Purpose: Advanced ion beam therapeutic techniques, such as hypofractionation, respiratory gating, or laser-based pulsed beams, have dose rate time structures which are substantially different 15 from those found in conventional approaches. The biological impact of the time structure is mediated through the β parameter in the linear quadratic (LQ) model. The aim of this study is to assess the impact of changes in the value of the β parameter on the treatment outcomes, also accounting for non instantaneous intra-fraction dose delivery or fractionation and comparing the effects of using different primary ions. with good results. Notably, in contrast to the original MKM formulation, the MCt-MKM explicitly predicts an ion and LET dependent β compatible with observations. The data from a split-dose experiment were used to experimentally determine the value of the parameter related to the cellular repair kinetics. Concerning the clinical case considered, an RBE decrease was observed, depending on the dose, ion and LET, exceeding up to 3% of the acute value in the case of a protraction in Conclusions:The present study provides a framework for exploiting the temporal effects of dose delivery. The results show the possibility of optimizing the treatment outcomes accounting for the 40 correlation between the specific dose rate time structure and the spatial characteristic of the LET distribution, depending on the ion type used.2 *

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Few attempts have been made to include the oxygen enhancement ratio (OER) in treatment planning for ion beam therapy, and systematic studies to evaluate the impact of hypoxia in treatment with the beam of different ion species are sorely needed. The radiobiological models used to quantify the OER in such studies are mainly based on the dose-averaged LET estimates, and do not explicitly distinguish between the ion species and fractionation schemes. In this study, a new type of OER modelling, based on the microdosimetric kinetic model, taking into account the specificity of the different ions, LET spectra, tissues and fractionation schemes, has been developed. The model has been benchmarked with published in vitro data, HSG, V79 and CHO cells in aerobic and hypoxic conditions, for different ion irradiation. The model has been included in the simulation of treatments for a clinical case (brain tumour) using proton, lithium, helium, carbon and oxygen ion beams. A study of the tumour control probability (TCP) as a function of oxygen partial pressure, dose per fraction and primary ion type has been performed. The modelled OER depends on both the LET and ion type, also showing a decrease for an increased dose per fraction with a slope that depends on the LET and ion type, in good agreement with the experimental data. In the investigated clinical case, a significant increase in TCP has been found upon increasing the ion charge. Higher OER variations as a function of dose per fraction have also been found for low-LET ions (up to 15% varying from 2 to 8 Gy(RBE) for protons). This model could be exploited in the identification of treatment condition optimality in the presence of hypoxia, including fractionation and primary particle selection.