The principles of Katz's cellular track structure radiobiological model

The cellular track structure theory (TST), introduced by Katz in 1968, applies the concept of action cross section as the probability of targets in the radiation detector being activated to elicit the observed endpoint (e.g. cell killing). The ion beam radiation field is specified by the charge Z, speed β (or energy), fluence and linear energy transfer (LET) of the ion, rather than by its total absorbed dose or dose-averaged LET. The detector is represented by radiosensitive elements of size a₀ and radiosensitivity D₀, its gamma-ray response being represented by c-hit or multi-target expressions rather than by the linear-quadratic formula. Key to TST is the D_δ(r) formula describing the radial distribution of delta-ray dose (RDD) around the ion path. This formula, when folded with the dose response of the detector and radially integrated, yields the 'point target' action cross section value, sPT. The averaged value of the cross section, σ, is obtained by radially integrating the a₀-averaged RDD. In the 'track width' regime which may occur at the distal end of the ion's path, the value of s may considerably exceed its geometrical value, πa²₀. Several scaling principles are applied in TST, resulting in its simple analytic formulation. Multi-target detectors, such as cells, are represented in TST by m, D₀, σ₀ (the 'saturation value' of the cross section which replaces a₀) and k (a 'detector saturation index'), as the fourth model parameter. With increasing LET of the ion, the two-component formulation of TST allows for successive transition from shouldered survival curves at low LET values to exponential ones at radiobiological effectiveness (RBE) maximum, followed by 'thin-down' at the end of the ion track. For a given cell line, having best-fitted the four model parameters (m, D₀, σ₀ and k) to an available data set of measured survival curves, TST is able to quantitatively predict cell survival and RBE for this cell line after any other ion irradiation. (authors)