Output factor constituents of a high-energy photon beam

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.

Study of head scatter factor in 4MV photon beam used in radiotherapy

The 4 MV photon beam offers equal build-up region behavior like Co-60 beam and it plays a major role in head and neck and pediatric radiotherapy. In this study an attempt is made to study the head scatter factor (SC) for 4 MV photon beam using locally designed PMMA and Brass miniphantoms. The SC is measured in combination of PMMA miniphantom with 0.6 cc chamber and Brass miniphantom with 0.6 cc and 0.13 cc chambers. The measured SC is compared with the literature data and it agrees within ± 1.98%. The study reveals that either 0.13 cc or 0.6 cc chamber with PMMA or Brass phantom materials can be used for SC measurements in a 4 MV photon beam. The variation of SSD does not alter the head scatter factor. The collimator exchange effect is found to be within 1, and it is less than that of other linear accelerators. It is also found that the presence of internal wedge has significant contribution to head scatter factor. The Phantom scatter factor is also calculated and it agrees within ±1% with published data.

Measurement of back-scattered radiation from micro multileaf collimator into the beam monitor chamber from a dual energy linear accelerator

Measurements designed to find the collimator backscatter into the beam monitor chamber from Micro Multileaf collimator of 6 MV photon beams of the Siemens Primus linear accelerator were made with the help of dose rate feedback control. The photons and electrons backscattered from the upper and lower secondary collimator jaws give rise to a significant increase in the ion charge measured by monitor chamber. This increase varies between the different accelerators. The output measurements were carried out in air at the isocenter. The effect of collimator backscatter was investigated by measuring the pulse width, number of beam pulses per monitor unit, monitor unit rate and dose for different mMLC openings. These measurements were made with and without dose rate feedback control, i.e., with constant electron beam current in the accelerator. Monitor unit rate (MU/min) was almost constant for all field sizes. The maximum variation between the open and the closed feedback control circuits was 2.5%. There was no difference in pulse width and negligible difference in pulse frequency. Maximum value of backscattered radiation from the micro Multileaf collimator into the beam monitor chamber was found to be 0.5%.

Ecliptic method for the determination of backscatter into the beam monitor chambers in photon beams of medical accelerators

A new method to measure the effect of the backscatter into the beam monitor chambers in linear accelerators is introduced from first principles. The technique, applicable to high-energy photon beams, is similar to the well-known telescopic method although here the heavy blocks are replaced by a very small, centred block on the shadow tray, thus the name 'ecliptic method'. This effect, caused mainly by backscattering from the secondary collimators, is known to be an output factor constituent and must be accounted for when detailed calculations involving the machine's head are required. Since its magnitude is generally small, experimental errors might obscure the behaviour of the phenomenon. Consequently, the procedure introduced goes along with an uncertainty assessment. Our theory was confirmed via measurements in cobalt-60 beams, where the studied effect does not contribute to the output factor. Measurements were also performed on our Saturne 41 linear accelerator and the results were qualitatively similar to those described elsewhere. The collimation systems were studied separately by varying one jaw setting while keeping the other at its maximum value. In the light of these results, we deduced an algorithm that can correlate the former data with the effect of backscattering to the beam monitor chambers for any rectangular field within 0.5%, which is of the order of the experimental uncertainty (0.6%). As we show, the experimental procedure is safe, simple, not invasive for the linac and requires only basic dosimetry equipment.

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.

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.

On empirical methods to determine scatter factors for irregular MLC shaped beams

Multileaf collimators (MLCs) are in clinical use for more than a decade and are a well accepted tool in radiotherapy. For almost each MLC design different empirical or semianalytical methods have been presented for calculating output ratios in air for irregularly shaped beams. However, until now no clear recommendations have been given on how to handle irregular fields shaped by multileaf collimators for independent monitor unit (MU) verification. The present article compares different empirical methods, which have been proposed for independent MU verification, to determine (1) output ratios in air (Sc) and (2) phantom scatter factors (Sp) for irregular MLC shaped fields. Ten dedicated field shapes were applied to five different types of MLCs (Elekta, Siemens, Varian, Scanditronix, General Electric). All calculations based on empirical relations were compared with measurements and with calculations performed by a treatment planning system with a fluence based algorithm. For most irregular MLC shaped beams output ratios in air could be adequately modeled with an accuracy of about 1%-1.5% applying a method based on the open field aperture defined by the leaf and jaw setting combined with the equivalent square formula suggested by Vadash and Bjärngard [P. Vadash and B. E. Bjärngard, Med. Phys. 20, 733-734 (1993)]. The accuracy of this approach strongly depends on the inherent head scatter characteristics of the accelerator in use and on the irregular field under consideration. Deviations of up to 3% were obtained for fields where leaves obscure central parts of the flattening filter. Simple equivalent square methods for Sp calculations in irregular fields did not provide acceptable results (deviations mostly >3%). Sp values derived from Clarkson integration, based on published tables of phantom scatter correction factors, showed the same accuracy level as calculations performed using a pencil beam algorithm of a treatment planning system (in a homogeneous media). The separation of head scatter and phantom scatter contributions is strongly recommended for irregular MLC shaped beams as both contributions have different factors of influence. With rather simple methods Sc and Sp can be determined for independent MU calculation with an accuracy better than 1.5% for most clinical situations encountered in conformal radiotherapy.

Monte Carlo modelling of external radiotherapy photon beams

An essential requirement for successful radiation therapy is that the discrepancies between dose distributions calculated at the treatment planning stage and those delivered to the patient are minimized. An important component in the treatment planning process is the accurate calculation of dose distributions. The most accurate way to do this is by Monte Carlo calculation of particle transport, first in the geometry of the external or internal source followed by tracking the transport and energy deposition in the tissues of interest. Additionally, Monte Carlo simulations allow one to investigate the influence of source components on beams of a particular type and their contaminant particles. Since the mid 1990s, there has been an enormous increase in Monte Carlo studies dealing specifically with the subject of the present review, i.e., external photon beam Monte Carlo calculations, aided by the advent of new codes and fast computers. The foundations for this work were laid from the late 1970s until the early 1990s. In this paper we will review the progress made in this field over the last 25 years. The review will be focused mainly on Monte Carlo modelling of linear accelerator treatment heads but sections will also be devoted to kilovoltage x-ray units and 60Co teletherapy sources.

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.

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.

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.

Backscatter towards the monitor ion chamber in high-energy photon and electron beams: charge integration versus Monte Carlo simulation

In some linear accelerators, the charge collected by the monitor ion chamber is partly caused by backscattered particles from accelerator components downstream from the chamber. This influences the output of the accelerator and also has to be taken into account when output factors are derived from Monte Carlo simulations. In this work, the contribution of backscattered particles to the monitor ion chamber response of a Varian 2100C linac was determined for photon beams (6, 10 MV) and for electron beams (6, 12, 20 MeV). The experimental procedure consisted of charge integration from the target in a photon beam or from the monitor ion chamber in electron beams. The Monte Carlo code EGS4/BEAM was used to study the contribution of backscattered particles to the dose deposited in the monitor ion chamber. Both measurements and simulations showed a linear increase in backscatter fraction with decreasing field size for photon and electron beams. For 6 MV and 10 MV photon beams, a 2-3% increase in backscatter was obtained for a 0.5 x 0.5 cm2 field compared to a 40 x 40 cm2 field. The results for the 6 MV beam were slightly higher than for the 10 MV beam. For electron beams (6, 12, 20 MeV), an increase of similar magnitude was obtained from measurements and simulations for 6 MeV electrons. For higher energy electron beams a smaller increase in backscatter fraction was found. The problem is of less importance for electron beams since large variations of field size for a single electron energy usually do not occur.

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%.

Dose calculations for external photon beams in radiotherapy

Dose calculation methods for photon beams are reviewed in the context of radiation therapy treatment planning. Following introductory summaries on photon beam characteristics and clinical requirements on dose calculations, calculation methods are described in order of increasing explicitness of particle transport. The simplest are dose ratio factorizations limited to point dose estimates useful for checking other more general, but also more complex, approaches. Some methods incorporate detailed modelling of scatter dose through differentiation of measured data combined with various integration techniques. State-of-the-art methods based on point or pencil kernels, which are derived through Monte Carlo simulations, to characterize secondary particle transport are presented in some detail. Explicit particle transport methods, such as Monte Carlo, are briefly summarized. The extensive literature on beam characterization and handling of treatment head scatter is reviewed in the context of providing phase space data for kernel based and/or direct Monte Carlo dose calculations. Finally, a brief overview of inverse methods for optimization and dose reconstruction is provided.

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.

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.

A single-variable method for the derivation of collimator scatter correction factors in symmetrical and asymmetrical X-ray beams

Using a minimal set of measured data, the collimator scatter correction factor of an asymmetrical collimated rectangular field (X1,X2;Y1,Y2) can be calculated from the product of one-dimensional factors, in combination with a correction term: Sc(X1,X2;Y1,Y2) = S(cx1)(X1)S(cx2)(X2)S(cy1)(Y1)S(cy2)(Y2) + c delta(X;Y). Two forms of the function delta(X;Y) were investigated.

A generalized solution for the calculation of in-air output factors in irregular fields

Three major contributors of scatter radiation to the in-air output of a medical linear accelerator are the flattening filter, wedge, and tertiary collimator. These were considered separately in the development of an algorithm to be used to set up an in-air output factor calculation formalism for open and wedge fields of irregular shape. A detector's eye view (DEV) field defined at the source plane was used to account for the effects of collimator exchange and the partial blockage of the flattening filter by the tertiary collimator in the determination of head scatter. An irregular field determined at the source plane by a DEV was segmented and mapped back into the detector plane by a field-mapping method. Field mapping was performed by using a geometric conversion factor and equivalent field relationships for head scatter. The scatter contribution of each segmented equivalent field at the detector plane was summed by Clarkson integration. The same methodology was applied for determining both tertiary collimator and wedge scatter contribution. However, the field size that determined the amount of scatter contribution was not the same for each component. For tertiary collimator scatter and external wedge scatter, a field projected to the detector plane was used directly. Comparisons of calculated and measured values for in-air output factors showed good agreement for both open and external wedge fields. This algorithm can also be used for multileaf collimator (MLC) fields irrespective of the position of the MLC (i.e., whether the MLC replaces one secondary collimator or is used as a tertiary collimator). The measurement and parameterization of tertiary collimator scatter is necessary to account for its contribution to the in-air output. Because a source-plane field is mapped into the detector plane, no additional dosimetric data acquisition is necessary for the calculation of head scatter.

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 sigma/R approximately equal to 0.9 was obtained, where sigma 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.

Measurement of backscatter to the monitor chamber of medical accelerators using target charge

A simple noninvasive method is described for determining the backscatter to a monitor chamber of a medical accelerator based on the measurement of charge deposited in the target. This method is compared quantitatively to the more elaborate telescopic method for photon beams of 6 MV and 15 MV on linear accelerators having mica and Kapton monitor chambers. The new target charge method gives results consistent with the telescopic method to within 0.3%.

Monitor chamber backscatter for intensity modulated radiation therapy using multileaf collimators

Backscattered radiation into the machine monitor chamber can affect the machine output variation, with changes in field size and shape. For intensity modulated radiation therapy (IMRT) where many field, which may have small dimensions, are summed to give an intensity modulated field, the magnitude of backscatter will be different due to both the backscattering surface area changing, and the delivered monitor units being larger than for the equivalent static field. The effect of backscatter variation with field size for a Philips SL15 accelerator has been investigated at 8 MV for static and IMRT fields both in the standard clinical operating condition where an anti-backscatter plate is fitted, and also for a case where the anti-backscatter plate has been removed. The results show that in the absence of the anti-backscatter plate the variation in output between a 4 cm by 4 cm field and a 40 cm by 40 cm field size due to backscattered radiation was 5% for static fields. The anti-backscatter plate reduced this variation to less than 1%. When the accelerator operated in IMRT mode, with the backscatter plate in place, changes in the output due to additional backscattered radiation were less than 0.3%. With the backscatter plate removed, the outputs were lower, indicating the presence of additional backscattered radiation. It can be concluded that for the Philips MLC and SL accelerator with its anti-backscatter plate, the effects of backscattered radiation can be ignored for both static and IMRT fields.

Calculating dose distributions and wedge factors for photon treatment fields with dynamic wedges based on a convolution/superposition method

A convolution/superposition based method was developed to calculate dose distributions and wedge factors in photon treatment fields generated by dynamic wedges. This algorithm used a dual source photon beam model that accounted for both primary photons from the target and secondary photons scattered from the machine head. The segmented treatment tables (STT) were used to calculate realistic photon fluence distributions in the wedged fields. The inclusion of the extra-focal photons resulted in more accurate dose calculation in high dose gradient regions, particularly in the beam penumbra. The wedge factors calculated using the convolution method were also compared to the measured data and showed good agreement within 0.5%. The wedge factor varied significantly with the field width along the moving jaw direction, but not along the static jaw or the depth direction. This variation was found to be determined by the ending position of the moving jaw, or the STT of the dynamic wedge. In conclusion, the convolution method proposed in this work can be used to accurately compute dose for a dynamic or an intensity modulated treatment based on the fluence modulation in the treatment field.

Blocked field effects on collimator scatter factors

In routine dosimetry we assume separability of the collimator (Sc) and phantom (Sp) scatter components that together comprise the total scatter factor (Sc,p). In practice, the addition of blocking also affects the photon fluence attributable to the treatment head and flattening filter in a complicated way. The reduced aperture blocks out some of the head scatter contribution, while the block and tray add back secondary scatter. In the following we present techniques for directly measuring the aperture effect on Sc in air or in a full-scatter phantom. The change in Sc is found to be a scaleable quantity that can be modelled as a simple linear fit to the ratio of projected open-to-blocked equivalent square fields. Measurements have been made for 6, 18 and 24 MV photon beams on one Varian 2500 and two Varian 2100c accelerators. Results indicate a progressive loss of collimator scatter contribution with increased field blocking that is amplified with increasing energy. Block and tray scatter only contribute significantly to Sc for large fields and treatment distances of 80 cm or less. Application of these corrections in monitor unit calculations is presented.

A dual source photon beam model used in convolution/superposition dose calculations for clinical megavoltage x-ray beams

A realistic model of photon beams generated by clinical linear accelerators has been incorporated in a convolution/superposition method to compute dose distributions in photon treatment fields. In this beam model, a primary photon source represents photons directly from the target, and an extra-focal photon source represents scattered photons from the primary collimator and the flattening filter. Monte Carlo simulation was used to study clinical linear accelerators producing photon beams. From the output of the Monte Carlo simulation, the fluence and spectral distributions of each photon component, as well as the geometrical characteristics of each photon source with respect to its distance to the isocenter and its source distribution, were analyzed. These quantities were used to reproduce realistic photon distributions in treatment fields, and thus to compute dose distributions using the convolution method. Our results showed that compared to the primary photon fluence, the extra-focal photon fluence from the primary collimator and the flattening filter was 11%-16% at the isocenter, among which 70% was contributed by the flattening filter. The variation of extra-focal photons in different treatment fields was predicted accurately by accounting for the finite size of the extra-focal source. Compared to measurements, dose distributions in photon treatment fields, including those of asymmetric jaw settings and at different SSDs were calculated accurately, particularly in the penumbral region, by using the convolution method with the new dual source photon beam model.

Calculating output factors for photon beam radiotherapy using a convolution/superposition method based on a dual source photon beam model

A realistic photon beam model based on Monte Carlo simulation of clinical linear accelerators was implemented in a convolution/superposition dose calculation algorithm. A primary and an extra-focal sources were used in this beam model to represent the direct photons from the target and the scattered photons from other head structures, respectively. The effect of the finite size of the extra-focal source was modeled by a convolution of the source fluence distribution with the collimator aperture function. Relative photon output in air (Sc) and in phantom (Scp) were computed using the convolution method with this new photon beam model. Our results showed that in a 10 MV photon beam, the Sc, Sp (phantom scatter factor), and Scp factors increased by 11%, 10%, and 22%, respectively, as the field size changed from 3 x 3 cm2 to 40 x 40 cm2. The variation of the Sc factor was contributed mostly by an increase of the extra-focal radiation with field size. The radiation backscattered into the monitor chamber inside the accelerator head affected the Sc by about 2% in the same field range. The output factors in elongated fields, asymmetric fields, and blocked fields were also investigated in this study. Our results showed that if the effect of the backscattered radiation was taken into account, output factors in these treatment fields can be predicted accurately by our convolution algorithm using the dual source photon beam model.

Differences in wedge factor determination in air using a PMMA mini-phantom or a brass build-up cap

The head scatter dose contribution to the output of a treatment machine has been determined for an open and wedged 60Co gamma-ray beam and for open and wedged x-ray beams of 4, 8, and 16 MV. From those data wedge factor values "in air" have been deduced, expressed as the ratio of the dose to water, measured in air, for the situation with and without wedge, for the same number of monitor units (or treatment time for 60Co). The measurements have been performed using a polymethyl-metacrylate (PMMA) and a graphite-walled ionization chamber inserted in a brass build-up cap and in a PMMA mini-phantom, respectively. Absolute wedge factor values deduced with both detector systems and based on the ratio of ionization chamber readings, differ for the investigated photon beams, up to 3.5% for the 4 MV x-ray beam. The deviations results from the difference in composition between the detector materials and water and can be taken into account by conversion of the ionization chamber readings for both the open and wedged photon beams to the absorbed dose to water. For the brass build-up cap detector system the ratio of the conversion factors for the wedged and open beam changes the ratio of the ionization chamber readings up to about 3.6% for the 4 MV x-ray beam. For the mini-phantom the conversion factors for the wedged and open beam are almost equal for all photon beams. Consequently, for that system wedge factors based on ionization chamber readings or dose values are the same. With respect to the wedge factor variation with field size a somewhat larger increase has been determined for the 60Co and 4 MV photon beam using the brass build-up cap: about 1% for field sizes varying between 5 cm x 5 cm and 15 cm x 15 cm. This effect has to be related to an apparent more pronounced variation of the head scatter dose contribution with field size for the wedged photon beams if the brass build-up cap detection system is used. It can be concluded that determination of wedge factors "in air" under reference irradiation conditions, performed with both the mini-phantom and brass build-up cap yields within 0.5% the same result if the wedge factors are based on a dose to water ratio. However, by using high-Z build-up materials the determination is more complicated because appropriate conversion factors are then required, while similar conversion factors can be ignored if more water equivalent build-up materials such as PMMA are applied.

Comparison of parametrization methods of the collimator scatter correction factor for open rectangular fields of 6-25 MV photon beams

PURPOSE

To facilitate the use of the collimator scatter correction factor, Sc, parametrization methods that relate Sc to the field size by fitting were investigated.

MATERIALS AND METHODS

Sc was measured with a mini-phantom for five types of dual photon energy accelerators with energies varying between 6 and 25 MV. Using these Sc-data six methods of parametrizing Sc for square fields were compared, including a third-order polynomial of the natural logarithm of the field size normalized to the field size of 10 cm2. Also five methods of determining Sc for rectangular fields were considered, including one which determines the equivalent field size by extending Sterling's method.

RESULTS

The deviations between measured and calculated Sc-values were determined for all photon beams and methods investigated in this study. The resulting deviations of the most accurate method varied between 0.07 and 0.42% for square fields and between 0.26 and 0.79% for rectangular fields. A recommendation is given as to how to limit the number of fields for which Sc should be measured in order to be able to accurately predict it for an arbitrary field size.

Dosimetric comparison of an integrated multileaf-collimator versus a conventional collimator

The dosimetric characteristics of both a conventional GE collimator (CC) and a GE multileaf collimator (MLC) are compared for different photon beam energies. The integrated GE MLC consists of 32 pairs of tungsten leaves, replacing the lower pair of jaws of the conventional collimator. Measurements were performed with the conventional collimator before this collimator was replaced by the MLC. All parts of the accelerator except the collimator remained the same. Leakage and transmission measurements show good agreement with the manufacturer's specification, stating a leakage between leaves of less than 1% for all energies and a transmission through leaves of less than 0.5%. The dosimetric characteristics of both collimators are very similar for square and rectangular fields. No significant change in beam quality, beam attenuation and depth of maximum dose could be detected within the measurement accuracy. The MLC output ratio variation is smaller than the one measured with the CC. The penumbra difference in the Y direction is less than 0.5 mm at a depth of 5 cm in phantom; in the X direction the penumbra is 1 mm larger for the MLC due to the rounded leaf fronts. As the two leaf banks replace the lower pair of collimator jaws the distance from the collimator end to the isocentre is similar for the two collimators, therefore the MLC does not reduce the flexibility of the treatment unit. For symmetrical and regular collimator settings the MLC can be treated as the CC.

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 3 cm x 3 cm up to 40 cm x 40 cm 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.

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 x 4 cm and 40 cm x 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 x 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.

Theoretical and experimental determination of phantom scatter factors for photon fields with different radial energy variation

The output factor used for monitor unit determination in radiotherapy can be divided into two factors: the head scatter factor and the phantom scatter factor. Theoretical and experimental phantom scatter factors have been compared for different beam qualities between 4 MV and 50 MV and field sizes from 5 cm x 5 cm to 30 cm x 30 cm. The theoretical data were obtained through a convolution method based on Monte Carlo calculated energy spectra and dose kernels. The calculations have been performed both for accelerators with a rather large energy variation within the field and for accelerators with a constant energy distribution in the field. Deviations between theoretical and experimental data were found to be less than 1%.

Measurement of photon beam backscatter from collimators to the beam monitor chamber using target-current-pulse-counting and telescope techniques

Backscattered radiation (BSR) arising from field-defining collimators and entering the beam monitor chamber (BMC) may contribute to observed variations in medical linear accelerator photon beam output with collimator setting. Measuring the magnitude of such contributions for particular accelerators under specified operating conditions is therefore important when attempting to understand and model accelerator head scatter. The present work was conducted to confirm some backscatter measurements for collimating jaws reported previously and to extend these to include other accelerators and a multileaf collimator (MLC). BSR reaching the BMC from the jaws of Clinac 600C, 2100C and 2300CD accelerators and from an MLC on the 2300CD was investigated using both target-current-pulse-counting and telescope methods. Our measurements show that for the Clinac 600C BSR-dependent output variations are negligible. However, for the 2100C and 2300CD BSR-dependent relative output increased in an almost linear fashion, by up to 2.4% for 15 and 18 MV beams, and by up to 1.7% for 6 MV beams, as the field size varied from 5 x 5 cm2 to 40 x 40 cm2. The magnitude of BSR dependent upon collimator location in the head, as expected, thereby contributing to the collimator exchange effect. An earlier study at our centre using the telescope method had reported higher BSR levels. This discrepancy was resolved when corrections for telescope block and room scatter, previously assumed negligible, were made.

Collimator (head) scatter at extended distances in linear accelerator-generated photon beams

PURPOSE

A calculation formalism is proposed to predict variation of head scatter as a function of field size and treatment distance.

METHODS AND MATERIALS

Assuming that the head scatter for the linear accelerator studied was contributed predominantly by the flattening filter, a formalism was devised to predict beam intensity as a function of distance from the target position. The method used the concept of an equivalent collimator field in which a given field at any distance can be equated to a field at the isocenter such that the extent of the flattening filter seen at the two positions is the same.

RESULTS

The equation derived from the concept of equivalent collimator field size predicated change in head scatter with distance to within 0.5% for collimator field sizes ranging from 8 x 8 to 40 x 40 cm and distances up to 300 cm from the target.

CONCLUSIONS

Considering flattening filter to be the main source of head scatter, the observed deviation from inverse square law for extended treatment distances can be accounted for by an equivalent collimator field size, which sees the same extent of the flattening filter at the isocenter as the field at the given distance.

The fraction of photons undergoing head scatter in x-ray beams

The output factor in air for a high-energy x-ray beam varies with the collimator setting. Collimator backscatter and obscuring of the source in the target contribute to this variation, but the main component is photon scatter in structures in the accelerator head. To determine the scatter-to-primary ratio, SPR, between the air kerma from such scattered photons and from those that originate directly from the source, it is essential to know the shape of this function SPR(c) of the square collimator opening c, especially for small c. To determine this, simulated head scatter was generated in lead blocks inside the head. By taking the ratio of the output factors for two such blocks of slightly different thickness, the effects of source obscuring and collimator backscatter were eliminated. Using the measured difference in transmission through the two lead blocks, the limiting value for c-->0 could be determined and hence the scatter-to-primary ratios SPR(c). The results could be fitted well with an error function, which then was applied to data measured for clinical beams of 6 and 25 MV. For c = 20 cm, SPR for one 6 MV beam was determined to be 0.016 without a flattening filter, 0.06 for the open beam, and 0.16 with the built-in wedge. At 25 MV, the SPR was higher, 0.09 and 0.20 for the open and wedged beams, respectively.

Head-scatter factors in blocked photon fields

The behavior of the head-scatter factor in shielded 6 and 25 MV X-ray beams from a Philips SL25 linear accelerator was investigated by measuring incident fluences by direct (in-air) and indirect (in-phantom) methods. It was found that perturbations in head-scatter produced by shielding blocks arranged to define a slit-shaped field are considerably less than 1% in unwedged beams, even when 80% of a 20 x 20 cm2 field is shielded. The results are independent of beam energy and orientation of the slit with respect to the collimator jaws. When a 60 degrees wedge is inserted, the head-scatter factor decreases by up to a few percent, depending on slit direction but not on energy. The contributions to head-scatter from the block tray and the shielding blocks are negligible.

Relative output factors of asymmetric megavoltage beams

A new method for calculating output factors of asymmetric therapy fields is presented. The method uses the output factors of symmetric fields, as well as off-axis ratios measured in air, to calculate the output factor for an arbitrary asymmetric field. Calculations have been checked by measurements in four photon beams (4-18 MV) of three different linear accelerators. The accuracy between the theory and the measurements is generally better than 1%. According to the preliminary results the method may also be suitable for megavoltage electron beams.

Wedge factor constituents of high-energy photon beams: head and phantom scatter dose components

The head and phantom scatter contribution to the output of a treatment machine have been determined for open and wedged 60Co gamma-ray beams and 4, 8, 16 and 25 MV X-ray beams, using an extended and a small-sized phantom. The wedge factor variation with field size and phantom depth have been analysed as a function of both scatter components. For the wedged beams a stronger increase of the head scatter contribution with field size, i.e. 4-9% for field sizes increasing from 5 cm x 5 cm to 20 cm x 20 cm, has been observed compared with open beams. This result indicates that the wedge factor variation with field size is related to a change of the primary photon fluence. Our study shows that the ratio of the head and phantom scatter contribution for the wedged and open beams remains unchanged for all beams except the 4 and 25 MV X-ray beam. This implies that, except for these latter energies, the variation of the wedge factor with phantom depth is determined by the wedge-induced change of the primary photon energy fluence. For the 4 and 25 MV X-ray beam it is shown that the wedge factor is also influenced by a change of the phantom scatter contribution. The wedge factor for the 25 MV X-ray beam is strongly influenced by the electron contamination for phantom depths up to 6 cm. For the 60Co and the 4 MV photon beam it is shown that the wedge factor decreases slightly with increasing source-to-skin distance due to a reduced contribution to the total dose from photons scattered in the wedge. For clinical use, an algorithm is given to calculate the wedge factor variation with field size and phantom depth.

A method for dose calculation for high energy photon beams based on measurements performed at reference depth

An algorithm is proposed to calculate the dose per monitor unit at any point along the beam axis for blocked or unblocked fields. The proposed formalism takes into consideration the beam measurements performed at the reference depth as recommended by most dosimetry protocols (5 cm or 10 cm depending on the beam quality). The only parameters which cannot be measured at the reference depth are the peak scatter factors, but they appear only as a ratio of two peak scatter factors for two slightly different field sizes. A correction factor is proposed when the distance of one shielding block to the beam axis is smaller than 5 cm. An agreement better than 1% has been obtained between calculations and measurements in the range of beam qualities, distances to the source and field sizes defined by typical collimators or shielding blocks, usually encountered in clinical practice.

The determination of phantom and collimator scatter components of the output of megavoltage photon beams: measurement of the collimator scatter part with a beam-coaxial narrow cylindrical phantom

The separation of the total scatter correction factor Sc,p in a collimator scatter component, Sc, and a phantom scatter component, Sp, has proven to be an useful concept in megavoltage photon beam dose calculations in situations which differ from the standard treatment geometry. A clinically applicable method to determine Sc is described. Measurements are carried out with an ionization chamber, placed at a depth beyond the range of contaminant electrons, in a narrow cylindrical polystyrene phantom with a diameter of 4 cm of which the axis coincides with the beam axis. Sc,p is measured in a full-scatter phantom and Sp can be derived from Sc,p and Sc. In order to obtain a reliable separation, i.e. excluding the influence of contaminant electrons, measurements of Sc,p have been carried out at depths of 5 cm for photon beams with a quality index (QI) up to and including 0.75 and a depth of 10 cm with QI larger than 0.75. These depths are in accordance with recommendations given in recent dosimetry protocols. The consistency of the method was checked by comparing calculated and measured values of Sc,p for a set of blocked fields for a range of photon beam energies from 60Co up to 25 MV showing a maximum deviation of 2%. The method can easily be implemented in existing procedures for the calculation of the number of monitor units to deliver a specified dose to a target volume.