The calculation of radial dose from heavy ions: predictions of biological action cross sections
The track structure model of heavy ion cross sections was developed by Katz and co-workers in the 1960s. In this model the action cross section is evaluated by mapping the dose-response of a detector to gamma rays (modeled from biological target theory) onto the radial dose distribution from delta rays about the path of the ion. This is taken to yield the radial distribution of probability for a "hit" (an interaction leading to an observable end-point). Radial integration of the probability yields the cross section. When different response from ions of different Z having the same stopping power is observed this model may be indicated. Since the 1960s there have been several developments in the computation of the radial dose distribution, in the measurement of these distributions, and in new radiobiological data against which to test the model. The earliest model, by Butts and Katz made use of simplified delta ray distribution functions, of simplified electron range-energy relations, and neglected angular distributions. Nevertheless it made possible the calculation of cross sections for the inactivation of enzymes and viruses, and allowed extension to tracks in nuclear emulsions and other detectors and to biological cells. It set the pattern for models of observable effects in the matter through which the ion passed. Here we outline subsequent calculations of radial dose which make use of improved knowledge of the electron emission spectrum, the electron range-energy relation, the angular distribution, and some considerations of molecular excitation, of particular interest both close to the path of the ion and the outer limits of electron penetration. These are applied to the modeling of action cross sections for the inactivation of several strains of E-coli and B. subtilis spores where extensive measurements in the "thin-down" region have been made with heavy ion beams. Such calculations serve to test the radial dose calculations at the outer limit of electron penetration. We lack data from which to test these calculations in regions close to the path of the ion aside from our earliest work on latent tracks in plastics, though it appears that the criterion then suggested for the threshold of track formation, of a minimal dose at a minimal distance (of about 20 angstroms, in plastics), remains valid.