A Generalised Formulation of Microdosimetric Quantities

The microdosimetric quantities energy imparted, lineal energy, and
specific energy are defined with reference to certain volumes but
are quantified in terms of frequency distributions of possible
values without regard to spatial interrelations. Computer
simulations of the patterns of energy deposits seem, therefore,
only loosely related to the microdosimetric distributions. In a
more general formulation one treats the specific energy and the
related microdosimetric quantities as point functions; one deals
then with the spatial distribution of their random values and not
merely with the frequency of different values. A further extension
of the formalism admits reference regions of vanishing size; the
inchoate distribution of energy deposits is then the limit case of
specific energy. The definitions are related to Matheron's concept
of the regularisation of a spatial variable; this is a convolution
process that permits a flexible mathematical treatment. One
resulting possibility is the definition of specific energy with
reference not to the conventional geometry of a sphere or a
cylinder but to a disperse region of support. This extension
provides distributions of specific energy that are relevant to
diffusion or transport processes and it can help to free
biophysical models from a one-sided fixation on the concept of
geometric targets. The formalism is applied also to the definition
of the proximity functions and the related spatial autocorrelation
functions.