Relations between scatter factor, quality index and attenuation for x-ray beams.

The relations between the attenuation factor, the normalized phantom scatter factor and the quality index are examined using a semiempirical formula for the dose on the central axis of an x-ray beam in water. The study is restricted to depths and field sizes sufficient for electron equilibrium. The results are compared with data in the recent literature. It is concluded that for x-ray beams in the energy range 4-25 MV the normalized scatter factors can be calculated from the dose-weighted average linear attenuation coefficient in water, determined from transmission measurements in a narrow-beam geometry or from the quality index.

Quality control of measured x-ray beam data.

The purpose of this study was to examine whether the quality of measured x-ray beam data can be judged from how well the data agree with a semiempirical formula. Tissue-phantom ratios (TPR) and output factors for several accelerators in the energy range 4-25 MV were fitted to the formula, separating the dose contributions from primary and phantom-scattered photons. The former was described by exponential attenuation in water, with beam hardening, and the latter by the scatter-to-primary dose ratio using two parameters related to the probability and the directional distribution of the scattered photons. Electron disequilibrium was not considered. Two approaches were evaluated. In one, the attenuation and hardening coefficients were determined from measurements in a narrow-beam geometry; in the other, they were extracted by the fitting procedure. Measured and fitted data agreed within +/- 2% in both cases. The differences were randomly distributed and had a standard deviation of typically 0.7%. Singular points with errors were easily identified. Systematic errors were revealed by increased standard deviation. However, when the attenuation was derived by the fitting algorithm, the attenuation coefficient deviated significantly from the experimental value. It is concluded that the semiempirical formula can serve to evaluate and verify beam data measured in water and that the physically most accurate description requires that the attenuation and hardening coefficients be determined in a narrow-beam geometry. The attenuation coefficient is an excellent measure of both the primary and the scatter dose component, i.e., of beam quality.

Dynamic universal wedge.

A computer-controlled equivalent of the universal wedge was designed by moving one collimator with step-wise constant velocity to produce the same primary-dose profile as a 20x20-cm2 conventional 58-deg wedge. It was used for smaller fields without changing the profile and combined with open beams to alter the wedge angle. Output factors in air and wedge factors in air and water were determined experimentally for the dynamic wedge and compared to predictions based on the assumption that the primary dose is proportional to the number of monitor units that the point of interest is in the open portion of the beam. This model was found to be accurate within about 2% and the deviations caused by head-scatter changes and collimator transmission after the moving collimator has passed. Measurements of the wedge factor in water indicated that the scatter factors for large wedged beams slightly exceeded those for open beams.

Scattered photons from wedges in high-energy x-ray beams.

The presence of a wedge increases the fraction of "head-scattered" photons in a high-energy x-ray beam. We have compared internal and external wedges for x-ray beam energies between 6 and 25 MV by determining their SPRw, i.e., the ratio of the dose contribution from photons scattered by the wedge and photons either coming directly from the target or scattered by other structures, including the flattening filter. Marked differences were observed. First, SPRw for the thickest external wedge (60 degrees) was 1.8% at a field size of 10 x 10 cm2 and mildly dependent on the photon energy, while SPRw for internal wedges for this field size varied between 4.4% and 5.4% depending mostly on the location and size of the wedge and marginally on the photon energy. Second, the variation of SPRw with the collimator setting c x c was different for the internal and external wedges. SPRw for the internal wedge approached a limiting value at large c and could be fitted with an error function, while SPRw for the external wedge increased quadratically with c. As a result, the difference in SPRw (c) for internal and external wedges is reduced for large fields.

Analysis of central-axis doses for high-energy x rays.

The purpose of this study was to improve on the analytical expressions used to describe central-axis doses for high-energy x-ray beams, in particular, the component due to phantom-scattered photons. The beams were characterized by quantities related to the physical processes, namely, transmission, head-scatter, and phantom-scatter factors, which were described separately with mathematical functions. Transmission in water was measured in a narrow beam and head scatter with a small phantom in air. The phantom-scatter factors, i.e., the ratios between total and primary dose, were deduced from measured central-axis doses per monitor unit. Based on previous work, it was assumed that this scatter factor is proportional to the depth d if the ratio between the depth and the field size s is constant. The proportionality constant was examined as a function of this ratio d/s and the effective linear attenuation coefficient mu. Two quality-dependent parameters were extracted. One expresses the probability of scatter and was numerically close to mu. The other, which has not previously been studied, reflects the directional distribution of the scattered photons and was also found to be a linear function of mu. Thus the scatter factors can be estimated if mu is known. Central-axis doses were described by these formulas with 2.5% maximum error at 6 MV, 0.8% at 25 MV. To achieve this result, only a few measurements were needed for selected d and s, which indicates that the model used for the scatter factor is realistic. When the method was applied to 10-MV and 15-MV x-ray beam data measured by another institution, about +/- 2% accuracy resulted.

Doses near the surface in high-energy x-ray beams.

In an irradiation with a high-energy x-ray beam, the absorbed dose near the surface is the combined result of incident contaminating electrons and phantom-generated electrons. We describe an experimental method to characterize these processes under conditions of longitudinal electron disequilibrium but lateral equilibrium. The equilibrium dose at large depths is extrapolated back towards the surface and compared with measured doses. The extrapolation uses an expression that is based on Monte Carlo-calculated kerma values. The technique was applied to a 6-MV and a 25-MV x-ray beam. The dose from phantom-generated electrons increased exponentially with depth from zero at the surface. The dose from contaminating electrons decreased rapidly with depth with an attenuation coefficient that was approximately equal to the corresponding coefficient for the increase of dose from phantom-generated electrons. The surface dose from contaminating electrons increased linearly with the side of the square field at 6 MV but an error-function agreed better with the data at 25 MV.

An equivalent-square formula for head-scatter factors.

A simple formula is evaluated for calculating the equivalent square collimator setting that gives the same headscatter factor as a given rectangular field. The expression requires that one parameter is determined experimentally. It is found that one single value of this parameter can be used for the six x-ray beams studied (two accelerators, two energies, with and without wedge).