate and stand-alone tool for 3D evaluation of dose distribution in irradiation with the GK unit, which can provide important, 3D plan evaluation criteria used in clinical practice.

MCNP-based computational model for the Leksell Gamma Knife

We have focused on the usage of MCNP code for calculation of Gamma Knife radiation field parameters with a homogenous polystyrene phantom. We have investigated several parameters of the Leksell Gamma Knife radiation field and compared the results with other studies based on EGS4 and PENELOPE code as well as the Leksell Gamma Knife treatment planning system Leksell GammaPlan (LGP). The current model describes all 201 radiation beams together and simulates all the sources in the same time. Within each beam, it considers the technical construction of the source, the source holder, collimator system, the spherical phantom, and surrounding material. We have calculated output factors for various sizes of scoring volumes, relative dose distributions along basic planes including linear dose profiles, integral doses in various volumes, and differential dose volume histograms. All the parameters have been calculated for each collimator size and for the isocentric configuration of the phantom. We have found the calculated output factors to be in agreement with other authors' works except the case of 4 mm collimator size, where averaging over the scoring volume and statistical uncertainties strongly influences the calculated results. In general, all the results are dependent on the choice of the scoring volume. The calculated linear dose profiles and relative dose distributions also match independent studies and the Leksell GammaPlan, but care must be taken about the fluctuations within the plateau, which can influence the normalization, and accuracy in determining the isocenter position, which is important for comparing different dose profiles. The calculated differential dose volume histograms and integral doses have been compared with data provided by the Leksell GammaPlan. The dose volume histograms are in good agreement as well as integral doses calculated in small calculation matrix volumes. However, deviations in integral doses up to 50% can be observed for large volumes such as for the total skull volume. The differences observed in treatment of scattered radiation between the MC method and the LGP may be important in this case. We have also studied the influence of differential direction sampling of primary photons and have found that, due to the anisotropic sampling, doses around the isocenter deviate from each other by up to 6%. With caution about the details of the calculation settings, it is possible to employ the MCNP Monte Carlo code for independent verification of the Leksell Gamma Knife radiation field properties.

Study of scattered photons from the collimator system of Leksell Gamma Knife using the EGS4 Monte Carlo Code

In the algorithm of Leksell GAMMAPLAN (the treatment planning software of Leksell Gamma Knife), scattered photons from the collimator system are presumed to have negligible effects on the Gamma Knife dosimetry. In this study, we used the EGS4 Monte Carlo (MC) technique to study the scattered photons coming out of the single beam channel of Leksell Gamma Knife. The PRESTA (Parameter Reduced Electron-Step Transport Algorithm) version of the EGS4 (Electron Gamma Shower version 4) MC computer code was employed. We simulated the single beam channel of Leksell Gamma Knife with the full geometry. Primary photons were sampled from within the 60Co source and radiated isotropically in a solid angle of 4pi. The percentages of scattered photons within all photons reaching the phantom space using different collimators were calculated with an average value of 15%. However, this significant amount of scattered photons contributes negligible effects to single beam dose profiles for different collimators. Output spectra were calculated for the four different collimators. To increase the efficiency of simulation by decreasing the semiaperture angle of the beam channel or the solid angle of the initial directions of primary photons will underestimate the scattered component of the photon fluence. The generated backscattered photons from within the 60Co source and the beam channel also contribute to the output spectra.

Effects of bone- and air-tissue inhomogeneities on the dose distributions of the Leksell Gamma Knife® calculated with PENELOPE

Monte Carlo simulation with PENELOPE (version 2003) is applied to calculate Leksell Gamma Knife dose distributions for heterogeneous phantoms. The usual spherical water phantom is modified with a spherical bone shell simulating the skull and an air-filled cube simulating the frontal or maxillary sinuses. Different simulations of the 201 source configuration of the Gamma Knife have been carried out with a simplified model of the geometry of the source channel of the Gamma Knife recently tested for both single source and multisource configurations. The dose distributions determined for heterogeneous phantoms including the bone- and/or air-tissue interfaces show non-negligible differences with respect to those calculated for a homogeneous one, mainly when the Gamma Knife isocentre approaches the separation surfaces. Our findings confirm an important underdosage (approximately 10%) nearby the air-tissue interface, in accordance with previous results obtained with the PENELOPE code with a procedure different from ours. On the other hand, the presence of the spherical shell simulating the skull produces a few per cent underdosage at the isocentre wherever it is situated.

Monte Carlo simulation of the Leksell Gamma Knife®: II. Effects of heterogeneous versus homogeneous media for stereotactic radiosurgery

The absence of electronic equilibrium in the vicinity of bone-tissue or air-tissue heterogeneity in the head can misrepresent deposited dose with treatment planning algorithms that assume all treatment volume as homogeneous media. In this paper, Monte Carlo simulation (PENELOPE) and measurements with a specially designed heterogeneous phantom were applied to investigate the effect of air-tissue and bone-tissue heterogeneity on dose perturbation with the Leksell Gamma Knife. The dose fall-off near the air-tissue interface caused by secondary electron disequilibrium leads to overestimation of dose by the vendor supplied treatment planning software (GammaPlan) at up to 4 mm from an interface. The dose delivered to the target area away from an air-tissue interface may be underestimated by up to 7% by GammaPlan due to overestimation of attenuation of photon beams passing through air cavities. While the underdosing near the air-tissue interface cannot be eliminated with any plug pattern, the overdosage due to under-attenuation of the photon beams in air cavities can be eliminated by plugging the sources whose beams intersect the air cavity. Little perturbation was observed next to bone-tissue interfaces. Monte Carlo results were confirmed by measurements. This study shows that the employed Monte Carlo treatment planning is more accurate for precise dosimetry of stereotactic radiosurgery with the Leksell Gamma Knife for targets in the vicinity of air-filled cavities.

A simplified model of the source channel of the Leksell Gamma Knife®: testing multisource configurations with PENELOPE

A simplification of the source channel geometry of the Leksell Gamma Knife (GK), recently proposed by the authors and checked for a single source configuration (Al-Dweri F M O, Lallena A M and Vilches M 2004 Phys. Med. Biol. 49 2687-703), has been used to calculate the dose distributions along the x, y and z axes in a water phantom with a diameter of 160 mm, for different configurations of the Gamma Knife, including 201, 150 and 102 unplugged sources. The code PENELOPE (v. 2001) has been used to perform the Monte Carlo simulations. In addition, the output factors for the 14, 8 and 4 mm helmets have been calculated. The results found for the dose profiles show a qualitatively good agreement with previous ones obtained with EGS4 and PENELOPE (v. 2000) codes and with the predictions of GammaPlan. The output factors obtained with our model agree within the statistical uncertainties with those calculated with the same Monte Carlo codes and with those measured with different techniques. Owing to the accuracy of the results obtained and to the reduction in the computational time with respect to full geometry simulations (larger than a factor 15), this simplified model opens the possibility of using Monte Carlo tools for planning purposes in the Gamma Knife.