On the Microdosimetric Treatment of One-Hit Detectors: Reply to R. Katz

Abstract

and f,(z) is the single-event microdosimetric spectrum. In Eq. (1), the factor exp(-az) represents the one-hit model, while f(z; D) describes the radiation field and is therefore unrelated to any model of radiation action or radiobiological assumption of any kind. In confronting the predictions of Eq. (1) with data one tests the model and not the microdosimetric spectrum. By and large the evaluation of microdosimetric spectra, fJ(z), and subsequently of expressions such as Eqs. (1) and (2), is a complicated process, and it becomes advantageous to have-whenever warranted-simpler approximations of these equations. (B) Katz's formulation of the response of one-hit detectors (2) is one such approximation. Under this simplified approach Eq. (3) is replaced with = -b0 2rb[ 1 e-aD(b)]db. (4) Here D(b) is the average absorbed dose in a sensitive volume (radius x) placed at impact parameter b from the axis of the particle, p is the density of the material, L = LET and bo is the maximum value of b for which D(b) is different from zero. The model, Eq. (4), is valid only when at least one of the following conditions is met: (a) x > bo or (b) az < 1 for the whole range of z. In the typical applications of this model a and x are taken as adjustable parameters to be obtained by fitting Eqs. (2) and (4) to the data. To test this model one must not only find values a and x which reproduce the data correctly but also verify that the parameters thus obtained remain within the range which makes the approximation, Eq. (4), valid. To omit this latter part of the test is an obvious fallacy. (C) The exact formulation of the one-hit model, Eqs. (2) and (3), does not fit the inactivation data for the ?x-174 bacteriophage (3). A likely conclusion is that the single-hit mechanism is not correct for this particular phage. The approximate model, Eqs. (2) and (4), can be made to fit the data only when the parameters a and x are given values which fail the test described above. Another, equivalent way of describing this result is: Eqs. (2) and (4) are a 2-parameter analytic model which fit the data but they do not represent the response of one-hit detectors to radiation. For scientists concerned with mechanisms of radiation action (rather than curve-fitting) this is a very important distinction.