Objective. To develop a new model (Mayo Clinic Florida microdosimetric kinetic model, MCF MKM) capable of accurately describing the in vitro clonogenic survival at low and high linear energy transfer (LET) using single-event microdosimetric spectra in a single target. Methodology. The MCF MKM is based on the ‘post-processing average’ implementation of the non-Poisson microdosimetric kinetic model and includes a novel expression to compute the particle-specific quadratic-dependence of the cell survival with respect to dose (β of the linear-quadratic model). A new methodology to a priori calculate the mean radius of the MCF MKM subnuclear domains is also introduced. Lineal energy spectra were simulated with the Particle and Heavy Ion Transport code System (PHITS) for ¹H, ⁴He, ¹²C, ²⁰Ne, ⁴⁰Ar, ⁵⁶Fe, and ¹³²Xe ions and used in combination with the MCF MKM to calculate the ion-specific LET-dependence of the relative biological effectiveness (RBE) for Chinese hamster lung fibroblasts (V79 cell line) and human salivary gland tumor cells (HSG cell line). The results were compared with in vitro data from the Particle Irradiation Data Ensemble (PIDE) and in silico results of different models. The possibility of performing experiment-specific predictions to explain the scatter in the in vitro RBE data was also investigated. Finally, a sensitivity analysis on the model parameters is also included. Main results. The RBE values predicted with the MCF MKM were found to be in good agreement with the in vitro data for all tested conditions. Though all MCF MKM model parameters were determined a priori, the accuracy of the MCF MKM was found to be comparable or superior to that of other models. The model parameters determined a priori were in good agreement with the ones obtained by fitting all available in vitro data. Significance. The MCF MKM will be considered for implementation in cancer radiotherapy treatment planning with accelerated ions.

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).

With more patients receiving external beam radiation therapy with protons, it becomes increasingly important to refine the clinical understanding of the relative biological effectiveness (RBE) for dose delivered during treatment. Treatment planning systems used in clinics typically implement a constant RBE of 1.1 for proton fields irrespective of their highly heterogeneous linear energy transfer (LET). Quality assurance tools that can measure beam characteristics and quantify or be indicative of biological outcomes become necessary in the transition towards more sophisticated RBE weighted treatment planning and for verification of the Monte Carlo and analytical based models they use. In this study the RBE for the CHO-K1 cell line in a passively delivered clinical proton spread out Bragg peak (SOBP) is determined both in vitro and using a silicon-on-insulator (SOI) microdosimetry method paired with the modified microdosimetric kinetic model. The RBE along the central axis of a SOBP with 2 Gy delivered at the middle of the treatment field was found to vary between 1.11–1.98 and the RBE for 10% cell survival between 1.07–1.58 with a 250 kVp x-ray reference radiation and between 1.19–2.34 and 0.95–1.41, respectively, for a Co60 reference. Good agreement was found between RBE values calculated from the SOI-microdosimetry-MKM approach and in vitro . A strong correlation between proton lineal energy and RBE was observed particularly in the distal end and falloff of the SOBP.

The relative biological effectiveness (RBE) calculations used during the planning of ion therapy treatments are generally based on the microdosimetric kinetic model (MKM) and the local effect model (LEM). The Mayo Clinic Florida MKM (MCF MKM) was recently developed to overcome the limitations of previous MKMs in reproducing the biological data and to eliminate the need for ion-exposed in vitro data as input for the model calculations. Since we are considering to implement the MCF MKM in clinic, this article presents (a) an extensive benchmark of the MCF MKM predictions against corresponding in vitro clonogenic survival data for 4 rodent and 10 cell lines exposed to ions from ¹H to ²³⁸U, and (b) a systematic comparison with published results of the latest version of the LEM (LEM IV). Additionally, we introduce a novel approach to derive an approximate value of the MCF MKM model parameters by knowing only the animal species and the mean number of chromosomes. The overall good agreement between MCF MKM predictions and in vitro data suggests the MCF MKM can be reliably used for the RBE calculations. In most cases, a reasonable agreement was found between the MCF MKM and the LEM IV.

Objective. Estimation of the probability density of the microdosimetric quantities in macroscopic matter is indispensable for applying the concept of microdosimetry to medical physics and radiological protection. The Particle and Heavy Ion Transport code System (PHITS) enables estimating the microdosimetric probability densities due to its unique hybrid modality between the Monte Carlo and analytical approaches called the microdosimetric function. It can convert the deposition energies calculated by the macroscopic Monte Carlo radiation transport simulation to microdosimetric probability densities in water using an analytical function based on the track-structure simulations. Approach. In this study, we improved this function using the latest track-structure simulation codes implemented in PHITS. The improved function is capable of calculating the probability densities of not only the conventional microdosimetric quantities such as lineal energy but also the number of ionization events occurring in a target site, the so-called ionization cluster size distribution, for arbitrary site diameters from 3 nm to 1 μm. Main results. The accuracy of the improved function was well verified by comparing the microdosimetric probability densities measured by tissue-equivalent proportional counters with the corresponding data calculated in this study. Test calculations for clonogenic cell survival using the improved function coupled with the modified microdosimetric kinetic model suggested a slight increase of its relative biological effectiveness compared with our previous estimations. As a new application of the improved function, we calculated the relative biological effectiveness of the single-strand break and double-strand break yields for proton irradiations using the updated PHITS coupled with the simplified DNA damage estimation model, and confirmed its equivalence in accuracy and its superiority in computational time compared to our previously proposed method based on the track-structure simulation. Significance. From these features, we concluded that the improved function could expand the application fields of PHITS by bridging the gap between microdosimetry and macrodosimetry.