Theoretical Microdosimetry

In Chapter II it was shown that the specific energy spectrum can be factorized in terms of a dose-dependent term and a z-dependent one. In regional microdosimetry a second factor that contributes to the shape of the microdosimetric distribution is the geometry of the site. The question then arises as to whether it would be possible to further factor out this contribution. This possibility is suggested by the fact that — in a homogeneous medium — one can regard the spectrum of energy deposition as resulting from the random overlap of two “objects”: the track (i.e. a collection of transfer points) and the site. As a matter of fact, this is precisely the way most theoretical microdosimetric distributions are generated, namely by randomly placing a site on a Monte-Carlo-generated track (see Section V.2). The interesting (and powerful) consequences of this viewpoint are examined in the following through a brief excursion in the domain of geometric probability. For a general introduction to this subject the book by Santalo (1976) may be consulted.