Monte Carlo simulation of the Leksell Gamma Knife: I. Source modelling and calculations in homogeneous media

Monte-Carlo techniques for radiotherapy applications I: introduction and overview of the different Monte-Carlo codes

Introduction:

The dose calculation plays a crucial role in many aspects of contemporary clinical radiotherapy treatment planning process. It therefore goes without saying that the accuracy of the dose calculation is of very high importance. The gold standard for absorbed dose calculation is the Monte-Carlo algorithm.

Methods:

This first of two papers gives an overview of the main openly available and supported codes that have been widely used for radiotherapy simulations.

Results:

The paper aims to provide an overview of Monte-Carlo in the field of radiotherapy and point the reader in the right direction of work that could help them get started or develop their existing understanding and use of Monte-Carlo algorithms in their practice.

Conclusions:

It also serves as a useful companion to a curated collection of papers on Monte-Carlo that have been published in this journal.

Monte-Carlo techniques for radiotherapy applications II: equipment and source modelling, dose calculations and radiobiology

Introduction:

This is the second of two papers giving an overview of the use of Monte-Carlo techniques for radiotherapy applications.

Methods:

The first paper gave an introduction and introduced some of the codes that are available to the user wishing to model the different aspects of radiotherapy treatment. It also aims to serve as a useful companion to a curated collection of papers on Monte-Carlo that have been published in this journal.

Results and Conclusions:

This paper focuses on the application of Monte-Carlo to specific problems in radiotherapy. These include radiotherapy and imaging beam production, brachytherapy, phantom and patient dosimetry, detector modelling and track structure calculations for micro-dosimetry, nano-dosimetry and radiobiology.

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.

Early Monitoring Response to Therapy in Patients with Brain Lesions Using the Cumulative SUV Histogram

Gamma Knife treatment is an alternative to traditional brain surgery and whole-brain radiation therapy for treating cancers that are inaccessible via conventional treatments. To assess the effectiveness of Gamma Knife treatments, functional imaging can play a crucial role. The aim of this study is to evaluate new prognostic indices to perform an early assessment of treatment response to therapy using positron emission tomography imaging. The parameters currently used in nuclear medicine assessments can be affected by statistical fluctuation errors and/or cannot provide information on tumor extension and heterogeneity. To overcome these limitations, the Cumulative standardized uptake value (SUV) Histogram (CSH) and Area Under the Curve (AUC) indices were evaluated to obtain additional information on treatment response. For this purpose, the absolute level of [11C]-Methionine (MET) uptake was measured and its heterogeneity distribution within lesions was evaluated by calculating the CSH and AUC indices. CSH and AUC parameters show good agreement with patient outcomes after Gamma Knife treatments. Furthermore, no relevant correlations were found between CSH and AUC indices and those usually used in the nuclear medicine environment. CSH and AUC indices could be a useful tool for assessing patient responses to therapy.

Monte Carlo Dose Calculation Using MRI Based Synthetic CT Generated by Fully Convolutional Neural Network for Gamma Knife Radiosurgery

The aim of this work is to study the dosimetric effect from generated synthetic computed tomography (sCT) from magnetic resonance (MR) images using a deep learning algorithm for Gamma Knife (GK) stereotactic radiosurgery (SRS). The Monte Carlo (MC) method is used for dose calculations. Thirty patients were retrospectively selected with our institution IRB's approval. All patients were treated with GK SRS based on T1-weighted MR images and also underwent conventional external beam treatment with a CT scan. Image datasets were preprocessed with registration and were normalized to obtain similar intensity for the pairs of MR and CT images. A deep convolutional neural network arranged in an encoder-decoder fashion was used to learn the direct mapping from MR to the corresponding CT. A number of metrics including the voxel-wise mean error (ME) and mean absolute error (MAE) were used for evaluating the difference between generated sCT and the true CT. To study the dosimetric accuracy, MC simulations were performed based on the true CT and sCT using the same treatment parameters. The method produced an MAE of 86.6 ± 34.1 Hundsfield units (HU) and a mean squared error (MSE) of 160.9 ± 32.8. The mean Dice similarity coefficient was 0.82 ± 0.05 for HU > 200. The difference for dose-volume parameter D95 between the ground true dose and the dose calculated with sCT was 1.1% if a synthetic CT-to-density table was used, and 4.9% compared with the calculations based on the water-brain phantom.

Monte carlo model and output factors of elekta infinity™ 6 and 10 MV photon beam

Aim

This study aimed to commission the Elekta Infinity™ working in 6 and 10 MV photon beam installed in Concord International Hospital, Singapore, and compare the OFs between MC simulation and measurement using PTW semiflex and microDiamond detector for small field sizes.

Material and Methods

There are two main steps in this study: modelling of Linac 6 and 10 MV photon beam and analysis of the output factors for field size 2 × 2-10 × 10 cm². The EGSnrc/BEAMnrc-DOSXYZnrc code was used to model and characterize the Linac and to calculate the dose distributions in a water phantom. The dose distribution and OFs were compared to the measurement data in the same condition.

Results

The commissioning process was only conducted for a 10 × 10 cm² field size. The PDD obtained from MC simulation showed a good agreement with the measurement. The local dose difference of PDDs was less than 2% for 6 and 10 MV. The initial electron energy was 5.2 and 9.4 MeV for 6 and 10 MV photon beam, respectively. This Linac model can be used for dose calculation in other situations and different field sizes because this Linac has been commissioned and validated using Monte Carlo simulation. The 10 MV Linac produces higher electron contamination than that of 6 MV.

Conclusions

The Linac model in this study was acceptable. The most important result in this work comes from OFs resulted from MC calculation. This value was more significant than the OFs from measurement using semiflex and microDiamond for all beam energy and field sizes because of the CPE phenomenon.

Beam penumbra reduction of Gamma Knife machine model 4C using Monte Carlo simulation

BACKGROUND AND OBJECTIVE

In small radiation fields used in stereotactic radiosurgery penumbra is an important portion of the field size especially when critical organs at risk are located near the treatment sites. This study was aimed to reduce penumbra width (90%-50% isodose lines) of Gamma Knife (GK) machine by investigating of source to diaphragm distance (SDD) and designing compensating filter.

METHODS

Compensating filters at the end of the helmet collimators with the aim of reducing penumbra as well as reducing hot spots appeared near the edge of beam were modeled using Monte Carlo simulation code. Moreover, the SDD parameter was increased as one of the effective factors on penumbra width.

RESULTS

Results showed that single beam penumbra width using optimal design of filters was decreased by 59.49%, 42.50%, 39.02% and 34.44% with attenuation of 30.53%, 13.67%, 11.43% and 9.82% for 4, 8, 14 and 18 mm field sizes, respectively.

CONCLUSIONS

The designed filters lead to considerable reductions in single beams penumbra width as well as a noticeable reduction in maximum dose emerged near the beam edge due to the curved lateral surface of filters.

Estimation of technical treatment accuracy in fractionated stereotactic radiosurgery

Aim:

The purpose of this study was to estimate technical treatment accuracy in fractionated stereotactic radiosurgery (fSRS) using the Extend™ system (ES) of Gamma Knife (GK).

Methods and materials:

The fSRS with GK relies on a re-locatable ES where the reference treatment position is estimated using repositioning check tool (RCT). A patient surveillance unit (PSU) monitors the head and neck movement of the patient during treatment and imaging. The quality assurance test of RCT was performed to evaluate a standard error (SE) associated with a measurement tool called digital probe. A ‘4-mm collimator shot’ dose plan for a head–neck phantom was investigated using EBT3 films. CT and MR distortion measurement studies were combined to evaluate SEimaging. The combined uncertainty from all measurements was evaluated using statistical methods, and the resultant treatment accuracy was investigated for the ES.

Results:

Four sets of RCT measurements and 20 observations of associated digital probe showed SERCT of ±0·0186 mm and SEdigital probe of ±0·0002 mm. The mean positional shift of 0·2752 mm (σ = 0·0696 mm) was observed for 20 treatment settings of the phantom. The differences between radiological and predefined isocentres were 0·4650 and 0·4270 mm for two independent experiments. SEimaging and SEdiode  tool were evaluated as ±0·1055 and ±0·0096 mm, respectively. An expanded uncertainty of ±0·2371 mm (at 95% confidence level) was observed with our system.

Conclusions:

The combined result of the positional shift and expanded uncertainty showed close agreement with film investigations.

Dosimetric evaluation of the Leksell GammaPlan™ Convolution dose calculation algorithm

The dosimetric accuracy of the Leksell GammaPlan Convolution calculation algorithm was evaluated through comparison with corresponding Monte Carlo (MC) dosimetric results. MC simulations were based on generated sector phase space files for the 4 mm, 8 mm and 16 mm collimator sizes, using a previous comprehensive Gamma Knife Perfexion^™ source model and validated using film dosimetry. Test cases were designed for the evaluation of the Convolution algorithm involving irradiation of homogeneous and inhomogeneous phantom geometries mimicking clinical cases, with radiation fields created using one sector (single sector), all sectors with the same (single shot) or different (composite shot) collimator sizes. Dose calculations using the Convolution algorithm were found to be in excellent agreement (gamma pass rate greater than 98%, applying 1%/1 mm local dose difference and distance agreement criteria), with corresponding MC calculations, indicating the accuracy of the Convolution algorithm in homogeneous and heterogeneous model geometries. While of minor clinical importance, large deviations were observed for the voxels laying inside air media. The calculated beam on times using the Convolution algorithm were found to increase (up to 7%) relative to the TMR 10 algorithm currently used in clinical practice, especially in a test case mimicking a brain metastasis close to the skull, in excellent agreement with corresponding MC calculations.

Penumbra width determination of single beam and 201 beams of Gamma Knife machine model 4C using Monte Carlo simulation

Background

One of the stereotactic radiosurgery techniques is Gamma Knife radiosurgery, in which intracranial lesions that are inaccessible or inappropriate for surgery are treated using 201 cobalt-60 sources in one treatment session. In this conformal technique, the penumbra width, which results in out-of-field dose in tumour-adjacent normal tissues should be determined accurately. The aim of this study is to calculate the penumbra widths of single and 201 beams for different collimator sizes of Gamma Knife machine model 4C using EGSnrc/BEAMnrc Monte Carlo simulation code and comparison the results with EBT3 film dosimetry data.

Methods and materials

In this study, simulation of Gamma Knife machine model 4C was performed based on the Monte Carlo codes of EGSnrc/BEAMnrc. To investigate the physical penumbra width (80−20%), the single beam and 201 beams profiles were obtained using EGSnrc/DOSXYZnrc code and EBT3 films located at isocentre point in a spherical Plexiglas head phantom.

Results

Based on the results, the single beam penumbra widths obtained from simulation data for 4, 8, 14 and 18 mm collimator sizes alongXaxis were 0·75, 0·77, 0·90 and 0·92 mm, respectively. The data for 201 beams obtained from simulation were 2·61, 4·80, 7·92 and 9·81 mm alongXaxis and 1·31, 1·60, 1·91 and 2·14 mm alongZaxis and from film dosimetry were 3·21, 4·90, 8·00 and 10·61 mm alongXaxis and 1·22, 1·69, 2·01 and 2·25 mm alongZaxis, respectively.

Conclusion

The differences between measured and simulated penumbra widths are in an acceptable range. However, for more precise measurement in the penumbra region in which dose gradient is high, Monte Carlo simulation is recommended.

Independent dose validation system for Gamma Knife radiosurgery, using a DICOM-RT interface and Geant4

Leksell GammaPlan was specifically designed for Gamma Knife (GK) radiosurgery planning, but it has limited accuracy for estimating the dose distribution in inhomogeneous areas, such as the embolization of arteriovenous malformations. We aimed to develop an independent patient dose validation system based on a patient-specific model, constructed using a DICOM-RT interface and the Geant4 toolkit. Leksell Gamma Knife Perfexion was designed in Geant4.10.00 and includes a DICOM-RT interface. Output factors for each collimator in a sector and dose distributions in a spherical water phantom calculated using a Monte Carlo (MC) algorithm were compared with the output factors calculated by the tissue maximum ratio (TMR) 10 algorithm and dose distributions measured using film, respectively. Studies using two types of water phantom and two patient simulation cases were evaluated by comparing the dose distributions calculated by the MC, the TMR and the convolution algorithms. The water phantom studies showed that if the beam size is small and the target is located in heterogeneous media, the dose difference could be up to 11%. In the two patient simulations, the TMR algorithm overestimated the dose by about 4% of the maximum dose if a complex and large bony structure was located on the beam path, whereas the convolution algorithm showed similar results to those of the MC algorithm. This study demonstrated that the in-house system could accurately verify the patient dose based on full MC simulation and so would be useful for patient cases where the dose differences are suspected.

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.

A fully automatic approach for multimodal PET and MR image segmentation in gamma knife treatment planning

BACKGROUND AND OBJECTIVES

Nowadays, clinical practice in Gamma Knife treatments is generally based on MRI anatomical information alone. However, the joint use of MRI and PET images can be useful for considering both anatomical and metabolic information about the lesion to be treated. In this paper we present a co-segmentation method to integrate the segmented Biological Target Volume (BTV), using [¹¹C]-Methionine-PET (MET-PET) images, and the segmented Gross Target Volume (GTV), on the respective co-registered MR images. The resulting volume gives enhanced brain tumor information to be used in stereotactic neuro-radiosurgery treatment planning. GTV often does not match entirely with BTV, which provides metabolic information about brain lesions. For this reason, PET imaging is valuable and it could be used to provide complementary information useful for treatment planning. In this way, BTV can be used to modify GTV, enhancing Clinical Target Volume (CTV) delineation.

METHODS

A novel fully automatic multimodal PET/MRI segmentation method for Leksell Gamma Knife^® treatments is proposed. This approach improves and combines two computer-assisted and operator-independent single modality methods, previously developed and validated, to segment BTV and GTV from PET and MR images, respectively. In addition, the GTV is utilized to combine the superior contrast of PET images with the higher spatial resolution of MRI, obtaining a new BTV, called BTV_MRI. A total of 19 brain metastatic tumors, undergone stereotactic neuro-radiosurgery, were retrospectively analyzed. A framework for the evaluation of multimodal PET/MRI segmentation is also presented. Overlap-based and spatial distance-based metrics were considered to quantify similarity concerning PET and MRI segmentation approaches. Statistics was also included to measure correlation among the different segmentation processes. Since it is not possible to define a gold-standard CTV according to both MRI and PET images without treatment response assessment, the feasibility and the clinical value of BTV integration in Gamma Knife treatment planning were considered. Therefore, a qualitative evaluation was carried out by three experienced clinicians.

RESULTS

The achieved experimental results showed that GTV and BTV segmentations are statistically correlated (Spearman's rank correlation coefficient: 0.898) but they have low similarity degree (average Dice Similarity Coefficient: 61.87 ± 14.64). Therefore, volume measurements as well as evaluation metrics values demonstrated that MRI and PET convey different but complementary imaging information. GTV and BTV could be combined to enhance treatment planning. In more than 50% of cases the CTV was strongly or moderately conditioned by metabolic imaging. Especially, BTV_MRI enhanced the CTV more accurately than BTV in 25% of cases.

CONCLUSIONS

The proposed fully automatic multimodal PET/MRI segmentation method is a valid operator-independent methodology helping the clinicians to define a CTV that includes both metabolic and morphologic information. BTV_MRI and GTV should be considered for a comprehensive treatment planning.

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.

MAGAT gel and EBT2 film-based dosimetry for evaluating source plugging-based treatment plan in Gamma Knife stereotactic radiosurgery

This work illustrates a procedure to assess the overall accuracy associated with Gamma Knife treatment planning using plugging. The main role of source plugging or blocking is to create dose falloff in the junction between a target and a critical structure. We report the use of MAGAT gel dosimeter for verification of an experimental treatment plan based on plugging. The polymer gel contained in a head‐sized glass container simulated all major aspects of the treatment process of Gamma Knife radiosurgery. The 3D dose distribution recorded in the gel dosimeter was read using a 1.5T MRI scanner. Scanning protocol was: CPMG pulse sequence with 8 equidistant echoes, TR=7 s, echo step=14 ms, pixel size=0.5 mm x 0.5 mm, and slice thickness of 2 mm. Using a calibration relationship between absorbed dose and spin‐spin relaxation rate (R2), we converted R2 images to dose images. Volumetric dose comparison between treatment planning system (TPS) and gel measurement was accomplished using an in‐house MATLAB‐based program. The isodose overlay of the measured and computed dose distribution on axial planes was in close agreement. Gamma index analysis of 3D data showed more than 94% voxel pass rate for different tolerance criteria of 3%/2 mm, 3%/1 mm and 2%/2 mm. Film dosimetry with GAFCHROMIC EBT 2 film was also performed to compare the results with the calculated TPS dose. Gamma index analysis of film measurement for the same tolerance criteria used for gel measurement evaluation showed more than 95% voxel pass rate. Verification of gamma plan calculated dose on account of shield is not part of acceptance testing of Leksell Gamma Knife (LGK). Through this study we accomplished a volumetric comparison of dose distributions measured with a polymer gel dosimeter and Leksell GammaPlan (LGP) calculations for plans using plugging. We propose gel dosimeter as a quality assurance (QA) tool for verification of plug‐based planning.

PACS number: 87.53.Ly, 87.55.‐x, 87.56.N‐

FLUKA Monte Carlo simulation for the Leksell Gamma Knife Perfexion radiosurgery system: homogeneous media

The purpose of this work is to investigate the capability of the FLUKA Monte Carlo (MC) code to simulate the Elekta Leksell Gamma Knife Perfexion (LGK-PFX) and reproduce the Treatment Planning System (TPS) Leksell GammaPlan version 8.2 (LGP) dose calculations for the case of a water equivalent phantom target. Thanks to the collaboration with Elekta Instruments AB, the collimation system geometry, the source positions and all the involved material have been simulated in detail. The relative linear dose distribution along the three coordinate axes, for each collimator size, and the Relative Output Factors (ROF) have been investigated. The simulation has been validated comparing simulated linear dose profiles with measurements performed with EBT radiochromic films. The acceptance criterion between experimental data and FLUKA results is based on the gamma index (GI) method. The FLUKA MC calculation for the ROF provided the values of 0.920 for the 8 mm collimators and 0.800 for the 4 mm collimators. These values are in good agreement with the Elekta reference data of 0.924 and 0.805 respectively. The percentage difference between calculated and reference values for the ROF is under 1% and within the FLUKA uncertainty. Also the simulated relative dose profiles show a good agreement with the LGP calculation expressed by means of the gamma index method. This established accuracy proves that FLUKA is a suitable and powerful tool in order to reproduce successfully the LGP calculations for the homogeneous media.

A contemporary review of stereotactic radiotherapy: inherent dosimetric complexities and the potential for detriment

OBJECTIVE

The advantages of highly localised, conformal treatments achievable with stereotactic radiotherapy (SRT) are increasingly being extended to extracranial sites as stereotactic body radiotherapy with advancements in imaging and beam collimation. One of the challenges in stereotactic treatment lies in the significant complexities associated with small field dosimetry and dose calculation. This review provides a comprehensive overview of the complexities associated with stereotactic radiotherapy and the potential for detriment.

METHODS

This study is based on a comprehensive review of literature accessible via PubMed and other sources, covering stereotactic radiotherapy, small-field dosimetry and dose calculation.

FINDINGS

Several key issues were identified in the literature. They pertain to dose prescription, dose measurement and dose calculation within and beyond the treatment field. Field-edge regions and penumbrae occupy a significant portion of the total field size. Spectral and dosimetric characteristics are difficult to determine and are compounded by effects of tissue inhomogeneity. Measurement of small-fields is made difficult by detector volume averaging and energy response. Available dosimeters are compared, and emphasis is given to gel dosimetry which offers the greatest potential for three-dimensional small-field dosimetry. The limitations of treatment planning system algorithms as applied to small-fields (particularly in the presence of heterogeneities) is explained, and a review of Monte Carlo dose calculation is provided, including simplified treatment planning implementations. Not incorporated into treatment planning, there is evidence that far from the primary field, doses to patients (and corresponding risks of radiocarcinogenesis) from leakage/scatter in SRT are similar to large fields.

CONCLUSIONS

Improved knowledge of dosimetric issues is essential to the accurate measurement and calculation of dose as well as the interpretation and assessment of planned and delivered treatments. This review highlights such issues and the potential benefit that may be gained from Monte Carlo dose calculation and verification via three-dimensional dosimetric methods (such as gel dosimetry) being introduced into routine clinical practice.

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.

Measurement of relative output factors for the 8 and 4 mm collimators of Leksell Gamma Knife Perfexion by film dosimetry

Three types of films, Kodak EDR2, Gafchromic EBT, and Gafchromic MD-V2-55, were used to measure relative output factors of 4 and 8 mm collimators of the Leksell Gamma Knife Perfexion. The optical density to dose calibration curve for each of the film types was obtained by exposing the films to a range of known doses. Ten data points were acquired for each of the calibration curves in the dose ranges from 0 to 4 Gy, 0 to 8 Gy, and 0 to 80 Gy for Kodak EDR2, Gafchromic EBT, and Gafchromic MD-V2-55 films, respectively. For the measurement of relative output factors, five films of each film type were exposed to a known dose. All films were scanned using EPSON EXPRESSION 10000 XL scanner with 200 dpi resolution in 16 bit gray scale for EDR2 film and 48 bit color scale for Gafchromic films. The scanned images were imported in the red channel for both Gafchromic films. The background corrections from an unexposed film were applied to all films. The output factors obtained from film measurements were in a close agreement both with the Monte Carlo calculated values of 0.924 and 0.805 for 8 and 4 mm collimators, respectively. These values are provided by the vendor and used as default values in the vendor's treatment planning system. The largest differences were noted for the Kodak EDR 2 films (-2.1% and -4.5% for 8 and 4 mm collimators, respectively). The best agreement observed was for EBT Gafchromic film (-0.8% and +0.6% differences for 8 and 4 mm collimators, respectively). Based on the present values, no changes in the default relative output factor values were made in the treatment planning system.

Analytical description of dose profile behaviour in Gamma Knife radiosurgery

Stereotactic Gamma Knife radiosurgery utilizes ionizing beams from (60)Co sources and relies on a combination of collimator sizes, weighting, etc to generate a high-dose region that is conformal with a designated target volume. Dose computation is typically performed by computer, but in this paper, single collimator dose profile behaviour is modelled analytically and then extended to accommodate multiple collimators of different weights with co-located isocentres. The dose profile from a single helmet is derived from a top-hat beam profile approximation and an idealized symmetric distribution of sources is used to represent the 201 sources within a collimating helmet. The results from the analysis are validated by an independent numerical model and also compared with those obtained by other groups using numerical and experimental methods. With respect to multiple collimators, the relationship between the size (full width half maximum) of the irradiated volume and relative collimator weighting is also examined using the simple analytical model. The simplicity of the mathematics clarifies the relationship between beam profile, dose profile and multiple collimator behaviour, and provides data that compare favourably with published literature.

Characterization of the radiation quality of60Co therapy units by the fraction of air kerma attributable to scattered photons

In this work we present a new parameter for characterizing the emitted photon spectra of (60)Co radiotherapy units. It is intended to propose this parameter for the revised DIN standard 6809-1. In the previous DIN regulation, it had been sufficient to state the nature of the radioactive material within the source. However, scatter processes within the radioactive material as well as the source housing and the collimator system influence the shape of the photon spectrum, with a noticeable contribution in the low-energy portion. The fraction of the air kerma for a given distance from the source, position and beam size in air comprising all contributions by scattered photons up to an upper energy limit for the emitted spectrum from (60)Co decay, will be proposed as a typical parameter. The new quantity, which is termed the 'fraction of air kerma attributable to scattered photons', P(E)(Scatter), has been calculated for E = 1.17 MeV and compared for four different Monte Carlo-simulated spectra of used (60)Co devices. Not included in this new formalism is the air kerma contribution by scattered photons in between the two lines of the (60)Co spectrum. A simple measurement procedure based on the signal ratio of two Farmer chamber detectors with different wall materials is discussed and its feasibility shown.

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.

Evaluation of dose delivery accuracy of Gamma Knife by polymer gel dosimetry

The BANG™ polymer gel dosimeter was used to evaluate 3D absorbed dose distributions in tissue delivered with Gamma Knife stereotactic radiosurgery systems. We compared dose distributions calculated with Leksell GammaPlan (LGP) treatment‐planning software with dose distributions measured with the polymer gel dosimeter for single‐shot irradiations. Head‐sized spherical glass vessels filled with the polymer gel were irradiated with Gamma Knife. The phantoms were scanned with a 1.0T MRI scanner. The Hahn spin‐echo sequence with two echoes was used for the MRI scans. Calibration relations between the spin‐spin relaxation rate and the absorbed dose were obtained by using small cylindrical vials, which were filled with the polymer gel from the same batch as for the spherical phantom. We made voxel‐by‐voxel comparisons of measured and calculated dose distributions for 31×31×31 dose matrix elements. With the 3D dose data we calculated the tumor control probability (TCP) and normal tissue complication probability (NTCP) for a simple model. For the maximum dose of 100 Gy, the mean and one standard deviation of differences between the measured and the calculated doses were the following: –0.38±4.63 Gy,1.49±2.77 Gy, and –1.03±4.18 Gy for 8‐mm, 14‐mm, and 18‐mm collimators, respectively. Tumor control probability values for measurements were smaller than the calculations by 0% to 7%, whereas NTCP values were larger by 7% to 24% for four of six experiments.

PACS numbers: 87.53.‐j, 87.53.Dq, 87.53.Ly

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.

Use of the Leksell Gamma Knife for localized small field lens irradiation in rodents

For most basic radiobiological research applications involving irradiation of small animals, it is difficult to achieve the same high precision dose distribution realized with human radiotherapy. The precision for irradiations performed with standard radiotherapy equipment is +/-2 mm in each dimension, and is adequate for most human treatment applications. For small animals such as rodents, whose organs and tissue structures may be an order of magnitude smaller than those of humans, the corresponding precision required is closer to +/-0.2 mm, if comparisons or extrapolations are to be made to human data. The Leksell Gamma Knife is a high precision radiosurgery irradiator, with precision in each dimension not exceeding 0.5 mm, and overall precision of 0.7 mm. It has recently been utilized to treat ocular melanoma and induce targeted lesions in the brains of small animals. This paper describes the dosimetry and a technique for performing irradiation of a single rat eye and lens with the Gamma Knife while allowing the contralateral eye and lens of the same rat to serve as the "control". The dosimetry was performed with a phantom in vitro utilizing a pinpoint ion chamber and thermoluminescent dosimeters, and verified by Monte Carlo simulations. We found that the contralateral eye received less than 5% of the administered dose for a 15 Gy exposure to the targeted eye. In addition, after 15 Gy irradiation 15 out of 16 animals developed cataracts in the irradiated target eyes, while 0 out of 16 contralateral eyes developed cataracts over a 6-month period of observation. Experiments at 5 and 10 Gy also confirmed the lack of cataractogenesis in the contralateral eye. Our results validate the use of the Gamma Knife for cataract studies in rodents, and confirmed the precision and utility of the instrument as a small animal irradiator for translational radiobiology experiments.

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

Monte Carlo simulations using the code PENELOPE have been performed to test a simplified model of the source channel geometry of the Leksell GammaKnife. The characteristics of the radiation passing through the treatment helmets are analysed in detail. We have found that only primary particles emitted from the source with polar angles smaller than 3 degrees with respect to the beam axis are relevant for the dosimetry of the Gamma Knife. The photon trajectories reaching the output helmet collimators at (x, v, z = 236 mm) show strong correlations between rho = (x2 + y2)(1/2) and their polar angle theta, on one side, and between tan(-1)(y/x) and their azimuthal angle phi, on the other. This enables us to propose a simplified model which treats the full source channel as a mathematical collimator. This simplified model produces doses in good agreement with those found for the full geometry. In the region of maximal dose, the relative differences between both calculations are within 3%, for the 18 and 14 mm helmets, and 10%, for the 8 and 4 mm ones. Besides, the simplified model permits a strong reduction (larger than a factor 15) in the computational time.

Benchmark of PENELOPE code for low-energy photon transport: dose comparisons with MCNP4 and EGS4

The expanding clinical use of low-energy photon emitting 125I and 103Pd seeds in recent years has led to renewed interest in their dosimetric properties. Numerous papers pointed out that higher accuracy could be obtained in Monte Carlo simulations by utilizing newer libraries for the low-energy photon cross-sections, such as XCOM and EPDL97. The recently developed PENELOPE 2001 Monte Carlo code is user friendly and incorporates photon cross-section data from the EPDL97. The code has been verified for clinical dosimetry of high-energy electron and photon beams, but has not yet been tested at low energies. In the present work, we have benchmarked the PENELOPE code for 10-150 keV photons. We computed radial dose distributions from 0 to 10 cm in water at photon energies of 10-150 keV using both PENELOPE and MCNP4C with either DLC-146 or DLC-200 cross-section libraries, assuming a point source located at the centre of a 30 cm diameter and 20 cm length cylinder. Throughout the energy range of simulated photons (except for 10 keV), PENELOPE agreed within statistical uncertainties (at worst +/- 5%) with MCNP/DLC-146 in the entire region of 1-10 cm and with published EGS4 data up to 5 cm. The dose at 1 cm (or dose rate constant) of PENELOPE agreed with MCNP/DLC-146 and EGS4 data within approximately +/- 2% in the range of 20-150 keV, while MCNP/DLC-200 produced values up to 9% lower in the range of 20-100 keV than PENELOPE or the other codes. However, the differences among the four datasets became negligible above 100 keV.

Modelling 6 MV photon beams of a stereotactic radiosurgery system for Monte Carlo treatment planning

The goal of this work is to build a multiple source model to represent the 6 MV photon beams from a Cyberknife stereotactic radiosurgery system for Monte Carlo treatment planning dose calculations. To achieve this goal, the 6 MV photon beams have been characterized and modelled using the EGS4/BEAM Monte Carlo system. A dual source model has been used to reconstruct the particle phase space at a plane immediately above the secondary collimator. The proposed model consists of two circular planar sources for the primary photons and the scattered photons, respectively. The dose contribution of the contaminant electrons was found to be in the order of 10(-3) of the total maximum dose and therefore has been omitted in the source model. Various comparisons have been made to verify the dual source model against the full phase space simulated using the EGS4/BEAM system. The agreement in percent depth dose (PDD) curves and dose profiles between the phase space and the source model was generally within 2%/1 mm for various collimators (5 to 60 mm in diameter) at 80 to 100 cm source-to-surface distances (SSD). Excellent agreement (within 1%/1 mm) was also found between the dose distributions in heterogeneous lung and bone geometry calculated using the original phase space and those calculated using the source model. These results demonstrated the accuracy of the dual source model for Monte Carlo treatment planning dose calculations for the Cyberknife system.

Monte Carlo modelling of external radiotherapy photon beams

An essential requirement for successful radiation therapy is that the discrepancies between dose distributions calculated at the treatment planning stage and those delivered to the patient are minimized. An important component in the treatment planning process is the accurate calculation of dose distributions. The most accurate way to do this is by Monte Carlo calculation of particle transport, first in the geometry of the external or internal source followed by tracking the transport and energy deposition in the tissues of interest. Additionally, Monte Carlo simulations allow one to investigate the influence of source components on beams of a particular type and their contaminant particles. Since the mid 1990s, there has been an enormous increase in Monte Carlo studies dealing specifically with the subject of the present review, i.e., external photon beam Monte Carlo calculations, aided by the advent of new codes and fast computers. The foundations for this work were laid from the late 1970s until the early 1990s. In this paper we will review the progress made in this field over the last 25 years. The review will be focused mainly on Monte Carlo modelling of linear accelerator treatment heads but sections will also be devoted to kilovoltage x-ray units and 60Co teletherapy sources.