Monte Carlo simulation of photon buildup factors for shielding materials in radiotherapy x-ray facilities

Linac primary barrier transmission for concrete: Monte Carlo calculations

Recent publications have called into question the accuracy of reference tenth-value layer (TVL) data cited in official reports for linac primary concrete barriers. Doubts have arisen based on both experimental and theoretical evidence. Most of the standard reference TVL values trace back to a publication that appeared in 1984 that used beam spectra that are not representative of modern linacs. This study reports a new set of TVL data for concrete based on modern linac beam spectra and a definition of the barrier transmission that is consistent with its use in shielding calculations. TVL values have been computed for concrete using Monte Carlo simulation for beam energies of 4, 6, 10, 15, and 18 MV. The barrier transmission depends on the field size at the barrier and the distance from the distal surface of the barrier to the point of observation. The TVL values reported here lead to barrier transmission values that are up to a factor of 4 larger than those in official reports. The air kerma rate beyond the barrier does not obey an inverse square law as the barrier now acts like a new (non-point) source of radiation. For distance greater than 0.3 m from the distal side of the barrier, inverse square predictions of the air kerma rate are low by up to a factor of 2. The average energy of the transmitted photons declines rapidly for all beam energies with increasing barrier thickness up to a thickness of about 50 cm and then slowly increases with increasing thickness.

Uncertainties in linac primary barrier transmission values

Primary barrier design for linac shielding depends very sensitively on tenth value layer (TVL) data. Inaccuracies can lead to large discrepancies between measured and calculated values of the barrier transmission. Values of the TVL for concrete quoted in several widely used standard references are substantially different than those calculated more recently. The older standard TVL data predict significantly lower radiation levels outside primary barriers than the more recently calculated values under some circumstances. The difference increases with increasing barrier thickness and energy, and it can be as large as a factor of 4 for 18 MV and concrete thickness of 200 cm. This may be due to significant differences in the beam spectra between the earlier and the more recent calculations. Measured instantaneous air kerma rates sometimes show large variations for the same energy and thickness. This may be due to confounding factors such as extra material on, or inside the barrier, variable field size at the barrier, density of concrete, and distal distance from the barrier surface. In some cases, the older TVL data significantly underestimate measured instantaneous air kerma rates, by up to a factor of 3, even when confounding factors are taken into account. This could lead to the necessity for expensive remediation. The more recent TVL values tend to overestimate the measured instantaneous dose rates. Reference TVL data should be computed in a manner that is mathematically consistent with their use in the calculation of air kerma rate outside barriers directly from the linac “dose” rate in MU/min.

Brachytherapy structural shielding calculations using Monte Carlo generated, monoenergetic data

PURPOSE

To provide a method for calculating the transmission of any broad photon beam with a known energy spectrum in the range of 20-1090 keV, through concrete and lead, based on the superposition of corresponding monoenergetic data obtained from Monte Carlo simulation.

METHODS

MCNP5 was used to calculate broad photon beam transmission data through varying thickness of lead and concrete, for monoenergetic point sources of energy in the range pertinent to brachytherapy (20-1090 keV, in 10 keV intervals). The three parameter empirical model introduced by Archer et al. ["Diagnostic x-ray shielding design based on an empirical model of photon attenuation," Health Phys. 44, 507-517 (1983)] was used to describe the transmission curve for each of the 216 energy-material combinations. These three parameters, and hence the transmission curve, for any polyenergetic spectrum can then be obtained by superposition along the lines of Kharrati et al. ["Monte Carlo simulation of x-ray buildup factors of lead and its applications in shielding of diagnostic x-ray facilities," Med. Phys. 34, 1398-1404 (2007)]. A simple program, incorporating a graphical user interface, was developed to facilitate the superposition of monoenergetic data, the graphical and tabular display of broad photon beam transmission curves, and the calculation of material thickness required for a given transmission from these curves.

RESULTS

Polyenergetic broad photon beam transmission curves of this work, calculated from the superposition of monoenergetic data, are compared to corresponding results in the literature. A good agreement is observed with results in the literature obtained from Monte Carlo simulations for the photon spectra emitted from bare point sources of various radionuclides. Differences are observed with corresponding results in the literature for x-ray spectra at various tube potentials, mainly due to the different broad beam conditions or x-ray spectra assumed.

CONCLUSIONS

The data of this work allow for the accurate calculation of structural shielding thickness, taking into account the spectral variation with shield thickness, and broad beam conditions, in a realistic geometry. The simplicity of calculations also obviates the need for the use of crude transmission data estimates such as the half and tenth value layer indices. Although this study was primarily designed for brachytherapy, results might also be useful for radiology and nuclear medicine facility design, provided broad beam conditions apply.