Clinical implementation of a two-component x-ray source model for calculation of head-scatter factors

Measurement and comparison of head scatter factor for 7 MV unflattened (FFF) and 6 MV flattened photon beam using indigenously designed columnar mini phantom

AIM

To measure and compare the head scatter factor for 7 MV unflattened and 6 MV flattened photon beam using a home-made designed mini phantom.

BACKGROUND

The head scatter factor (Sc) is one of the important parameters for MU calculation. There are multiple factors that influence the Sc values, like accelerator head, flattening filter, primary and secondary collimators.

MATERIALS AND METHODS

A columnar mini phantom was designed as recommended by AAPM Task Group 74 with high and low atomic number material for measurement of head scatter factors at 10 cm and d max dose water equivalent thickness.

RESULTS

The Sc values measured with high-Z are higher than the low-Z mini phantoms observed for both 6MV-FB and 7MV-UFB photon energies. Sc values of 7MV-UFB photon beams were smaller than those of the 6MV-FB photon beams (0.6-2.2% (Primus), 0.2-1.4% (Artiste) and 0.6-3.7% (Clinac iX (2300CD))) for field sizes ranging from 10 cm × 10 cm to 40 cm × 40 cm. The SSD had no influence on head scatter for both flattened and unflattened beams. The presence of wedge filters influences the Sc values. The collimator exchange effects showed that the opening of the upper jaw increases Sc irrespective of FF and FFF.

CONCLUSIONS

There were significant differences in Sc values measured for 6MV-FB and unflattened 7MV-UFB photon beams over the range of field sizes from 10 cm × 10 cm to 40 cm × 04 cm. Different results were obtained for measurements performed with low-Z and high-Z mini phantoms.

Comparison of Head Scatter Factor for 6MV and 10MV flattened (FB) and Unflattened (FFF) Photon Beam using indigenously Designed Columnar Mini Phantom

To measure and compare the head scatter factor for flattened (FB) and unflattened (FFF) of 6MV and 10MV photon beam using indigenously designed mini phantom. A columnar mini phantom was designed as recommended by AAPM Task Group 74 with low and high atomic number materials at 10 cm (mini phantom) and at approximately twice the depth of maximum dose water equivalent thickness (brass build-up cap). Scatter in the accelerator (Sc) values of 6MV-FFF photon beams are lesser than that of the 6MV-FB photon beams (0.66-2.8%; Clinac iX, 2300CD) and (0.47-1.74%; True beam) for field sizes ranging from 10 × 10 cm² to 40 × 40 cm². Sc values of 10MV-FFF photon beams are lesser (0.61-2.19%; True beam) than that of the 10MV-FB photons beams for field sizes ranging from 10 × 10 cm² to 40 × 40 cm². The SSD had no influence on head scatter for both flattened and unflattened beams and irrespective of head design of the different linear accelerators. The presence of field shaping device influences the Sc values. The collimator exchange effect reveals that the opening of the upper jaw increases Sc irrespective of FB or FFF photon beams and different linear accelerators, and it is less significant in FFF beams. Sc values of 6MV-FB square field were in good agreement with that of AAPM, TG-74 published data for Varian (Clinac iX, 2300CD) accelerator. Our results confirm that the removal of flattening filter decreases in the head scatter factor compared to flattened beam. This could reduce the out-of-field dose in advanced treatment delivery techniques.

Multisource modeling of flattening filter free (FFF) beam and the optimization of model parameters

PURPOSE

With the introduction of flattening filter free (FFF) linear accelerators to radiation oncology, new analytical source models for a FFF beam applicable to current treatment planning systems is needed. In this work, a multisource model for the FFF beam and the optimization of involved model parameters were designed.

METHODS

The model is based on a previous three source model proposed by Yang et al. ["A three-source model for the calculation of head scatter factors," Med. Phys. 29, 2024-2033 (2002)]. An off axis ratio (OAR) of photon fluence was introduced to the primary source term to generate cone shaped profiles. The parameters of the source model were determined from measured head scatter factors using a line search optimization technique. The OAR of the photon fluence was determined from a measured dose profile of a 40 x 40 cm2 field size with the same optimization technique, but a new method to acquire gradient terms for OARs was developed to enhance the speed of the optimization process. The improved model was validated with measured dose profiles from 3 x 3 to 40 x 40 cm2 field sizes at 6 and 10 MV from a TrueBeam STx linear accelerator. Furthermore, planar dose distributions for clinically used radiation fields were also calculated and compared to measurements using a 2D array detector using the gamma index method.

RESULTS

All dose values for the calculated profiles agreed with the measured dose profiles within 0.5% at 6 and 10 MV beams, except for some low dose regions for larger field sizes. A slight overestimation was seen in the lower penumbra region near the field edge for the large field sizes by 1%-4%. The planar dose calculations showed comparable passing rates (> 98%) when the criterion of the gamma index method was selected to be 3%/3 mm.

CONCLUSIONS

The developed source model showed good agreements between measured and calculated dose distributions. The model is easily applicable to any other linear accelerator using FFF beams as the required data include only the measured PDD, dose profiles, and output factors for various field sizes, which are easily acquired during conventional beam commissioning process.

[Estimation of collimator scatter factor, S(c), of rectangular fields by a saturation model]

We estimated collimator scatter factor, S(c), of symmetric rectangular fields of any size by applying a two-component scatter model to measured in-air output data in width and length directions of measured rectangles. The in-air output was measured for symmetric rectangles with combined width and length sizes of 7 x 7 and 6 x 6 using 10 MV and 4 MV X-rays of Varian's Clinac 2100 C/D, respectively. The model consists of scatter components from the primary collimator and flattening filter and from the collimator jaws: the former shows a saturation curve and the latter increases linearly with enlarging field size. This model was fitted to the measured dataset firstly in the width and secondly in the length directions of rectangles; then, by compiling interpolated matrix data, the S(c) table of symmetric rectangles was constructed. In addition, using this S(c) table, values of S(c) were calculated for a few asymmetric rectangles by Day's method, and were in good agreement with measured values. Therefore, we think that our method is practical and precise for constructing the S(c) table of symmetric rectangles from measured data, and that using this table, the S(c) of any asymmetric rectangles may be calculated.

Measurements of in-air output ratios for a linear accelerator with and without the flattening filter

The in-air output ratio (Sc) for photon beams from linear accelerators describes the change of in-air output as a function of the collimator settings. The physical origin of the Sc is mainly due to the change in scattered radiation that can reach the point of measurement as the geometry of the head changes. The flattening filter (FF) and primary collimator are the major sources of scattered radiation. The change in amount of backscattered radiation from the collimator into the beam-monitoring chamber also contributes to the variation of output. In this work, we measured the Sc and backscatter factors (Sb) into the beam-monitoring chamber for a linear accelerator with and without the FF. We measured the Sc with a Farmer-type chamber in a miniphantom at the depth of 10 g/cm2 for 6- and 18-MV x-ray beams from a Varian Clinac 2100EX linear accelerator. The Sb were measured with a universal pulse counter and a diode array with build-in counting hardware and software. The head scatter component (Sh) was then derived from the relationship Sc= Sh x Sb, where Sb was the linear fit of measured results. Significant differences were observed for Sc with and without the FF. Within the range of experimental uncertainty, the Sb was similar with and without the FF. The variations in Sh differed significantly over the range of field sizes of 3 X 3 to 40 X 40 cm2 with and without the FF; for the 6-MV beam, it was 8% vs 3%, and for the 18-MV beam, 7% vs 1%. By analyzing the contributions of backscatter factor and total in-air output ratios with and without the FF, we directly gained insight into the contributions of different components to the total variations in Sc of a linear accelerator. Sc, Sb, and Sh are basic and useful dosimetric quantities for delivery of intensity-modulated radiation therapy using a linear accelerator operating in a mode without the FF.

Measurement of head scatter factors of linear accelerators with columnar miniphantoms

The measurement of linear accelerator head scatter factors or in-air output factors, Sc, with columnar miniphantoms is refined in this work. Columnar miniphantoms are constructed from water equivalent materials: solid water and M3, and materials with higher mass density and atomic number: copper and lead. The change in the value of Sc from a 4-cm X 4-cm to a 40-cm X 40-cm field is different by 22% +/- 3%, 18% +/- 2%, and 10% +/- 3% for 6, 15, and 23 MV x rays, respectively, when measured with water equivalent or lead miniphantoms of 10 gm/cm2 depth. Based on measurements of transmission factors in solid-water miniphantoms of different depths, it is demonstrated that the beam energy spectra decreases in energy with increased field size. These changes in beam energy spectra alter the transmission and scatter of radiation and buildup of the dose in the miniphantom even if the miniphantom is made of water-equivalent material. These changes underlie the alteration in Sc when measured by miniphantoms fabricated from materials of different atomic number. It is shown that miniphantoms designed with a depth just adequate to stop contamination electrons will minimize these distortions due to transmission and scatter of radiation and buildup of dose in the miniphantom. Use of a miniphantom constructed from water-equivalent material with a depth appropriate for the x-ray energy being measured is the preferred method for determining Sc for dosimetry in water.

Comparison of the ESTRO formalism for monitor unit calculation with a Clarkson based algorithm of a treatment planning system and a traditional "full-scatter" methodology

The ESTRO formalism for monitor unit (MU) calculations was evaluated and implemented to replace a previous methodology based on dosimetric data measured in a full-scatter phantom. This traditional method relies on data normalised at the depth of dose maximum (Zm), as well as on the utilisation of the BJR 25 table for the conversion of rectangular fields into equivalent square fields. The treatment planning system (TPS) was subsequently updated to reflect the new beam data normalised at a depth ZR of 10 cm. Comparisons were then carried out between the ESTRO formalism, the Clarkson-based dose calculation algorithm on the TPS (with beam data normalised at Zm and ZR), and the traditional "full-scatter" methodology. All methodologies, except for the "full-scatter" methodology, separated head-scatter from phantom-scatter effects and none of the methodologies; except for the ESTRO formalism, utilised wedge depth dose information for calculations. The accuracy of MU calculations was verified against measurements in a homogeneous phantom for square and rectangular open and wedged fields, as well as blocked open and wedged fields, at 5, 10, and 20 cm depths, under fixed SSD and isocentric geometries for 6 and 10 MV. Overall, the ESTRO Formalism showed the most accurate performance, with the root mean square (RMS) error with respect to measurements remaining below 1% even for the most complex beam set-ups investigated. The RMS error for the TPS deteriorated with the introduction of a wedge, with a worse RMS error for the beam data normalised at Zm (4% at 6 MV and 1.6% at 10 MV) than at ZR (1.-9% at 6 MV and 1.1% at 10 MV). The further addition of blocking had only a marginal impact on the accuracy of this methodology. The "full-scatter" methodology showed a loss in accuracy for calculations involving either wedges or blocking, and performed worst for blocked wedged fields (RMS errors of 7.1% at 6 MV and 5% at 10 MV). The origins of these discrepancies were quantified and the shortcomings of these MU calculation methodologies are discussed in the paper.

Modelling of output factors for conformal megavoltage X-ray beams

A method is described for calculating the output from conformally shaped megavoltage X-ray beams. The model has been developed for Varian accelerators but is shown to work for accelerators from another manufacturer. The use of dynamic wedging and both static and dynamic multileaf collimated beams are included in the model. For any linear accelerator, the data required are a set of measured output factors for square beams, an in-air profile and a limited number of readily available parameters defining the geometry of the head of the accelerator. The three components of the output, namely primary, head scatter and phantom scatter are modelled and calculated individually for any point in a beam. An optimization procedure is developed that automatically determines the eight parameters required to model an accelerator in order for these calculations to be performed. The performance of the method is demonstrated for shaped beams using asymmetric and multileaf collimation, both with and without wedging, and for a range of beam energies. The model has been incorporated into a computer program that is used clinically.

Derivation of the distribution of extrafocal radiation for head scatter factor calculation

Head scatter factors for high energy photon beams from linear accelerators can be modeled using a two-source model consisting of focal and extrafocal radiation. The focal radiation can be approximated as a point source, and the distribution of the extrafocal radiation is a two-dimensional (2D) radial symmetric function. Various methods, including analytical, Monte Carlo, and empirical trial functions, have been used to determine the radial symmetric function of extrafocal radiation distribution. This article describes a method for directly determining the extrafocal radiation distribution without assuming any empirical trial function. The extrafocal radiation distribution is determined with measured head scatter factors for rectangular fields defined by the lower jaw (X) fixed at 40 cm and the upper jaw (Y) varying from 3 to 40 cm. The derivatives of the measured head scatter factors, with respect to the Y jaw position projected in the plane of extrafocal radiation, are proportional to the one-dimensional (1D) projection (also called the line spread function) of the extrafocal radiation distribution. Two methods are used to solve the radial function of extrafocal radiation from the 1D projection. The first method uses a 2D filtered backprojection algorithm, originally developed for parallel beam computed tomography reconstruction, to directly derive the radial dependence of the extrafocal radiation distribution. The method has been applied to 6 and 18 MV photon beams from a Siemens linear accelerator and has been tested by comparing measured and calculated head scatter factors for square and rectangular fields. The second method uses a Fourier transform followed by a Fourier-Bessel transform to solve the problem. The distributions of extrafocal radiation derived from these two methods are virtually identical.

A widely tested model for head scatter influence on photon beam output

PURPOSE

To construct and test a semi-analytical model describing the effects on Monitor Unit (MU) verification caused by scattering in the treatment head. The implementation of the model should be accomplished using a small set of experimental data. Furthermore, the model should include a geometry dependent estimation of the resulting uncertainty.

MATERIAL AND METHODS

The input required by the created model consists of basic treatment head geometry and 10 measured output factors in air (OFair) for square fields. It considers primary energy fluence, scattered radiation from an extra-focal source and from secondary collimators, as well as backscatter to the monitor chamber. Measurements and calculations were performed in open symmetric and asymmetric fields at points located both on and off the collimator axis, as well as at arbitrary treatment distances. The model has been verified for 19 photon beams in the range from 4 up to 50 MV, provided by nine different treatment units from six manufacturers.

RESULTS

The presented model provided results with errors smaller than 1% (2 S.D.) in typical clinical situations for all beams tested. In more exceptional situations, i.e. combinations of unconventional treatment head designs, very elongated fields, and dosimetry points far away from the isocenter, the total uncertainty increased to approximately 2%. The spread in the results was further analysed in order to create a method for predicting the uncertainties under different treatment conditions.

CONCLUSIONS

A general head scatter model that is easy to implement has been developed and can be used as the basis for computerised MU verification. The model handles all commercially available treatment units adequately and also includes an estimation of the resulting uncertainty.

A virtual photon energy fluence model for Monte Carlo dose calculation

The presented virtual energy fluence (VEF) model of the patient-independent part of the medical linear accelerator heads, consists of two Gaussian-shaped photon sources and one uniform electron source. The planar photon sources are located close to the bremsstrahlung target (primary source) and to the flattening filter (secondary source), respectively. The electron contamination source is located in the plane defining the lower end of the filter. The standard deviations or widths and the relative weights of each source are free parameters. Five other parameters correct for fluence variations, i.e., the horn or central depression effect. If these parameters and the field widths in the X and Y directions are given, the corresponding energy fluence distribution can be calculated analytically and compared to measured dose distributions in air. This provides a method of fitting the free parameters using the measurements for various square and rectangular fields and a fixed number of monitor units. The next step in generating the whole set of base data is to calculate monoenergetic central axis depth dose distributions in water which are used to derive the energy spectrum by deconvolving the measured depth dose curves. This spectrum is also corrected to take the off-axis softening into account. The VEF model is implemented together with geometry modules for the patient specific part of the treatment head (jaws, multileaf collimator) into the XVMC dose calculation engine. The implementation into other Monte Carlo codes is possible based on the information in this paper. Experiments are performed to verify the model by comparing measured and calculated dose distributions and output factors in water. It is demonstrated that open photon beams of linear accelerators from two different vendors are accurately simulated using the VEF model. The commissioning procedure of the VEF model is clinically feasible because it is based on standard measurements in air and water. It is also useful for IMRT applications because a full Monte Carlo simulation of the treatment head would be too time-consuming for many small fields.

A three-source model for the calculation of head scatter factors

Accurate determination of the head scatter factor Sc is an important issue, especially for intensity modulated radiation therapy, where the segmented fields are often very irregular and much less than the collimator jaw settings. In this work, we report an Sc calculation algorithm for symmetric, asymmetric, and irregular open fields shaped by the tertiary collimator (a multileaf collimator or blocks) at different source-to-chamber distance. The algorithm was based on a three-source model, in which the photon radiation to the point of calculation was treated as if it originated from three effective sources: one source for the primary photons from the target and two extra-focal photon sources for the scattered photons from the primary collimator and the flattening filter, respectively. The field mapping method proposed by Kim et al. [Phys. Med. Biol. 43, 1593-1604 (1998)] was extended to two extra-focal source planes and the scatter contributions were integrated over the projected areas (determined by the detector's eye view) in the three source planes considering the source intensity distributions. The algorithm was implemented using Microsoft Visual C/C++ in the MS Windows environment. The only input data required were head scatter factors for symmetric square fields, which are normally acquired during machine commissioning. A large number of different fields were used to evaluate the algorithm and the results were compared with measurements. We found that most of the calculated Sc's agreed with the measured values to within 0.4%. The algorithm can also be easily applied to deal with irregular fields shaped by a multileaf collimator that replaces the upper or lower collimator jaws.

Implementation of an in vivo diode dosimetry program and changes in diode characteristics over a 4-year clinical history

An in vivo dosimetry system that used n-type semiconductor diodes with integral build-up caps was introduced into the clinic. Measurements were made on the entrance surface of the patient and were compared to calculated diode readings expected from monitor units delivered by each beam. A method is given for calibration and correction for changes in diode sensitivity, dose-per-pulse effects, collimated field-size (head-scatter factor), wedges, compensators, and scatter from blocks and block trays. Clinically relevant temperature corrections are determined based on temperature measurements made with the diode used as a thermistor. Changes in diode characteristics over 4 years of clinical use are presented. With proper correction for clinical variables it is shown that difference between calculated and measured diode readings are within +/- 1% for phantom measurements and within +/- 3% for clinical measurements at a 95% confidence level. The correlation of dose measurements on the patient surface to dose inside a target volume is discussed.

Analysing collimator structure effects in head-scatter calculations for IMRT class fields using scatter raytracing

The frequent blocking of the irradiated volume in intensity modulated radiation therapy (IMRT) makes the head-scatter fraction of the incident photon fluence more significant than that in conventional therapy with open fields. On the other hand. certain collimator configurations block scatter photons directed to a given observation point while allowing primary photons to be transmitted. The 'anomalous blocking' makes the primary field a poor indicator of the scatter fluence. Since large MU-to-cGy ratios in IMRT can magnify head-scatter uncertainties, it becomes necessary to accurately model both the effective scatter source and the collimator structure that limits the scatter reaching the irradiated volume. First we obtain a dual-source model, using a Taylor series expansion to derive the effective scatter source distribution from the data measured for the Elekta SL20 linac equipped with a multi-leaf collimator (MLC). Then, using a raytracing algorithm, we calculate the transmission of scatter rays from the effective scatter source plane to points in the patient plane. The method can account for the anomalous blocking of scatter by the MLC leaves and the backup diaphragms. For a variety of collimator settings tested, the calculations agree with measurements to an accuracy of 0.002psi10 x 10, where psi10 x 10 is the total (primary + scatter) photon fluence of an open 10 x 10 cm2 field for the same MU delivered. Although the significance of collimator structure in IMRT depends strongly on fields shapes employed for the delivery, potential cumulative errors on the order of a few per cent can be avoided in fluence calculations if the proposed method is used.

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.

Modeling the output ratio in air for megavoltage photon beams

The output ratio in air, OR, for a high-energy x-ray beam describes how the incident central axis photon fluence varies with collimator setting. For field sizes larger than 3 x 3 cm2, its variation is caused by the scatter of photons in structures in the accelerator head (primarily the flattening filter and the wedge, if one is used) and by the backscatter of radiation into the monitor ionization chamber. The objective of this study was to evaluate the use of an analytical function to parametrize OR for square collimator setting c: OR = (1 + a1.c).[1 + a2.erf(c/lambda)2].H0. For open beams, these parameters can be attributed to explicit physical meanings within the systematical uncertainty of the model: a1 accounts for backscatter into the monitor, a2 is the maximum scatter-to-primary ratio for head-scattered photons, and lambda represents the effective width of the "source" of head-scatter photons. H0 is a constant that sets OR = 1 for c = 10 cm. This formula also fits OR for wedge beams and a Co-60 unit, although the fitting parameters lose their physical interpretations. To calculate the output ratio for a rectangular field, cx x cy, an equivalent square can be used: c = (1 + k).cy x cx/(k.cx + cy), where k is a constant. The study included a number of different accelerators and a cobalt-60 unit. The fits for square fields agreed with measurements with a standard deviation (SD) of less than 0.5%. Using k = lx.(f - ly)/ly.(f - lx), where lx and ly are the source-to-collimator distances and f is the source-to-detector distance, measurements and calculations agreed within a SD of 0.7% for rectangular fields. Sufficient data for the three parameters are presented to suggest constraints that can be used for quality assurance of the measured output ratio in air.

Independent checking of the delivered dose for high-energy X-rays using a hand-held PC

BACKGROUND AND PURPOSE

The requirements on the delivered dose in radical radiation therapy are extremely high. The dose should be within a few percent and also delivered with high accuracy in space. Vendors and users have successfully managed to implement radiation therapy systems, which are able to achieve these demands with high accuracy and reproducibility. These systems include computerized tomography scanners, treatment planning systems, simulators, treatment machines, and record and verify systems. More and more common are also computer networks to assure data integrity when transferring information between the systems. Even if these systems are commissioned and kept under quality assurance programs to maintain their accuracy, errors may be introduced. Especially, the human factor is an uncontrolled parameter that may introduce errors. Thus, unintentional changes or incorrect handling of data may occur during clinical use of the equipment. Having an independent dose calculation system implemented in the daily quality assurance process may assure a high quality of treatments and avoidance of severe errors.

MATERIALS AND METHODS

To accomplish this, a system of equations for calculating the absorbed dose to the prescription point from the set-up information, has been compiled into a dose-calculation engine. The model is based on data completely independent of the treatment planning system (TPS). The fundamental parameter in the dose engine is the linear attenuation coefficient for the primary photons. This parameter can readily be determined experimentally. The dose calculation engine has been programmed into a hand-held PC allowing direct calculation of the dose to the prescription point when the first treatment is delivered to the patient.

RESULTS AND CONCLUSION

The model is validated with measurements and is shown to be within +/-1.0% (1 SD). Comparison against a state-of-the-art TPS shows an average difference of 0.3% with a standard deviation of +/-2.1%. An action level covering 95% of the cases has been chosen, i.e. +/-4.0%. Deviations larger than this are with a high probability due to erroneous handling of the patient set-up data. This system has been implemented into the daily clinical quality control program.

Modeling the extrafocal radiation and monitor chamber backscatter for photon beam dose calculation

A simple analytical approach has been developed to model extrafocal radiation and monitor chamber backscatter for clinical photon beams. Model parameters for both the extrafocal source and monitor chamber backscatter are determined simultaneously using conventional measured data, i.e., in-air output factors for square and rectangular fields defined by the photon jaws. The model has been applied to 6 MV and 15 MV photon beams produced by a Varian Clinac 2300C/D accelerator. Contributions to the in-air output factor from the extrafocal radiation and monitor chamber backscatter, as predicted by the model, are in good agreement with the measurements. The model can be used to calculate the in-air output factors analytically, with an accuracy of 0.2% for symmetric or asymmetric rectangular fields defined by jaws when the calculation point is at the isocenter and 0.5% when the calculation point is at an extended SSD. For MLC-defined fields, with the jaws at the recommended positions, calculated in-air output factors agree with the measured data to within 0.3% at the isocenter and 0.7% at off-axis positions. The model has been incorporated into a Monte Carlo dose algorithm to calculate the absolute dose distributions in patients or phantoms. For three MLC-defined irregular fields (triangle shape, C-shape, and L-shape), the calculations agree with the measurements to about 1% even for points at off-axis positions. The model will be particularly useful for IMRT dose calculations because it accurately predicts beam output and penumbra dose.

An empirical model for megavoltage x-ray output factors

An empirical model of the factors that determine the central axis dose at 10 cm depth in water for 4 MV, 6 MV and 18 MV photon beams is presented. Backscattering from the variable collimators into the dose monitoring ionization chamber can cause a variation of -0.5% to +1.8% in the dose per monitor unit in accelerators with an electron facility. Forward emission towards the isocentre from the beam flattening filter and upper collimators is more dependent on the position of the upper variable collimator blades than the lower blades, so that they are not interchangeable in determining output factors, which can differ by up to 2%. The model includes the product of the monitor backscatter factor, normalized phantom scatter factor, normalized head scatter factor and inverse square law, corrected for the displacement of the virtual x-ray focus from the target. It can predict the dose to -/+0.83% for 4 MV, -/+0.80% for 6 MV photons and -/+0.82% for 18 MV photons. The normalized head scatter factor is a second-order polynomial of the modified equivalent square collimator, whose coefficients do not vary significantly with x-ray energy. The model was tested by comparison with independent measurements of output factor and generally agreed to around 1%.

A practical method for the calculation of multileaf collimator shaped fields output factors

Output factors of multileaf-collimator (MLC) shaped radiation fields were measured for a commercial linear accelerator whose MLC leaves form parts of the upper collimator system. The approach of taking into account the reduced phantom scatter due to the MLC shaping on the output factor has previously been shown to be inadequate for this type of machine because of the effect of the MLC leaves on the collimator factor [Palta et al., Med. Phys. 23, 1219-1224(1996)]. In this article, we present two forms of the collimator factor that give satisfactory agreement with measured values of the output factors of MLC-shaped fields. The present method should be directly applicable to other linacs of similar MLC configuration. For clinical treatment planning, we believe the method is practical and accurate enough to be satisfactory. The equation for calculating the output factor requires only peak scatter and output factors of the machine. These are normally measured during machine commissioning.

Changes in incident photon fluence of 6 and 18 MV x rays caused by blocks and block trays

When a block and tray are placed in a x-ray beam the dose to a point in a phantom is changed by the following factors: (1) attenuation of photon and electron fluence from the head of the accelerator by the tray and the block, (2) decrease in the scatter in the phantom by a reduction in the phantom volume that receives radiation, and (3) generation of scatter off the tray and block. This third factor is generally ignored in dosimetry calculation but has been measured in this work. Measurements of incident photon fluence for 6 and 18 MV x rays were made with a columnar miniphantom of 10 cm depth. The tray factor for a 9 mm thick Lexan tray is found to be variable and to increase by 1.8% due to scatter off the tray when the field size is increased from a 3cm x 3 cm to 40cm x 40 cm field. Also, it was found that scatter off a block could increase the incident photon fluence by as much as 2%. The magnitude of this block scatter depends on the length of the inner edge of the opening in the block and on amount of block that is being irradiated, the overlap of the block by the radiation field. The total block-tray factor can be as much as 3% larger than the single-value tray factor measured with a 10cm x 10cm field that is traditionally used. An analytical equation is developed that accurately models the block-tray factor.

Effect of electron contamination on scatter correction factors for photon beam dosimetry

Physical quantities for use in megavoltage photon beam dose calculations which are defined at the depth of maximum absorbed dose are sensitive to electron contamination and are difficult to measure and to calculate. Recently, formalisms have therefore been presented to assess the dose using collimator and phantom scatter correction factors, Sc and Sp, defined at a reference depth of 10 cm. The data can be obtained from measurements at that depth in a miniphantom and in a full scatter phantom. Equations are presented that show the relation between these quantities and corresponding quantities obtained from measurements at the depth of the dose maximum. It is shown that conversion of Sc and Sp determined at a 10 cm depth to quantities defined at the dose maximum such as (normalized) peak scatter factor, (normalized) tissue-air ratio, and vice versa is not possible without quantitative knowledge of the electron contamination. The difference in Sc at dmax resulting from this electron contamination compared with Sc values obtained at a depth of 10 cm in a miniphantom has been determined as a multiplication factor, Scel, for a number of photon beams of different accelerator types. It is shown that Scel may vary up to 5%. Because in the new formalisms output factors are defined at a reference depth of 10 cm, they do not require Scel data. The use of Sc and Sp values, defined at a 10 cm depth, combined with relative depth-dose data or tissue-phantom ratios is therefore recommended. For a transition period the use of the equations provided in this article and Scel data might be required, for instance, if treatment planning systems apply Sc data normalized at d(max).

Photon output factor calculation from the inverse of the sector-integration equation

A method to predict rectangular field output factors (OFs) of photon open beams for the Saturne 41 linear accelerator has been developed. The procedure is similar to the sector-integration method but the radiotherapy quantities corresponding to circular fields (circular functions) are calculated from one-dimensional OFs. In this case the one-dimensional OFs are defined as rectangular field OFs, where one side remains constant and equal to the maximum field size. The circular quantities are numerically obtained by inversion of the sector-integration equation which relates both the one-dimensional OFs and the circular function. Two one-dimensional OFs were used to take into account the asymmetry between the x and y collimator systems (collimator exchange effect). The resulting pair of circular functions corresponds to the x and y collimator systems, respectively. They contain all the information relative to head, air, and medium (phantom) scatter and, consequently, there is no need to account for the geometry of the head or fitting parameters. Using the sector-integration method, the OFs for any rectangular field can be calculated by integrating the obtained circular functions. To improve results, a procedure is given to account for corner collimators overlapping. Results agree with data to within approximately 0.4% at 6-15 MV photon beams. The proposed method is thus clinically acceptable for routine calculation. Furthermore, the circular function calculation algorithm could be extended to other radiotherapy quantities.

Two-effective-source method for the calculation of in-air output at various source-to-detector distances in wedged fields

A simple algorithm was developed for calculation of the in-air output at various source-to-detector distances (SDDs) on the central axis for wedged fields. In the algorithm we dealt independently with two effective sources, one for head scatter and the other for wedge scatter. Varian 2100C with 18 and 8 MV photon beams was used to examine this algorithm. The effective source position for head scatter for wedged fields was assumed to be the same as that for open fields, and the effective source position for wedge scatter was assumed to be a certain distance upstream from the physical location of the wedge. The shift of the effective source for wedge scatter, w, was found to be independent of field size. Moreover, we observed no systematic dependency of w on wedge angle or beam energy. One value, w = 5.5 cm, provided less than 1% difference in in-air outputs through the whole experimental range, i.e., 6 x 6 to 20 x 20 cm2 field size (15 x 20 cm2 for 60 degrees wedge), 15 degrees-60 degrees wedge angle, 80-130 cm SDD, and both 18 and 8 MV photon beams. This algorithm can handle the case in which use of a tertiary collimator with an external wedge makes the field size for the determination of wedge scatter different from that for head scatter. In this case, without the two-effective-source method, the maximum of 4.7% and 2.6% difference can be given by the inverse square method and one-effective-source method in a 45 degrees wedged field with 18 MV. Differences can be larger for thicker wedges. Enhanced dynamic wedge (EDW) fields were also examined. It was found that no second effective source is required for EDW fields.

Measurements of head-scatter factors with cylindrical build-up caps and columnar miniphantoms

Head-scatter factors, Sh, also referred to as output factors, are measured in-air with an ion chamber and a semiconductor diode fitted with cylindrical build-up caps and columnar miniphantoms fabricated from materials of different atomic number. Sh increases with field size less rapidly when cylindrical build-up caps are constructed from high atomic number materials. This is a consequence of a net scatter of contamination electrons away from the detector. Ion chambers and diodes give identical results when the same type of build-up caps are used. Contamination electrons can be avoided by the use of columnar miniphantoms that have sufficient wall thickness in the radial direction. This radial wall thickness is characterized in this work for 6, 10, and 18 MV x-ray beams. Sh increases with field size less rapidly when columnar miniphantoms are constructed from high atomic number materials. This is due to the decrease in the average energy of photons at large field sizes. It is concluded that to obtain Sh for dosimetry in water, cylindrical build-up caps and columnar miniphantoms should be constructed from material with an atomic number close to that of water.