Systematic uncertainties in the Monte Carlo calculation of ion chamber replacement correction factors

In a previous study [Med. Phys. 35, 1747-1755 (2008)], the authors proposed two direct methods of calculating the replacement correction factors (P-repl or p(cav)p(dis)) for ion chambers by Monte Carlo calculation. By "direct" we meant the stopping-power ratio evaluation is not necessary. The two methods were named as the high-density air (HDA) and low-density water (LDW) methods. Although the accuracy of these methods was briefly discussed, it turns out that the assumption made regarding the dose in an HDA slab as a function of slab thickness is not correct. This issue is reinvestigated in the current study, and the accuracy of the LDW method applied to ion chambers in a Co-60 photon beam is also studied. It is found that the two direct methods are in fact not completely independent of the stopping-power ratio of the two materials involved. There is an implicit dependence of the calculated P-repl values upon the stopping-power ratio evaluation through the choice of an appropriate energy cutoff Delta, which characterizes a cavity size in the Spencer-Attix cavity theory. Since the Delta value is not accurately defined in the theory, this dependence on the stopping-power ratio results in a systematic uncertainty on the calculated P-repl values. For phantom materials of similar effective atomic number to air, such as water and graphite, this systematic uncertainty is at most 0.2% for most commonly used chambers for either electron or photon beams. This uncertainty level is good enough for current ion chamber dosimetry, and the merits of the two direct methods of calculating P-repl values are maintained, i.e., there is no need to do a separate stopping-power ratio calculation. For high-Z materials, the inherent uncertainty would make it practically impossible to calculate reliable P-repl values using the two direct methods.