Dosimetry of asymmetric x-ray collimators

Validation of the geometric equivalent field concept in total scatter factor calculations, for half-, quarter- and off-isocenter asymmetric square fields

OBJECTIVE

Monitor unit (MU) verification for any symmetric or asymmetric field is performed using a total scatter factor (Scp ), that is calculated based on the geometric equivalent square field (GESF) concept. In this study, we measured the Scp of various asymmetric square fields (ASFs ) and their respective GESFs.

METHODS

Square half-fields (SHFs ), square quarter-fields (SQFs ) and square off-isocenter fields (SOFs ), with sizes ranging from 3×3 cm2 to 20×20 cm2 were created, by varying the collimator jaws of two Varian iX Linacs (6/18 and 6/23 MV). A semi-flex ion chamber was used to measure Scp at a depth of 10 cm within a water phantom, at the effective field center (EFC) of all ASFs , and at the isocenter (IC) of their respective GESFs. The later Scp values were corrected by the off-axis ratio [OAR(r)] of the 40×40 cm2 field size, where r is the distance between EFC and IC.

RESULTS

The results show that the Scp (EFC) is independent of the type of the ASF (SHF, SQF, or SOF) and no significant difference exists between the 18 and 23 MV beams. Compared with the Scp (IC), the Scp (EFC) increased with increasing r, by up to 2% and 4% for 18/23 and 6 MV, respectively.

CONCLUSIONS

The GESF concept provides acceptable accuracy (< 2%) for the calculation of Scp of the ASFs used in most clinical situations (except from SOF with EFC at large r), and thus can be used in MU verification calculations.

Monitor unit calculations for external photon and electron beams: Report of the AAPM Therapy Physics Committee Task Group No. 71

A protocol is presented for the calculation of monitor units (MU) for photon and electron beams, delivered with and without beam modifiers, for constant source-surface distance (SSD) and source-axis distance (SAD) setups. This protocol was written by Task Group 71 of the Therapy Physics Committee of the American Association of Physicists in Medicine (AAPM) and has been formally approved by the AAPM for clinical use. The protocol defines the nomenclature for the dosimetric quantities used in these calculations, along with instructions for their determination and measurement. Calculations are made using the dose per MU under normalization conditions, D'0, that is determined for each user's photon and electron beams. For electron beams, the depth of normalization is taken to be the depth of maximum dose along the central axis for the same field incident on a water phantom at the same SSD, where D'0 = 1 cGy/MU. For photon beams, this task group recommends that a normalization depth of 10 cm be selected, where an energy-dependent D'0 ≤ 1 cGy/MU is required. This recommendation differs from the more common approach of a normalization depth of dm, with D'0 = 1 cGy/MU, although both systems are acceptable within the current protocol. For photon beams, the formalism includes the use of blocked fields, physical or dynamic wedges, and (static) multileaf collimation. No formalism is provided for intensity modulated radiation therapy calculations, although some general considerations and a review of current calculation techniques are included. For electron beams, the formalism provides for calculations at the standard and extended SSDs using either an effective SSD or an air-gap correction factor. Example tables and problems are included to illustrate the basic concepts within the presented formalism.

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

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

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

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

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.

Abutment region dosimetry for the monoisocentric three-beam split field technique in the head and neck region using asymmetrical collimators

Creating non-divergent field edges using asymmetric collimators and a single isocentre can improve matchline dosimetry owing to decreased reliance on operator skills and avoidance of couch movement. However, asymmetic jaws have an associated tolerance that can cause abutment to be misaligned. The matching area dose for monoisocentric three-beam split fields commonly used in head and neck cancer treatments using mismatched and matched collimators is the subject of this work. X-ray verification film was exposed in a solid-water phantom, and the dose at the matching area was evaluated using mismatched and matched collimators. In the case of mismatched (consistently overlapped) collimators, digital displays of an asymmetric collimator position within the tolerance indicated in the manufacturer's specifications were investigated for the three-beam split field technique. The effect of this technique on the junctional dose was also determined using matched collimators. Although the collimators showed a consistent overlap, a perfect dose distribution could be obtained at the matching area. The three-beam split field technique yielded an 8% overdose at the matchline using matched collimators. In conclusion, an awareness of the effects of the abutting technique and digital display tolerance is necessary to achieve good junction uniformity using asymmetric collimators.

Sensitivity of megavoltage photon beam Monte Carlo simulations to electron beam and other parameters

The BEAM code is used to simulate nine photon beams from three major manufacturers of medical linear accelerators (Varian, Elekta, and Siemens), to derive and evaluate estimates for the parameters of the electron beam incident on the target, and to study the effects of some mechanical parameters like target width, primary collimator opening, flattening filter material and density. The mean energy and the FWHM of the incident electron beam intensity distributions (assumed Gaussian and cylindrically symmetric) are derived by matching calculated percentage depth-dose curves past the depth of maximum dose (within 1% of maximum dose) and off-axis factors (within 2sigma at 1% statistics or less) with measured data from the AAPM RTC TG-46 compilation. The off-axis factors are found to be very sensitive to the mean energy of the electron beam, the FWHM of its intensity distribution, its angle of incidence, the dimensions of the upper opening of the primary collimator, the material of the flattening filter and its density. The off-axis factors are relatively insensitive to the FWHM of the electron beam energy distribution, its divergence and the lateral dimensions of the target. The depth-dose curves are sensitive to the electron beam energy, and to its energy distribution, but they show no sensitivity to the FWHM of the electron beam intensity distribution. The electron beam incident energy can be estimated within 0.2 MeV when matching either the measured off-axis factors or the central-axis depth-dose curves when the calculated uncertainties are about 0.7% at the 1 sigma level. The derived FWHM (+/-0.1 mm) of the electron beam intensity distributions all fall within 1 mm of the manufacturer specifications except in one case where the difference is 1.2 mm.

Three-dimensional radiotherapy of head and neck and esophageal carcinomas: a monoisocentric treatment technique to achieve improved dose distributions

The specific aim of three-dimensional conformal radiotherapy is to deliver adequate therapeutic radiation dose to the target volume while concomitantly keeping the dose to surrounding and intervening normal tissues to a minimum. The objective of this study is to examine dose distributions produced by various radiotherapy techniques used in managing head and neck tumors when the upper part of the esophagus is also involved. Treatment planning was performed with a three-dimensional (3-D) treatment planning system. Computerized tomographic (CT) scans used by this system to generate isodose distributions and dose-volume histograms were obtained directly from the CT scanner, which is connected via ethernet cabling to the 3-D planning system. These are useful clinical tools for evaluating the dose distribution to the treatment volume, clinical target volume, gross tumor volume, and certain critical organs. Using 6 and 18 MV photon beams, different configurations of standard treatment techniques for head and neck and esophageal carcinoma were studied and the resulting dose distributions were analyzed. Film validation dosimetry in solid-water phantom was performed to assess the magnitude of dose inhomogeneity at the field junction. Real-time dose measurements on patients using diode dosimetry were made and compared with computed dose values. With regard to minimizing radiation dose to surrounding structures (i.e., lung, spinal cord, etc.), the monoisocentric technique gave the best isodose distributions in terms of dose uniformity. The mini-mantle anterior-posterior/posterior-anterior (AP/PA) technique produced grossly non-uniform dose distribution with excessive hot spots. The dose measured on the patient during the treatment agrees to within +/- 5 % with the computed dose. The protocols presented in this work for simulation, immobilization and treatment planning of patients with head and neck and esophageal tumors provide the optimum dose distributions in the target volume with reduced irradiation of surrounding non-target tissues, and can be routinely implemented in a radiation oncology department. The presence of a real-time dose-measuring system plays an important role in verifying the actual delivery of radiation dose.

Dosimetric assessment of nonperfectly abutted fields using asymmetric collimators

The abutment of adjacent fields has been facilitated through the use of asymmetric collimators. Conceptually, the abutment yields a perfectly uniform dose distribution across the junction, provided the asymmetric jaw is set precisely at the beam central axis. However, the asymmetric jaw has an associated tolerance, which can cause the abutment to be misaligned. This study examined the dose distribution at the junction of nonperfectly abutted fields. The abutment of fields was carried out using an asymmetric collimation of 5 x 10 cm, with an asymmetric jaw positioned at the beam central axis. A film was initially exposed using this field with the collimator set at 90 degrees. The collimator was then rotated 180 degrees and the same film was exposed for the second time to create the field abutment. Positioning the asymmetric jaw with respect to the beam central axis set the amount of gap and overlap between the abutted fields. The dose distribution was measured for asymmetric jaw positioning of -2, -1, 0, + 1, and +2 mm from the beam central axis. In addition, the dose distribution was also computed mathematically by summing the 2 dose profiles with defined gap or overlap. A field mismatch of +/-1 mm would result in a dose nonuniformity of 17%, and a +/-2 mm mismatch would produce a 35% dose nonuniformity.

Dose calculations for asymmetric fields defined by independent collimators using symmetric field data

Several methods have been developed for the dosimetry of asymmetric radiation fields formed by independently moving collimator jaws. Three of these methods, based on different principles and modified to comply with our set of available data, are utilized for the calculation of asymmetric field dose profiles. All three methods use output factors and per cent depth doses or tissue maximum ratios of symmetric fields. In the first method, calculation of the off-centre ratio (OCR) of the asymmetric field is based on the symmetric field from which the asymmetric is originated, by setting the one jaw in an asymmetrical position. In the second method the OCR of the symmetric field is used for the OCR calculation of the asymmetric field of the same size; whereas the third method does not allow for the asymmetric OCR calculation. The results obtained using data for the 6 MV photon beam of a Philips SL-20 linear accelerator indicate that both the first and second method can accurately reproduce asymmetric field profiles from symmetric field data; the third method does not allow for penumbra reproduction, but it is accurate at the central part of the asymmetric field. The problems encountered in the application of the three methods are reported and their accuracy is compared.

Dose calculation for asymmetric photon fields with independent jaws and multileaf collimators

We have developed a simple method for dose calculation in dual asymmetric open and irregular fields with four independent jaws and multileaf collimators. Our calculation method extends the scatter correction method of Kwa et al. [Med. Phys. 21, 1599-1604 (1994)] based on the principle of Day's equivalent-field calculation. The scatter correction factor was determined by the ratio of the derived doses of a smaller asymmetric open field or irregular field to a larger symmetric field. The algorithm with the scatter correction method can be calculated from output factors, tissue maximum ratios, and off-axis ratios for conventional symmetric fields. The doses calculated by this method were compared with the measured doses for various asymmetric open and irregular fields. The agreement between the calculated and measured doses for 4 and 10 MV photon beams was within 0.5% at the geometric center of the asymmetric open fields. For the asymmetric irregular fields with the same geometrical center, agreement within 1% was found in most cases.

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.

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

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

Analytical considerations of beam hardening in medical accelerator photon spectra

Beam hardening is a well-known phenomenon for therapeutic accelerator beams passing through matter in narrow beam geometry. This study assesses quantitatively the magnitude of beam hardening of therapeutic beams in water. A formal concept of beam hardening is proposed which is based on the decrease of the mean attenuation coefficient with depth. On the basis of this concept calculations of beam hardening effects are easily performed by means of a commercial spreadsheet program. Published accelerator spectra and the tabulated values of attenuation coefficients serve as input for these calculations. It is shown that the mean attenuation coefficient starts at depth zero with an almost linear decrease and then slowly levels off to a limit value. A similar behavior is found for the beam hardening coefficient. A physically reasonable, semianalytical model is given which fits the data better than previously published functions. The energy dependence of the initial attenuation coefficient is evaluated and shown. It fits well to published experimental data. The initial beam hardening coefficient, however, shows no energy dependence. Its mean value (eta0) approximately 0.006 cm(-1)) is also in close agreement to the measured data.

The single-isocentre treatment of head and neck cancer: time gain using MLC and automatic set-up

PURPOSE

In this manuscript, we studied the difference in the treatment time required to execute a single-isocentre three-field irradiation of the head and neck, using either tray-mounted cerrobend blocks or a multileaf collimator (MLC) for field shaping and automatic set-up.

MATERIALS AND METHODS

A total of twenty consecutive, unselected patients (16 males, four females), were eligible for this study because the dose they were to received was 44 Gy (2 Gy/fraction) to the head, neck and supraclavicular regions. Patients were randomly allocated to one of two treatment groups. The first group (n = 11) was treated on a Philips SL-75 linear accelerator (SL-75), using 5 MV photons and tray-mounted cerrobend blocks. The second group (n = 9) was treated on a Philips SL-25 linear accelerator (SL-25-MLC), using 6 MV photons and a MLC. Patients of the second group were treated using the automatic set-up facility of the SL-25-MLC, without entering the treatment room between consecutive fields.

RESULTS

Overall treatment time was significantly shorter on the SL-25-MLC than on the SL-75 (P < 0.0001). The difference in total treatment-execution time was in the range of 157 s per treatment session. The largest difference was observed in the set-up time. There was an average of a 125 s time gain per treatment day (P < 0.0001) in favour of the SL-25-MLC.

CONCLUSIONS

Compared to tray-mounted cerrobend blocks, a MLC and automatic set-up results in a significant time advantage when a single isocentre technique is used to treat head and neck cancer.

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.

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 generic off-axis energy correction for linac photon beam dosimetry

Cooperative clinical trial group protocols frequently require off-axis point dose calculations. The Radiological Physics Center uses the calculative technique developed by Hanson et al. [Med. Phys. 7, 145-146 (1980); 7, 147-150 (1980)] to verify these calculations. In order to correct for off-axis energy changes, this technique requires off-axis half-value layer data, HVL, as a function of off-axis ray angle for the specific beam. This paper presents a formulism based on HVL mesurements on a limited number of therapy beams, which allows the calculation of an off-axis energy-correction factor for any clinical photon beam created by a linear accelerator using conventional flattening filters.

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.

Output ratios in a miniphantom for asymmetric fields shaped by a multileaf collimator

The integrated GE multileaf collimator (MLC) provides the ability to achieve 'double' asymmetric fields: each of the 64 leaves allow an over-axis travel of 10 cm and the Y-jaws allow 20 cm. A formalism has recently been proposed by the authors to calculate the output ratio in a miniphantom for this type of MLC by the product of independent leaf and jaw correction factors. The original proposed formalism was restricted to regular or irregular fields including the collimator rotational axis. Introducing 'reduced coordinates' for the correction factors in the present work this formalism is extended to asymmetric fields where central leaves or jaws overlap the collimator axis. The extended formalism is applied to asymmetric square, rectangular and irregular fields. For all fields checked at a given off-axis position, measured and calculated output ratios agree within 1% for 6, 18 and 25 MV photon beams. To relate output ratios normalized to off-axis points with output ratios on-axis, off-axis ratios are derived from film and miniphantom measurements. Both off-axis ratios agree to within 1% for 6 and 25 MV photon beams; a maximum deviation of 1.3% is observed at 18 MV. Calculated products of output ratios and off-axis ratios derived from films are compared with measurements for asymmetric square, rectangular and irregular fields, and agree mostly within 1% for all energies checked; maximum deviations of 1.3 and 1.6% are observed for 6 and 18 MV photon beams.

Commissioning the Varian Enhanced Dynamic Wedge using the RAHD treatment planning system

Procedures to commission and verify the Varian Enhanced Dynamic Wedge for use with the RAHD Treatment Planning System are presented. Emphasis is placed on minimizing the time and equipment required to verify that acceptable beam data is used in the planning process.

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.

Linear accelerator photon beam quality at off-axis points

Transmitted intensity through water was measured in a narrow-beam geometry for different energy x-ray beams from commercial accelerators. In order to accurately obtain the attenuation coefficient of the incident beam using transmission data, a novel formula was developed based on consideration of beam hardening in phantom. The value of the attenuation coefficient obtained by fitting transmission data to this formula was found to be independent of the absorber thickness used in experiments, whereas the attenuation coefficient obtained from the traditional formula, I(x) = I0 exp(-mux), changed by up to 7% with absorber thickness for a given beam. The beam hardening coefficient obtained from our formula indicates that the attenuation coefficient in water changes by about 0.33% per cm near the surface for the high-energy photon beams studied. Variations in beam quality with off-axis distance were subsequently investigated using the new formula. Results show that the attenuation coefficient at the water surface increased by about 15% for 15 and 18 MV beams, and by 11%-13% for 6 MV beams, when the off-axis distance at 100 cm from the source was changed from 0 to 18 cm. Consideration of the physics of bremsstrahlung production suggests that these variations should be mainly determined by the shape of the flattening filter, i.e., by the path length of rays traversing the filter in different directions. This expectation was confirmed by observing that the attenuation coefficient at the phantom surface can be related to the ray path of the beam in the flattening filter using the new transmission formula.

Clinical use of asymmetric collimators

PURPOSE

To illustrate some of the radiation treatment techniques with asymmetric collimators in one field dimension.

METHODS AND MATERIALS

Treatment planning for various sites is done with an in-house developed treatment planning system. Dose distributions in the central plane are illustrated.

RESULTS

The use of asymmetric collimation, in addition to being a replacement for cerrobend and lead blocks, can facilitate treatment setup with boost fields and with half-beam asymmetric fields as in matching two adjacent fields, in avoiding nearby critical organ or tissue, and in tangential breast treatment. The use of asymmetric collimators would alter the dose distribution across the radiation field and should be accounted for during treatment planning. In conjunction with arc rotation or multiple asymmetric fields, two-dimensional conformal radiotherapy is possible.

CONCLUSION

The full potential of asymmetric collimation requires the use of a proper treatment planning algorithm. Some of the treatment techniques with asymmetric collimation in one field dimension are shown here.

10 MV x-ray zero-area phantom scatter correction factors (Sp) obtained using three extrapolation methods

Three sets of 10 MV x-ray zero-area phantom scatter correction factors (Sp) have been obtained using three methods. The three methods are all based on the Bjärngard-Petti extrapolation principle. The three sets of data assume lateral CPE (charged particle equilibrium) for the primary absorbed dose. Using the most reliable set of data, a set of 10 MV x-ray SMRs (scatter-maximum ratios) is produced and parameterized. With respect to the zero-area Sp correction factor at a depth of 2.5 cm, the parameterized expression gives Sp (0; 2.5) = 0.931 and a Rice-Chin Monte Carlo simulation gives Sp (0; 2.5) = 0.927. The former is only 0.4% larger than the latter.

Verification of a simple point dose calculation method for a dual energy linear accelerator with asymmetric jaws

Certain fundamental dosimetrical parameters involving the applications of asymmetric jaws were investigated. The nominal accelerating potentials (NAPs) were found to decrease from 5.1 to 4.2 and from 18.0 to 13.4 for the 6 and 18 MV beams, respectively, as the off-axis distance (OAD) increases from 0.0 to 15.0 cm. The relative beam intensity increases from 1.00 to 1.07 at OAD of 15.0 cm for the 6 MV beam, and to 1.02 at OAD of 7.0 cm for the 18 MV beam. The percentage depth doses (PDDs) for half-blocked fields of 4 x 4 cm, 10 x 10 cm and 20 x 20 cm were found to deviate from those of corresponding symmetric fields by less than 2% down to the depth of 35.0 cm. The field size factor (FSF) for the asymmetric field from 4 x 4 cm to 20 x 20 cm deviates less than 1.0% from those of the corresponding symmetric fields. The equivalent square concept was found to be applicable to asymmetric fields within 1% error if the jaw exchange effect is taken into consideration. The measured point doses for half-blocked fields of 4 x 4 cm, 10 x 10 cm and 20 x 20 cm for both 6 and 18 MV were within 3% of the calculated dose based on a published dose calculation method which employs symmetric field beam parameters, such as field size factor (FSF), percentage depth dose (PDD), and off-axis correction factors (OAFs). The efficacy of this point dose calculation method is discussed.

Dosimetric verification of open asymmetric photon fields calculated with a treatment planning system based on dose-to-energy-fluence concepts

Output normalized dose profiles for asymmetric open photon fields has been calculated using a commercial treatment planning system (TPS) based on a dose-to-energy-fluence concept. The model does not require any additional measurements for off-axis fields. Calculations are compared with measurements for quadratic fields of 5 cm x 5 cm up to 20 cm x 20 cm, with their geometric field centre positioned 10 cm off-axis in the in-plane direction. The measurements include depth doses and profiles in-plane as well as cross-plane for nominal photon energies of 4, 6 and 18 MV x-rays. Both calculated and measured doses are normalized with respect to a 10 cm x 10 cm reference field, therefore making it possible to compare not only the relative distributions but also the absolute dose levels; that is, calculation of monitor units is included. The calculated depth-dose curves are generally in good agreement with measured data with an accuracy at the absolute dose level of 2% at depths beyond the dose maximum. The cross-plane profiles are calculated with an accuracy better than 3% within the field. The 'tilt' towards the collimator central axis of the in-plane profiles is predicted by the model, but is somewhat overestimated at large depths. The system provides the possibility to separate the primary and scattered parts of the dose and the cause of this tilting was studied by comparing calculated phantom-scattering and head-scattering dose profiles for a symmetric 40 cm x 20 cm field to dose profiles for an asymmetric 20 cm x 20 cm field. The tilting is shown to originate from a change both in phantom scattering and in head scattering compared to the case of symmetrical fields. The results indicate that the investigated TPS can calculate dose distributions in open asymmetric fields with a high degree of accuracy, typically better than 2-3%.

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.

Comparison of measured and calculated dose for asymmetric x-ray beams defined by independently movable collimators

Linear accelerators with x-ray collimators that move independently are becoming increasingly common for treatment with asymmetric fields. In an asymmetric field, the center of the treatment field is away from the true central axis where dosimetric data are normally obtained. In this paper we present a simplified approach to the calculation of dose for asymmetric fields. We use central axis tissue-maximum ratio, off-axis factor in phantom and relative field-size factor in phantom to calculate dose. The accuracy of our calculations has been compared with ion-chamber measurements for 6 and 15 MV x-ray beams. Measurements were made at 5, 10, and 15 cm off-axis for a 20 cm x 20 cm asymmetric field at dmax and 6 cm depths in a solid-water phantom using a 0.6 cc Farmer chamber. Agreement within 3% was found at the measurement points.

Study of dosimetric penumbra due to multileaf collimation on a medical linear accelerator

PURPOSE

Investigations of dosimetric penumbra produced by multileaf collimation on a medical linear accelerator are presented.

METHODS AND MATERIALS

Multileaf collimators (MLCs) can be designed with at least three different shaped leaf-end profiles: straight, divergent, and curved. Assessment of the dosimetric effects of the collimator edge profiles was implemented using a fast Fourier transform (FFT) convolution algorithm. Accelerator source intensity was considered to have a Gaussian distribution. The calculated dose profile, for a source-to-surface distance of 100 cm and at depth of 10 cm in a water phantom, was fitted to a penumbral-forming function from which the penumbral width between 80% and 20% of the central axis dose was obtained.

RESULTS

Calculation performed at various field sizes showed that curved collimator leaf-end produces a wider penumbra than the diverging collimator leaf-side. Film measurements agreed with the calculations within an uncertainty of less than 2 mm. The effect of backup jaws for the MLC and of the lower pair of diverging diaphragms on dosimetric penumbra was also investigated.

CONCLUSIONS

This study is useful for characterizing collimator edge effects and for optimizing new collimator designs.

Tissue compensation using dynamic collimation on a linear accelerator

PURPOSE

The availability of computer-controlled collimators on some accelerators has led to techniques for dynamic beam modification, mainly to simulate beam wedge filters. This work addresses the practical aspects of dynamic tissue compensation in one dimension using available treatment-planning software.

METHODS AND MATERIALS

Data derived from the treatment-planning program is used with an iterative calculational routine to determine the monitor unit settings needed for the collimator-controlling computer. The method was first tested by simulating a 60 degrees physical wedge. Further studies were carried out on a specially fabricated plastic phantom that modeled the sagittal contour of the upper torso, neck, and lower head regions.

RESULTS

Dynamic wedge point doses generated by the planning program agreed within 1% with the values directly measured in a polystyrene phantom. In the patient phantom, dynamic collimation achieved calculated dose uniformity within 0.5% in a reference plane near the phantom midline. A comparison of computer-generated and measured point doses in this case showed agreement within 3%.

CONCLUSIONS

Dynamic collimation can provide effective compensation for contours that vary primarily along one direction. A conventional treatment-planning program can be used to plan dynamic collimation and deliver a prescribed dose with reliable accuracy.

A method for delivering accurate and uniform radiation dosages to the head and neck with asymmetric collimators and a single isocenter

PURPOSE

To investigate the use of asymmetric collimators and a single isocenter for delivering a uniform, accurate dose of radiation to the head, neck, and supraclavicular lymph nodes.

METHODS AND MATERIALS

A linear accelerator with a pair of asymmetric collimators is required for this technique. An isocenter was placed at the junction of the lateral head and neck fields and the anterior supraclavicular field. The asymmetric collimators were set longitudinally, by collimator rotation if necessary. The collimators split the radiation beam to all portals. Dose uniformity was measured at the junction with films in solid-water phantoms.

RESULTS

Film dosimetry showed a uniform dose at the junction without hot or cold regions. A digital display tolerance of +/- 1.0 mm for a field size maintained an acceptable uniform dose (+/- 5% dose variation) at the junction. The single isocenter and asymmetric collimators reduced field setup time by half. No table rotation was required to match fields.

CONCLUSION

The asymmetric collimators lead to easy and accurate patient setup. The absence of the trapezoid effect resulted in the complete coverage of the submandibular and cervical nodes without any hot spots.

Applications of asymmetric collimation on linear accelerators

Frequency of use of asymmetric collimation (AC) at an academic radiation oncology center equipped with AC-capable linear accelerators was determined, and the type of use was cataloged. Records of patients beginning radiation treatment at U.C. Davis Cancer Center within a 3-month period (3/1/92 to 5/31/92) were reviewed. Forty-seven percent of 102 patients and 56% of 123 courses of treatment involved AC. Six common uses of AC were identified: beam-split field matching, planned boosts, other field size changes, adjustments to match divergent fields, matchline feathering, and opposed tangential fields. This study demonstrates that asymmetric collimation is a useful and powerful clinical treatment tool with widespread applications to radiation therapy.

Calculation models for determining the absorbed dose in water phantoms in off-axis planes of rectangular fields of open and wedged photon beams

Beam models are proposed for the calculation of the dose in off-axis planes of rectangular photon fields, when the data set used in the treatment planning system is based on the simple storage model of Milan and Bentley. For open beams the model separates the off-axis ratio into an envelope profile and two boundary profiles. The envelope profile gives the field intensity of the maximal position of the jaws and has rotational symmetry. The boundary profiles describe the boundaries of the field actually formed by the jaws. In the case of a wedged beam, the model also separates the off-axis ratio into envelope profiles and boundary profiles. To determine these profiles for the non-wedge direction from open beam profiles, the wedge thickness is converted to an equivalent water thickness. In the case of an asymmetric field, the boundary profiles are shifted to the field centre. Results of calculation with these models have been compared with measurements and the simple multiplication of profiles, which has often been used with the Milan-Bentley model. The new models agree within a few per cent with the measurements and are a great improvement compared to the simple multiplication of profiles.

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.

Postoperative radiotherapy for chondrosarcoma of the L1 vertebral body: a case report

A 51-year-old man presented with a low-grade chondrosarcoma of the L1 vertebral body, which had been completely resected. Radiotherapy was indicated; however, the close proximity of critical structures such as the spinal cord and the kidneys complicated the delivery of the high radiation dose required. In this paper we present the clinical and technical aspects of the radiotherapy technique used to treat this patient; we also describe the patient immobilization and radiation dose verification techniques used. The patient was treated with 18 MV photons using multiple field arc rotations with fields asymmetric with respect to the rotational axis of the collimator head. The spinal cord was aligned along the horizontal axis of the linear accelerator isocenter, and the patient was immobilized using a 10 degrees styrofoam wedge combined with an Alpha Cradle mold. In this manner, the patient was stabilized in a comfortable position, which facilitated the daily check of the isocenter position within the patient. Radiation dose verification was carried out with films in an anthropomorphic phantom and with an ionization chamber in a water phantom. These measurements confirmed the accuracy of the isodose distributions calculated for the treatment with asymmetric fields in the arc therapy mode. The use of this technique in conjunction with the positioning device permitted the delivery of 64 Gy to the L1 vertebral body with relatively low doses to the critical structures, amounting to 32 Gy at the surface of the spinal cord and less than 16 Gy to half of both kidneys.

Independent collimator dosimetry for a dual photon energy linear accelerator

PURPOSE

The independent collimator feature in medical linear accelerators can define radiation fields that are asymmetric with respect to the flattening filter and oblique to the incident surface. Prior to clinical implementation, it is necessary to evaluate the dosimetry of this non-standard treatment delivery technique. An investigation of the independent collimator dosimetry for 6 MV and 18 MV x-ray beams has been undertaken.

METHODS AND MATERIALS

Dose to tissue in free space, percent depth dose and dose distribution were measured and compared to that for symmetric field collimation.

RESULTS

The dosimetry results were consistent for both photon modes. Dose in free space with asymmetric collimation can be calculated from the corresponding symmetric field dose in free space to within 1.2 +/- 0.7% by applying an appropriate off-axis factor. Asymmetric field percent depth dose differs from symmetric field percent depth dose on average by 1.1 +/- 0.7% for 6 MV and by 0.7 +/- 0.5% for 18 MV for field sizes ranging from 5 x 5 to 20 x 20, centered 3 cm and 10 cm off-axis. The measured isodose curves demonstrate divergence effects and reduced doses (less than 3%) adjacent to the field edge closest to the flattening filter center. This dose asymmetry result is identical to that from secondary collimation.

CONCLUSION

The methodology for clinical implementation of the independent collimator feature is straightforward. However, accurate representation of the isodose distributions by commercial radiotherapy treatment planning systems requires special dose calculation algorithms.

Three-field isocentric breast irradiation using asymmetric jaws and a tilt board

Perfect abutment of medial and lateral tangential breast portals with the adjacent supraclavicular field may be achieved with ease. A simple and safe approach was developed using a tilt board and new technology that is standard on a popular linear accelerator. The patient is secured on a tilt board as a means to level the chest wall. Isocenter is placed at depth on the matchline, where asymmetric jaws are used to produce non-divergent field edges and a perfect abutment. This is done without the need for table or collimator rotations, beam-splitters, or vertical cephalad blocks. The dorsal beam edge of the tangents is made coplanar by rotating the gantry more than 180 degrees. This procedure produces a dosimetrically sharp field edge and eliminates concern about block transmission and excess dose to the contralateral breast. Set-up is fast, and the steps involved are simple and few. Advantages and limitations of this technique are presented.

Photon beam dosimetry at a blocked beam edge using diffusion approximation

A simple analytical model is presented for the transport of secondary electrons at a photon beam edge using the energy averaged solution of the Boltzmann equation, originally developed for beta-ray dosimetry at a plane interface. Dose at a point under a block is assumed to be due to secondary electrons and the scattered photons generated from the primary photon beam. The diffusion approximation is used for the secondary electron transport at a virtual plane interface created by the block. The dose from the scattered photon component is treated as decaying exponentially with distance from the beam edge. Comparisons made with the model and measurements are in general agreement for high energy accelerator beams.

A standardized multifield irradiation technique for breast tumours using asymmetrical collimators and beam angulation

Combined angulation and asymmetrical collimator matching techniques are used for field alignment in breast irradiation. A local regional irradiation technique has been developed that allows a uniform dose distribution to the entire target volume. The localization is characterized by simple measurement of a few patient co-ordinates. The equipment settings to produce a theoretical exact field alignment are calculated by a special computer program. These settings guide the simulation. We have designed the method such that the technique is standardized for all patients receiving breast and lymph node irradiation. This allows an easy, accurate and fast patient throughput at the simulator and accelerators.

The use of an universal wedge for asymmetric fields

Beam collimators on newer linear accelerators may be collimated asymmetric to the central axis. The asymmetric beam has a non-flat profile adjusted to yield fields whose half widths are not symmetric about the central axis. While some treatment planning systems modify their programs to mimic the nonuniformity, ideally it is preferred to have a flat profile under the open beam. We have developed a universal wedge that can be used to flatten the field for a variety of jaw sizes and positions and energies for the Varian 2100C. The wedge flattens the field to +/- 3% over 80% of the field.

A technique for treating local breast cancer using a single set-up point and asymmetric collimation

Using both pairs of asymmetric jaws of a linear accelerator local-regional breast cancer may be treated from a single set-up point. This point is placed at the abutment of the supraclavicular fields with the medial and lateral tangential fields. Positioning the jaws to create a half-beam superiorly permits treatment of the supraclavicular field. Positioning both jaws asymmetrically at midline to define a single beam in the inferoanterior quadrant permits treatment of the breast from medial and lateral tangents. The highest possible matching accuracy between the supraclavicular and tangential fields is inherently provided by this technique. For treatment of all fields at 100 cm source to axis distance (SAD) the lateral placement and depth of the set-up point may be determined by simulation and simple trigonometry. We elaborate on the clinical procedure. For the technologists treatment of all fields from a single set-up point is simple and efficient. Since the tissue at the superior border of the tangential fields is generally firmer than in mid-breast, greater accuracy in day-to-day set-up is permitted. This technique eliminates the need for table angles even when tangential fields only are planned. Because of half-beam collimation the limit to the tangential field length is 20 cm. Means will be suggested to overcome this limitation in the few cases where it occurs. Another modification is suggested for linear accelerators with only one independent pair of jaws.

Dynamic beam shaping

Computer control of independent collimator jaw positions and dose is combined with multiple-field summation techniques to design optimized radiation field profiles. Clinically relevant examples are shown for dynamic wedges and compensated mantle fields. Calculation, measurement, and verification techniques are discussed.

Calculation and measurements of absorbed dose in total body irradiation

A method which is simple, reliable, and rapid to use in clinical routine for basic dose calculation in total body irradiation (TBI) has been tested with 8 MV x-rays. The dosimetry follows, as far as possible, national and international recommendations for conventional radiotherapy. The dose rate at different locations and depths is calculated from the absorbed dose rate at dose maximum for a phantom size of 30 x 30 x 30 cm in the TBI field (Dc), an inverse square law factor (SAD2/SPD2), the tissue-maximum ratio (TMR), an equivalent phantom and patient size correction factor (A), a factor for lack of back-scattering material (B), an off-axis output correction factor (O), and a factor that corrects for off-axis variations in effective photon beam energy and for oblique beam penetration of the patient (R). The collimator opening is constant for all patient sizes. It is shown that TMR, A, B and R can be measured in conventional geometry in ordinary phantoms but at an extended distance, while Dc, O and SAD2/SPD2 must be measured in TBI geometry. Tests in Humanoid phantoms showed an agreement in measured and planned AP/2 doses of 2% or better. If the calculation method is used for lower photon energies or in other TBI geometries it may be necessary to correct for the elliptical shape of the patient and for back-scattered radiation from the walls or floor.