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Purpose: To present a closed formalism calculating charged particle radiationdamage induced in DNA. The formalism is valid for all types of chargedparticles and due to its closed nature is suited to provide fast conversion ofdose to DNA-damage. Methods: The induction of double strand breaks inDNA--strings residing in irradiated cells is quantified using a single particlemodel. This leads to a proposal to use the cumulative Cauchy distribution toexpress the mix of high and low LET type damage probability generated by asingle particle. A microscopic phenomenological Monte Carlo code is used to fitthe parameters of the model as a function of kinetic energy related to thedamage to a DNA molecule embedded in a cell. The model is applied for fourparticles: electrons, protons, alpha--particles, and carbon ions. A geometricinterpretation of this observation using the impact ionization mean free pathas a quantifier, allows extension of the model to very low energies. Results:The mathematical expression describes the model adequately using a chi--squaretest ($\chi^2/NDF < 1$). This applies to all particle types with an almostperfect fit for protons, while the other particles seem to result in somediscrepancies at very low energies. The implementation calculating a strictversion of the RBE based on complex damage alone is corroborated byexperimental data from the measured RBE. The geometric interpretation generatesa unique dimensionless parameter $k$ for each type of charged particle. Inaddition, it predicts a distribution of DNA damage which is different from thecurrent models.

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