Monitor unit calculations for wedged asymmetric photon beams

Algorithms for calculating monitor units (MUs) in wedged asymmetric high-energy photon beams as implemented in treatment planning systems have their limitations. Therefore an independent method for MU calculation is necessary. The aim of this study was to develop an empirical method to determine MUs for points at the centre of wedged fields, asymmetric in two directions. The method is based on the determination of an off-axis factor (OAF) that corrects for the difference in dose between wedged asymmetric and wedged symmetric beams with the same field size. Measurements were performed in a water phantom irradiated with 6 and 18 MV photon beams produced by Elekta accelerators, which are fitted with an internal motorized wedge that has a complex shape. The OAF perpendicular to the wedge direction changed significantly with depth for the 18 MV beam. Dose values measured for a set of 18 test cases were compared with those calculated with our method. The maximum difference found was 6.5% and in 15 cases this figure was smaller than 2.0%. The analytical method of Khan and the empirical method of Georg were also tested and showed errors up to 12.8%. It can be concluded that our simple formalism is able to calculate MUs in wedged asymmetric fields with an acceptable accuracy in most clinical situations.     

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.     

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

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

Errors in off-axis treatment planning for a 4-MeV machine

Computer treatment planning systems allow dose computation in planes parallel to the central one (off-axis plans). The beam data may consist of, e.g., percentage depth doses along the central axis plus off-axis ratios (OAR) at several depths. In some systems, the calculation of an off-axis plan is based on the assumption that the OAR can be represented by a separable function: OAR(x,y) = f(x).g(y), where x and y are the symmetry axes perpendicular to the beam axis and the functions f and g are equal for a square open field. The errors of this assumption for a 4-MeV machine were measured for open fields and wedged fields at five different depths. The measured dose was compared with that predicted by the above equation for 50%, 75%, and 88% of the half field width from the beam axis. Maximum deviation of more than 10% was observed with the probable error of the measurement being 1%.     

Verification of treatment parameter transfer by means of electronic portal dosimetry

Electronic portal imaging devices (EPIDs) are mainly used for patient setup verification during treatment but other geometric properties like block shape and leaf positions are also determined. Electronic portal dosimetry allows dosimetric treatment verification. By combining geometric and dosimetric information, the data transfer between treatment planning system (TPS) and linear accelerator can be verified which in particular is important when this transfer is not carried out electronically. We have developed a pretreatment verification procedure of geometric and dosimetric treatment parameters of a 10 MV photon beam using an EPID. Measurements were performed with a CCD camera-based iView EPID, calibrated to convert a greyscale EPID image into a two-dimensional absolute dose distribution. Central field dose calculations, independent of the TPS, are made to predict dose values at a focus-EPID distance of 157.5 cm. In the same EPID image, the presence of a wedge, its direction, and the field size defined by the collimating jaws were determined. The accuracy of the procedure was determined for open and wedged fields for various field sizes. Ionization chamber measurements were performed to determine the accuracy of the dose values measured with the EPID and calculated by the central field dose calculation. The mean difference between ionization chamber and EPID dose at the center of the fields was 0.8 +/- 1.2% (1 s.d.). Deviations larger than 2.5% were found for half fields and fields with a jaw in overtravel. The mean difference between ionization chamber results and the independent dose calculation was -0.21 +/- 0.6% (1 s.d.). For all wedged fields, the presence of the wedge was detected and the mean difference in actual and measured wedge direction was 0 +/- 3 degrees (1 s.d.). The mean field size differences in X and Y directions were 0.1 +/- 0.1 cm and 0.0 +/- 0.1 cm (1 s.d.), respectively. Pretreatment monitor unit verification is possible with high accuracy and also geometric parameters can be verified using the same EPID image.     

Calculation of a pencil beam kernel from measured photon beam data

Usually, pencil beam kernels for photon beam calculations are obtained by Monte Carlo calculations. In this paper, we present a method to derive a pencil beam kernel from measured beam data, i.e. central axis depth doses, phantom scatter factors and off-axis ratios. These data are usually available in a radiotherapy planning system. The differences from other similar works are: (a) the central part of the pencil beam is derived from the measured penumbra of large fields and (b) the dependence of the primary photon fluence on the depth caused by beam hardening in the phantom is taken into account. The calculated pencil beam will evidently be influenced by the methods and instruments used for measurement of the basic data set. This is of particular importance for an accurate prediction of the absorbed dose delivered by small fields. Comparisons with measurements show that the accuracy of the calculated dose distributions fits well in a 2% error interval in the open part of the field, and in a 2 mm isodose shift in the penumbra region.     

Evaluation of the first commercial Monte Carlo dose calculation engine for electron beam treatment planning

The purpose of this study is to perform a clinical evaluation of the first commercial (MDS Nordion, now Nucletron) treatment planning system for electron beams incorporating Monte Carlo dose calculation module. This software implements Kawrakow's VMC++ voxel-based Monte Carlo calculation algorithm. The accuracy of the dose distribution calculations is evaluated by direct comparisons with extensive sets of measured data in homogeneous and heterogeneous phantoms at different source-to-surface distances (SSDs) and gantry angles. We also verify the accuracy of the Monte Carlo module for monitor unit calculations in comparison with independent hand calculations for homogeneous water phantom at two different SSDs. All electron beams in the range 6-20 MeV are from a Siemens KD-2 linear accelerator. We used 10,000 or 50,000 histories/cm2 in our Monte Carlo calculations, which led to about 2.5% and 1% relative standard error of the mean of the calculated dose. The dose calculation time depends on the number of histories, the number of voxels used to map the patient anatomy, the field size, and the beam energy. The typical run time of the Monte Carlo calculations (10,000 histories/cm2) is 1.02 min on a 2.2 GHz Pentium 4 Xeon computer for a 9 MeV beam, 10 x 10 cm2 field size, incident on the phantom 15 x 15 x 10 cm3 consisting of 31 CT slices and voxels size of 3 x 3 x 3 mm3 (total of 486,720 voxels). We find good agreement (discrepancies smaller than 5%) for most of the tested dose distributions. We also find excellent agreement (discrepancies of 2.5% or less) for the monitor unit calculations relative to the independent manual calculations. The accuracy of monitor unit calculations does not depend on the SSD used, which allows the use of one virtual machine for each beam energy for all arbitrary SSDs. In some cases the test results are found to be sensitive to the voxel size applied such that bigger systematic errors (>5%) occur when large voxel sizes interfere with the extensions of heterogeneities or dose gradients because of differences between the experimental and calculated geometries. Therefore, user control over voxelization is important for high accuracy electron dose calculations.     

Separation of dose-gradient effect from beam-hardening effect on wedge factors in photon fields

It is known experimentally that a wedge transmission factor depends upon the field size and depth of measurement in particular. Dependence of the transmission upon depth has been attributed to a hardening of the incident beam through the filter, which preferentially absorbs the low-energy photon of the bremsstrahlung component of that beam. We have attempted to separate this hardening effect from that of increased phantom scatter due to dose gradient induced by the wedge filter. Using an experimental wedge machined from cerrobend, the filter transmission at depth is measured and redefined relative to an "equally hardened" beam, obtained by filtering through a flat slab of equal thickness at the center of the wedge. Results of the Co-60, 4-, and 8-MV wedged beams indicate that nearly half of the increase in the transmission at depth is due to the effect of dose-gradient scatter in polystyrene phantom. Based on a simple relationship between primary and scattering radiation, an algebraic presentation is indeed in support of the dose gradient resulting in apparent increase in the wedge factors, at depth.     

Evaluation of a commercial three-dimensional electron beam treatment planning system

We evaluated a commercial three-dimensional (3D) electron beam treatment planning system (CADPLAN V.2.7.9) using both experimentally measured and Monte Carlo calculated dose distributions to compare with those predicted by CADPLAN calculations. Tests were carried out at various field sizes and electron beam energies from 6 to 20 MeV. For a homogeneous water phantom the agreement between measured and CADPLAN calculated dose distributions is very good except at the phantom surface. CADPLAN is able to predict hot and cold spots caused by a simple 3D inhomogeneity but unable to predict dose distributions for a more complex geometry where CADPLAN underestimates dose changes caused by inhomogeneity. We discussed possible causes for the inaccuracy in the CADPLAN dose calculations. In addition, we have tested CADPLAN treatment monitor unit and electron cut-out factor calculations and found that CADPLAN predictions generally agree with manual calculations.     

Treatment planning for asymmetric jaws on a commercial TP system.

In this work, the accuracy of the asymmetric jaws planning feature in a commercial treatment planning (TP) system is assessed. In the latest version of this software, the off-axis beam quality variation is handled by a function g(d,r), which is derived from measured horizontal beam profiles at four different depths. The calculated and measured isodoses for a 6-MV linear accelerator with asymmetric jaws agree to +/- 0.5% along the central axis and to within 2 mm at the beam edge. Formulas for treatment time calculations using the output data reported by the computer program are described, as well as formulas for manual calculations based on pregenerated data tables. Doses calculated based on these formulas are compared to measurement and the accuracy is +/- 1% and +/- 2% for the computer and manual calculations, respectively. It is concluded that this version of the treatment planning system as well as the treatment time calculation formulas can be used adequately for asymmetric jaw computerized and manual treatment planning.     

Partially wedged radiation beams

To increase dose homogeneity within certain radiotherapy targets, we defined a partially wedged radiation beam as a beam with wedge modification in one part of the field only. Partially wedged beams may be beneficial in cases with curved surfaces inside parts of the beam only, where they may compensate for missing tissue and/or for variations in depth to the target region. Possible sites suitable for partially wedged beams include urinary bladder and tangential breast irradiation. Customized partially wedged beams were delivered applying dynamic collimation techniques. Two different linear detector arrays, a semiconductor diode array and an ionization chamber array, were used independently in the same standard water tank to verify that the partially wedged beams were delivered according to the definition. Dose calculations of partial wedge fields were implemented in our treatment planning system and compared with the measured dose distributions. We re-planned a representative treatment plan for both advanced urinary bladder cancer and tangential breast irradiation using partially wedged beams. For both patients the target dose homogeneity was improved, and the doses to surrounding critical normal tissues were reduced.     

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 Bj?rngard [P. Vadash and B. E. Bj?rngard, 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.     

Extension of CadPlan algorithm to model the dose distribution under a motorized wedge.

The CadPlan treatment planning system models the dose distribution in the non-wedge direction under a wedged field by converting the wedge thickness to an equivalent water thickness. The algorithm estimates the off-axis ratio (OAR) in the non-wedged direction using the open field OAR at a depth deeper by this equivalent water thickness. This model has been shown to work well for a Siemens Mevatron KD-2 Linac. However, the motorized wedge of the Elekta (formerly Philips) accelerators is tapered off-axis to give a flat dose profile in the non-wedged direction. The CadPlan model assumes that the wedge has a uniform thickness in the non-wedged direction and so cannot model the off-axis dose for the motorized wedge. For a 4 MV beam of a SL75/5 accelerator this leads to a 7% overestimate and a 9% underestimate of the OAR under the thin and thick edge of the wedge respectively. For 6 and 18 MV beams of a SL20 accelerator and a 6 MV beam of a SL75/5 accelerator, the model underestimates the OAR in the order of 10% under the thick end of the wedge. We have shown that by appropriate modification of the effective water thickness values at off-axis distances, the algorithm models the OAR in the non-wedged direction to within 2.5% of the measured values for the 4, 6 and 18 MV beams, for the Elekta motorized wedge.     

Methods for beam data acquisition offered by a mini-phantom

Mini-phantoms are an important tool for measurement of basic head scatter parameters in high-energy photon beams, and recently they have also been used for beam quality specification. Therefore the feasibility and reliability of basic beam parameter acquisition using only a mini-phantom is checked in 6, 18 and 25 MV photon beams. These parameters include head scatter correction factors, phantom scatter correction factors, total scatter correction factors, wedge factors, off-axis ratios, as well as beam attenuation coefficients and beam hardening coefficients. In order to specify beam quality variations and beam quality modifications by a wedge, two different methods are compared: the first method uses a constant source to chamber distance of 1 m, the second method refers to narrow beam geometry. Mu values derived with two different beam quality specification methods show a systematic deviation. However, relative variations of the attenuation coefficient within the beam and the associated beam quality modifications observed with the two methods show good agreement in open and wedged beams. Phantom scatter correction factors are calculated from measured head scatter correction factors and total scatter correction factors as well as from attenuation coefficients. Measured and calculated phantom scatter correction factors agree within 1% with the values given in literature. For 18 and 25 MV photon beam, wedge factors measured in water or in the mini-phantom agree within 0.5%, but maximum deviations of approximately 1.5% are observed at 6 MV for the largest field sizes. It is demonstrated that the determination of several beam data related to full scatter conditions does not necessarily require the availability of a full scatter phantom. The mini-phantom is a reliable but very cheap and simple tool. It offers versatile possibilities to measure, check and verify basic beam parameters in high-energy photon beams.     

Generalized monitor unit calculation for the Varian enhanced dynamic wedge field

The generalized monitor unit (MU) calculation equation for the Varian enhanced dynamic wedge (EDW) is derived. The assumption of this MU calculation method is that the wedge factor of the EDW at the center of the field is a function of field size, the position of the center of the field in the wedge direction, and the final position of the moving jaw. The wedge factors at the center of the field in both symmetric and asymmetric fields are examined. The difference between calculated and measured wedge factors is within 1.0%. The method developed here is easy to implement. The only datum required in addition to the standard set of conventional physical wedge implementation data is the off-axis output factor for the open field in the reference condition. The off-center point calculation is also examined. For the off-center point calculation, the dose profile in the wedge direction for the largest EDW field is used to obtain the relative off-center ratio in any smaller wedge field. The accuracy of the off-center point calculation decreases when the point of calculation is too close to the field edge.     

Theoretical considerations of monitor unit calculations for intensity modulated beam treatment planning

A treatment planning system to compute intensity modulated radiotherapy (IMRT) treatments using inverse planning was investigated. The system was designed to optimize the intensity patterns required to treat a specified target volume with specified normal structure constraints. A beam model that uses the convolution of pencil beams was used to compute the dose distributions. A multileaf collimator leaf-setting sequence intended to produce the intensity pattern was computed along with the monitor units required to deliver each of a number of fixed-gantry modulated fields. Computer calculations are commonly verified using an independent manual procedure. It is difficult to calculate treatment delivery monitor units for this variant of IMRT using manual methods. Since manual calculations are not feasible, it is important both to understand and to verify the calculation of treatment monitor units by the planning system algorithm. A formal analysis was made of the dose calculation model and the monitor unit calculation embedded in the algorithm. Experimental verification of the dose delivered by plans computed with the methodology demonstrated an agreement of better than 4% between the dose model and measurements.     

Testing of the analytical anisotropic algorithm for photon dose calculation

The analytical anisotropic algorithm (AAA) was implemented in the Eclipse (Varian Medical Systems) treatment planning system to replace the single pencil beam (SPB) algorithm for the calculation of dose distributions for photon beams. AAA was developed to improve the dose calculation accuracy, especially in heterogeneous media. The total dose deposition is calculated as the superposition of the dose deposited by two photon sources (primary and secondary) and by an electron contamination source. The photon dose is calculated as a three-dimensional convolution of Monte-Carlo precalculated scatter kernels, scaled according to the electron density matrix. For the configuration of AAA, an optimization algorithm determines the parameters characterizing the multiple source model by optimizing the agreement between the calculated and measured depth dose curves and profiles for the basic beam data. We have combined the acceptance tests obtained in three different departments for 6, 15, and 18 MV photon beams. The accuracy of AAA was tested for different field sizes (symmetric and asymmetric) for open fields, wedged fields, and static and dynamic multileaf collimation fields. Depth dose behavior at different source-to-phantom distances was investigated. Measurements were performed on homogeneous, water equivalent phantoms, on simple phantoms containing cork inhomogeneities, and on the thorax of an anthropomorphic phantom. Comparisons were made among measurements, AAA, and SPB calculations. The optimization procedure for the configuration of the algorithm was successful in reproducing the basic beam data with an overall accuracy of 3%, 1 mm in the build-up region, and 1%, 1 mm elsewhere. Testing of the algorithm in more clinical setups showed comparable results for depth dose curves, profiles, and monitor units of symmetric open and wedged beams below dmax. The electron contamination model was found to be suboptimal to model the dose around dmax, especially for physical wedges at smaller source to phantom distances. For the asymmetric field verification, absolute dose difference of up to 4% were observed for the most extreme asymmetries. Compared to the SPB, the penumbra modeling is considerably improved (1%, 1 mm). At the interface between solid water and cork, profiles show a better agreement with AAA. Depth dose curves in the cork are substantially better with AAA than with SPB. Improvements are more pronounced for 18 MV than for 6 MV. Point dose measurements in the thoracic phantom are mostly within 5%. In general, we can conclude that, compared to SPB, AAA improves the accuracy of dose calculations. Particular progress was made with respect to the penumbra and low dose regions. In heterogeneous materials, improvements are substantial and more pronounced for high (18 MV) than for low (6 MV) energies.     

Measurement of dose distributions using film in therapeutic electron beams

The feasibility of using film dosimetry data as the input data for patient treatment planning was evaluated. The central-axis depth dose and the off-axis ratios obtained from film measurements in a solid phantom were compared with those of ion-chamber measurements in water. Two techniques were used to generate isodose distributions. The first technique used only the film data, i.e., the central-axis depth dose and the off-axis ratios used for the reconstruction were determined from the film optical density (corrected for film nonlinearity). In the second technique, the central-axis depth dose measured by an ion chamber in a water phantom was combined with the off-axis ratios measured using film in the "solid water" phantom. The resulting isodose distributions from both techniques were compared with the ion-chamber measurements in water for 7-, 12-, and 18-MeV electrons, and the second technique showed better agreement with the ion-chamber measurements than did the first technique. The differences were within a clinically acceptable range.