C. K. Ross

Comparison of measured and Monte Carlo calculated dose distributions from the NRC linac

We have benchmarked photon beam simulations with the EGS4 user code BEAM [Rogers et al., Med. Phys. 22, 503-524 (1995)] by comparing calculated and measured relative ionization distributions in water from the 10 and 20 MV photon beams of the NRC linac. Unlike previous calculations, the incident electron energy is known independently to 1%, the entire extra-focal radiation is simulated, and electron contamination is accounted for. The full Monte Carlo simulation of the linac includes the electron exit window, target, flattening filter, monitor chambers, collimators, as well as the PMMA walls of the water phantom. Dose distributions are calculated using a modified version of the EGS4 user code DOSXYZ which additionally allows scoring of average energy and energy fluence in the phantom. Dose is converted to ionization by accounting for the (L/rho)water(air) variation in the phantom, calculated in an identical geometry for the realistic beams using a new EGS4 user code, SPRXYZ. The variation of (L/rho)water(air) with depth is a 1.25% correction at 10 MV and a 2% correction at 20 MV. At both energies, the calculated and the measured values of ionization on the central axis in the buildup region agree within 1% of maximum ionization relative to the ionization at 10 cm depth. The agreement is well within statistics elsewhere. The electron contamination contributes 0.35(+/- 0.02) to 1.37(+/- 0.03)% of the maximum dose in the buildup region at 10 MV and 0.26(+/- 0.03) to 3.14(+/- 0.07)% of the maximum dose at 20 MV. The penumbrae at 3 depths in each beam (in g/cm2), 1.99 (dmax, 10 MV only), 3.29 (dmax, 20 MV only), 9.79 and 19.79, agree with ionization chamber measurements to better than 1 mm. Possible causes for the discrepancy between calculations and measurements are analyzed and discussed in detail.

The effective point of measurement of ionization chambers and the build-up anomaly in MV x-ray beams.

A precision experimental investigation of the effective point of measurement (EPOM) of ion chambers in megavoltage beams has been carried out. A one-dimensional scanning phantom system was developed with an overall accuracy in the positioning of a chamber of better than 0.15 mm. Depth-dose data were acquired for a 25 MV beam from an Elekta Precise linac (field sizes of 10 x 10 cm and 25 x 25 cm) for measurement depths in the range 0.6-6 cm. The results confirmed the Monte Carlo calculations of an earlier theoretical investigation by Kawrakow [Med. Phys. 33, 1829-1839 (2006)] that the standard shift for cylindrical chambers, recommended in dosimetry protocols of -0.6r (where r is the internal radius of the cavity), is incorrect. A wide range of ion chambers were investigated and it was found that errors of up to 1.4 mm could occur for certain chamber designs (although typical errors for common chambers were around 0.5 mm). A comparison between measurements and Monte Carlo simulations showed that once the correct EPOM is used, the details of the linac geometry are correct, and the parameters of the electron beam striking the bremsstrahlung target have been adequately determined, the EGSnrc Monte Carlo package is capable of reproducing the experimental data to 0.2 mm or better. The investigation also confirmed that for the highest accuracy depth-dose curves in megavoltage photon beams one should use a well-guarded parallel-plate ion chamber. Three chamber designs were tested here and found to be satisfactory-the Scanditronix-Wellhöfer NACP-02, PTW Roos and Exradin All.

Electron beam dose distributions near standard inhomogeneities

At a recent workshop on electron beam dose planning, a set of standard geometries was defined to facilitate the comparison of electron beam treatment planning algorithms and dosimetric measurements. The geometries consist of one-, two- or three-dimensional inhomogeneities embedded near the entrance surface of a water phantom. In the three-dimensional case, the inhomogeneities are small cylinders of air or aluminium located on the beam axis. The authors have used a small (1 mm square by 0.1 mm thick) p-type silicon detector to measure the dose distributions behind these inhomogeneities for broad beams of 10 and 20 MeV electrons. The effect of the inhomogeneities is to perturb the dose in their vicinity by as much as 50% over a range of a few millimetres. These results provide a stringent test of techniques for calculating dose distributions. Current clinical algorithms do not accurately predict the dose distributions, but detailed Monte Carlo simulations are shown to be in good agreement with the experimental results.

Fricke dosimetry: the difference between G(Fe3+) for 60Co gamma-rays and high-energy x-rays.

A calibration of the Fricke dosimeter is a measurement of epsilon G(Fe3+). Although G(Fe3+) is expected to be approximately energy independent for all low-LET radiation, existing data are not adequate to rule out the possibility of changes of a few per cent with beam quality. When a high-precision Fricke dosimeter, which has been calibrated for one particular low-LET beam quality, is used to measure the absorbed dose for another low-LET beam quality, the accuracy of the absorbed dose measurement is limited by the uncertainty in the value of G(Fe3+). The ratio of G(Fe3+) for high-energy x-rays (20 and 30 MV) to G(Fe3+) for 60Co gamma-rays, G(Fe3+)MV(Co), was measured to be 1.007(+/-0.003) (confidence level of 68%) using two different types of water calorimeter, a stirred-water calorimeter (20 MV) and a sealed-water calorimeter (20, 30 MV). This value is consistent with our calculations based on the LET dependence of G(primary products) and, as well, with published measurements and theoretical treatments of G(Fe3+).

Angular distribution of bremsstrahlung from 15‐MeV electrons incident on thick targets of Be, Al, and Pb

Bremsstrahlung spectra from thick cylindrical targets of Be, Al, and Pb have been measured at angles of 0 degrees, 1 degree, 2 degrees, 4 degrees, 10 degrees, 30 degrees, 60 degrees, and 90 degrees relative to the beam axis for electrons of 15-MeV incident energy. The spectra are absolute (photons per incident electron) and have a 145-keV lower-energy cutoff. The target thickness were nominally 110% of the electron CSDA range. A thin transmission detector, calibrated against a toroidal current monitor, was placed upstream of the target to measure the beam current. The spectrometer was a 20-cm-diam by 25-cm-long cylindrical NaI detector. Measured spectra were corrected for pile-up, background, detector response, detector efficiency, attenuation in materials between the target and detector and collimator effects. Spectra were also calculated using the EGS4 Monte Carlo system for simulating the radiation transport. There was excellent agreement between the measured and calculated spectral shapes. The measured yield of photons per incident electron was 9% and 7% greater than the calculated yield for Be and Al, respectively, and 2% less for Pb, all with an uncertainty of +/- 5%. There was no significant angular variation in the ratio of the measured and calculated yields. The angular distributions of bremsstrahlung calculated using available analytical theories dropped off more quickly with angle than the measured distributions. The predictions of the theories would be improved by including target-scattered photons.

Forward‐directed bremsstrahlung of 10‐ to 30‐MeV electrons incident on thick targets of Al and Pb

Bremsstrahlung spectra from thick targets of Al and Pb have been measured absolutely (photons per incident electron) along the beam axis for electrons of 10-, 15-, 20-, 25-, and 30-MeV incident energy. The spectra have a 220-keV low-energy cutoff. The targets were cylinders with nominal thicknesses of 110% of the electron CSDA range. A thin transmission detector, calibrated against a toroidal current monitor, was placed upstream of the target to measure the beam current. The spectrometer was a 20-cm diameter by 25-cm-long cylindrical NaI detector. Measured spectra were corrected for pile-up, background, detector response, detector efficiency, attenuation in materials between the target and detector and the collimator effect. Spectra were calculated using the EGS4 Monte Carlo system for simulating the radiation transport. The simulation model included the small amount of material upstream of the target. This material contributed about 40% of the spectrum, but its presence or absence had little effect on the calculated bremsstrahlung yield. The shapes of the measured and calculated spectra were in excellent agreement. The ratio of the total number of photons in each measured spectrum to those in the corresponding calculated spectrum varied from 0.97 +/- 0.06 to 1.12 +/- 0.06, depending largely on the atomic number of the target. Absolute spectral measurements in the literature agreed with our calculations of spectral shape but showed a range of +/- 30% in the number of photons per incident electron relative to the calculated values, which is contrary to our result.

The role of humidity and other correction factors in the AAPM TG‐21 dosimetry protocol

A detailed derivation is presented of the formulas required to determine Ngas and Dmed in the AAPM TG-21 dosimetry protocol. This protocol specifies how to determine the absorbed dose in an electron or photon beam when using exposure or absorbed dose calibrated ion chambers. It is shown that the expression given in TG-21s recent letter of clarification is incorrect. Accounting for humidity correctly increases, by 0.4%, all absorbed dose determinations using an exposure calibrated ion chamber. Taking into account other correction factors in the equation for exposure could also have varying, but significant effects (possibly over 1%). These are the stem scatter correction, the axial nonuniformity correction and the electrode correction for electrodes made of different materials from the wall. Attention is drawn to differences in the definitions of the exposure and absorbed dose calibration factors, Nx and ND, respectively, as supplied by the NBS and the NRCC.

An investigation of the photon energy dependence of the EPR alanine dosimetry system

The electron paramagnetic resonance (EPR) alanine dosimetry system is based on EPR measurements of radicals formed in alanine by ionizing radiation. The system has been studied to determine its energy dependence for photons in the 10-30 MV region relative to those of 60Co and to find out if the system would be suitable for dosimetry comparisons. The irradiations were carried out at the National Research Council, Ottawa, Canada and the doses ranged from 8 to 54 Gy. The EPR measurements were performed at the University of Oslo, Norway. The ratio of the slope of the alanine reading versus dose-to-water curve for a certain linac photon beam quality and the corresponding slope for a reference 60Co gamma-radiation gives an experimental measure of the relative dose-to-water response of the EPR alanine dosimetry system. For calculating the linear regression coefficients of these alanine reading versus dose curves, the method of weighted least squares was used. This method is assumed to produce more accurate regression coefficients when applied to EPR dosimetry than the common method of standard least squares. The overall uncertainty on the ratio of slopes was between 0.5 and 0.6% for all three linac energies. The relative response for all the linac beams compared to cobalt was less than unity: by about 0.5% for the 20 and 30 MV points but by more than 1% for the 10 MV point. The given standard uncertainties negate concluding that there is any significant internal variation in the measured response as a function of beam quality between the three linac energies. Thus, we calculated the average dose response for all three energies and found that the alanine response is 0.8% (+/-0.5%) lower for high energy x-rays than for 60Co gamma-rays. This result indicates a small energy dependence in the alanine response for the high-energy photons relative to 60Co which may be significant. This result is specific to our dosimetry system (alanine with 20% polyethylene binder pressed into a particular shape) including its waterproofing sleeve of PMMA (2 mm thick); however, we expect that this result may apply to other similar detectors.

A direct comparison of water calorimetry and Fricke dosimetry

Considerable effort has been devoted to measuring the absorbed dose to water using water calorimetry. Most of these efforts have been hampered by a lack of adequate knowledge of the heat defect of water. We argue that there is now sufficient information to establish with considerable confidence the heat defect of high-purity water containing various dissolved gases. For the present work we used water saturated with a 50/50 mixture of H2 and O2 gases, for which the heat defect is calculated to be -2.1%. As a test of this assignment, we have compared the absorbed dose to water as measured using water calorimetry with that obtained from Fricke dosimetry. The water calorimeter consisted of a small sealed vessel containing 100 ml of stirred water saturated with a 50/50 mixture of H2 and O2 gases. It was irradiated with 20 MV x-rays at a dose rate of about 0.4 Gy s-1. The same vessel was then filled with Fricke dosemeter solution, and irradiated under identical conditions. Our Fricke dosimetry is based on the Svensson and Brahme value of epsilon G (3.515 x 10(-3) 1 cm-1 J-1) and agrees to within 0.2% with the dose to water for 60Co gamma-rays obtained via graphite calorimetry. We find that for 20 MV x-rays, the dose to water determined by water calorimetry is 1.006 +/- 0.004 times the dose determined by Fricke dosimetry. Within 0.6(+/- 0.4)%, this result supports the calculated heat defect of -2.1% for water saturated with a 50/50 mixture of H2 and O2 gases.

A comparison of absorbed dose standards for high-energy X-rays

An indirect comparison of the absorbed dose to water standards of the PTB and the NRC was carried out for 18/20 MV X-rays using five ionization chambers as transfer instruments. The absorbed dose standard of the PTB is based on the total absorption of 5.6 MeV electrons in Fricke solution. The NRC standard uses Fricke solution whose calibration is based on measurements made with a water calorimeter and a calculation of the heat defect. For high-energy X-rays, the difference found between the standards of 0.4% is within the expected uncertainties. The comparison was linked to existing 60Co absorbed dose to water and air kerma standards by comparing measurements of those quantities at the PTB, NRC and BIPM. Agreement was better than 0.7% in all cases. For the ionization chambers used in this study, the absorbed dose calibration factors for 18/20 MV X-rays are about 2% lower than those for 60Co gamma-rays.