Application of Monte Carlo simulation to cavity theory based on the virtual electron source concept

A cavity theory based on the application of the electron transport equation in the cavity and the surrounding medium, referred to as L-L cavity theory in this paper, is discussed. The L-L cavity theory is a very detailed theory that considers electron production in the cavity as well as in the wall, and is applicable to all cavity sizes. The main idea of this cavity theory is that the effect of the cavity on the energy deposition of electrons inside it can be attributed to a virtual electron source uniformly distributed in the cavity. Monte Carlo calculations have been used to determine the effect of the virtual electron source on the relative ionization density in the cavity. In particular, the Monte Carlo method has been used to compute the parameter k(E, a), which is the fraction of the energy deposited in the cavity relative to the initial energy of electrons, given an electron source uniformly distributed in the cavity. The total energy deposition of the virtual electron source in the cavity may also be obtained. The calculated results agree well with the experimental results from Attix et al (Attix F H, Vergne L D and Ritz V H 1958 J. Res. NBS 60 235-43) and show that the L-L cavity theory gives a more accurate prediction of the cavity response at low energies than do other cavity theories.     

Monte Carlo modelling of diode detectors for small field MV photon dosimetry: detector model simplification and the sensitivity of correction factors to source parameterization

The goal of this work was to examine the use of simplified diode detector models within a recently proposed Monte Carlo (MC) based small field dosimetry formalism and to investigate the influence of electron source parameterization has on MC calculated correction factors. BEAMnrc was used to model Varian 6?MV jaw-collimated square field sizes down to 0.5 cm. The IBA stereotactic field diode (SFD), PTW T60016 (shielded) and PTW T60017 (un-shielded) diodes were modelled in DOSRZnrc and isocentric output ratios (OR(fclin)(detMC)) calculated at depths of d = 1.5, 5.0 and 10.0 cm. Simplified detector models were then tested by evaluating the percent difference in (OR(fclin)(detMC)) between the simplified and complete detector models. The influence of active volume dimension on simulated output ratio and response factor was also investigated. The sensitivity of each MC calculated replacement correction factor (k(fclin,fmsr)(Qclin,Qmsr)), as a function of electron FWHM between 0.100 and 0.150 cm and energy between 5.5 and 6.5 MeV, was investigated for the same set of small field sizes using the simplified detector models. The SFD diode can be approximated simply as a silicon chip in water, the T60016 shielded diode can be modelled as a chip in water plus the entire shielding geometry and the T60017 unshielded diode as a chip in water plus the filter plate located upstream. The detector-specific (k(fclin,fmsr)(Qclin,Qmsr)), required to correct measured output ratios using the SFD, T60016 and T60017 diode detectors are insensitive to incident electron energy between 5.5 and 6.5 MeV and spot size variation between FWHM = 0.100 and 0.150 cm. Three general conclusions come out of this work: (1) detector models can be simplified to produce OR(fclin)(detMC) to within 1.0% of those calculated using the complete geometry, where typically not only the silicon chip, but also any high density components close to the chip, such as scattering plates or shielding material is necessary to be included in the model, (2) diode detectors of smaller active radius require less of a correction and (3) (k(fclin,fmsr)(Qclin,Qmsr)) is insensitive to the incident the electron energy and spot size variations investigated. Therefore, simplified detector models can be used with acceptable accuracy within the recently proposed small field dosimetry formalism.     

Modelling pencil-beam divergence with the electron pencil-beam redefinition algorithm.

The electron pencil-beam redefinition algorithm (PBRA), which is used to calculate electron beam dose distributions, assumes that the virtual source of each pencil beam is identical to that of the broad beam incident on the patient. In the present work, a virtual source specific for each pencil beam is modelled by including the source distance as a pencil-beam parameter to be redefined with depth. To incorporate a variable pencil-beam source distance parameter, the transport equation was reformulated to explicitly model divergence resulting in the algorithm divPBRA. Allowing the virtual source position to vary with individual pencil beams is expected to better model the effects of heterogeneities on local electron fluence divergence (or convergence). Selected experiments from a measured data set developed at The University of Texas M D Anderson Cancer Center were used to evaluate the accuracy of the dose calculated using divPBRA. Results of the calculation showed that the theory accurately predicted the virtual source position in regions of side-scatter equilibrium and predicted reasonable virtual source positions in regions lacking side-scatter equilibrium (i.e. penumbra and in the vicinity and shadow of internal heterogeneities). Results of the evaluation showed the dose accuracy of divPBRA to be marginally better to that of PBRA, except in regions of extremely sharp dose perturbations, where the divPBRA calculations were significantly greater than the measured data. Dose calculations using divPBRA took 45% longer than those using PBRA. Therefore, we concluded that divPBRA offers no significant advantage over PBRA for the purposes of clinical treatment planning. However, the results were promising and divPBRA might prove useful if further modelling were to include large-angle scattering, low-energy delta rays and brehmsstrahlung.     

Monte Carlo dose calculations of beta-emitting sources for intravascular brachytherapy: a comparison between EGS4, EGSnrc, and MCNP

The dose parameters for the beta-particle emitting 90Sr/90Y source for intravascular brachytherapy (IVBT) have been calculated by different investigators. At a distant distance from the source, noticeable differences are seen in these parameters calculated using different Monte Carlo codes. The purpose of this work is to quantify as well as to understand these differences. We have compared a series of calculations using an EGS4, an EGSnrc, and the MCNP Monte Carlo codes. Data calculated and compared include the depth dose curve for a broad parallel beam of electrons, and radial dose distributions for point electron sources (monoenergetic or polyenergetic) and for a real 90Sr/90Y source. For the 90Sr/90Y source, the doses at the reference position (2 mm radial distance) calculated by the three code agree within 2%. However, the differences between the dose calculated by the three codes can be over 20% in the radial distance range interested in IVBT. The difference increases with radial distance from source, and reaches 30% at the tail of dose curve. These differences may be partially attributed to the different multiple scattering theories and Monte Carlo models for electron transport adopted in these three codes. Doses calculated by the EGSnrc code are more accurate than those by the EGS4. The two calculations agree within 5% for radial distance <6 mm.     

Determination of effective electron source size using multislit and pinhole cameras

Two independent methods have been utilized for determination of effective source sizes for 6, 12, and 20 MeV electron beams generated by a Varian 2100C linear accelerator. First, a multislit camera has been constructed using parallel aluminum plates and plastic strip spacers, similar to the beam-spot camera for the photon source imaging. Second, pinhole imaging was performed using a lead plate with a small hole on the central axis of the beam. The plate thickness and the hole diameter varied with electron energy. The cameras were positioned directly at the opening of the movable photon collimator. The size of the source distribution from each camera was characterized by its full width at half-maximum (FWHM) value. The measured values of FWHM are different for each camera because of their different imaging principles. For the multislit camera, the measured FWHM values were (6.3 +/- 0.4) cm for the 6 MeV beam, (3.6 +/- 0.4) cm for 12 MeV, and (2.7 +/- 0.4) cm for 20 MeV. For the pinhole camera the measured values of FWHM were (7.9 +/- 0.6) cm for 6 MeV, (4.5 +/- 0.4) cm for 12 MeV, and (3.0 +/- 0.4) cm for the 20 MeV beam. Additionally, the effective source position was derived from output measurements at different values of the SSD, which were fitted to the inverse square law.     

Electron beam characteristics of the 50-MeV racetrack microtron.

Electron beams in the MM50 racetrack microtron are generated by computer controlled scanning of a well-focused electron pencil beam. The treatment head is optimized to give a minimum of scatter between the source position and the collimator plane by a general minimization of all scattering material in the beam and by replacement of the air in the treatment head by helium, which has a much lower linear scattering power than air. A double-focused multileaf collimator with a 31-cm collimator to patient distance is used both for electron and photon collimation. In general, no extra electron collimation is needed for the standard SSD of 100 cm. To make irregular field collimation at a distance this far from the patient possible, a number of requirements have to be fulfilled regarding the virtual source position and the spatial and angular distribution of the initial electron beam. The virtual source position has been found to be at a fixed position for different irradiation parameters. This is important for the use of the light field in electron beam treatment but also for achieving a high degree of accuracy in the dosimetry. Scatter from the multileaf collimator has not been found to give any significant contribution to the radiation field or to the monitor output factor of the MM50. Experimental dose distribution data on the MM50 have been compared to data both from other types of treatment units and to Monte Carlo simulations.     

Characteristics of bremsstrahlung in electron beams

Clinical electron beams contain an admixture of bremsstrahlung produced in structures in the accelerator head, in field-defining cerrobend or lead cutouts, and in the irradiated patient or water phantom. Accurate knowledge of these components is important for dose calculations and treatment planning. In this study, the bremsstrahlung components are separated for electron beams (energy 6-22 MeV, diameter 0-5 cm) using measurements in water and calculations. The results show that bremsstrahlung from the accelerator head dominates and increases with field size for electron beams generated by accelerators equipped with scattering foils. The bremsstrahlung from the field-defining cerrobend accounts for 10% to 30% of the total bremsstrahlung and decreases with increasing beam radius. The bremsstrahlung is softer than the x-ray beams of corresponding nominal energy since the latter are hardened by the flattening filter. For the 6, 12, and 22 MeV electron beams, the effective attenuation coefficients in water for the bremsstrahlung are 0.058, 0.050, and 0.043 cm(-1). The depths of maximum dose at 100 cm SSD are 0.8, 1.7, and 3.0 cm. The position of the virtual source of the bremsstrahlung shifts downstream from the nominal source position by 20, 13, 5.6 cm, respectively. The lateral bremsstrahlung dose distribution is more forward-peaked for higher electron energy. The bremsstrahlung components could be described for any machine by a set of simple measurements and can be modeled by an analytical expression.     

The diagnostic capability of x-ray scattering parameters for the characterization of breast cancer

PURPOSE: The evaluation of the diagnostic capability of easy to measure x-ray scattering profile characterization parameters for the detection of breast cancer in excised samples. The selected parameters are the full width at half maximum (FWHM) and area under the x-ray scattering profile of breast tissue in addition to the ratio of scattering intensities (I2/I1%) at 1.6 nm(-1) to that at 1.1 nm(-1) (corresponding to scattering from soft and adipose tissues, respectively). Methods: A histopathologist is asked to classify 36 excised breast tissue samples into healthy or malignant. A conventional x-ray diffractometer is used to acquire the scattering profiles of the investigated samples. The values of three profile characterization parameters are calculated and the diagnostic capability of each is evaluated by determining the optimal cutoffs of scatter diagrams, calculating the diagnostic indices, and plotting the receiver operating characteristic (ROC) curves. Results: At the calculated optimal cutoff for each of the examined parameters, the sensitivity ranged from 78% (for area under curve) up to 94% (for FWHM), the specificity ranged from 94% [for I2/I1% and area under curve] up to 100% (for FWHM), and the diagnostic accuracy ranged from 86% (for area under curve) up to 97% (for FWHM). The area under the ROC curves is greater than 0.95 for all of the investigated parameters, reflecting a highly accurate diagnostic performance. Conclusions: The discussed tests offered a means to quantitatively evaluate the performance of the suggested breast tissue x-ray scattering characterization parameters. The performance results are promising, indicating that the evaluated parameters would be considered a tool for fast, on spot probing of breast cancer in excised tissue samples.     

Radiological characterization and water equivalency of genipin gel for x-ray and electron beam dosimetry

The genipin radiochromic gel offers enormous potential as a three-dimensional dosimeter in advanced radiotherapy techniques. We have used several methods (including Monte Carlo simulation), to investigate the water equivalency of genipin gel by characterizing its radiological properties, including mass and electron densities, photon interaction cross sections, mass energy absorption coefficient, effective atomic number, collisional, radiative and total mass stopping powers and electron mass scattering power. Depth doses were also calculated for clinical kilovoltage and megavoltage x-ray beams as well as megavoltage electron beams. The mass density, electron density and effective atomic number of genipin were found to differ from water by less than 2%. For energies below 150 keV, photoelectric absorption cross sections are more than 3% higher than water due to the strong dependence on atomic number. Compton scattering and pair production interaction cross sections for genipin gel differ from water by less than 1%. The mass energy absorption coefficient is approximately 3% higher than water for energies <60 keV due to the dominance of photoelectric absorption in this energy range. The electron mass stopping power and mass scattering power differ from water by approximately 0.3%. X-ray depth dose curves for genipin gel agree to within 1% with those for water. Our results demonstrate that genipin gel can be considered water equivalent for kilovoltage and megavoltage x-ray beam dosimetry. For megavoltage electron beam dosimetry, however, our results suggest that a correction factor may be needed to convert measured dose in genipin gel to that of water, since differences in some radiological properties of up to 3% compared to water are observed. Our results indicate that genipin gel exhibits greater water equivalency than polymer gels and PRESAGE formulations.     

Electron contamination from different materials in high energy photon beams

Relative lateral electron surface dose distributions from filters and air in high energy photon beams were determined using the Fermi-Eyges theory of multiple scattering. The model includes transmission and angular scattering in materials and in air. Backscatter from the phantom was also estimated. The variation of surface dose with different parameters such as atomic number, thickness and position of material, field size and photon energy was investigated. The calculated data show good agreement with experiment. For 60Co gamma rays, electron filters of medium atomic number give the lowest surface dose, whereas for higher energies a low to medium atomic number material should be used, especially for short material-phantom distances and large field sizes. The contribution to surface dose can be reduced by over 30% by placing a thin foil of high atomic number after a low to medium atomic number filter, thus scattering some electrons from the beam. For 60Co gamma rays the air is often the dominant source of contaminating electrons because of high multiple scatter loss at this energy, while for higher photon energies the beam flattening filter is the main electron source because of the small emission angle of the electrons and the small scattering power at high energies.     

Sensitivity of megavoltage photon beam Monte Carlo simulations to electron beam and other parameters

The BEAM code is used to simulate nine photon beams from three major manufacturers of medical linear accelerators (Varian, Elekta, and Siemens), to derive and evaluate estimates for the parameters of the electron beam incident on the target, and to study the effects of some mechanical parameters like target width, primary collimator opening, flattening filter material and density. The mean energy and the FWHM of the incident electron beam intensity distributions (assumed Gaussian and cylindrically symmetric) are derived by matching calculated percentage depth-dose curves past the depth of maximum dose (within 1% of maximum dose) and off-axis factors (within 2sigma at 1% statistics or less) with measured data from the AAPM RTC TG-46 compilation. The off-axis factors are found to be very sensitive to the mean energy of the electron beam, the FWHM of its intensity distribution, its angle of incidence, the dimensions of the upper opening of the primary collimator, the material of the flattening filter and its density. The off-axis factors are relatively insensitive to the FWHM of the electron beam energy distribution, its divergence and the lateral dimensions of the target. The depth-dose curves are sensitive to the electron beam energy, and to its energy distribution, but they show no sensitivity to the FWHM of the electron beam intensity distribution. The electron beam incident energy can be estimated within 0.2 MeV when matching either the measured off-axis factors or the central-axis depth-dose curves when the calculated uncertainties are about 0.7% at the 1 sigma level. The derived FWHM (+/-0.1 mm) of the electron beam intensity distributions all fall within 1 mm of the manufacturer specifications except in one case where the difference is 1.2 mm.     

Electron beam collimation with focused and curved leaf end MLCs--experimental verification of Monte Carlo optimized designs

In general, electron beams from conventional accelerators using applicators with lead alloy inserts are not suitable for advanced conformal radiation therapy. However, interesting electron treatments have been demonstrated on a few advanced accelerators. These accelerators have been equipped with helium filled treatment heads and computer controlled MLCs that produce clinically useful energy modulated electron beams or mixed photon electron beams in an automated sequence. This study analyzes the characteristics of different MLC designs, curved and focused leaf ends in helium filled treatment heads, with respect to their effect on electron beams. In addition, this study analyzes the effects that different treatment head designs have on the output factor due to collimator scattering and shielding of secondary sources during treatment. The investigation of the different treatment head designs was performed with the Monte Carlo package BEAM and was verified by experimental methods. The results show that the difference between curved leaf ends and focused ends is negligible in most practical cases. The results also show the importance of scattering foil optimization in the optimization of parameters such as penumbra, virtual source position, and in the reduction of the output variation. In all cases, the experimental data verifies the calculations.     

Monte Carlo modeling of a high-sensitivity MOSFET dosimeter for low- and medium-energy photon sources

Metal-oxide-semiconductor field effect transistor (MOSFET) dosimeters are increasingly utilized in radiation therapy and diagnostic radiology. While it is difficult to characterize the dosimeter responses for monoenergetic sources by experiments, this paper reports a detailed Monte Carlo simulation model of the High-Sensitivity MOSFET dosimeter using Monte Carlo N-Particle (MCNP) 4C. A dose estimator method was used to calculate the dose in the extremely thin sensitive volume. Efforts were made to validate the MCNP model using three experiments: (1) comparison of the simulated dose with the measurement of a Cs-137 source, (2) comparison of the simulated dose with analytical values, and (3) comparison of the simulated energy dependence with theoretical values. Our simulation results show that the MOSFET dosimeter has a maximum response at about 40 keV of photon energy. The energy dependence curve is also found to agree with the predicted value from theory within statistical uncertainties. The angular dependence study shows that the MOSFET dosimeter has a higher response (about 8%) when photons come from the epoxy side, compared with the kapton side for the Cs-137 source.     

Anisotropy functions for low energy interstitial brachytherapy sources: an EGS4 Monte Carlo study

Anisotropy functions for low energy interstitial brachytherapy sources are examined. Absolute dose rates around 103Pd seed model 200 and 125I seed models 6702 and 6711 have been estimated by means of the EGS4 Monte Carlo simulation system. The DLC-136/PHOTX cross section library, water molecular form factors, bound Compton scattering and Doppler broadening of the Compton-scattered photon energy were considered in the calculations. Following the formalism developed by the Interstitial Brachytherapy Collaborative Working Group, anisotropy functions, F(r, theta), have been calculated. Our Monte Carlo results were compared against a limited set of measured data selected from the literature and other Monte Carlo results. Binding corrections and phantom material selection have been found to have no influence on the anisotropy function. The accuracy of the geometrical source models used for the Monte Carlo calculations was validated against experimental measurements of in-air relative fluence at 100 cm from the source. More detailed knowledge about the geometrical design of 103Pd seed model 200 is needed in order to improve the agreement with experimentally measured in-air fluence. Values for in-air fluence of 125I model 6702 are sensitive to source position within the inner seed cylinder. Excellent agreement between calculated and measured in-air fluence is found for 125I model 6711. It was observed that using in-air relative fluence at 100 cm from the source to calculate the anisotropy function yields a less anisotropic dose distribution at distances close to the source than full Monte Carlo simulation, in contradiction with experimental data. Our results have estimated statistical uncertainties of 1%-3% at the 1sigma level within clinically relevant regions, but contain systematic uncertainties related to the assumed geometrical details.     

A study on virtual source position for electron beams from a Mevatron MD linear accelerator.

The virtual source position (VSP) for electron beams of energies 5, 7, 9 10, 12 and 14 MeV and for the applicators (cones) available in the department have been measured for a Mevatron MD class linear accelerator. Different methods of obtaining the virtual source position for electron beams have been investigated in the present study. The results obtained have been compared with those of other workers. It is observed that the VSP is very much machine dependent and needs to be measured for each linear accelerator. The effect of shielding on virtual source position for the type of applicators available in the department has also been investigated.     

Dual scattering foil design for poly-energetic electron beams

The laser wakefield acceleration (LWFA) mechanism can accelerate electrons to energies within the 6-20 MeV range desired for therapy application. However, the energy spectrum of LWFA-generated electrons is broad, on the order of tens of MeV. Using existing laser technology, the therapeutic beam might require a significant energy spread to achieve clinically acceptable dose rates. The purpose of this work was to test the assumption that a scattering foil system designed for a mono-energetic beam would be suitable for a poly-energetic beam with a significant energy spread. Dual scattering foil systems were designed for mono-energetic beams using an existing analytical formalism based on Gaussian multiple-Coulomb scattering theory. The design criterion was to create a flat beam that would be suitable for fields up to 25 x 25 cm2 at 100 cm from the primary scattering foil. Radial planar fluence profiles for poly-energetic beams with energy spreads ranging from 0.5 MeV to 6.5 MeV were calculated using two methods: (a) analytically by summing beam profiles for a range of mono-energetic beams through the scattering foil system, and (b) by Monte Carlo using the EGS/BEAM code. The analytic calculations facilitated fine adjustments to the foil design, and the Monte Carlo calculations enabled us to verify the results of the analytic calculation and to determine the phase-space characteristics of the broadened beam. Results showed that the flatness of the scattered beam is fairly insensitive to the width of the input energy spectrum. Also, results showed that dose calculated by the analytical and Monte Carlo methods agreed very well in the central portion of the beam. Outside the useable field area, the differences between the analytical and Monte Carlo results were small but significant, possibly due to the small angle approximation. However, these did not affect the conclusion that a scattering foil system designed for a mono-energetic beam will be suitable for a poly-energetic beam with the same central energy. Further studies of the dosimetric properties of LWFA-generated electron beams will be done using Monte Carlo methods.     

The proton chemical shifts and the conformations of the unbranched paraffin hydrocarbon C44H90 in solution

The temperature dependence of the proton chemical-shift difference between the methyl and methylene groups in the unbranched paraffin hydrocarbon C₄₄H₉₀ was calculated by using Pople's approximation and the Monte Carlo method, and the calculated results could interpret the experimental behavior in carbon tetrachloride solution. From these results, it was estimated that the energy difference between the trans and gauche states is 1880–2300 J/mol, and the four-bond interaction energy is 5270–6275 J/mol. The estimated values agree with those obtained from comparison of the calculated and observed average-dimension and its temperature coefficient by Abe et al. Further, the calculated chemical-shift difference was associated with the unperturbed dimension and its temperature coefficient.     

Monte Carlo dose calculations using MCNP4C and EGSnrc/BEAMnrc codes to study the energy dependence of the radiochromic film response to beta-emitting sources

The energy dependence of the radiochromic film (RCF) response to beta-emitting sources was studied by dose theoretical calculations, employing the MCNP4C and EGSnrc/BEAMnrc Monte Carlo codes. Irradiations with virtual monochromatic electron sources, electron and photon clinical beams, a (32)P intravascular brachytherapy (IVB) source and other beta-emitting radioisotopes ((188)Re, (90)Y, (90)Sr/(90)Y,(32)P) were simulated. The MD-55-2 and HS radiochromic films (RCFs) were considered, in a planar or cylindrical irradiation geometry, with water or polystyrene as the surrounding medium. For virtual monochromatic sources, a monotonic decrease with energy of the dose absorbed to the film, with respect to that absorbed to the surrounding medium, was evidenced. Considering the IVB (32)P source and the MD-55-2 in a cylindrical geometry, the calibration with a 6 MeV electron beam would yield dose underestimations from 14 to 23%, increasing the source-to-film radial distance from 1 to 6 mm. For the planar beta-emitting sources in water, calibrations with photon or electron clinical beams would yield dose underestimations between 5 and 12%. Calibrating the RCF with (90)Sr/(90)Y, the MD-55-2 would yield dose underestimations between 3 and 5% for (32)P and discrepancies within +/-2% for (188)Re and (90)Y, whereas for the HS the dose underestimation would reach 4% with (188)Re and 6% with (32)P.     

The mass angular scattering power method for determining the kinetic energies of clinical electron beams.

A method for determining the kinetic energy of clinical electron beams is described. The method is based on the measurement in air of the spatial spread of a pencil electron beam which is produced from the broad clinical electron beam. As predicted by the Fermi-Eyges theory, the dose distribution measured in air on a plane, perpendicular to the incident direction of the initial pencil electron beam, is Gaussian. The square of its spatial spread is related to the mass angular scattering power which in turn is related to the kinetic energy of the electron beam. The measured spatial spread may thus be used to determine the mass angular scattering power, which is then used to determine the kinetic energy of the electron beam from the known relationship between mass angular scattering power and kinetic energy. Energies obtained with the mass angular scattering power method agree with those obtained with the electron range method. The angular scattering power method is relatively cumbersome, but allows us to determine the kinetic energies of electron beams from first principles, in contrast to the empirical methods based on range measurements in water.