A closed parameterization of DNA-damage by charged particles as a function of energy - A geometrical approach

Purpose: To present a closed formalism calculating charged particle radiation damage induced in DNA. The formalism is valid for all types of charged particles and due to its closed nature is suited to provide fast conversion of dose to DNA-damage. Methods: The induction of double strand breaks in DNA--strings residing in irradiated cells is quantified using a single particle model. This leads to a proposal to use the cumulative Cauchy distribution to express the mix of high and low LET type damage probability generated by a single particle. A microscopic phenomenological Monte Carlo code is used to fit the parameters of the model as a function of kinetic energy related to the damage to a DNA molecule embedded in a cell. The model is applied for four particles: electrons, protons, alpha--particles, and carbon ions. A geometric interpretation of this observation using the impact ionization mean free path as a quantifier, allows extension of the model to very low energies. Results: The mathematical expression describes the model adequately using a chi--square test ($\chi^2/NDF < 1$). This applies to all particle types with an almost perfect fit for protons, while the other particles seem to result in some discrepancies at very low energies. The implementation calculating a strict version of the RBE based on complex damage alone is corroborated by experimental data from the measured RBE. The geometric interpretation generates a unique dimensionless parameter $k$ for each type of charged particle. In addition, it predicts a distribution of DNA damage which is different from the current models.