Using matrix summation method for three dimensional dose calculation in brachytherapy

AimThe purpose of this study is to calculate radiation dose around a brachytherapy source in a water phantom for different seed locations or rotation the sources by the matrix summation method.BackgroundMonte Carlo based codes like MCNP are widely used for performing radiation transport calculations and dose evaluation in brachytherapy. But for complicated situations, like using more than one source, moving or rotating the source, the routine Monte Carlo method for dose calculation needs a long time running.Materials and methodsThe MCNPX code has been used to calculate radiation dose around a ¹⁹²Ir brachytherapy source and saved in a 3D matrix. Then, we used this matrix to evaluate the absorbed dose in any point due to some sources or a source which shifted or rotated in some places by the matrix summation method.ResultsThree dimensional (3D) dose results and isodose curves were presented for ¹⁹²Ir source in a water cube phantom shifted for 10 steps and rotated for 45 and 90° based on the matrix summation method. Also, we applied this method for some arrays of sources.ConclusionThe matrix summation method can be used for 3D dose calculations for any brachytherapy source which has moved or rotated. This simple method is very fast compared to routine Monte Carlo based methods. In addition, it can be applied for dose optimization study.     

A Monte Carlo study on dose distribution evaluation of Flexisource 192Ir brachytherapy source

Aim

The aim of this study is to evaluate the dose distribution of the Flexisource ¹⁹²Ir source.

Background

Dosimetric evaluation of brachytherapy sources is recommended by task group number 43 (TG. 43) of American Association of Physicists in Medicine (AAPM).

Materials and methods

MCNPX code was used to simulate Flexisource ¹⁹²Ir source. Dose rate constant and radial dose function were obtained for water and soft tissue phantoms and compared with previous data on this source. Furthermore, dose rate along the transverse axis was obtained by simulation of the Flexisource and a point source and the obtained data were compared with those from Flexiplan treatment planning system (TPS).

Results

The values of dose rate constant obtained for water and soft tissue phantoms were equal to 1.108 and 1.106, respectively. The values of the radial dose function are listed in the form of tabulated data. The values of dose rate (cGy/s) obtained are shown in the form of tabulated data and figures. The maximum difference between TPS and Monte Carlo (MC) dose rate values was 11% in a water phantom at 6.0 cm from the source.

Conclusion

Based on dosimetric parameter comparisons with values previously published, the accuracy of our simulation of Flexisource ¹⁹²Ir was verified. The results of dose rate constant and radial dose function in water and soft tissue phantoms were the same for Flexisource and point sources. For Flexisource ¹⁹²Ir source, the results of TPS calculations in a water phantom were in agreement with the simulations within the calculation uncertainties. Furthermore, the results from the TPS calculation for Flexisource and MC calculation for a point source were practically equal within the calculation uncertainties.     

Monte Carlo dose calculation of GZP6 60Co stepping source based on a matrix shift technique

Background

As a routine method for stepping source simulation, a Monte Carlo program is run according to the number of steps and then the summation of dose from each run is taken to obtain total dose distribution. This method is time consuming.

Aim

As an alternative method, a matrix shift based technique was applied to simulate a stepping source for brachytherapy.

Materials and methods

The stepping source of GZP6 brachytherapy unit was simulated. In a matrix shift method, it is assumed that a radiation source is stationary and instead the data matrix is shifted based on the number of steps. In this study, by running MCNPX program for one point and calculation of the dose matrix using the matrix shift method, the isodose curves for the esophageal cancer tumor lengths of 4 and 6 cm were obtained and compared with the isodose curves obtained by running MCNPX programs in each step position separately (15 and 23 steps for esophageal cancer tumor lengths of 4 and 6 cm, respectively).

Results

The difference between the two dose matrixes for the stepping and matrix shift methods based on the average dose differences are 3.85 × 10⁻⁴ Gy and 5.19 × 10⁻⁴ Gy for treatment length of 4 cm and 6 cm, respectively. Dose differences are insignificant and these two methods are equally valid.

Conclusions

The matrix shift method presented in this study can be used for calculation of dose distribution for a brachytherapy stepping source as a quicker tool compared to other routine Monte Carlo based methods.     

A Monte Carlo approach to calculate dose distribution around the lineal brachytherapy sources.

Monte Carlo means the statistical methods used to solve stochastic or deterministic physical or mathematical problems. The use of this technique for solving deterministic problems is indicated whenever there is no analytical solution for the problem or when this solution is very difficult or when the use of numerical methods requires an excessive amount of CPU-time. This paper describes the application of Monte Carlo methods using a computer program, called ISODOSE, which calculates isodose curves around linear radioactive sources to be used in brachytherapy treatment-planning. Brachytherapy is a special form of cancer treatment in which the radioactive source is placed near or inside the tumor, in order to produce cancer tissue necrosis. The program is written in C language, and the results will be compared to similar data obtained from a commercially available program at Hospital do Cancer de Recife (Brazil), radiation therapy institute. The use of Monte Carlo techniques in the ISODOSE program allows for plotting isodose curves around linear sources, and it is especially more precise near the borders of the source (singularities), taking less time than it would be possible by using deterministic methods. The ISODOSE program can be used for brachytherapy planning in small clinics in Recife and adjacent areas.     

Application of Monte Carlo calculations for validation of a treatment planning system in high dose rate brachytherapy

AimThe accuracy of treatment planning systems is of vital importance in treatment outcomes in brachytherapy. In the current study the accuracy of dose calculations of a high dose rate (HDR) brachytherapy treatment planning system (TPS) was validated using the Monte Carlo method.Materials and methodsThree ⁶⁰Co sources of the GZP6 afterloading brachytherapy system were modelled using MCNP4C Monte Carlo (MC) code. The dose distribution around all the sources was calculated by MC and a dedicated treatment planning system. The results of both methods were compared.ResultsThere was good agreement (<2%) between TPS and MC calculated dose distributions except at a point near the sources (<1 cm) and beyond the tip of the sources.ConclusionsOur study confirmed the accuracy of TPS calculated dose distributions for clinical use in HDR brachytherapy.     

A Study on the Dose Distributions in Various Materials from an Ir-192 HDR Brachytherapy Source

Dose distributions of (192)Ir HDR brachytherapy in phantoms simulating water, bone, lung tissue, water-lung and bone-lung interfaces using the Monte Carlo codes EGS4, FLUKA and MCNP4C are reported. Experiments were designed to gather point dose measurements to verify the Monte Carlo results using Gafchromic film, radiophotoluminescent glass dosimeter, solid water, bone, and lung phantom. The results for radial dose functions and anisotropy functions in solid water phantom were consistent with previously reported data (Williamson and Li). The radial dose functions in bone were affected more by depth than those in water. Dose differences between homogeneous solid water phantoms and solid water-lung interfaces ranged from 0.6% to 14.4%. The range between homogeneous bone phantoms and bone-lung interfaces was 4.1% to 15.7%. These results support the understanding in dose distribution differences in water, bone, lung, and their interfaces. Our conclusion is that clinical parameters did not provide dose calculation accuracy for different materials, thus suggesting that dose calculation of HDR treatment planning systems should take into account material density to improve overall treatment quality.     

Detailed analysis of dose difference in using water as tissue-equivalent material in 252Cf brachytherapy

AimThe purpose of this study is to analyse how small variations in the elemental composition of soft tissue lead to differences in dose distributions from a ²⁵²Cf brachytherapy source and to determine the error percentage in using water as a tissue-equivalent material.BackgroundWater is normally used as a tissue-equivalent phantom material in radiotherapy dosimetry.Materials and methodsNeutron energy spectra, neutron and gamma-ray dose rate distributions were calculated for a ²⁵²Cf AT source located at the center of a spherical phantom filled with various types of tissue compositions: adipose, brain, muscle, International Commission on Radiation Units and Measurements (ICRU) report No. 44 9-component soft tissue and water, using Monte Carlo simulation.ResultsThe obtained results showed differences between total dose rates in various tissues relative to water varying between zero and 4.94%. The contributions of neutron and total gamma ray doses to these differences are, on average, 81% and 19%, respectively. It was found that the dose differences between various soft tissues and water depend not only on the soft tissue composition, but also on the beam type emitted from the ²⁵²Cf source and the distance from the source.ConclusionAssuming water as a tissue-equivalent material, although leads to overestimation of dose rate (except in the case of adipose tissue), is acceptable and suitable for use in ²⁵²Cf brachytherapy treatment planning systems based on the recommendation by the ICRU that the uncertainties in dose delivery in radiotherapy should be lower than 5%.     

Radiation protection from external exposure to radionuclides: A Monte Carlo data handbook

The availability of a resource collecting dose factors for the evaluation of the absorbed doses from external exposure during the manipulation of radioactive substances is fundamental for radiological protection purposes. Monte Carlo simulations are useful for the accurate calculation of dose distributions in complex geometries, particularly in presence of extended spectra of multi-radiation sources. We considered, as possible irradiation scenarios, a point source, a uniform planar source resembling a contaminated surface, several source volumes contained in plastic or glass receptacles, and the direct skin contamination case, implementing the corresponding Monte Carlo simulations in GAMOS (GEANT4-based Architecture for Medicine-Oriented Simulations). A set of 50 radionuclides was studied, focusing the attention on those ones mainly used in nuclear medicine, both for diagnostic and therapeutic purposes, in nuclear physics laboratories and for instrument calibration. Skin dose equivalents at 70 μm of depth and deep dose equivalents at 10 mm of depth are reported for different configurations and organized in easy-to-read tables.     

Monte Carlo Dosimetry of the 60Co BEBIG High Dose Rate for Brachytherapy

Introduction

The use of high-dose-rate brachytherapy is currently a widespread practice worldwide. The most common isotope source is ¹⁹²Ir, but ⁶⁰Co is also becoming available for HDR. One of main advantages of ⁶⁰Co compared to ¹⁹²Ir is the economic and practical benefit because of its longer half-live, which is 5.27 years. Recently, Eckert & Ziegler BEBIG, Germany, introduced a new afterloading brachytherapy machine (MultiSource^®); it has the option to use either the ⁶⁰Co or ¹⁹²Ir HDR source. The source for the Monte Carlo calculations is the new ⁶⁰Co source (model Co0.A86), which is referred to as the new BEBIG ⁶⁰Co HDR source and is a modified version of the ⁶⁰Co source (model GK60M21), which is also from BEBIG.

Objective and Methods

The purpose of this work is to obtain the dosimetry parameters in accordance with the AAPM TG-43U1 formalism with Monte Carlo calculations regarding the BEBIG ⁶⁰Co high-dose-rate brachytherapy to investigate the required treatment-planning parameters. The geometric design and material details of the source was provided by the manufacturer and was used to define the Monte Carlo geometry. To validate the source geometry, a few dosimetry parameters had to be calculated according to the AAPM TG-43U1 formalism. The dosimetry studies included the calculation of the air kerma strength S _k, collision kerma in water along the transverse axis with an unbounded phantom, dose rate constant and radial dose function. The Monte Carlo code system that was used was EGSnrc with a new cavity code, which is a part of EGS++ that allows calculating the radial dose function around the source. The spectrum to simulate ⁶⁰Co was composed of two photon energies, 1.17 and 1.33 MeV. Only the gamma part of the spectrum was used; the contribution of the electrons to the dose is negligible because of the full absorption by the stainless-steel wall around the metallic ⁶⁰Co. The XCOM photon cross-section library was used in subsequent simulations, and the photoelectric effect, pair production, Rayleigh scattering and bound Compton scattering were included in the simulation. Variance reduction techniques were used to speed up the calculation and to considerably reduce the computer time. The cut-off energy was 10 keV for electrons and photons. To obtain the dose rate distributions of the source in an unbounded liquid water phantom, the source was immersed at the center of a cube phantom of 100 cm³. The liquid water density was 0.998 g/cm³, and photon histories of up to 10¹⁰ were used to obtain the results with a standard deviation of less than 0.5% (k = 1). The obtained dose rate constant for the BEBIG ⁶⁰Co source was 1.108±0.001 cGyh^-1U^-1, which is consistent with the values in the literature. The radial dose functions were compared with the values of the consensus data set in the literature, and they are consistent with the published data for this energy range.     

A Monte Carlo study on dose distribution validation of GZP6 60Co stepping source

Aim

Stepping source in brachytherapy systems is used to treat a target lesion longer than the effective treatment length of the source. Cancerous lesions in the cervix, esophagus and rectum are examples of such a target lesion.

Background

In this study, the stepping source of a GZP6 afterloading intracavitary brachytherapy unit was simulated using Monte Carlo (MC) simulation and the results were used for the validation of the GZP6 treatment planning system (TPS).

Materials and methods

The stepping source was simulated using MCNPX Monte Carlo code. Dose distributions in the longitudinal plane were obtained by using a matrix shift method for esophageal tumor lengths of 8 and 10 cm. A mesh tally has been employed for the absorbed dose calculation in a cylindrical water phantom. A total of 5 × 10⁸ photon histories were scored and the MC statistical error obtained was at the range of 0.008–3.5%, an average of 0.2%.

Results

The acquired MC and TPS isodose curves were compared and it was shown that the dose distributions in the longitudinal plane were relatively coincidental. In the transverse direction, a maximum dose difference of 7% and 5% was observed for tumor lengths of 8 and 10 cm, respectively.

Conclusion

Considering that the certified source activity is given with ±10% uncertainty, the obtained difference is reasonable. It can be concluded that the accuracy of the dose distributions produced by GZP6 TPS for the stepping source is acceptable for its clinical applications.     

Effect of air cavities on the dose delivered to the lung during high-dose brachytherapy

In the treatment of lung cancer using the radiotherapy technique of intracavitary brachytherapy with an¹⁹²Ir source, the lung is normally assumed to be entirely composed of a homogenous mass of soft tissue. The aim of this study is to investigate whether there is the possibility that the air cavities in the lung influence the dose delivered to the lung at a prescribed distance from the source. The Monte Carlo code MCNP-4A was used to model the dose delivered by both¹⁹²Ir and¹⁹⁸Au as a function of treatment medium, density and composition, photon energy, and distance from the source. The suitability of MCNP-4A for this study was tested by producing depth-dose profiles for photons in water and comparing these to calculated profiles produced using well-documented methods.     

Comparison between beta radiation dose distribution due to LDR and HDR ocular brachytherapy applicators using GATE Monte Carlo platform

Eye applicators with 90Sr/90Y and 106Ru/106Rh beta-ray sources are generally used in brachytherapy for the treatment of eye diseases as uveal melanoma. Whenever, radiation is used in treatment, dosimetry is essential. However, knowledge of the exact dose distribution is a critical decision-making to the outcome of the treatment. The Monte Carlo technique provides a powerful tool for calculation of the dose and dose distributions which helps to predict and determine the doses from different shapes of various types of eye applicators more accurately. The aim of this work consisted in using the Monte Carlo GATE platform to calculate the 3D dose distribution on a mathematical model of the human eye according to international recommendations. Mathematical models were developed for four ophthalmic applicators, two HDR 90Sr applicators SIA.20 and SIA.6, and two LDR 106Ru applicators, a concave CCB model and a flat CCB model. In present work, considering a heterogeneous eye phantom and the chosen tumor, obtained results with the use of GATE for mean doses distributions in a phantom and according to international recommendations show a discrepancy with respect to those specified by the manufacturers. The QC of dosimetric parameters shows that contrarily to the other applicators, the SIA.20 applicator is consistent with recommendations. The GATE platform show that the SIA.20 applicator present better results, namely the dose delivered to critical structures were lower compared to those obtained for the other applicators, and the SIA.6 applicator, simulated with MCNPX generates higher lens doses than those generated by GATE.     

Dosimetric characterization of an 192Ir brachytherapy source with the Monte Carlo code PENELOPE

Monte Carlo calculations are highly spread and settled practice to calculate brachytherapy sources dosimetric parameters. In this study, recommendations of the AAPM TG-43U1 report have been followed to characterize the Varisource VS2000 ¹⁹²Ir high dose rate source, provided by Varian Oncology Systems.In order to obtain dosimetric parameters for this source, Monte Carlo calculations with PENELOPE code have been carried out. TG-43 formalism parameters have been presented, i.e., air kerma strength, dose rate constant, radial dose function and anisotropy function. Besides, a 2D Cartesian coordinates dose rate in water table has been calculated. These quantities are compared to this source reference data, finding results in good agreement with them.The data in the present study complement published data in the next aspects: (i) TG-43U1 recommendations are followed regarding to phantom ambient conditions and to uncertainty analysis, including statistical (type A) and systematic (type B) contributions; (ii) PENELOPE code is benchmarked for this source; (iii) Monte Carlo calculation methodology differs from that usually published in the way to estimate absorbed dose, leaving out the track-length estimator; (iv) the results of the present work comply with the most recent AAPM and ESTRO physics committee recommendations about Monte Carlo techniques, in regards to dose rate uncertainty values and established differences between our results and reference data.The results stated in this paper provide a complete parameter collection, which can be used for dosimetric calculations as well as a means of comparison with other datasets from this source.     

Deterministic model for the transport of energetic particles: Application in the electron radiotherapy

A new deterministic method for calculating the dose distribution in the electron radiotherapy field is presented. The aim of this work was to validate our model by comparing it with the Monte Carlo simulation toolkit, GEANT4. A comparison of the longitudinal and transverse dose deposition profiles and electron distributions in homogeneous water phantoms showed a good accuracy of our model for electron transport, while reducing the calculation time by a factor of 50. Although the Bremsstrahlung effect is not yet implemented in our model, we propose here a method that solves the Boltzmann kinetic equation and provides a viable and efficient alternative to the expensive Monte Carlo modeling.     

Calculation of the 3-D dose distribution surrounding a 103Pd stent

Purpose: This study was designed to assess the suitability of a ¹⁰³Pd-implanted stent for use in intravascular brachytherapy. Materials and methods: A stent was modeled as a superposition of 201 identical struts and the EGS4/DOSRZ Monte Carlo code was used to calculate the dose distribution for each strut. To verify the simulation parameters, doses along the transverse axis of a Model 200 ¹⁰³Pd interstitial seed were calculated and compared to those calculated by the TG43 method. Results: Dose profiles within 1 mm of the stent's outer surface were heterogeneous and reflected the stent's structure. For a 2-mm outer-diameter ¹⁰³Pd-implanted stent, ∼2.68×10⁷ Bq were required to deliver 31.5 Gy in 28 days at a distance of 0.5 mm along the perpendicular bisector from the stent's outer surface. The Monte Carlo simulation of the ¹⁰³Pd seed showed relative doses within 7% of the values calculated by the TG43 method. Conclusion: The dosimetry about a ¹⁰³Pd-implanted stent suggests that the stent is suitable for use in intravascular brachytherapy.     

Dosimetric penumbra effects in catheter-based intravascular brachytherapy using a centered photon or beta line source

Purpose: In catheter-based intravascular brachytherapy, either photon or beta emitters are often used in a linear arrangement so that blood vessels of 10-30 mm lengths can be treated. With a line source, the dose gradient in the radial direction and longitudinal direction depend on the type of radionuclides used in the treatment. The purpose of this study was to investigate the dose fall-off at the edges of a linear source in a blood vessel for different types of photon and beta emitters.Materials/Methods: Dose distributions were calculated on cylindrical blood vessels of various radii. Radioactive sources of 192Ir, 125I, 103Pd, 188Re, 32P, and 90Y/Sr were studied. All the sources were assumed to be in the form of a line. The dose rate at a point in space produced by a radioactive source was computed by integrating the point dose rate kernel of the corresponding radionuclide over the radioactive line. The point dose rate kernel was computed with Monte Carlo simulation of radiation transport. The edge effects were characterized with three newly defined quantities: longitudinal dose uniformity (LDU), effective coverage length (ECL), and margin length (ML). LDU was defined as the ratio of dose at a distance along the long axis of the vessel to the dose at center. ECL was defined as the length over which the LDU was greater than 0.95. ML was defined as half of the length difference between source length L and ECL, which is essentially the length segment at each edge that is covered by the source physical length but is being underdosed.Results: All beta emitters provided more uniform dose distributions and covered a larger portion of blood vessels longitudinally than photon emitters. Typical MLs were 2-3 mm for beta emitters and 4-6 mm for gamma emitters. As the radial depth of the point of interest increased, both the LDU and ECL decreased and ML increased. The ML increased from 2 to 3 mm for beta emitters and from 4 to 6 mm for photon emitters when the radial depth of the point of interest increased from 1.5 to 2.5 mm (typical proximal and distal media points for a 3-mm diameter lumen). The ML increased with increasing source length for all radionuclides. For beta emitters the ML increased initially from 1.5 mm to more than 2.5 mm as source length increased from 5 to 10 mm. When the source length was longer than 15 mm, the ML remains nearly constant, about 3 mm. For photon emitters, ML increased continuously from 1.5 mm to more than 6.0 mm, as source length increased from 5 to 50 mm.Conclusions: A formalism to quantify the dose uniformity along the length of a blood vessel undergoing catheter-based intravascular brachytherapy has been developed. This formalism was used to study the edge effects at the ends of several beta and photon sources. The results indicated that for a centered source the ML at each end due to penumbra effects was about 2 to 3 mm for beta emitters; about 4-6 mm for photon emitters. The ML increases as the radial depth of point of interest in the vessel increases. The ML increases also with increasing source length, especially for photon sources.     

Influence of Metal of the Applicator on the Dose Distribution during Brachytherapy

This study explores how the metal materials of the applicator influence the dose distribution when performing brachytherapy for cervical cancer. A pinpoint ionization chamber, Monte Carlo code MCNPX, and treatment planning system are used to evaluate the dose distribution for a single Ir-192 source positioned in the tandem and ovoid. For dose distribution in water with the presence of the tandem, differences among measurement, MCNPX calculation and treatment planning system results are <5%. For dose distribution in water with the presence of the ovoid, the MCNPX result agrees with the measurement. But the doses calculated from treatment planning system are overestimated by up to a factor of 4. This is due to the shielding effect of the metal materials in the applicator not being considered in the treatment planning system. This result suggests that the treatment planning system should take into account corrections for the metal materials of the applicator in order to improve the accuracy of the radiation dose delivered.     

Calculation of dose components in head phantom for boron neutron capture therapy.

Application of neutrons to cancer treatment has been a subject of considerable clinical and research interest since the discovery of the neutron by Chadwick in 1932 (3). Boron neutron capture therapy (BNCT) is a technique of radiation oncology which is used in treating brain cancer (glioblastoma multiform) or melanoma and that consists of preferentially loading a compound containing 10B into the tumor location, followed by the irradiation of the patient with a beam of neutron. Dose distribution for BNCT is mainly based on Monte Carlo simulations. In this work, the absorbed dose spatial distribution resultant from an idealized neutron beam incident upon ahead phantom is investigated using the Monte Carlo N-particles code, MCNP 4B. The phantom model used is based on the geometry of a circular cylinder on which sits an elliptical cylinder capped by half an ellipsoid representing the neck and head, both filled with tissue-equivalent material. The neutron flux and the contribution of individual absorbed dose components, as a function of depths and of radial distance from the beam axis (dose profiles) in phantom model, is presented and discussed. For the studied beam the maximum thermal neutron flux is at a depth of 2 cm and the maximum gamma dose at a depth of 4 cm.