Calculation of depth dose and dose per monitor unit for irregularly shaped electron fields

Planar dose calculation of electron therapy

Purpose.The aim of this study is to determine the planar dose distribution of irregularly-shaped electron beams at their maximum dose depth (zmax) using the modied lateral build-up ratio (LBR) and curve-fitting methods.Methods.Circular and irregular cutouts were created using Cerrobend alloy for a 14 × 14 cm2applicator. Percentage depth dose (PDD) at the standard source-surface-distance (SSD = 100 cm) and point dose at different SSD were measured for each cutout. Orthogonal profiles of the cutouts were measured atzmax. Data were collected for 6, 9, 12, and 15 MeV electron beam energies on a VERSA HDTMLINAC using the IBA Blue Phantom23D water phantom system. The planar dose distributions of the cutouts were also measured atzmaxin solid water using EDR2 films.Results.The measured PDD curves were normalized to a normalization depth (d0) of 1 mm. The lateral-buildup-ratio (LBR), lateral spread parameter (σR(z)), and effective SSD (SSDeff) for each cutout were calculated using the PDD of the open applicator as the reference field. The modified LBR method was then employed to calculate the planar dose distribution of the irregular cutouts within the field at least 5 mm from the edge. A simple curve-fitting model was developed based on the profile shapes of the circular cutouts around the field edge. This model was used to calculate the planar dose distribution of the irregular cutouts in the region from 3 mm outside to 5 mm inside the field edge. Finally, the calculated planar dose distribution was compared with the film measurement.Conclusions.The planar dose distribution of electron therapy for irregular cutouts atzmaxwas calculated using the improved LBR method and a simple curve-fitting model. The calculated profiles were within 3% of the measured values. The gamma passing rate with a 3%/3 mm and 10% dose threshold was more than 96%.

[Investigation of the Usefulness of Monte Carlo Simulation in Electron Beam Therapy Using Body Surface Lead Cutout]

PURPOSE

The purpose of this study was to understand the PDD and OAR during electron beam therapy using lead cutout on the body surface.

METHODS

The Monte Carlo code PHITS version 3.24 was used to simulate PDD and OAR. The simulation results were compared with actual measurements using a silicon diode detector to evaluate the validity of the simulation results.

RESULTS

The simulated PDD and OAR parameters of the linac agreed with the measured values within 2 mm. When the lead cutout on the body surface was used, all parameters except for R100 agreed with the measured values within 2 mm. The cutout sizes of the broad-beam square irradiation fields were 3 cm for 6 MeV, 5 cm for 12 MeV, and 8 cm for 18 MeV when the lead cutout on the body surface was used.

CONCLUSION

The Monte Carlo simulation was useful for understanding the PDD and OAR of the lead cutout irradiation fields, which are difficult to measure.

The Study of Field Equivalence Determined by the Modeled Percentage Depth Dose in Electron Beam Radiation Therapy

Introduction

This study presents an empirical method to model the curve of electron beam percent depth dose (PDD) by using the primary-tail function in electron beam radiation therapy. The modeling parameters N and n can be used to predict the minimal side length when the field size is reduced below that required for lateral scatter equilibrium (LSE) in electron radiation therapy.

Methods and Materials

The electrons' PDD curves were modeled by the primary-tail function in this study. The primary function included the exponential function and the main parameters of N and μ, while the tail function was composed of a sigmoid function with the main parameter of n. The PDD of five electron energies was modeled by the primary and tail function by adjusting the parameters of N, μ, and n. The R₅₀ and R_p can be derived from the modeled straight line of 80% to 20% region of PDD. The same electron energy with different cone sizes was also modeled by the primary-tail function. The stopping power of different electron energies in different depths can also be derived from the parameters N, μ, and n.

Results

The main parameters N and n increase but μ decreases in the primary-tail function for characterizing the electron beam PDD when the electron energy increased. The relationship of parameter n, N, and ln(−μ) with electron energy are n = 31.667E₀ − 88, N = 0.9975E₀ − 2.8535, and ln(−μ) = −0.1355E₀ − 6.0986, respectively. Percent depth dose was derived from the percent reading curve by multiplying the stopping power relevant to the depth in water at a certain electron energy. The stopping power of different electron energies can be derived from n and N with the following equation: stopping power = (−0.042ln(N_E0) + 1.072)e^{(−n_E0 · 5 · 10−5 + 0.0381)·x}, where x is the depth in water. The lateral scatter equivalence (LSE) of the clinical electron beam can be described by the parameters E₀, n, and N in the equation of S_eq = (n_E0 − N_E0)^0.288/(E₀/n_E0)^0.0195. The LSE was compared with the root mean square scatter angular distribution method and shows the agreement of depth dose distributions within ±2%.

Conclusions

The PDD of the electron beam at different energies and cone sizes can be modeled with an empirical model to deal with what is the minimal field size without changing the percent depth dose when approximate LSE is given in centimeters of water.

Validation of spline modeling for calculation of electron insert factors for varian linear accelerators

There are several methods available in the literature for predicting the insert factor for clinical electron beams. The purpose of this work was to build on a previously published technique that uses a bivariate spline model generated from elliptically parameterized empirical measurements. The technique has been previously validated for Elekta linear accelerators for limited clinical electron setups. The same model is applied to Varian machines to test its efficacy for use with these linear accelerators. Insert factors for specifically designed elliptical cutouts were measured to create spline models for 6, 9, 12, 16, and 20 MeV electron energies for four different cone sizes at source-to-surface distances (SSD) of 100, 105, and 110 cm. Insert factor validation measurements of patient cutouts and clinical standard cutouts were acquired to compare to model predictions. Agreement between predicted insert factors and validation measurements averaged 0.8% over all energies, cones, and clinical SSDs, with an uncertainty of 0.6% (1SD), and maximum deviation of 2.1%. The model demonstrated accurate predictions of insert factors using the minimum required amount of input data for small cones, with more input measurements required for larger cones. The results of this study provide expanded validation of this technique to predict insert factors for all energies, cones, and SSDs that would be used in most clinical situations. This level of accuracy and the ease of creating the model necessary for the insert factor predictions demonstrate its acceptability to use clinically for Varian machines.

Characterization of irregular electron beam for boost dose after whole breast irradiation

Irradiating a tumor bed with boost dose after whole breast irradiation helps reducing the probability of local recurrence. However, the success of electron beam treatment with a small area aiming to cover a superficial lesion is a dual challenge as it requires an adequate dosimetry beside a double check for dose coverage with an estimation of various combined uncertainty of tumor location and losing lateral electron equilibrium within small field dimensions.

Aim of work

this work aims to measure the electron beam fluence within different field dimensions and the deviation from measurement performed in standard square electron applicator beam flatness and symmetry, then to calculate the average range of the correction factor required to overcome the loss of lateral electron equilibrium.

Material and method

the electron beam used in this work generated from the linear accelerator model ELEKTA Precise and dosimetry system used were a pair of PTW Pin Point ion chambers for electron beam dosimetry at standard conditions and assessment of beam quality at a reference depth of measurement, with an automatic water phantom, then a Roos ion chamber was used for absolute dose measurement, and PTW 2Darray to investigate the beam fluence of four applicators 6, 10, 14 and 20 cm² and 4 rectangular cutouts 6 × 14, 8 × 14, 6 × 17 and 8 × 17 cm², the second part was clinical application which was performed in a precise treatment planning system and examined boost dose after whole breast irradiation.

Results

revealed that lower energy (6MeV and 8MeV) showed the loss of lateral electron equilibrium and deviation from measurements of a standard applicator more than the high energy (15 MeV) which indicated that the treatment of superficial dose with 6MeV required higher monitor unit to allow for the loss of lateral electron equilibrium and higher margin as well.

Practical lookup tables for ensuring target coverage in a clinical setup for skin cancer electron therapy

Aim

To create practical lookup tables containing percent depth dose (PDD) and profile parameters of electron beams and to demonstrate clinical application of the lookup tables to skin cancer treatment to ensure target coverage in a clinical setup.

Materials and methods

For 6 and 9 MeV electron energies, PDDs and profiles at clinically relevant depths [i.e., R95 (distal depth of 95% maximum dose), R90, R85 and R80] were measured in water at 100 cm source-to-surface distance for an 10×10 cm2 open field and circular cutouts with diameters of 4, 5, 6, 7 and 8 cm. Then PDD parameters along with profile parameters such as width of isodose lines and penumbra at the clinically relevant depths were determined. Output factors for the cutouts were measured at dmax in water and solid water.

Results

With PDD and profile parameters, dosimetry lookup tables were generated. Based upon the lookup tables, target coverage at prescribed depths was retrospectively reviewed for three skin cancer cases. The lookup tables suggested larger cutouts for adequate target coverage.

Findings

Dosimetry lookup tables for electron beam therapy should include profile parameters at clinically relevant depths and be provided to clinicians to ensure target coverage in a clinical setup.

Convolution-based modified Clarkson integration (CMCI) for electron cutout factor calculation

Electron therapy is widely used to treat shallow tumors because of its characteristic sharp dose fall‐off beyond a certain range. A customized cutout is typically applied to block radiation to normal tissues. Determining the final monitor unit (MU) for electron treatment requires an output factor for the cutout, which is usually generated by measurement, especially for highly irregular cutouts. However, manual measurement requires a lengthy quality assurance process with possible errors. This work presents an accurate and efficient cutout output factor prediction model, convolution‐based modified Clarkson integration (CMCI), to replace patient‐specific output factor measurement. Like the Clarkson method, we decompose the field into basic sectors. Unlike the Clarkson integration method, we use annular sectors for output factor estimation. This decomposition method allows calculation via convolution. A 2D distribution of fluence is generated, and the output factor at any given point can be obtained. We applied our method to 10 irregularly shaped cutouts for breast patients for 6E, 9E, and 15E beams and compared the results with measurements and the electron Monte Carlo (eMC) calculation using the Eclipse planning system. While both the CMCI and eMC methods showed good agreement with chamber measurements and film measurements in relative distributions at the nominal source to surface distance (SSD) of 100 cm, eMC generated larger errors than the CMCI method at extended SSDs, with up to −9.28% deviations from the measurement for 6E beam. At extended SSD, the mean absolute errors of our method relative to measurements were 0.92 and 1.14, while the errors of eMC were 1.42 and 1.79 for SSD 105 cm and 110 cm, respectively. These results indicate that our method is more accurate than eMC, especially for low‐energy beams, and can be used for MU calculation and as a QA tool for electron therapy.

Some computer graphical user interfaces in radiation therapy

In this review, five graphical user interfaces (GUIs) used in radiation therapy practices and researches are introduced. They are: (1) the treatment time calculator, superficial X-ray treatment time calculator (SUPCALC) used in the superficial X-ray radiation therapy; (2) the monitor unit calculator, electron monitor unit calculator (EMUC) used in the electron radiation therapy; (3) the multileaf collimator machine file creator, sliding window intensity modulated radiotherapy (SWIMRT) used in generating fluence map for research and quality assurance in intensity modulated radiation therapy; (4) the treatment planning system, DOSCTP used in the calculation of 3D dose distribution using Monte Carlo simulation; and (5) the monitor unit calculator, photon beam monitor unit calculator (PMUC) used in photon beam radiation therapy. One common issue of these GUIs is that all user-friendly interfaces are linked to complex formulas and algorithms based on various theories, which do not have to be understood and noted by the user. In that case, user only needs to input the required information with help from graphical elements in order to produce desired results. SUPCALC is a superficial radiation treatment time calculator using the GUI technique to provide a convenient way for radiation therapist to calculate the treatment time, and keep a record for the skin cancer patient. EMUC is an electron monitor unit calculator for electron radiation therapy. Instead of doing hand calculation according to pre-determined dosimetric tables, clinical user needs only to input the required drawing of electron field in computer graphical file format, prescription dose, and beam parameters to EMUC to calculate the required monitor unit for the electron beam treatment. EMUC is based on a semi-experimental theory of sector-integration algorithm. SWIMRT is a multileaf collimator machine file creator to generate a fluence map produced by a medical linear accelerator. This machine file controls the multileaf collimator to deliver intensity modulated beams for a specific fluence map used in quality assurance or research. DOSCTP is a treatment planning system using the computed tomography images. Radiation beams (photon or electron) with different energies and field sizes produced by a linear accelerator can be placed in different positions to irradiate the tumour in the patient. DOSCTP is linked to a Monte Carlo simulation engine using the EGSnrc-based code, so that 3D dose distribution can be determined accurately for radiation therapy. Moreover, DOSCTP can be used for treatment planning of patient or small animal. PMUC is a GUI for calculation of the monitor unit based on the prescription dose of patient in photon beam radiation therapy. The calculation is based on dose corrections in changes of photon beam energy, treatment depth, field size, jaw position, beam axis, treatment distance and beam modifiers. All GUIs mentioned in this review were written either by the Microsoft Visual Basic.net or a MATLAB GUI development tool called GUIDE. In addition, all GUIs were verified and tested using measurements to ensure their accuracies were up to clinical acceptable levels for implementations.

Parameterization of electron beam output factor

Electron beam dose distribution is dependent on the beam energy and complicated trajectory of particles. Recent treatment planning systems using Monte Carlo calculation algorithm provide accurate dose calculation. However, double check of monitor units (MUs) based on an independent algorithm is still required. In this study, we have demonstrated single equation that reproduces the measured relative output factor (ROF) that can be used for MU calculation for electron radiotherapy. Electron beams generated by an iX (Varian Medical Systems) and a PRIMUS (Siemens) accelerator were investigated. For various energies of electron beams, the ROF at respective dmax were measured using diode detector in a water phantom at SSD of 100 cm. Curve fitting was performed with an exponential generalized equation ROF = α(β - e(-γR)) including three variables (α, β, γ) as a function of field radius and electron energy. The correlation coefficients between the ROF measured and that calculated by the equation were greater than 0.998. For ROF of Varian electron beams, the average values of all fitting formulas were applied for two of the constants; α and β. The parameter γ showed good agreement with the quadratic approximation as a function of mean energy at surface (E0). The differences between measured and calculated ROF values were within ± 3% for beams with cutout radius of ≥ 1.5 cm for electron beams with energies from 6 MeV to 15 MeV. The proposed formula will be helpful for double-check of MUs, as it requires minimal efforts for MU calculation.

Output calculation of electron therapy at extended SSD using an improved LBR method

PURPOSE

To calculate the output factor (OPF) of any irregularly shaped electron beam at extended SSD.

METHODS

Circular cutouts were prepared from 2.0 cm diameter to the maximum possible size for 15 × 15 applicator cone. In addition, two irregular cutouts were prepared. For each cutout, percentage depth dose (PDD) at the standard SSD and doses at different SSD values were measured using 6, 9, 12, and 16 MeV electron beam energies on a Varian 2100C LINAC and the distance at which the central axis electron fluence becomes independent of cutout size was determined. The measurements were repeated with an ELEKTA Synergy LINAC using 14 × 14 applicator cone and electron beam energies of 6, 9, 12, and 15 MeV. The PDD measurements were performed using a scanning system and two diodes-one for the signal and the other a stationary reference outside the tank. The doses of the circular cutouts at different SSDs were measured using PTW 0.125 cm(3) Semiflex ion-chamber and EDR2 films. The electron fluence was measured using EDR2 films.

RESULTS

For each circular cutout, the lateral buildup ratio (LBR) was calculated from the measured PDD curve using the open applicator cone as the reference field. The effective SSD (SSDeff) of each circular cutout was calculated from the measured doses at different SSD values. Using the LBR value and the radius of the circular cutout, the corresponding lateral spread parameter [σR(z)] was calculated. Taking the cutout size dependence of σR(z) into account, the PDD curves of the irregularly shaped cutouts at the standard SSD were calculated. Using the calculated PDD curve of the irregularly shaped cutout along with the LBR and SSDeff values of the circular cutouts, the output factor of the irregularly shaped cutout at extended SSD was calculated. Finally, both the calculated PDD curves and output factor values were compared with the measured values.

CONCLUSIONS

The improved LBR method has been generalized to calculate the output factor of electron therapy at extended SSD. The percentage difference between the calculated and the measured output factors of irregularly shaped cutouts in a clinical useful SSD region was within 2%. Similar results were obtained for all available electron energies of both Varian 2100C and ELEKTA Synergy machines.

Monitor unit calculations for external photon and electron beams: Report of the AAPM Therapy Physics Committee Task Group No. 71

A protocol is presented for the calculation of monitor units (MU) for photon and electron beams, delivered with and without beam modifiers, for constant source-surface distance (SSD) and source-axis distance (SAD) setups. This protocol was written by Task Group 71 of the Therapy Physics Committee of the American Association of Physicists in Medicine (AAPM) and has been formally approved by the AAPM for clinical use. The protocol defines the nomenclature for the dosimetric quantities used in these calculations, along with instructions for their determination and measurement. Calculations are made using the dose per MU under normalization conditions, D'0, that is determined for each user's photon and electron beams. For electron beams, the depth of normalization is taken to be the depth of maximum dose along the central axis for the same field incident on a water phantom at the same SSD, where D'0 = 1 cGy/MU. For photon beams, this task group recommends that a normalization depth of 10 cm be selected, where an energy-dependent D'0 ≤ 1 cGy/MU is required. This recommendation differs from the more common approach of a normalization depth of dm, with D'0 = 1 cGy/MU, although both systems are acceptable within the current protocol. For photon beams, the formalism includes the use of blocked fields, physical or dynamic wedges, and (static) multileaf collimation. No formalism is provided for intensity modulated radiation therapy calculations, although some general considerations and a review of current calculation techniques are included. For electron beams, the formalism provides for calculations at the standard and extended SSDs using either an effective SSD or an air-gap correction factor. Example tables and problems are included to illustrate the basic concepts within the presented formalism.

Dose calculation for electron therapy using an improved LBR method

PURPOSE

To calculate the percentage depth dose (PDD) of any irregularly shaped electron beam using a modified lateral build-up ratio (LBR) method.

METHODS

Percentage depth dose curves were measured using 6, 9, 12, and 15 MeV electron beam energies for applicator cone sizes of 6 × 6, 10 × 10, 14 × 14, and 20 × 20 cm(2). Circular cutouts for each cone were prepared from 2.0 cm diameter to the maximum possible size for each cone. In addition, three irregular cutouts were prepared.

RESULTS

The LBR for each circular cutout was calculated from the measured PDD curve using the open field of the 14 × 14 cm(2) cone as the reference field. Using the LBR values and the radius of the circular cutouts, the corresponding lateral spread parameter [σR(z)] of the electron shower was calculated. Unlike the commonly accepted assumption that σR(z) is independent of cutout size, it is shown that its value increases linearly with circular cutout size (R). Using this characteristic of the lateral spread parameter, the PDD curves of irregularly shaped cutouts were calculated. Finally, the calculated PDD curves were compared with measured PDD curves.

CONCLUSIONS

In this research, it is shown that the lateral spread parameter σR(z) increases with cutout size. For radii of circular cutout sizes up to the equilibrium range of the electron beam, the increase of σR(z) with the cutout size is linear. The percentage difference of the calculated PDD curve from the measured PDD data for irregularly shaped cutouts was under 1.0% in the region between the surface and therapeutic range of the electron beam. Similar results were obtained for four electron beam energies (6, 9, 12, and 15 MeV).

Determination of square equivalent field for rectangular field in electron therapy

Equivalent field for electron beams is considered by using pencil beam theory. According to the Fermi-Eyges model the dose distribution of an electron pencil beam has a Gaussian profile. For this function determination of mean square radial displacement scattering of electrons is important. In this study the contribution of back scatter electron has been taken into account by using the multiple scattering theories for calculating mean square radial displacement scattering. The dimension of standard equivalent field depends on depth and shape of treatment field. Here the depth under study is the depth that mean square radial displacement scattering is extremum and the shape of treatment field is rectangular. In this study four energies were used 6, 9,12 and 15 MeV electron beams of 2100C/D Varian Linac. Findings of this study are based on analytical calculations, which are in good agreement with other experimental data. The findings of this study that were resulted from formula, shows, for all circular fields of radius ≥LSE (lateral scattering equilibrium) were considered broad field and equivalent. For validating the findings, Percentage Depth Dose (PDD) and Output factors were measured in 15 MeV electron beams for 7 × 3-cm, 6 × 4-cm and 4 × 2-cm and their equivalent squares and equivalent circular fields and compared.

The effects of cutouts on output, mean energy and percentage depth dose of 12 and 14 MeV electrons

Electron field-shaping cerrobend cutouts on the linear accelerator applicator have some effects on the output and percentage depth dose. These effects which arise from the lateral scatter nonequilibrium are particularly evident in higher energies and in cutouts with smaller radius. Dose measurements for circular, square, and triangular cutouts as well as open field was performed in a 10 × 10 cm applicator, using plane parallel type ion chamber with a 100 cm source surface distance. The Percentage Depth Doses curves were drawn and the outputs were measured for each of these cutouts. The output factors, normalized to open 10 × 10 cm field, varied between 0.891 and 0.996 depending on the energy, cutout shape, and cavity area. With the use of cutouts, R₁₀₀ shifted toward the surface. The shifts ranged from 9 to 0 mm and from 13 to 0 mm for 12 and 14 MeV, respectively, depending on the shape and cavity area. For R₉₀, R₈₀, and R₅₀ the ranges for observed shifts narrowed down and practically no shifts were observed for R₂₀. We present these changes in the form of predictive formulas, which would be useful in clinical applications.

Recommendations for clinical electron beam dosimetry: supplement to the recommendations of Task Group 25

The goal of Task Group 25 (TG-25) of the Radiation Therapy Committee of the American Association of.Physicists in Medicine (AAPM) was to provide a methodology and set of procedures for a medical physicist performing clinical electron beam dosimetry in the nominal energy range of 5-25 MeV. Specifically, the task group recommended procedures for acquiring basic information required for acceptance testing and treatment planning of new accelerators with therapeutic electron beams. Since the publication of the TG-25 report, significant advances have taken place in the field of electron beam dosimetry, the most significant being that primary standards laboratories around the world have shifted from calibration standards based on exposure or air kerma to standards based on absorbed dose to water. The AAPM has published a new calibration protocol, TG-51, for the calibration of high-energy photon and electron beams. The formalism and dosimetry procedures recommended in this protocol are based on the absorbed dose to water calibration coefficient of an ionization chamber at 60Co energy, N60Co(D,w), together with the theoretical beam quality conversion coefficient k(Q) for the determination of absorbed dose to water in high-energy photon and electron beams. Task Group 70 was charged to reassess and update the recommendations in TG-25 to bring them into alignment with report TG-51 and to recommend new methodologies and procedures that would allow the practicing medical physicist to initiate and continue a high quality program in clinical electron beam dosimetry. This TG-70 report is a supplement to the TG-25 report and enhances the TG-25 report by including new topics and topics that were not covered in depth in the TG-25 report. These topics include procedures for obtaining data to commission a treatment planning computer, determining dose in irregularly shaped electron fields, and commissioning of sophisticated special procedures using high-energy electron beams. The use of radiochromic film for electrons is addressed, and radiographic film that is no longer available has been replaced by film that is available. Realistic stopping-power data are incorporated when appropriate along with enhanced tables of electron fluence data. A larger list of clinical applications of electron beams is included in the full TG-70 report available at http://www.aapm.org/pubs/reports. Descriptions of the techniques in the clinical sections are not exhaustive but do describe key elements of the procedures and how to initiate these programs in the clinic. There have been no major changes since the TG-25 report relating to flatness and symmetry, surface dose, use of thermoluminescent dosimeters or diodes, virtual source position designation, air gap corrections, oblique incidence, or corrections for inhomogeneities. Thus these topics are not addressed in the TG-70 report.

An enhanced sector integration model for output and dose distribution calculation of irregular concave shaped electron beams

A comprehensive method of output factor and dose distribution calculation for electron beams has been developed. It allows one to calculate the output factors and isodose distributions in water of arbitrary shaped electron fields with excellent accuracy even for the cases of concaved, small, elongated beams, and extended source to surface distances (SSDs). The method requires two sets of data: Depth dose distribution per monitor unit for circular cutouts and depth dose distributions per monitor unit for circular blocks (plugs), both for two SSDs, one reference of 100 cm and second extended one. The method has been extensively tested using a combination of different irregular cutouts and various SSDs for the 6 and 9 MeV electron beams. The calculated values agreed with the measured data well within 1% for output factors and below 1 for gamma (gamma test) for isodose distributions. The computer program has been developed to facilitate the method for practical application. The method has been used for almost 8 years considerably cutting workload in the department.

The nth root percent depth dose method for calculating monitor units for irregularly shaped electron fields

This study outlines an improved method for calculating dose per monitor unit values for irregularly shaped electron fields using the nth root percent depth dose method. This method calculates the percent depth dose and output factors for an irregularly shaped electron field directly from the measured electron beam percent depth dose curves and output factors for circular fields. The percent depth dose curves and output factors for circular fields are normalized and measured at a fixed depth of maximum dose for a reference field, respectively. When compared with the sector integral lateral buildup ratio method, the percent depth dose data calculated using the nth root method accounts more accurately for the change in lateral scatter with decreasing field size. Therefore, it provides more accurate values of dose per monitor unit at different depths for all type of field shapes and beam energies. For beam energies in the range of 6-21 MeV, the differences between measured and calculated dose per monitor unit values, at different depths, were found to be within +/- 1.0% when the nth root percent depth dose method was used for calculation and 12.6% when the sector integral lateral buildup ratio method was used. The nth root percent depth dose method was tested and compared with the sector integral lateral buildup ratio method for ten clinically used irregularly shaped inserts (cutouts). For small irregularly shaped fields, a maximum difference of 2% was found between calculated dose per monitor unit values and measurements when the nth root percent depth dose method was used; this difference changed to 7% when comparisons were made between measurements and calculations based on the sector integral lateral buildup ration method. For large irregular fields this difference was found to be within 1.5% and 3.5%, respectively.

Effect of electron beam obliquity on lateral buildup ratio: a Monte Carlo dosimetry evaluation

The impact of the oblique electron beam on the lateral buildup ratio (LBR), used in the electron pencil beam model to predict the per cent depth dose (PDD) and dose per monitor unit (MU) for an irregular electron field, was examined using Monte Carlo simulation. The EGSnrc-based Monte Carlo code was used to model electron beams produced by a Varian 21 EX linear accelerator for different beam energies, angles of obliquity and field sizes. The Monte Carlo phase space model was verified by measurements using electron diode and radiographic film. For PDDs of oblique electron beams, it is found that the depth of maximum dose (d(m)) shifts towards the surface as the beam obliquity increases. Moreover, for increasing the beam angle of obliquity, the depth doses just beyond d(m) decrease with depth. The depth doses then increase eventually in a deeper depth close to the practical range. The LBRs and pencil beam radial spread function, calculated using PDDs with different field sizes, are found varying with electron beam energies, angles of obliquity and cutout diameters. It is found that LBR increases along the normalized depth when the beam angle of obliquity increases. This results in a decrease of the radial spread function with an increase of beam obliquity. When the size of the electron field increases, the variation of LBR with beam angle of obliquity decreases. It should be noted that when calculating dose per MU for an oblique electron beam with an irregular field misunderstanding and neglecting the effect of beam obliquity would lead to a significant deviation. A database of LBRs for oblique electron beams can be created using Monte Carlo simulation conveniently and is recommended when an oblique beam is used in electron radiotherapy.

Calculation of lateral buildup ratio using Monte Carlo simulation for electron radiotherapy

Monte Carlo simulation was used to calculate the lateral buildup ratio (LBR) used in estimating the percentage depth dose (PDD) and dose per monitor unit for an irregular shaped cutout field in electron radiotherapy. Monte Carlo code BEAMnrc/EGSnrc was used to build a simulation model for a Varian 21 EX linear accelerator producing clinical electron beams with energies of 4, 6, 9, 12, and 16 MeV. The model is optimized by adjusting the incident electron energy within the Monte Carlo simulation so that the calculated PDD curves agree with the measurement within +/-2%. The LBR is calculated from the PDD curves for different diameters of circular cutouts. Although Monte Carlo simulation requires a longer time to create a LBR database compared to measurement using scanning water tank and dosimeter, the simulation models for different electron energies, applicators, and cutouts are very similar. As the calculations can be carried out in a batch mode automatically run by a computer, human efforts in carrying out measurements in the treatment room and fabricating the circular cutouts in the mold room are greatly saved. Moreover, the simulation avoids human error in the experimental setup and can better handle the electron scattering affecting accuracy in the measurement. Using Monte Carlo simulation to calculate the LBR is proved to be useful in the commissioning of the electron beams for electron radiotherapy.

A modified method of calculating the lateral build-up ratio for small electron fields

This note outlines an improved method of calculating dose per monitor unit values for small electron fields using Khan's lateral build-up ratio (LBR). This modified method obtains the LBR directly from the ratio of measured, surface normalized, electron beam percentage depth dose curves. The LBR calculated using this modified method more accurately accounts for the change in lateral scatter with decreasing field size. The LBR is used along with Khan's dose per monitor unit formula to calculate dose per monitor unit values for a set of small fields. These calculated dose per monitor unit values are compared to measured values to within 3.5% for all circular fields and electron energies examined. The modified method was further tested using a small triangular field. A maximum difference of 4.8% was found.

Review of electron beam therapy physics

For over 50 years, electron beams have been an important modality for providing an accurate dose of radiation to superficial cancers and disease and for limiting the dose to underlying normal tissues and structures. This review looks at many of the important contributions of physics and dosimetry to the development and utilization of electron beam therapy, including electron treatment machines, dose specification and calibration, dose measurement, electron transport calculations, treatment and treatment-planning tools, and clinical utilization, including special procedures. Also, future changes in the practice of electron therapy resulting from challenges to its utilization and from potential future technology are discussed.

A graphical user interface for an electron monitor unit calculator using a sector-integration algorithm and exponential curve-fitting method

A new electron monitor unit (MU) calculator program called "eMUc" was developed to provide a convenient electron MU calculation platform for the physics and radiotherapy staff in electron radiotherapy. The program was written using the Microsoft Visual Basic.net framework and has a user-friendly front-end window with the following features: (1) Apart from using the well-known polynomial curvefitting method for the interpolation and extrapolation of relative output factors (ROFs), an exponential curve-fitting method was used to obtain better results. (2) A new algorithm was used to acquire the radius in each angular segment in the irregular electron field during the sector integration. (3) A comprehensive graphical user interface running on the Microsoft Windows operating system was used. (4) Importing irregular electron cutout field images to the calculator program was simplified by using only a commercial optical scanner. (5) Interlocks were provided when the input patient treatment parameters could not be handled by the calculator database accurately. (6) A patient treatment record could be printed out as an electronic file or hard copy and transferred to the patient database. The data acquisition mainly required ROF measurements using various circular cutouts for all the available electron energies and applicators for our Varian 21 EX linear accelerator. To verify and implement the calculator, the measured results using our specific designed irregular and clinical cutouts were compared to those predicted by the calculator. Both agreed well with an error of +/-2%.

Experimental verification of the application of lateral buildup ratio on the 4-MeV electron beam

The lateral buildup ratio (LBR) used to estimate the depth dose distribution of electron beams for an irregular cutout field was obtained for a 4‐MeV energy beam from a Varian 21 EX linear accelerator. The depth‐dose curves for a group of circular cutout fields starting from a 2‐cm diameter were measured. Electron diodes were used in a large water tank to measure the LBR values for 6, 9, 12, and 16 MeV electron beam energies and a 10×10cm2 applicator. The results agreed with the published data. When the same equipment, setup, and technique were used to determine the LBR values for the 4‐MeV energy beam, the values were only reasonable, being within the clinical treatment range (i.e., LBR <1) for the smallest 6×6cm2 applicator. The calculated LBR values were clinically unacceptable for the circular cutout fields with a diameter larger than 2 cm with the 10×10cm2 applicator. The difficulty in the LBR measurement may be due to the significant contribution of scattered electrons from the beam defining system. This study also focused on how well the sigma values for the 4‐MeV beam can predict depth‐dose curves for other field sizes and whether the values are applicator‐dependent.

PACS numbers: 87.53.Fs; 87.53.Hv; 87.66.Jj

A graphical user interface for an electron monitor unit calculator using a sector-integration algorithm and exponential curve-fitting method

A new electron monitor unit (MU) calculator program called “eMUc” was developed to provide a convenient electron MU calculation platform for the physics and radiotherapy staff in electron radiotherapy. The program was written using the Microsoft Visual Basic.net framework and has a user‐friendly front‐end window with the following features: (1) Apart from using the well‐known polynomial curve‐fitting method for the interpolation and extrapolation of relative output factors (ROFs), an exponential curve‐fitting method was used to obtain better results. (2) A new algorithm was used to acquire the radius in each angular segment in the irregular electron field during the sector integration. (3) A comprehensive graphical user interface running on the Microsoft Windows operating system was used. (4) Importing irregular electron cutout field images to the calculator program was simplified by using only a commercial optical scanner. (5) Interlocks were provided when the input patient treatment parameters could not be handled by the calculator database accurately. (6) A patient treatment record could be printed out as an electronic file or hard copy and transferred to the patient database. The data acquisition mainly required ROF measurements using various circular cutouts for all the available electron energies and applicators for our Varian 21 EX linear accelerator. To verify and implement the calculator, the measured results using our specific designed irregular and clinical cutouts were compared to those predicted by the calculator. Both agreed well with an error of ±2%.

PACS number(s): 87.53.Fs; 87.53.Hv; 87.66.‐a

Final Aperture Superposition Technique applied to fast calculation of electron output factors and depth dose curves

The Final Aperture Superposition Technique (FAST) is described and applied to accurate, near instantaneous calculation of the relative output factor (ROF) and central axis percentage depth dose curve (PDD) for clinical electron beams used in radiotherapy. FAST is based on precalculation of dose at select points for the two extreme situations of a fully open final aperture and a final aperture with no opening (fully shielded). This technique is different than conventional superposition of dose deposition kernels: The precalculated dose is differential in position of the electron or photon at the downstream surface of the insert. The calculation for a particular aperture (x-ray jaws or MLC, insert in electron applicator) is done with superposition of the precalculated dose data, using the open field data over the open part of the aperture and the fully shielded data over the remainder. The calculation takes explicit account of all interactions in the shielded region of the aperture except the collimator effect: Particles that pass from the open part into the shielded part, or visa versa. For the clinical demonstration, FAST was compared to full Monte Carlo simulation of 10 x 10, 2.5 x 2.5, and 2 x 8 cm2 inserts. Dose was calculated to 0.5% precision in 0.4 x 0.4 x 0.2 cm3 voxels, spaced at 0.2 cm depth intervals along the central axis, using detailed Monte Carlo simulation of the treatment head of a commercial linear accelerator for six different electron beams with energies of 6-21 MeV. Each simulation took several hours on a personal computer with a 1.7 Mhz processor. The calculation for the individual inserts, done with superposition, was completed in under a second on the same PC. Since simulations for the pre calculation are only performed once, higher precision and resolution can be obtained without increasing the calculation time for individual inserts. Fully shielded contributions were largest for small fields and high beam energy, at the surface, reaching a maximum of 5.6% at 21 MeV. Contributions from the collimator effect were largest for the large field size, high beam energy, and shallow depths, reaching a maximum of 4.7% at 21 MeV. Both shielding contributions and the collimator effect need to be taken into account to achieve an accuracy of 2%. FAST takes explicit account of the shielding contributions. With the collimator effect set to that of the largest field in the FAST calculation, the difference in dose on the central axis (product of ROF and PDD) between FAST and full simulation was generally under 2%. The maximum difference of 2.5% exceeded the statistical precision of the calculation by four standard deviations. This occurred at 18 MeV for the 2.5 x 2.5 cm2 field. The differences are due to the method used to account for the collimator effect.

Measurements of output factors with different detector types and Monte Carlo calculations of stopping-power ratios for degraded electron beams

The aim of the present study was to investigate three different detector types (a parallel-plate ionization chamber, a p-type silicon diode and a diamond detector) with regard to output factor measurements in degraded electron beams, such as those encountered in small-electron-field radiotherapy and intraoperative radiation therapy (IORT). The Monte Carlo method was used to calculate mass collision stopping-power ratios between water and the different detector materials for these complex electron beams (nominal energies of 6, 12 and 20 MeV). The diamond detector was shown to exhibit excellent properties for output factor measurements in degraded beams and was therefore used as a reference. The diode detector was found to be well suited for practical measurements of output factors, although the water-to-silicon stopping-power ratio was shown to vary slightly with treatment set-up and irradiation depth (especially for lower electron energies). Application of ionization-chamber-based dosimetry, according to international dosimetry protocols, will introduce uncertainties smaller than 0.3% into the output factor determination for conventional IORT beams if the variation of the water-to-air stopping-power ratio is not taken into account. The IORT system at our department includes a 0.3 cm thin plastic scatterer inside the therapeutic beam, which furthermore increases the energy degradation of the electrons. By ignoring the change in the water-to-air stopping-power ratio due to this scatterer, the output factor could be underestimated by up to 1.3%. This was verified by the measurements. In small-electron-beam dosimetry, the water-to-air stopping-power ratio variation with field size could mostly be ignored. For fields with flat lateral dose profiles (>3 x 3 cm2), output factors determined with the ionization chamber were found to be in close agreement with the results of the diamond detector. For smaller field sizes the lateral extension of the ionization chamber hampers its use. We therefore recommend that the readily available silicon diode detector should be used for output factor measurements in complex electron fields.

Monte Carlo calculations of output factors for clinically shaped electron fields

We report on the use of the EGS4/BEAM Monte Carlo technique to predict the output factors for clinically relevant, irregularly shaped inserts as they intercept a linear accelerator's electron beams. The output factor for a particular combination—energy, cone, insert, and source‐to‐surface distance (SSD)—is defined in accordance with AAPM TG‐25 as the product of cone correction factor and insert correction factor, evaluated at the depth of maximum dose. Since cone correction factors are easily obtained, we focus our investigation on the insert correction factors (ICFs). An analysis of the inserts used in routine clinical practice resulted in the identification of a set of seven “idealized” shapes characterized by specific parameters. The ICFs for these shapes were calculated using a Monte Carlo method (EGS4/BEAM) and measured for a subset of them using an ion chamber and well‐established measurement methods. Analytical models were developed to predict the Monte Carlo–calculated ICF values for various electron energies, cone sizes, shapes, and SSDs. The goodness‐of‐fit between predicted and Monte Carlo–calculated ICF values was tested using the Kolmogorov–Smirnoff statistical test. Results show that Monte Carlo–calculated ICFs match the measured values within 2.0% for most of the shapes considered, except for few highly elongated fields, where deviations up to 4.0% were recorded. Predicted values based on analytical modeling agree with measured ICF values within 2% to 3% for all configurations. We conclude that the predicted ICF values based on modeling of Monte Carlo–calculated values could be introduced in clinical use.

PACS numbers: 87.53.Wz, 87.53.Hv

Application of measured pencil beam parameters for electron beam model evaluation

Most current electron beam models, as are used in commercial treatment planning systems, combine measured broad beam central axis depth dose data with measured or modeled functions to approximate radial scatter and heterogeneity effects. In this paper, we extend a recently developed pencil beam model to calculate doses outside the field edge and doses in heterogeneous media. We have also explored use of this model as a tool for evaluating commercial electron planning programs. The algorithm we have developed, based on the concept of the lateral buildup ratio (LBR), enables calculation of dose at any point in an irregular electron field, and is capable of generating both on- and off-axis depth dose curves and isodose profiles. This model includes the effects of density and mass-angular scattering power in measured broad beam central axis depth dose data, which when combined with small field reference data, can be used to generate LBR ratios. From these ratios one can infer the depth dependent, effective pencil beam radial spread parameter a in water or other materials, which can be used to model any arbitrary field. We have used this approach to calculate fractional depth doses for small fields incident on aluminum and cork, which we have then compared against measurements and the calculations of several commercial planning systems.

A two-source model for electron beams: calculation of relative output factors

A two-source model for the calculation of relative output factors (ROF) for clinical applications of electron beams has been developed. The model consists of (1) an effective extended source above the final field-defining aperture (cutout) plane and (2) a source due to scattering from the aperture. Calculations are based on Fermi-Eyges theory and a pencil beam algorithm with parameters determined independently for each major scattering component. The model predicts a modified inverse square law for determining the dose rate for the electron beams. It also generalizes the "square-root method" and "one-dimensional method" that are often used clinically for ROF calculations. A computer program based on the model has been developed to calculate ROF for irregular fields. The predictions of ROF values have been compared with measurements on a Varian CLINAC 2100C/D accelerator for different cutout size, energies, applicators, and SSDs for square fields, rectangular fields, circular fields, and irregular fields. The agreement between prediction and measurement of the ROF for these wide range of conditions is generally within 1% for energies from 6 to 20 MeV. This two-source model can be used for clinical applications and it requires a minimal set of measured input data.

Monte Carlo calculation of output factors for circular, rectangular, and square fields of electron accelerators (6-20 MeV)

Monte Carlo (MC) techniques can be used to build a simulation model of an electron accelerator to calculate output factors for electron fields. This can be useful during commissioning of electron beams from a linac and in clinical practice where irregular fields are also encountered. The Monte Carlo code BEAM/EGS4 was used to model electron beams (6-20 MeV) from a Varian 2100C linear accelerator. After optimization of the Monte Carlo simulation model, agreement within 1% to 2% was obtained between calculated and measured (with a Si diode) lateral and depth dose distributions or within 1 mm in the penumbral regions. Output factors for square, rectangular, and circular fields were measured using two different plane-parallel ion chambers (Markus and NACP) and compared to MC simulations. The agreement was usually within 1% to 2%. This study was not primarily concerned with minimizing the simulation time required to obtain output factors but some considerations with respect to this are presented. It would be particularly useful if the MC model could also be used to calculate output factors for other, similar linacs. To see if this was possible, the primary electron energies in the MC model were retuned to model a recently commissioned similar linac. Good agreement between calculated and measured output factors was obtained for most field sizes for this second accelerator.

Field equivalence for clinical electron beams

The concept of field equivalence for electron beams is examined using a pencil beam theory applied to circular fields. It is shown that a circular field can be found for a field of any size, shape and energy for which the depth dose distribution is approximately equivalent. The usefulness of the concept in clinical dosimetry is discussed.

Electron spectra derived from depth dose distributions

The technique of extracting electron energy spectra from measured distributions of dose along the central axis of clinical electron beams is explored in detail. Clinical spectra measured with this simple spectroscopy tool are shown to be sufficient in accuracy and resolution for use in Monte Carlo treatment planning. A set of monoenergetic depth dose curves of appropriate energy spacing, precalculated with Monte Carlo for a simple beam model, are unfolded from the measured depth dose curve. The beam model is comprised of a point electron and photon source placed in vacuum with a source-to-surface distance of 100 cm. Systematic error introduced by this model affects the calculated depth dose curve by no more than 2%/2 mm. The component of the dose due to treatment head bremsstrahlung, subtracted prior to unfolding, is estimated from the thin-target Schiff spectrum within 0.3% of the maximum total dose (from electrons and photons) on the beam axis. Optimal unfolding parameters are chosen, based on physical principles. Unfolding is done with the public-domain code FERDO. Comparisons were made to previously published spectra measured with magnetic spectroscopy and to spectra we calculated with Monte Carlo treatment head simulation. The approach gives smooth spectra with an average resolution for the 27 beams studied of 16+/-3% of the mean peak energy. The mean peak energy of the magnetic spectrometer spectra was calculated within 2% for the AECL T20 scanning beam accelerators, 3% for the Philips SL25 scattering foil based machine. The number of low energy electrons in Monte Carlo spectra is estimated by unfolding with an accuracy of 2%, relative to the total number of electrons in the beam. Central axis depth dose curves calculated from unfolded spectra are within 0.5%/0.5 mm of measured and simulated depth dose curves, except near the practical range, where 1%/1 mm errors are evident.

Calculation of depth dose and dose per monitor unit for irregularly shaped electron fields: an addendum

Electron beam output (dose/MU) is generally specified at the depth of maximum dose (zmax). The location of this point depends on beam energy, field size and field shape. Useful relationships have been developed to estimate zmax as a function of field size and beam energy. The formalism uses a pencil beam theory applied to circular fields.