An improved biological weighting function (IBWF) is proposed to phenomenologically relate microdosimetric lineal energy probability density distributions with the relative biological effectiveness (RBE) for the in vitro clonogenic cell survival (surviving fraction = 10%) of the most commonly used mammalian cell line, i.e. the Chinese hamster lung fibroblasts (V79). The IBWF, intended as a simple and robust tool for a fast RBE assessment to compare different exposure conditions in particle therapy beams, was determined through an iterative global-fitting process aimed to minimize the average relative deviation between RBE calculations and literature in vitro data in case of exposure to various types of ions from ¹ H to ²³⁸ U. By using a single particle- and energy- independent function, it was possible to establish an univocal correlation between lineal energy and clonogenic cell survival for particles spanning over an unrestricted linear energy transfer range of almost five orders of magnitude (0.2 keV µ m ⁻¹ to 15 000 keV µ m ⁻¹ in liquid water). The average deviation between IBWF-derived RBE values and the published in vitro data was ∼14%. The IBWF results were also compared with corresponding calculations ( in vitro RBE ₁₀ for the V79 cell line) performed using the modified microdosimetric kinetic model (modified MKM). Furthermore, RBE values computed with the reference biological weighting function (BWF) for the in vivo early intestine tolerance in mice were included for comparison and to further explore potential correlations between the BWF results and the in vitro RBE as reported in previous studies. The results suggest that the modified MKM possess limitations in reproducing the experimental in vitro RBE ₁₀ for the V79 cell line in case of ions heavier than ²⁰ Ne. Furthermore, due to the different modelled endpoint, marked deviations were found between the RBE values assessed using the reference BWF and the IBWF for ions heavier than ² H. Finally, the IBWF was unchangingly applied to calculate RBE values by processing lineal energy density distributions experimentally measured with eight different microdosimeters in 19 ¹ H and ¹² C beams at ten different facilities (eight clinical and two research ones). Despite the differences between the detectors, irradiation facilities, beam profiles (pristine or spread out Bragg peak), maximum beam energy, beam delivery (passive or active scanning), energy degradation system (water, PMMA, polyamide or low-density polyethylene), the obtained IBWF-based RBE trends were found to be in good agreement with the corresponding ones in case of computer-simulated microdosimetric spectra (average relative deviation equal to 0.8% and 5.7% for ¹ H and ¹² C ions respectively).

Experimental studies of microdosimetry in therapeutic ion beams have been performed using several detectors. The differences among the microdosimeters lie on the shapes, the site sizes, and the material. The present study proposes a method to extract from the heterogeneous information collected with the different microdosimeters a univocal specification of the radiation quality of the radiation field. Historically the specification of the radiation quality is provided either in terms of linear energy transfer (LET) or in terms of lineal energy, y . The first part of this study focuses on identifying the correlation between the distributions of LET and the lineal energy spectra as well as the correspondence between their mean values calculated from the frequency and dose distributions. The evaluation is inspired by the method of LET analysis described by Kellerer (1972 Phys. Med. Biol . 17 232–40) with adaptation to the peculiarities of ion-beam therapy where the pristine irradiation is unidirectional and made of a single species of essentially mono-energetic ions. The second objective of this study is to interpret the spectra collected by a slab and perform the necessary conversion to estimate what the spectrum would be if it was collected by a detector different in shape, material, or size. An example is provided using as starting point the simulated lineal energy spectrum of carbon ions impinging a slab detector of graphite and applying the method to convert it to the spectra that would be obtained in the same radiation field with spherical, cylindrical, and slab detectors made of water.

The specific advantages of ion beams for application in tumor therapy are attributed to their different macroscopic and microscopic energy deposition pattern as compared to conventional photon radiation. On the macroscopic scale, the dose profile with a Bragg peak at the highest depths and small lateral scattering allow a better conformation of the dose to the tumor. On the microscopic scale, the localized energy deposition around the trajectory of the particles leads to an enhanced biological effectiveness, typically expressed in terms of clinically significant relative biological effectiveness (RBE). Experimental investigations reveal complex dependencies of RBE on many physical and biological parameters, as e.g. ion species, dose, position in the field, and cell or tissue type. In order to complement the experimental work, different approaches are used for the characterization of the specific physical and biological properties of ion beams. In a set of two papers, which are linked by activities within a European HORIZON 2020 project about nuclear science and application (ENSAR2), we describe recent developments in two fields playing a key role in characterizing the increased biological effectiveness. These comprise the biophysical modelling of RBE and the microdosimetric measurements in complex radiation fields. This second paper focuses on microdosimeters and on the importance of providing the instrumental measurement of the spectra of the imparted energy. The relevance of microdosimetric quantities, complementary to the absorbed dose is emphasized. This parts provides an overview of the microdosimetric concepts and the recent experimental developments in the field of microdosimetry applied to ion beam therapy. Finally, a non-exhaustive, dedicated section in included to emphasize the relevance of Monte Carlo simulations as tool for the design of the microdosimetric detectors and for the interpretation of the experimental results. For the two distinctive clinical beams of protons and carbon ions, the lineal-energy parameters are correlated to the clinical concept of Linear Energy Transfer (LET) and RBE. The possibilities of applying experimental microdosimetry in ion-beam therapy are discussed considering the consolidated irradiation characteristics as well as the most recent developments.

Microdosimetry is increasingly adopted in the characterization of proton and carbon ion beams used in cancer therapy. Spectra and mean values of lineal energy calculated in frequency and dose are seen by many as the tools which, by complementing dosimetric measurements, allow for the most complete characterization of the therapeutic radiation fields. The urgency is now to consolidate the experience and converge to commonly accepted methodologies. In this context, the purpose of this work is to study the effects of the energy-loss straggling and the delta-ray escape, considering slab-sensitive volumes; these are, in fact, the typical shapes of solid-state microdosimeters, which are widely used in investigating light ion therapy beams. The method considers the energy distribution of delta rays resulting from the collision of the impinging ion and, taking into account the escape, convolutes it with itself as many times as the expected number of collisions in the sensitive volume thickness. The resulting distribution is compared to the experimental microdosimetric spectrum showing a substantially good agreement. The extension of the methodology to a wider range of ion energy and detector characteristics is instrumental for a detector-independent microdosimetric assessment of the radiation fields.

Objective. Microdosimetry is gaining increasing interest in particle therapy. Thanks to the advancements in microdosimeter technologies and the increasing number of experimental studies carried out in hadron therapy frameworks, it is proving to be a reliable experimental technique for radiation quality characterisation, quality assurance, and radiobiology studies. However, considering the variety of detectors used for microdosimetry, it is important to ensure the consistency of microdosimetric results measured with different types of microdosimeters. Approach. This work presents a novel multi-thickness microdosimeter and a methodology to characterise the radiation quality of a clinical carbon-ion beam. The novel device is a diamond detector made of three sensitive volumes (SVs) of different thicknesses: 2, 6 and 12 µm. The SVs, which operate simultaneously, were accurately aligned and laterally positioned within 3 mm. This alignment allowed for a comparison of the results with a negligible impact of the SVs alignment and their lateral positioning, ensuring the homogeneity of the measured radiation quality. An experimental campaign was carried out at MedAustron using a carbon-ion beam of typical clinical energy (284.7 MeV u⁻¹). Main results. The measurement results allowed for a meticulous interpretation of its radiation quality, highlighting the effect of the SV thickness. The consistency of the microdosimetric spectra measured by detectors of different thicknesses is discussed by critically analysing the spectra and the differences observed. Significance. The methodology presented will be highly valuable for future experiments investigating the effects of the target volume size in radiobiology and could be easily adapted to the other particles employed in hadron therapy for clinical (i.e. protons) and for research purposes (e.g. helium, lithium and oxygen ions).

Ion-beam therapy faces a growing demand of tools able to map radiation quality within the irradiated volume. Although analytical computations and simulations provide useful estimations of dose and radiation quality, the direct measure of those parameters would improve ion-beam therapy in particular when deep-seated tumours are irradiated, tissue composition and density are variable or organs at risk are near the tumour. Several ion-beam therapy facilities are studying detectors and procedures for measuring the radiation quality on a microdosimetric as well as a nanodosimetric scale. Simplicity and miniaturisation of the devices are essential for measurements first in phantoms and thereafter during therapy, particularly for intra-cavity detectors. MedAustron is studying solid-state detectors based on a single crystal chemical vapour deposition diamond. In collaboration with Italian National Institute for Nuclear Physics (INFN), Tor Vergata and Legnaro; INFN-microdosimetry and track structure project; Austrian Institute of Technology, Vienna; and Italian National agency for new technologies, energy and sustainable economic development, Rome, prototypes have been developed to characterise radiation quality in sizes equivalent to one micrometre of biological tissue.