On charged particle equilibrium violation in external photon fields

In a recent paper by Bouchard et al. [Med. Phys. 36(10), 4654-4663 (2009)], a theoretical model of quality correction factors for idealistic so-called plan-class specific reference (PCSR) fields was proposed. The reasoning was founded on the definition of PCSR fields made earlier by Alfonso et al. [Med. Phys. 35(11), 5179-5186 (2008)], requiring the beam to achieve charged particle equilibrium (CPE), in a time-averaged sense, in the reference medium. The relation obtained by Bouchard et al. was derived using Fano's theorem (1954) which states that if CPE is established in a given medium, the dose is independent of point-to-point density variations. A potential misconception on the achievability of the condition required by Fano (1954) might be responsible for false practical conclusions, both in the definition of PCSR fields as well as the theoretical model of quality correction factor.

In this paper, the practical achievability of CPE in external beams is treated in detail. The fact that this condition is not achievable in single or composite deliveries is illustrated by an intuitive method and is also formally demonstrated.

Fano's theorem is not applicable in external beam radiation dosimetry without (virtually) removing attenuation effects, and therefore, the relation conditionally defined by Bouchard et al. (2009) cannot be valid in practice. A definition of PCSR fields in the recent formalism for nonstandard beams proposed by Alfonso et al. (2008) should be modified, revising the criterion of CPE condition. The authors propose reconsidering the terminology used to describe standard and nonstandard beams. The authors argue that quality correction factors of intensity modulated radiation therapy PCSR fields (i.e., k(Q(pcsr),Q) (f(pcsr),f(ref) )) could be unity under ideal conditions, but it is concluded that further investigation is necessary to confirm that hypothesis.