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Introduction The study of the interaction of charged particles with living matter is of prime importance to the fields of radiotherapy, radioprotection and space radiobiology. Particle accelerators and their associated equipments are proven to be helpful tools in performing basic science in all of these fields. Indeed, they can accelerate virtually any ions to a given energy and flux and let them interact with living matter either in vivo or in vitro. Usually radiobiological and radiotherapy studies are performed with a broad beam configuration, as homogeneous as possible over a given irradiation field. This uniform beam follows Poisson’s law in term of particle number delivered to the cells. However, even if Poisson’s distribution is well known and understood, its effects on different endpoints such as survival fraction in case of in vitro clonogenic assay or treatment planning systems (TPS) for external radiotherapy have not yet been taken into account. In this context, we describe here the current status of a Monte Carlo (MC) code that models the in vitro irradiation of a monolayer of adherent cells with a broad beam of charged particles. This MC code predicts survival fraction for different doses, and estimates and radiosensitivity parameters. Simulations are benchmarked to experimental survival curves obtained for A549 adenocarcinoma lung cancer cells with protons, alphas and carbon ions. The need to perform microbeam irradiations to obtain input parameters is discussed.
Materials and methods Physical and biological inputs are needed. First the dose and the linear energy transfer (LET in keV/µm) are required. These values are used to calculate the fluence (particles/cm²). Together with the cell and nucleus areas, these parameters fix the mean number of particles per nucleus. The LET is calculated using an external program, SRIM (Stopping and Range of Ions in Matter) , knowing the cell thickness. The value at the cell mid-plane is chosen and assumed not to vary too much throughout the cell layer. The number of double strand breaks (DSBs) per Gy and per cell is also needed and extracted from the MCDS (Monte Carlo Damage Simulation) program . The user may tune the DSB repair probability input and the number of cells to be tested. Lastly, two parameters are required to handle the low-dose hypersensitivity (HRS): the G2-phase proportion in the cell population and a threshold dose at which HRS is overcome. HRS has been shown to be mainly expressed by G2-phase cells [3, 4]. Cell morphology was assessed by nuclear and membrane staining (CellMask Orange (Invitrogen) and DRAQ5 (Cell Signaling)). G2-phase proportion was determined by flow cytometry (propidium iodide staining).
Results and discussion Outputs of the model are in good agreement with experimental data  for alphas, 25 keV/µm protons and carbon ions. The survival fraction of A549 cells exposed to 10 keV/µm protons exhibit HRS in the low dose region. The high-dose behavior of the 10 keV/µm protons survival curve is also reproduced by the model. The simulation of the low-dose region reproduces the hypersensitivity trend but should be improved. In the current status of our computer program, some input parameters were obtained experimentally (e.g. G2-phase proportion or cell morphology), whereas some others can be tuned by the user (e.g. DSB repair probability or HRS threshold dose). It would be desirable that all input parameters would be either predicted or experimentally determined. For instance, DSB repair probability could be assessed by analyzing the intensity with time of p-H2AX radiation induced foci . That kind of measurements could be performed after irradiation with a microbeam setup. Indeed, the Poisson dose distribution linked to the broad beam setup would make it difficult to determine the DSBs kinetics precisely. The same observation can be done for the assessment of the HRS dose threshold. Further work is needed to obtain DSBs kinetics experimentally, to improve the simulation of the DSBs repair and to implement the bystander effect.