Maximum dose angle for oblique incidence on primary beam protective barriers in the design of medical radiation therapy facilities

Primary barrier determinations for the shielding of medical radiation therapy facilities are generally made assuming normal beam incidence on the barrier, since this is geometrically the most unfavorable condition for that shielding barrier whenever the occupation line is allowed to run along the barrier. However, when the occupation line (for example, the wall of an adjacent building) runs perpendicular to the barrier (especially roof barrier), then two opposing factors come in to play: increasing obliquity angle with respect to the barrier increases the attenuation, while the distance to the calculation point decreases, hence, increasing the dose. As a result, there exists an angle ( α max ) for which the equivalent dose results in a maximum, constituting the most unfavorable geometric condition for that shielding barrier. Based on the usual NCRP Report No. 151 model, this article presents a simple formula for obtaining α max , which is a function of the thickness of the barrier ( t E ) and the equilibrium tenth-value layer ( TVL e ) of the shielding material for the nominal energy of the beam. It can be seen that α max increases for increasing TVL e (hence, beam energy) and decreases for increasing t E , with a range of variation that goes from 13 to 40 deg for concrete barriers thicknesses in the range of 50–300 cm and most commercially available teletherapy machines. This parameter has not been calculated in the existing literature for radiotherapy facilities design and has practical applications, as in calculating the required unoccupied roof shielding for the protection of a nearby building located in the plane of the primary beam rotation.