Expanding microdosimetry from radiation field characterization to radiobiological damage modeling

Besides the general introduction given above, the main features and quantities of the common thread of the whole work, namely microdosimetry, are given in Part \ref{microdosimetry}. Moreover, an overview of the most useful details of the experiments, Monte Carlo simulations, data analysis and machine learning techniques used throughout the whole work are presented in Part \ref{part:tools}. Finally, the core of this thesis can be divided into three main parts, focusing on different aspects of microdosimetry. A summary of the three parts is given below.\\ \subsection*{Microdosimetric radiation field characterization} Several data-taking campaigns using a commercial TEPC have been carried out, performing experiments to characterize the radiation quality in different positions inside a water phantom, both in- and off-beam. In the experiments, we mainly aimed at studying the radiation fields coming from secondary particles and scattered primary particles in the so called \textit{out-of-field} region, that would correspond to the normal tissues around the irradiated tumour in a clinical scenario.\\ A set of measurements have been taken at the Trento Protontherapy Center with a monoenergetic therapeutic proton beam and a \textit{Spread Out Bragg Peak} (SOBP). In both cases, we evaluated the radiation quality and assessed in addition the potential radiobiological damage in the different regions. Analogous measurements have been also performed with ions heavier than protons, namely helium and oxygen. Finally, microdosimetry finds also an application in space radioprotection. In this perspective, two experimental data campaigns have been carried out at GSI \textit{Helmholtz Centre for Heavy Ion Research} in Darmstadt (Germany), with the goal of assessing microdosimetric energy depositions spectra of neutrons.\\ \subsection*{Hybrid Detector for Microdosimetry (HDM): a new tool for extending the microdosimetric information} A feature shared by every microdosimeter is that the \textit{lineal energy} y (microdosimetric counterpart of the LET) of each particle is obtained by dividing the energy deposition $\epsilon$ with the mean chord length $l$ traversed in the detector. While $\epsilon$ is directly measured, the value of $l$ is calculated as the average path travelled by the particle inside the detector, and thus depends both on the detector geometry and on specific assumptions on the radiation field (typically considered isotropic and uniform). To investigate the validity of this approximation, we performed Monte Carlo calculations using GEANT4 toolkit. We analyzed the track length distributions of all particles traversing the TEPC and found that the mean chord was not always a good representative of the whole population. In order to experimentally achieve the real track length information without relying on the mean chord length approximation, we designed a new hybrid 2-stage microdosimeter (HDM: hybrid detector for microdosimetry) composed of a spherical TEPC followed by four Low Gain Avalanche Detectors (LGADs). HDM provides lineal energy spectra in tissue-equivalent with an event-by-event measurement of the path length and a submillimetric spatial resolution. To assess the detector performances, in the feasibility study we tested different configurations (distance between detectors, number of strips in a single LGAD) and studied HDM response when irradiated with protons and carbon ions at different water depths. We found out that the detection efficiency is the most critical issue. To improve it, we exploited modern \textit{Machine Learning} (ML) techniques, and developed a model composed by two modules: the first one aims at improving the detector efficiency, filling the missing spatial point values on the LGADs; the second one reconstructs the tracks of the particles to calculate microdosimetric spectra using the real track length. \subsection*{The Generalized Stochastic Microdosimetric Model (GSM$^2$)} Currently, the only two radiobiological models used in clinical applications are the Microdosimetric Kinetic Model (MKM) and the Local Effect Model (LEM). The main limitation shared by both models is the assumption that all physical and biological variables follow a Poisson distribution. This hypothesis neglects stochastic fluctuations of energy deposition both from cell to cell and within dose fractions. Although some generalizations to overcome the Poissonian assumption have been developed, \cite{bellinzona2021linking}, a comprehensive stochastic description of the radiation-induced DNA damage formation and dynamics accounting for both spatial and temporal features of the dose deposition are still missing.\\ To overcome this limitation, we have developed the generalized stochastic microdosimetry model (GSM$^2$) \cite{cordoni2021generalized}. By modeling the probability distribution of DNA damages, GSM$^2$ provides a general probabilistic framework to describe the damage formation and evolution.\\ One of the most relevant strengths of GSM$^2$ is the capability to efficiently treat the different levels of spatio-temporal stochasticity for an irradiation. An extensive study of the cell survival probability for acute irradiation conditions (as it is the case in particle therapy) has been carried out in this part, showing GSM$^2$ potentiality to provide a better ground for the mechanistic interpretation of cell killing compared to the existing models. As a relevant consequence, we showed how GSM$^2$ provides a generalization to the multi-hit model, that accounts for non-Poissonian effects and damage repair. In addition, a separate work focusing on the different level of stochasticities and their effect on the cell survival curve has been carried out.\\ Finally, GSM$^2$ provided an ideal mathematical framework for the information provided by HDM, being able to account for the whole microdosimetric distribution to predict survival curves, instead of using just mean values like the majority of existing RBE models.\\