A new approach to modeling the microdosimetry of proton therapy beams

To revisit the formulation of the mean chord length in microdosimetry and replace it by the particle mean free path appropriate for modelings in radiobiology.

We perform a collision-by-collision followed by event-by-event Geant4 Monte Carlo simulation and calculate double-averaged stepping length, 〈〈l〉〉, for a range of target sizes from mm down to μm and depth in water. We consider 〈〈l〉〉 to represent the particle mean free path.

We show that 〈〈l〉〉 continuously drops as a function of depth and asymptotically saturates to a minimum value in low energies, where it exhibits a universal scaling behavior, independent of particle nominal beam energy. We correlate 〈〈l〉〉 to linear density of DNA damage, complexities of initial lethal lesions and illustrate a relative difference between predictive RBEs in model calculations using mean chord length vs the proposed mean free path. We demonstrate consistency between rapid increase in RBE within and beyond the Bragg peak and 〈〈l〉〉, a decreasing function of depth.

An interplay between localities in imparted energy at nanometer scale and subsequent physio-chemical processes, causalities and pathways in DNA damage requires substitution of geometrical chord length of cell nuclei by mean-free path of proton and charged particles to account for a mean distance among sequential collisions in DNA materials. To this end, the event averaging over cell volume in the current microdosimetry formalism must be superseded by the collision averaging scored within the volume. The former, is fundamentally a global attribute of the cell nuclei surfaces and boundaries and is characterized by their membrane diameters, hence such global indices are not appropriate to quantitatively represent the radiobiological strength of the particles and their RBE variabilities that is associated with the sensitivities to local structure of the collisions and their spatio-temporal collective patterns in DNA materials.