Relative Biological Effectiveness (RBE) of Monoenergetic Protons: Comparison of Empirical and Biophysical Models  
[PERSON]  
1 Medical Physics Laboratory, Department of Medicine, University of Ioannina, 45110 Ioannina, Greece; [EMAIL_ADDRESS] (D.D. ); [EMAIL_ADDRESS] (A.P. ); [EMAIL_ADDRESS] (I.K.) [PERSON]  
1 Medical Physics Laboratory, Department of Medicine, University of Ioannina, 45110 Ioannina, Greece; [EMAIL_ADDRESS] (D.D. ); [EMAIL_ADDRESS] (A.P. ); [EMAIL_ADDRESS] (I.K.) [PERSON]  
1 Medical Physics Laboratory, Department of Medicine, University of Ioannina, 45110 Ioannina, Greece; [EMAIL_ADDRESS] (D.D. ); [EMAIL_ADDRESS] (A.P. ); [EMAIL_ADDRESS] (I.K.) [PERSON]  
2 Department of Radiation Oncology, University of Washington, Seattle, WA 98195, USA; [EMAIL_ADDRESS] 23 Radiation Oncology Division, Fred Hutchinson Cancer Center, Seattle, WA 98109, USA 34 Medical Physics Laboratory, Medical School, National and Kapodistrian University of Athens, 15784 Athens, Greece 4  
[PERSON]  
4 Correspondence: [EMAIL_ADDRESS]; Tel. : +30-26510077414441  
may be sufficient in many clinical settings, although plans optimized with a constant, spatially invariant RBE are most likely sub-optimal in terms of the therapeutic ratio for PBT, i.e., overestimating the RBE-weighted dose (RWD) on target while underestimating the RWD to OAR of most concern [5,6]. Published studies imply significant deviations from a constant RBE of 1.1 [1, 7, 8, 9, 10, 11, 12]. These studies provide evidence that RBE is not spatially invariant--rather, it varies within the target volume depending on several factors, including target size, treatment delivery technique and other physical and biological parameters [2]. RBE values that exceed 1.1 at the end of a proton track (i.e., low-energy protons distal to the Bragg peak) are not uncommon in PBT, due to the change in the radiation quality of the beam [13, 14, 15]. Radiation quality (type and energy of radiation) leads to distinct spatial patterns of energy depositions in (sub) cellular dimensions (DNA helix, chromosomes, cell nucleus) that in turn change the relative effectiveness of a dose of one type of radiation relative to another [14,16]. These differences in the biological effectiveness of different types of radiation are often quantified relative to the linear energy transfer (LET) of the relevant charged particle(s). LET is a measure of the ionization density per unit distance traveled by an ion in matter, and tends to increase with decreasing ion kinetic energy. Therefore, ions at the end of their path exhibit a higher LET and are expected to be more effective in causing localized DNA damage and cell death than lower LET radiations [13, 17, 18, 19]. The adoption of a constant, spatially invariant proton RBE of 1.1 runs counter to fundamental physics and a large body of published in vitro, in vivo and clinical evidence [1, 9, 10, 11]. Several proton RBE models have been developed in recent years that attempt to incorporate tissue-specific and variable-with-LET RBE into PBT treatment planning. Most proton RBE models are empirical (or phenomenological) and derived from linear-quadratic (LQ) model fits to measured data for in vitro cell survival [20]. In contrast, biophysical (or mechanistic-inspired) models, like the theory of dual radiation action (TDRA) and the micro-crosimetric kinetic model (MKM) [18,21], seek a connection between the stochastic energy deposition pattern on microscopic (subcellular) target volumes and reproductive cell survival [18]. Other biophysical approaches, like the Repair-Misrepair Fixation (RMF) model, relate reproductive cell death to the pairwise interaction of DSB from an independently validated Monte Carlo model, thus using microdosimetric concepts indirectly [17, 22, 23]. The TDRA and MKM models employ the microdosimetric (i.e., stochastic) analogue of LET, lineal energy (\(y\)) [24].