Technical Note: Minimizing geometrical uncertainties of cylindrical well-type ionization chamber measurements: There is an optimal chamber length.

Abstract

The response of well-type ionization chambers used, for example, in brachytherapy and nuclear medicine, depends on the location of the source. In cases where the source length is variable (typically in nuclear medicine), it is also dependent on length of the source. Here, the combined effect on chamber sensitivity of both source position and length is investigated in detail. This analysis is important if nominal values for source location and length are prescribed as (arbitrary but fixed) values in order to precisely define a chamber's sensitivity. During measurement, the actual values for source location and length can deviate from the nominal ones, altering sensitivity and thus giving rise to measurement uncertainties which, in turn, directly affect the doses administered to patients. Our aim is to investigate these uncertainties and minimize them with an optimized ion chamber design. An analytical model for the chamber response is used to describe the variation of chamber sensitivity with respect to the two parameters, source position and length. The influence of the relative magnitude of uncertainty in both parameters is also accounted for. The effect of their combined variation on chamber sensitivity is required to be minimal and, employing differential geometry tools, a relationship is derived between them and the optimal height of the ionization chamber's sensitive volume. This relationship provides the chamber height h which minimizes its response variation for given nominal value of source location (quantified as insertion depth d) and prescribed source length l: h=2d-ρ(ρ)l, where ρ=δd/δl is defined as the quotient of uncertainty in insertion depth, δd, and uncertainty in source length, δl, and ρρ=4/9+ρ21+4ρ2, so that the optimal ionization chamber length varies between h=2d-12l and h=2d-23l. Alternatively, if h is given, suitable combinations of d and l can be deduced. The analysis presented here provides a tool for reducing the uncertainty budget of any cylindrically designed ionization chambers utilized for measuring extended on-axis sources. In particular, these results can be applied to a calibration-type ionization chamber design recently proposed for the cross-calibration of unsealed radionuclides.