A Generalised Formulation of Microdosimetric Quantities Medizin - Open Access LMU - Teil 07/22

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.