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

Empirical method for modeling the percent depth dose curves of electron beam in radiation therapy

Introduction: This study presents an empirical method to model the electron beam percent depth dose curve (PDD) using the primary and tail functions in radiation therapy. The modeling parameters N and n can be used to derive the depth relative stopping power of the electron energy in radiation therapy.

Methods and Materials: The electrons PDD curves were modeled with the primary-tail function in this study. The primary function included exponential function and main parameters of N, µ while the tail function was composed by a sigmoid function with the main parameter of n. The PDD for five electron energies were modeled by the primary and tail function by adjusting the parameters of N, µ and n. The R50 and Rp 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 with the primary-tail function. The stopping power for different electron energies at different depths can also be derived from the parameters of N, µ and n. Percent ionization depth curve can then be derived from the percent depth dose by dividing its depth relevant stopping power for comparing with the original water phantom measurement.

Results: The main parameters N, n increase, but µ decreases in primary-tail function when electron energy increased. The relationship of parameters n, N and LN(-µ) with electron energy are n = 31.667 E0 - 88, N = 0.9975 E0 - 2.8535, LN(-µ) = -0.1355 E0 - 6.0986, respectively. Stopping power of different electron energy can be derived from n and N with the equation: stopping power = (−0.042 ln N E 0 + 1.072)e(−n−E0·5·10−5+0.0381·d), where d is the depth in water. Percent depth dose was derived from the percent reading curve by multiplying the stopping power relevant to the depth in water at certain electron energy.

Conclusion: The PDD of electrons at different energies and field sizes can be modeled with an empirical model to deal with the stopping power calculation. The primary-tail equation provides a uncomplicated solution than a pencil beam or other numerical algorism for investigators to research the behavior of electron beam in radiation therapy.

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.

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.

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.

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 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

The clinical implementation of a method for calculating the output factor and per cent depth dose for an electron beam

A modified sector-integration method has been developed that predicts electron beam output factor at any point on the beam central axis, for a given source to surface distance (SSD), as a function of the geometry of the irradiated field. The main concept of this method is that with the arbitrary field shape divided into small sectors, the individual contributions from each sector can be calculated based on the sector radius, using a dataset consisting of circular inserts of standard radii. A computer program was developed based on this algorithm. The program interfaces to a digital camera that is used to capture the shape of the electron insert. We compared the calculated and the measured output factors and per cent depth doses (PDDs) at different SSDs for various rectangular inserts and a typical irregularly shaped insert used in our clinic. To determine the geometric limitations of this algorithm, a series of rectangular inserts were designed with the long-to-short axis ratio between 1:1 and 7:1. The agreement between calculation and measurement for the electron output and PDD was generally within 2% (or 2 mm) for energies from 6 to 20 MeV.

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.

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.