Bengt E. Bjärngard

The Dosimetry of Ionizing Radiation

This book presents summaries of the current information on subtopics in dosimetry of ionizing radiation; each accompanied by an extensive reference list.

Attenuation in high‐energy x‐ray beams

Attenuation factors in water have been measured by a narrow-beam technique in various portions of x-ray beams with nominal energies of 6 and 25 MV, with and without a wedge in the beam. The results were analyzed in terms of an attenuation coefficient mu for small water thicknesses and a beam-hardening coefficient eta that describes the change in attenuation per unit depth. The variation of mu within the field was significant, about 0.5% per centimeter at 6 MV and 0.8% per centimeter at 25 MV for open beams. The heavy wedge used in these experiments caused significant (about 10%) beam hardening at 6 MV, softened the beam somewhat at 25 MV, and increased the variation of mu within the field to 3%-5%. These effects should be taken into account in dose calculations, and correction factors can be designed based on the variation of mu with off-axis radius for open beams and with off-axis position for wedged beams. The experimental technique, based on two measurements with the beam going through a water tank with either 26- or 50-cm path length, was simple and highly reproducible. The beam hardening with depth in water, i.e., the value of eta, was readily determined but found to be clinically insignificant.

THE HEAD-SCATTER FACTOR FOR SMALL FIELD SIZES

The head-scatter factors H were examined for four different linear accelerators and were found to be similar at field sizes larger than 3 x 3 cm2. Sharply reduced values for small collimator openings were observed for all the accelerators. It is concluded that the head-scatter (or collimator-scatter) factor has two major components. Scatter of photons in various structures in the beam path, especially the flattening filter, causes a slow (about 10%) increase with increased collimator opening. Insertion of a built-in wedge may double this number. When the collimators are closed, they ultimately block photons from the periphery of the source. This may cause a considerable reduction of the primary photon fluence and typically affects fields smaller than 3 x 3 cm2. The effect can be used to estimate the source size, with results that correlate with the design of the bending magnet.

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).

X‐ray source and the output factor

When the collimator setting of a linear accelerator is made sufficiently small, the output factor in air, R, is greatly reduced because the collimators obstruct the periphery of the x-ray source. This has been utilized to examine the size of the source by varying the width y of a narrow field and determining how R(y) varies. The sources diameters in the two principal directions were clearly influenced by the design of the accelerators. The x-ray sources of two accelerators with bending magnets were found to be noncircular while that of a linear accelerator without a magnet showed circular symmetry. The position of the source relative to the axis of collimator rotation was determined by measuring R for offset narrow fields. For one of the accelerators, the source was initially moving and off the central axis by about 2 mm for the first five monitor units. The results correlated well with sharpness in portal-film images. The technique can serve to evaluate the major source characteristics in acceptance testing and quality control.

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.

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

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

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.

Head‐scatter factors and effective x‐ray source positions in a 25‐MV linear accelerator

The behavior of the effective source position and the correction factor associated with the collimator opening (head-scatter factor) were investigated for the 6- and 25-MV x-ray beams of a linear accelerator. The primary photon fluence was measured in air for square field sizes from 5 x 5 cm to 40 x 40 cm at distances from the nominal source of 80 to 140 cm, for open and wedged fields (wedge angle 60 deg). An inverse-square analysis shows that, for open fields, the effective source position of the accelerator is about the same (approximately 1 cm downstream) at 6 and 25 MV, for all field sizes. For the wedged fields, the effective source position depends on field size and ranges from about 2 to 4 cm. The head-scatter correction factors for given collimator settings were found to be essentially independent of distance at both energies.

Experimental determination of the dose kernel in high-energy x-ray beams.

A semiempirical method to characterize the pencil-beam dose kernel is presented. Results from measurements are described by mathematical models of the applicable physical processes. The measurements were made with 6 and 25 MV x-ray beams from a linear accelerator. Broad-beam notations were used consistently, and the pencil-beam quantities were obtained by differentiation. The results were compared to pencil-beam kernels calculated by Monte Carlo techniques. The analysis of the measured data included a number of approximations. It was assumed that all the constituent pencil beams in the field are parallel, i.e., the divergence is ignored. Furthermore, the lateral variations of the incident photon fluence and the energy spectrum were disregarded. Monte Carlo calculations, on the other hand, are based on an average energy spectrum over the field, and are free from divergence and variations in the incident photon fluence. Measured and Monte Carlo calculated pencil beams nevertheless agreed well, and the approximations mentioned caused at maximum 2.7% discrepancies for the largest field size at 6 MV.