Head Scatter Factor Research Articles

SU-FF-T-327: Comparison of Characteristics of Electron Beams Generated by Siemens and Varian Linear Accelerators

Purpose: To compare the electron beam data for Siemens and Varian accelerators. Method and Materials: Beam data for the electron beams for at least 4 linear accelerators are compared in seven categories: (1) percent depth dose for open beam and small circular cutouts, (3) phantom scatter factor, (4) head scatter factor as a function of cone size and SSD, (5) cone factors, (6) distance factor and (7) virtual source position. Results: PDD for broad beams is in good agreement among all accelerators. However, PDD for small circular cutouts of the two Siemens Oncor accelerators are different from the other accelerators with their mean energy shifted by 2 MeV. The phantom scatter factor, defined as the ratio of blocking factor in water at reference depth and head scatter factor in air, for the same cone size and radius, is a function of radius and nominal electron energy only, regardless of linac makers with a maximum and standard deviation of 10% (for the smallest cutout of 1cm) and 2.3%, respectively. The head scatter factor H is defined as the ratio of in-air energy fluence between circular cutout with radius r and open cone for the same cone size and source-to-detector distance. The renormalized H is a function of electron energy and cutout radius. The cone factor for all energies, among all accelerators agreed within 1.9% among the Varian accelerators and 1.7% within the Siemens accelerators. The distance factors varied up to 10% for the smallest energy (6e) and up to 3.4% for the 21e. The virtual position varied by 3.8cm and 6.5cm for the Siemens and Varian accelerators, respectively. Conclusion: Accelerators from the same manufacturer, with the same nominal energy, can be treated as “identical” for conventional treatment except for small circular cutouts and large SSDs, where variations of 10% are observed.

SU-FF-T-316: Modifications to the “three-Source Model” for the Calculation of Head Scatter Factors for Small Field Sizes

Purpose: The three-source model proposed by Yang et al.1 when applied to Siemens PRIMUS 6 MV beam over-estimated head scatter by 10–200% for field sizes less than 2 cm × 2 cm and elongated narrow beams. This necessitated the development of a modified approach Method and Materials: The complete theoretical background for the three-source model can be found in the published literature1 in which the total energy fluence at the point of calculation can be divided into three components. The primary component Cp has been chosen around 90% in the model. A modified approach is proposed to the three-source model with the primary source component Cp having growth function that grows exponentially with radius of the beam in the Sp plane. The primary source function was integrated in the Sp plane using the formula, ; rs < r3 where Cp2, Cp3 and r3 are fitting coefficients. Results: The measured head scatter factors for smaller field sizes including the rectangular fields where the exchanged collimator jaw positions have been compared with both three-source model and modified three-source model for Siemens PRIMUS 6 MV beam. It was observed that the accuracy of the modified model is improved and is within 10% of the measurements for small field sizes. Conclusion: In routine IMRT treatments, about 10–15% of the segmented fields use small or elongated fields. The modified approach to the three-source model improves the accuracy of the head scatter factors calculation significantly for field sizes below 2 cm × 2cm.

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.

777 poster A comparison of head scatter factors for fields defined by MLC and head scatter factors defined by photon jaws: the effect on MU calculations for IMRT

777 poster A comparison of head scatter factors for fields defined by MLC and head scatter factors defined by photon jaws: the effect on MU calculations for IMRT

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 (Sc,w) for any rectangular field and for any irregular MLC shaped beam. This method was based on open field output ratios in air (Sc) for a field with the same collimator setting, and a relation fw between Sc,w and Sc. The relation fw can be determined from measured output ratios in air for a few open and wedged fields including the maximum wedged field size. The function fw 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 Sc,w/Sc 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.

Dosimetry of small x‐ray beams for stereotactic radiotherapy

The dosimetry of small width) x‐ray beams, such as those used in stereotactic radiotherapy, is much more complex than that of those used in routine clinical treatments. A thorough understanding of the properties of both small beams and small detectors is necessary to determine the optimum detector to use in each measurement situation. Accurate and reproducible experimental methods must also be developed to measure absolute and relative doses, obtain precise beam data and subsequently verify the delivered treatment dose. This work is an investigation of the above aspects of small beam dosimetry, with particular reference to the types of small fields used for stereotactic radiotherapy in the Edinburgh Cancer Centre. These are fields formed by circular stereotactic collimators (12.5 to 40 mm diameter), used in conjunction with arc therapy for the treatment of small brain lesions. Several detectors were compared in the measurement of percentage depth doses, tissue maximum ratios, off axis ratios, head scatter and relative output factors, on a 6 MV linac. This included the testing of three new, commercially available detectors. Clinical beam data were obtained via detector comparison and recommendations made as to the best methodology for each measurement parameter. The most accurate and reproducible technique for head scatter factors was extended to smaller stereotactic collimators (5 to 10 mm diameter) and square fields with widths of 10 to 20 mm. These were shaped with both the movable linac collimators and the multileaf collimator and the results will be applied to the measurement of the small subfields used in intensity modulated radiotherapy (IMRT). A verification phantom was designed to be compatible with the stereotactic head frame and the properties of various small detectors were investigated for use in the phantom to measure point doses in both single arcs and multiple non‐coplanar plans. The recommendations on beam data acquisition and dose verification were applied to two additional linacs. On all machines, the dose to the isocenter was verified in several typical treatment plans to within 2% of the calculated dose, for all clinical collimators. The results confirm the accuracy of the measurement processes used. The verification technique also provides the basis for a proposed audit of dosimetry in all stereotactic centers in the UK.

298 poster Calculation of head scatter factor for our 6MV beam using the two source model

298 poster Calculation of head scatter factor for our 6MV beam using the two source model

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.

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%.

ミニファントムを用いたヘッド散乱係数の測定法の評価

ミニファントムを用いたヘッド散乱係数の測定法の評価

Monitor unit calculation on the beam axis of open and wedged asymmetric high-energy photon beams

An ESTRO booklet and a report of the Netherlands Commission on Radiation Dosimetry have been published recently describing empirical methods for monitor unit (MU) calculations in symmetrical high-energy photon beams. Both documents support the same basic ideas; firstly the separation of head scatter and volume scatter components and secondly the determination of head scatter quantities in a mini-phantom. Based on these ideas the methods previously described for MU calculations in symmetrical beams are extended to asymmetrical open and wedged beams in isocentric treatment conditions. All required dosimetric parameters (normalized head scatter factors, phantom scatter correction factors, wedge factors, off-axis ratios, quality index, and depth dose parameters) are determined as a function of beam axis position in order to study their off-axis dependence. Measurements are performed for 6 MV and 18 MV photon beams provided by two different dual-energy linear accelerators, a GE Saturne 42 and a Varian 2100 CD linac.

Calculation of head scatter factors at isocenter or at center of field for any arbitrary jaw setting.

The purpose of this work is to calculate the head scatter factors for any arbitrary jaw setting by using two different semi-empirical methods. The head scatter factor at the center of field (COF) for any arbitrary jaw setting can be defined as H(COF)(X1,X2,Y1,Y2,r)=DairCOF(XI1,X2,Y1,Y2,r)/ [Dair(5,5,5,5,0)*OAR(r)], where X1, X2, Y1, and Y2 are the jaw positions; r is the distance between COF and isocenter (IC); OAR(r) is the Off-Axis-Ratio; DairCOF(X1,X2,Y1,Y2,r) is the dose in air measured at COF; Dair(5,5,5,5,0) is the dose in air measured at IC for the 10 x 10 cm2 field. In certain clinical situations, doses are prescribed at IC instead of COF for asymmetric fields. In these cases, head scatter factors should be determined at IC. It is found that the head scatter factors at IC for asymmetric fields [H(IC)(X1,X2,Y1,Y2)] are lower than H(COF)(X1,X2,Y1,Y2,r) for the same jaw setting by up to 4%. The values of H(IC)(X1,X2,Y1,Y2) and H(COF)(X1,X2,Y1,Y2,r) for a variety of jaw settings were measured using a miniphantom of 3-cm diameter for a 6- and a 18-MV photon beams. An equivalent square formula, derived presently at the source plane for any jaw setting, was used to calculate H(COF)(X1,X2,Y1,Y2,r). The calculation and the measurement agree within +/-1% (+/-0.5% for most clinical situations). To calculate H(IC)(X1,X2,Y1,Y2), we have generalized the Day's "quarter-field" method, i.e., H(IC)(X1,X2,Y1,Y2) = [H(X1,X1,Y1,Y1) + H(X1,X1,Y2,Y2) + H(X2,X2,Y1,Y1) + H(X2,X2,Y2,Y2)]/4. We found that the calculation and the measurement agree within +/-0.8% for the beams studied.

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.

The equivalent square concept for the head scatter factor based on scatter from flattening filter

The equivalent field relationship between square and circular fields for the head scatter factor was evaluated at the source plane. The method was based on integrating the head scatter parameter for projected shaped fields in the source plane and finding a field that produced the same ratio of head scatter to primary dose on the central axis. A value of was obtained, where was one-half of the side length of the equivalent square and R was the radius of the circular field. The assumptions were that the equivalent field relationship for head scatter depends primarily on the characteristics of scatter from the flattening filter, and that the differential scatter-to-primary ratio of scatter from the flattening filter decreases linearly with the radius, within the physical radius of the flattening filter. Lam and co-workers showed empirically that the area-to-perimeter ratio formula, when applied to an equivalent square formula at the flattening filter plane, gave an accurate prediction of the head scatter factor. We have analytically investigated the validity of the area-to-perimeter ratio formula. Our results support the fact that the area-to-perimeter ratio formula can also be used as the equivalent field formula for head scatter at the source plane. The equivalent field relationships for wedge and tertiary collimator scatter were also evaluated.

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

A calculation method is described, which presumes that linac output has two components. One component is direct x rays from the target and the remaining component is an extra-focal, distributed source of radiation that is scattered from the flattening filter, primary collimator, and the jaws of the moveable collimator. This calculation method gives values for output factors that differ from measured values by no more than 0.5% for field widths from 4 to 40 cm, rectangular fields with long to short axis ratios as great as 10, symmetric and asymmetric fields, and source-to-axis distances from 65 to 360 cm. While this calculation method has great accuracy and flexibility, a minimal amount of input data is required: (1) measured output factors at a source-to-axis distance of 100 cm for square fields; (2) positions of the collimator with respect to the x-ray source target; and (3) output factors measured at various source-to-axis distances for a 10 cm x 10 cm field.

An equivalent square field formula for determining head scatter factors of rectangular fields

A simple formula is derived for the calculation of an equivalent square field that gives the same head scatter factor as a given rectangular field. This formula is based strictly on the configuration of a medical linear accelerator treatment head. The geometric parameters used are the distances between the target and the top of each field-defining aperture. The formula accounts for both the effect of field elongation and the collimator exchange effect. This method predicts the output to within 1% accuracy for both open and wedged fields and does not require any new measured data other than the field size dependence of head scatter for a range of square field sizes. Interestingly, the formula we derived has the same format as the formula that was empirically obtained by Vadash and Bjärngard [Med. Phys. 20, 733-734 (1993)].

Build-up cap materials for measurement of photon head-scatter factors

The suitability of high-Z materials as build-up caps for head-scatter measurements has been investigated. Build-up caps are often used to enable characterization of fields too small for a mini-phantom. We have studied lead and brass build-up caps with sufficiently large wall thicknesses, as compared to the range of contaminating electrons originating in the accelerator head, and compared them with build-up caps made of ionization chamber equivalent materials, i.e. graphite. The results were also compared with measurements taken using square and cylindrical polystyrene mini-phantoms. Field sizes ranging from up to were studied for nominal photon energies of 4, 6, 10 and 18 MV. The results show that the use of lead and brass build-up caps produces normalized head-scatter data slightly different from graphite build-up caps for large fields at high photon energies. At lower energies, however, no significant differences were found. The intercomparison between the two different plastic mini-phantoms and graphite caps showed no differences.

Measurements of basic parameters in wedged high-energy photon beams using a mini-phantom

Basic dosimetric quantities necessary to specify wedged beams (beam quality, wedge factors, output ratios) are obtained by measurements performed in a narrow coaxial mini-phantom for 6, 18 and 25 MV photon beams. To express beam quality, an attenuation coefficient is derived from measurements in a mini-phantom at 20 and 10 cm depth. Wedge factors and output ratios are measured as a function of field size at 10 cm water-equivalent depth. In open beams one observes beam softening with increasing distance from the collimator axis for all energies. With an inserted wedge a beam hardening is observed at 6 MV. This beam hardening decreases at 18 MV while at 25 MV a slight beam softening is detected. Larger variations of output ratios with field sizes are observed with a wedge than without a wedge. An equivalent square formula for head-scatter factors can be used with a good accuracy for rectangular wedged fields. For irregular wedged fields a method is proposed to calculate the product of the output ratio and the wedge factor. Measurements and calculations agree within 1% for all irregular wedged fields checked.

Off-axis primary-dose measurements using a mini-phantom.

The characterization of the incident photon beam is usually divided into its dependence on collimator setting (head-scatter factor) and off-axis position (primary off-axis ratio). These parameters are normally measured "in air" with a build-up cap thick enough to generate full dose build-up at the depth of dose maximum. In order to prevent any influence from contaminating electrons, it has been recommended that head-scatter measurements are carried out using a mini-phantom rather than a conventional build-up cap. Due to the volume of the mini-phantom, the effects from attenuation and scatter are not negligible. In relative head-scatter measurements these effects cancel and the head scatter is thus a good representation of the variation of the incident photon beam with collimator setting. However, in off-axis measurements, attenuation and scatter conditions vary due to beam softening and do not cancel in the calculation of the primary off-axis ratio. The purpose of the present work was to estimate the effects from attenuation and phantom scatter in order to determine their influence on primary off-axis ratio measurements. We have characterized the off-axis beam-softening effect by means of narrow-beam transmission measurements to obtain the effective attenuation coefficient as a function of off-axis position. We then used a semi-analytical expression for the phantom-scatter calculation that depends solely on this attenuation coefficient. The derived formalism for relative "in air" measurements using a mini-phantom is clear and consistent, which enables the user to separately calculate the effects from scatter and attenuation. For the investigated beam qualities, 6 and 18 MV, our results indicate that the effects from attenuation and scatter in the mini-phantom nearly cancel (the combined effect is less than 1%) within 12.5 cm from the central beam axis. Thus, no correction is needed when the primary off-axis ratio is measured with a mini-phantom.

Semi-conductor detectors in output factor measurements

Background and purpose: Output factors are generally measured with cylindrical ionization chambers. It was investigated if Si-diodes of p-type instead could be used. The advantage would be the small detector size and the robust construction of the detector. Materials and methods: Two types of diodes were studied, one with a shielding layer of tungsten specially made to reduce the excess response for scattered photons and one standard diode without any extra shielding. The measurements were performed at accelerating potentials between 4 and 50 MV and beam sizes between 4 cm × 4 cm and 40 cm × 40 cm. Results: The results showed that both types of diodes are suitable for measurements of head scatter factors in mini-phantoms. However, the diodes were found inappropriate for measurement of output factors for large fields in extended water phantoms. For small fields (<10 cm × 10 cm) a small detector is advantageous and no errors due to the scatter contribution were seen. Conclusions: An cylindrical ionization chamber is the best choice for output factor measurements in extended water phantoms for large field sizes while diodes are an alternative in small fields. There were negligible differences between the detectors in head scatter measurements in mini phantoms.