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.     

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.     

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.     

Description and dosimetric verification of the PEREGRINE Monte Carlo dose calculation system for photon beams incident on a water phantom

PEREGRINE is a three-dimensional Monte Carlo dose calculation system written specifically for radiotherapy. This paper describes the implementation and overall dosimetric accuracy of PEREGRINE physics algorithms, beam model, and beam commissioning procedure. Particle-interaction data, tracking geometries, scoring, variance reduction, and statistical analysis are described. The BEAM code system is used to model the treatment-independent accelerator head, resulting in the identification of primary and scattered photon sources and an electron contaminant source. The magnitude of the electron source is increased to improve agreement with measurements in the buildup region in the largest fields. Published measurements provide an estimate of backscatter on monitor chamber response. Commissioning consists of selecting the electron beam energy, determining the scale factor that defines dose per monitor unit, and describing treatment-dependent beam modifiers. We compare calculations with measurements in a water phantom for open fields, wedges, blocks, and a multileaf collimator for 6 and 18 MV Varian Clinac 2100C photon beams. All calculations are reported as dose per monitor unit. Aside from backscatter estimates, no additional, field-specific normalization is included in comparisons with measurements. Maximum discrepancies were less than either 2% of the maximum dose or 1.2 mm in isodose position for all field sizes and beam modifiers.     

Dose uncertainties in photon pencil kernel calculations at off-axis positions

The purpose of this study was to investigate the specific problems associated with photon dose calculations in points located at a distance from the central beam axis. These problems are related to laterally inhomogeneous energy fluence distributions and spectral variations causing a lateral shift in the beam quality, commonly referred to as off-axis softening (OAS). We have examined how the dose calculation accuracy is affected when enabling and disabling explicit modeling of these two effects. The calculations were performed using a pencil kernel dose calculation algorithm that facilitates modeling of OAS through laterally varying kernel properties. Together with a multi-source model that provides the lateral energy fluence distribution this generates the total dose output, i.e., the dose per monitor unit, at an arbitrary point of interest. The dose calculation accuracy was evaluated through comparisons with 264 measured output factors acquired at 5, 10, and 20 cm depth in four different megavoltage photon beams. The measurements were performed up to 18 cm from the central beam axis, inside square fields of varying size and position. The results show that calculations including explicit modeling of OAS were considerably more accurate, up to 4%, than those ignoring the lateral beam quality shift. The deviations caused by simplified head scatter modeling were smaller, but near the field edges additional errors close to 1% occurred. When enabling full physics modeling in the dose calculations the deviations display a mean value of -0.1%, a standard deviation of 0.7%, and a maximum deviation of -2.2%. Finally, the results were analyzed in order to quantify and model the inherent uncertainties that are present when leaving the central beam axis. The off-axis uncertainty component showed to increase with both off-axis distance and depth, reaching 1% (1 standard deviation) at 20 cm depth.     

Clinical dosimetry for implementation of a multileaf collimator.

In order to initiate the use of a multileaf collimator (MLC) in the clinic, a set of technical procedures needs to be available sufficient to create MLC leaf settings and to deliver an accurate dose of radiation through the MLC-shaped field. Dosimetry data for clinical use of the MLC were measured. Dosimetric characteristics included central axis percent depth dose, output factors, and penumbra. In this paper, it has been concluded that a dose control monitor unit calculation procedure that has been applied to the use of conventional secondary field-shaping blocks can be applied to the multileaf collimator dosimetry. The multileaf collimator penumbra (20% to 80%) is only slightly wider (1-3 mm) than the penumbra of the conventional collimator jaws. Beam's-eye-view comparisons made between the isodose curves in fields shaped by conventional Cerrobend blocks and isodose curves in fields shaped by the multileaf collimator demonstrated that the 50% isodose line at 10-cm depth exhibited the discrete steps of the multileaf collimator leaves, but that the 90% and 10% isodose curves of the multileaf were close to those shaped by Cerrobend blocks.     

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 practical method to calculate head scatter factors in wedged rectangular and irregular MLC shaped beams for external and internal wedges

Factor based methods for absorbed dose or monitor unit calculations are often based on separate data sets for open and wedged beams. The determination of basic beam parameters can be rather time consuming, unless equivalent square methods are applied. When considering irregular wedged beams shaped with a multileaf collimator, parametrization methods for dosimetric quantities, e.g. output ratios or wedge factors as a function of field size and shape, become even more important. A practical method is presented to derive wedged output ratios in air (S(c,w)) for any rectangular field and for any irregular MLC shaped beam. This method was based on open field output ratios in air (S(c)) for a field with the same collimator setting, and a relation f(w) between S(c,w) and S(c). The relation f(w) can be determined from measured output ratios in air for a few open and wedged fields including the maximum wedged field size. The function f(w) and its parametrization were dependent on wedge angle and treatment head design, i.e. they were different for internal and external wedges. The proposed method was tested for rectangular wedged fields on three accelerators with internal wedges (GE, Elekta, BBC) and two accelerators with external wedges (Varian). For symmetric regular beams the average deviation between calculated and measured S(c,w) / S(c) ratios was 0.3% for external wedges and about 0.6% for internal wedges. Maximum deviations of 1.8% were obtained for elongated rectangular fields on the GE and ELEKTA linacs with an internal wedge. The same accuracy was achieved for irregular MLC shaped wedged beams on the accelerators with MLC and internal wedges (GE and Elekta), with an average deviation < 1% for the fields tested. The proposed method to determine output ratios in air for wedged beams from output ratios of open beams, combined with equivalent square approaches, can be easily integrated in empirical or semi-empirical methods for monitor unit calculations.     

Characteristics of the high-energy photon beam of a 25-MeV accelerator

The CGR Saturne 25 is an isocentrically mounted standing wave medical linear accelerator that produces dual-energy photon beams and a scanned electron beam with six selectable energies between 4 and 25 MeV. The highest energy photon beam is nominally referred to as 23 MV. For this beam the mean energy of the accelerated electron beam on the 1.3 radiation length (4 mm) tungsten x-ray target is found to be approximately 21 MeV, with the energy acceptance stated to be +/- 5%. The electron beam traverses a 270 degrees bending magnet upstream of the x-ray production target. The resulting bremsstrahlung beam passes through a combination steel and lead flattening filter, 4-cm maximum thickness. Dosimetric data for the 23-MV beam are presented with respect to rectangular field output factor, depth of maximum dose as a function of field size, surface and buildup dose, central axis percent depth dose, tissue-phantom ratios, beam profile, applicability of inverse square, and block transmission. Some data are also presented on the effect of different flattening filter designs on apparent beam energy.     

Monitor unit settings for intensity modulated beams delivered using a step-and-shoot approach

Two linear accelerators have been commissioned for delivering IMRT treatments using a step-and-shoot approach. To assess beam startup stability for 6 and 18 MV x-ray beams, dose delivered per monitor unit (MU), beam flatness, and beam symmetry were measured as a function of the total number of MU delivered at a clinical dose rate of 400 MU per minute. Relative to a 100 MU exposure, the dose delivered per MU by both linear accelerators was found to be within +/-2% for exposures larger than 4 MU. Beam flatness and symmetry also met accepted quality assurance standards for a minimum exposure of 4 MU. We have found that the performance of the two machines under study is well suited to the delivery of step-and-shoot IMRT. A system of dose calculation has also been commissioned for applying head scatter corrections to fields as small as 1x1 cm2. The accuracy and precision of the relative output calculations in water was validated for small fields and fields offset from the axis of collimator rotation. For both 6 and 18 MV x-ray beams, the dose per MU calculated in a water phantom agrees with measured data to within 1% on average, with a maximum deviation of 2.5%. The largest output factor discrepancies were seen when the actual radiation field size deviated from the set field size. The measured output in water can vary by as much 16% for 1x1 cm2 fields, when the measured field size deviates from the set field size by 2 mm. For a 1 mm deviation, this discrepancy was reduced to 8%. Steps should be taken to ensure collimator precision is tightly controlled when using such small fields. If this is not possible, very small fields should not contribute to a significant portion of the treatment, or uncertainties in the collimator position may effect the accuracy of the dose delivered.     

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.     

An analysis of equivalent fields for electron beam central-axis dose calculations.

The concepts of the equivalent square or circular field have long been used in dose calculations for photon beams. These concepts allow data measured for square or circular fields to be extended to calculate, for example, the percentage depth doses or output factors of rectangular or irregular fields. It has been pointed out in the past that an electron beam equivalent field dimension varies with depth and, thus, will have questionable utility. As the equivalent square and circle have proven to be useful in photon beam dose calculations, the work described in this paper has sought to analyze conditions under which equivalent fields may be useful for electron beam dose calculations. Equivalent square field dimensions and circular field radii are derived using the Fermi-Eyges theory and are compared to a number of approximate equivalent fields that have been applied to electron dose calculations. Calculations are also compared with measurements presented in the literature. It is shown that the accuracy of an electron dose calculation using these approximate equivalent fields diminishes with a decreasing degree of lateral scatter equilibrium at the central axis and only becomes accurate once equilibrium is established. As the central-axis dose under this latter condition is in any event independent of field shape or size, the equivalent field approach becomes unnecessary. Because of this and other restrictions discussed, it is concluded that the equivalent fields analyzed here should not be used for electron beam dose calculations.     

Irregular field calculation on the central beam axis of photon beams using sector-integration

A method is proposed for calculation of irregular field factors on the central beam axis and homogeneous medium for x-ray beams. The irregular field factor is introduced as the ratio of the output of a field with and without blocks on the central beam axis. The algorithm is based on the sector-integration method and the circular field quantities are calculated from in-phantom measurements. These circular field quantities are the output per beam monitor unit for circular fields defined by a hypothetical secondary collimator and reduced to a circular field by blocking. A derivation of the sector-integration equation is given from first principles. As it is shown, the circular field quantities are evaluated from data measured for rectangular, block shaped fields. Such quantities contain all beam components, including photons scattered from the blocks, the block tray, and photons scattered in the phantom. Consequently, the so called primary and secondary beam components are readily incorporated in this approach. Once the circular field quantities have been determined from rectangular field data, the irregular field factors for other geometry can be calculated. Irregular field factors for square, rectangular and circular block-shaped fields were calculated for 6 MV photon beams and compared with measured values. The results agree within 0.7%, even for heavy blocked field cases, i.e., a 40 x 40 cm2 collimator field blocked to a 5 x 5 cm2 field. The method was tested for a particular source to surface distance, depth, phantom composition, and source to block distance. Calculation of irregular field factors in another set up conditions requires the measurement of the appropriate input data.     

Calculation of electron beam dose distributions for arbitrarily shaped fields

A method for the calculation of absorbed dose distributions of arbitrarily shaped electron beams is presented. Isodose distributions and output factors of treatment fields can be predicted with good accuracy, without the need for any dose measurement in the actual field. A Gaussian pencil beam model is employed with two different pencil beams for each electron beam energy. The values of the parameters of the pencil beam dose distributions are determined from a set of measurements of broad beam distributions; in this way the influence of electrons scattered by the applicator walls is taken into account. The dose distribution of electrons scattered from high atomic number metal frames, which define the treatment field contour at the skin, is calculated separately and added. This calculation is based on experimentally derived data. The method has been tested for beams with 6, 10, 14 and 20 MeV electron energy. The distance between calculated and measured isodose lines with values between 10 and 90% is under 0.3 cm. The difference between calculated and measured output factors does not exceed 2%.     

Dosimetric characterization of the 18-MV photon beam from the Siemens Mevatron 77 linear accelerator

A comprehensive set of dosimetric measurements has been made on the Mevatron 77.80.67 18-MV photon beam. Percentage depth dose, dose in the buildup region, field size dependence of output, transmission through lead, tray attenuation, and isodose curves for the open and wedged fields were measured using an ionization chamber in water and polystyrene phantoms. These dosimetric measurements sufficiently characterized the beam to permit clinical use. The depth dose at 10-cm depth for a 10 X 10 cm2 field at 100-cm source-to-skin distance (SSD) is 80.9%, which meets design specifications. Central axis depth-dose data were fitted to within 0.5% by a set of polynomial equations utilizing a two-dimensional linear regression analysis. Tissue-maximum ratios calculated from depth-dose data agree with measured data to within 2%. Output differences as large as 2.5% were measured for rectangular fields depending on which collimator jaws defined the long dimension of the field. The field size dependence of output was fit to within +/- 0.1% by a linear regression. The half-value thickness of the beam was measured to be 13 mm of lead.     

Field-size dependence of doses of therapeutic carbon beams

To estimate the physical dose at the center of spread-out Bragg peaks (SOBP) for various conditions of the irradiation system, a semiempirical approach was applied. The dose at the center of the SOBP depends on the field size because of large-angle scattering particles in the water phantom. For a small field of 5 x 5 cm2, the dose was reduced to 99.2%, 97.5%, and 96.5% of the dose used for the open field in the case of 290, 350, and 400 MeV/n carbon beams, respectively. Based on the three-Gaussian form of the lateral dose distributions of the carbon pencil beam, which has previously been shown to be effective for describing scattered carbon beams, we reconstructed the dose distributions of the SOBP beam. The reconstructed lateral dose distribution reproduced the measured lateral dose distributions very well. The field-size dependencies calculated using the reconstructed lateral dose distribution of the therapeutic carbon beam agreed with the measured dose dependency very well. The reconstructed beam was also used for irregularly shaped fields. The resultant dose distribution agreed with the measured dose distribution. The reconstructed beams were found to be applicable to the treatment-planning system.     

Film dosimetry of small electron beams for routine radiotherapy planning

The characteristics of very small fields, 1 X 1 and 2 X 2 cm, of electron beams of nominal energies, 5, 7, 10, 12, 15, and 18 MeV have been studied and compared to a 10 X 10 cm field. A parallel-plate ion chamber and film have been used to obtain various dose parameters. The central axis depth dose measurements, field flatness, uniformity index, and relative output factors are presented. It was found that satisfactory results for determining the relative output factor can be obtained from film data using a scanning densitometer. It is our conclusion that film dosimetry is acceptable in determining the necessary clinical parameters needed to treat patients with fields as small as 2 X 2 cm. For the 1 X 1 cm field size and for the electron energies greater than 10 MeV, there was substantial disagreement between the ion chamber and film data in the buildup region as well as the regions beyond the depth of maximum dose to the depth of 90% dose.     

Accuracy limits of the equivalent field method for irregular photon fields

A mathematical approach is developed to evaluate the accuracy of the equivalent field method using basic clinical photon beam data. This paper presents an analytical calculation of dose errors arising when field equivalencies, calculated at a certain reference depth, are translated to other depths. The phantom scatter summation is expressed as a Riemann-Stieltjes integral and two categories of irregular fields are introduced: uniform and multiform. It is shown that multiform fields produce errors whose magnitudes are nearly twice those corresponding to uniform fields in extreme situations. For uniform field shapes, the maximum, local, relative dose errors, when the equivalencies are calculated at 10 cm depth on the central axis and translated to a depth of 30 cm, are 3.8% and 8.8% for 6 MV and cobalt-60 photon beams, respectively. In terms of maximum dose those errors are within 1-2%. This supports the conclusion that the equivalencies between rectangular fields, which are examples of uniform fields, are applicable to dose ratio functions irrespective of beam energy. However, the magnitude of such errors could be of importance when assessing the exit dose for in vivo monitoring. This work provides a better understanding of the influence of the irregular field shapes on the accuracy of the equivalent field method.     

Dose errors due to charge storage in electron irradiated plastic phantoms

Commercial plastics used for radiation dosimetry are good electrical insulators . Used in electron beams, these insulators store charge and produce internal electric fields large enough to measurably alter the electron dose distribution in the plastic. The reading per monitor unit from a cylindrical ion chamber imbedded in a polymethylmethacrylate (PMMA) or polystyrene phantom will increase with accumulated electron dose, the increase being detectable after about 20 Gy of 6-MeV electrons. The magnitude of the effect also depends on the type of the plastic, the thickness of the plastic, the wall thickness of the detector, the diameter and depth of the hole in the plastic, the energy of the electron beam, and the dose rate used. Effects of charge buildup have been documented elsewhere for very low energy electrons at extremely high doses and dose rates. Here we draw attention to the charging effects in plastics at the dose levels encountered in therapy dosimetry where ion chamber or other dosimeter readings may easily increase by 5% to 10% and where a phantom, once charged, will also affect subsequent readings taken in 60Co beams and high-energy electron and x-ray beams for periods of several days to many months. It is recommended that conducting plastic phantoms replace PMMA and polystyrene phantoms in radiation dosimetry.     

Lateral loss and dose discrepancies of multileaf collimator segments in intensity modulated radiation therapy

In the step-and-shoot technique delivery of intensity modulated radiation therapy (IMRT), each static field consists of a number of beamlets, some of which may be very small. In this study, we measured the dose characteristics for a range of field sizes: 2 x 2 to 12 x 10 cm2 for 6 and 15 MV x rays. For a given field length, a number of treatment fields are set up by sequentially increasing the field width using a multi leaf collimator. A set of fields is delivered with the accelerator operated in the IMRT mode. Using an ion chamber, the output factors at 1 cm and 3 cm laterally from a field edge are measured at different depths in a solid water phantom. Our results show that with insufficient lateral distance in at least one direction, the absorbed dose never reaches the equilibrium values, and can be significantly lower for very small field sizes. For example, the output factor of the 2 x 2 cm2 field relative to 10 x 10 cm2 at d(max0 is 0.832 and 0.790 for 6 MV and 15 MV x rays, respectively. Multiple output factor curves are obtained for different field lengths and different buildup conditions. Thus under nonequilibrium conditions, output factors are critically dependent on the field size and the conventional method of determining the equivalent square does not apply. Comparison of output factors acquired in the commissioning of the accelerator with those measured in the present study under conditions of nonequilibrium shows large discrepancies between the two sets of measurements. Thus monitor units generated by a treatment planning system using beam data commissioned with symmetric fields may be underestimated by > 5%, depending on the size and shape of the segments. To facilitate manual MU calculation as an independent check in step-and-shoot IMRT, the concept of effective equivalent square (EES) is introduced. Using EES, output factors can be calculated using existing beam data for fields with asymmetric collimator settings and under conditions of lateral disequilibrium.