Primary dose in photon beams with lateral electron disequilibrium

Abstract

It is shown that in narrow monoenergetic photon beams under conditions of lateral electron disequilibrium, primary absorbed dose P(r) is a simple function of beam radius r: P(r) = P lambda.(1 - e(-gamma.r)), where P lambda is the primary dose in broad beams for which complete lateral electron equilibrium exists, and gamma depends on photon energy and absorbing medium. This formula was evaluated using Monte-Carlo-generated data for the primary dose in water from monoenergetic photons in the energy range from 2 to 8 MeV. The primary dose was studied in beams of radii 0.006 cm less than r less than 5.0 cm and within the depth interval 0.5 cm less than or equal to d less than or equal to 24 cm. It was concluded that the saturation equation above provides an accurate description of the primary dose from monoenergetic photon beams, as judged by comparison with Monte Carlo results.

Viability of an isocentric cobalt‐60 teletherapy unit for stereotactic radiosurgery

“…Due to its lower energy, a cobalt-60 photon beam, in comparison with a 10 MV photon beam, requires a lower electron range to reach lateral electronic equilibrium, thus producing sharper penumbras for identical source sizes. 19,20 This geometrical and physical ''penumbra sharpening'' effect counteracts the large source size ''penumbra broadening'' effect, reducing the beam penumbra difference between the cobalt-60 and the 10 MV linac beams studied.…”

Measurement of head scatter factors of linear accelerators with columnar miniphantoms

“…The primary dose on the beam central axis is determined by the incident photon beam and can be separated into modifying factors as follows: [45][46][47][48][49] P͑d,c͒ = P 0 T͑d,c͒H͑c͒BF͑r mp ,c͒, P͑d r ,c r ͒ = P O T͑d r ,c r ͒H͑c r ͒BF͑r mp ,c r ͒, P͑d,c͒ = P͑d r ,c r ͒ ͫ T͑d,c͒ T͑d r ,c r ͒ ͬͫ H͑c͒ H͑c r ͒ ͬͫ BF͑r mp ,c͒ BF͑r mp ,c r ͒ ͬ , ͑2͒…”

“…where SF is the scatter factor, which is equal to ͑1+S / P͒. The primary dose on the beam central axis is determined by the incident photon beam and can be separated into modifying factors as follows: [45][46][47][48][49] P͑d,c͒ = P 0 T͑d,c͒H͑c͒BF͑r mp ,c͒, where d is the depth of the dose point, c is the collimator setting of the accelerator, d r is the reference depth ͑usually 10 cm͒, c r is the reference collimator setting ͑usually 10 cmϫ 10 cm͒, P 0 is a proportionality constant that represents the primary dose if it could be measured without attenuation or partial buildup, P͑d r , c r ͒ is the primary dose in the reference geometry, r mp is the radius of the miniphantom, T is the transmission of the miniphantom, H͑c͒ is the accelerator relative photon fluence and is equal to unity for c = c r , and BF͑r mp , c͒ ͑Refs. 46 and 47͒ is the buildup-factor correction for the existence of lateral electron disequilibrium in thin walls of the miniphantom.…”

“…where bb ͑c͒ is the broad-beam 34,50 attenuation coefficient of the miniphantom material. In this presentation the possibility is included that the beam energy changes with c and consequently bb change with c. The buildup factor is given by 46,47 BF͑r mp ,c͒ = 1 − exp…”

Tissue–air ratios for narrow gamma‐ray beams

“…This is so because the energy spectrum of charged particles resulting from first photon interactions in phantom material remains independent of phantom depth. 6,7 As a consequence, the primary dose ratio of Eq. ͑3͒, P o (d,r)/P o (d m ,r), is expected to be independent of r, as shown in Fig.…”