Analytical model of ionization and energy deposition by proton beams in subcellular compartments

Abstract

We present an analytical model to evaluate in a fast, simple and effective manner the energy delivered by proton beams moving through a cell model made of nucleus and cytoplasm, taking into account the energy carried by the secondary electrons generated along the proton tracks. The electronic excitation spectra of these subcellular compartments have been modelled by means of an empirical parameterization of their dielectric properties. The energy loss rate and target ionization probability induced by swift protons are evaluated by means of the dielectric formalism. With the present model we have quantified the energy delivered, the specific energy, and the number of ionizations produced per incoming ion in a typical human cell by a typical hadrontherapy proton beam having energies usually reached around the Bragg peak (below 20 MeV). We find that the specific energy per incoming ion delivered in the nucleus and in the cytoplasm are rather similar for all the proton energy range analyzed.