Segment-averaged LET concept and analytical calculation from microdosimetric quantities in proton radiation therapy

Abstract

Purpose: This work introduces the concept of segment-averaged linear energy transfer (LET) as a new approach to average distributions of LET of proton beams based on a revisiting of microdosimetry theory. The concept of segment-averaged LET is then used to generate an analytical model from Monte Carlo simulations data to perform fast and accurate calculations of LET distributions for proton beams and material: The distribution of energy imparted by a proton beam into a representative biological structure or site is influenced by the distributions of (1) LET, (2) segment length, which is the section of the proton track in the site, and (3) energy straggling of the proton beam. The distribution of LET is thus generated by the LET of each component of the beam in the site. However, the situation when the LET of each single proton varies appreciably along its path in the site is not defined. Therefore, a new distribution can be obtained if the particle track segment is decomposed into smaller portions in which LET is roughly constant. We have called “segment distribution” of LET the one generated by the contribution of each portion. The average of that distribution is called segment-averaged LET. This quantity is obtained in the microdosimetry theory from the average and standard deviation of the distributions of energy imparted to the site, segment length and energy imparted per collision. All this information is calculated for protons of clinically relevant energies by means of Geant4-DNA microdosimetric simulations. Finally, a set of analytical functions is proposed for each one of the previous quantities. The presented model functions are fitted to data from Geant4-DNA simulations for monoenergetic beams from 100 keV to 100 MeV and for spherical sites of 1 μm, 5 μm and 10 μm in diameter. Results: The average differences along the considered energy range between calculations based on our analytical models and MC for segment-averaged dose-averaged restricted LET are -0.2 ± 0.7 keV/μm for the 1 μm case, 0.0 ± 0.9 keV/μm for the 5 μm case and -0.3 ± 1.1 keV/μm for the 10 μm case, respectively. All average differences are below the average standard deviation (1σ) of the MC calculations. Conclusions: A new way of averaging LET for a proton beam is performed to incorporate the effects produced by the variation of stopping power of each individual proton along microscopic biological structures. An analytical model based on MC simulations allows for fast and accurate calculations of segment-averaged dose-averaged restricted LET for proton beams, which otherwise would need to be calculated from exhaustive MC simulations of clinical plans.