Objective.The, a new tool implemented in the GATE Monte Carlo platform, aims to calculate the biological dose and its associated uncertainty for hadrontherapy treatment plans. This tool is designed to facilitate the validation of biophysical models and optimize clinical treatment planning by providing accurate biological dose distributions.Approach.Theutilizes pre-calculated databases of the linear-quadratic coefficients (and) of cell survival curves, derived from biophysical models such as the modified MicroKinetic Model (mMKM) and the nanodosimetry and oxidative stress model. These databases cover hydrogen, helium, lithium, carbon, and oxygen ions, with energy ranges from 0.1 MeV uto 1000 MeV u. The algorithm computes the biological dose using the linear-quadratic coefficients and their uncertainties, while optimizing Monte Carlo simulation parameters. Two step-size limitation methods in Geant4 (StepLimiter and StepFunction) were evaluated to balance accuracy and computation time in spread out Bragg peak (SOBP) dose distributions for proton and carbon-ion beams.Main results.The StepFunction method proved more efficient than the StepLimiter, achieving a 30.6-fold acceleration factor for protons and a 2-fold acceleration factor for carbon ions while maintaining a maximum relative difference of 2% in SOBP. Optimal parameters for StepFunction were identified as (,) for the clinical proton beam and (,) for the clinical carbon-ion beam. The calculatedandcoefficients and relative biological effectiveness values (1.2-1.5 for protons, 2-3 for carbon ions) aligned with literature. Application to a clinical carbon-ion treatment plan created by Raystation allowed us to validate theand to demonstrate the tool's capability to generate physical and biological dose maps and dose volume histograms.Significance.Theenables direct comparison of biophysical models, supporting the integration of biological dose calculations into clinical practice. By optimizing simulation parameters, it reduces computation time without compromising accuracy, thus enhancing the feasibility of biological dose-based treatment planning in hadrontherapy.

Background and Purpose:Helium ion therapy offers favorable dose distributions and potential biological advantages over photon and proton therapies, yet data on cellular response in clinically relevant Spread-Out Bragg Peak (SOBP) configurations remain limited. This study measured the surviving fraction of radioresistant human laryngeal squamous cell carcinoma (SQ20B) cells irradiated in a helium SOBP and compared experimental results with predictions from NanOx, a nanodosimetry and oxidative stress model implemented in Monte Carlo simulations. Materials and Methods:SQ20B cells were irradiated at three positions along a helium SOBP using a passive beamline. Survival fractions were measured for doses between 1 and 4 Gy. The setup was simulated in GATE, and survival was predicted using the NanOx model via the Biodose Actor. Relative biological effectiveness (RBE) was derived from linear quadratic fits using photon reference parameters. Results:NanOx predicted decreasing survival towards the distal edge, with surviving fractions at 4 Gy of 11%, 7%, and 4% at the proximal edge, plateau, and distal edge, respectively. Experimentally, fitted surviving fractions at 4 Gy were 10%, 12%, and 8%, showing no spatial trend. Deviations between model predictions and experimental averages ranged from 20 to 37%. Experimental RBE values ranged from 2.1 to 2.4, in reasonable agreement with NanOx predictions (2.1-2.9). Conclusions:In this SQ20B cell model under the present experimental conditions, NanOx predictions differed from experimental data by 20-37% depending on position. These results support further validation of the model in a broader range of cell lines and helium ion irradiation configurations.

BACKGROUND:To understand and predict the therapeutic efficacy of targeted alpha therapy (TAT), nano- and microdosimetry are needed to consider the very heterogeneous dose deposition at cellular and subcellular levels. PURPOSE:The objective of this study is to theoretically evaluate the importance of cell internalization of alpha-emitters on relevant dosimetric and biological endpoints. METHODS:Isolated cells and realistic 3D multi-cellular geometries (spheroids modeled with CPOP) were generated as well as distributions of alpha-emitters corresponding to various cellular internalization cases. The alpha particles emitted were tracked with Geant4 (Monte Carlo) simulations. We calculated mean specific energies deposited into each cell nucleus ( Z n $Z_n$ ), cell survival fractions using the NanOx biophysical model, values of relative biological effectiveness (RBE) and tumor control probabilities (TCP) for each scenarios. The impact of spheroid compaction and size, alpha particle energy and radionuclide daughter diffusion was studied. The impact of the heterogeneous distribution of a number of alpha particles per cell was also studied, using a lognormal probability law. RESULTS:For a given activity per cell (APC), the radionuclide distribution had a critical influence on Z n $Z_n$ in isolated cancerous cells or small spheroids ( < $<$ 50  μ m $\mu{\rm m}$ radius), while its impact was relatively low in larger and more compact spheroids, with a maximum variation of 30% between the distributions. For an average 10% cell survival, RBE was found to be approximately between 2.3 and 3.3, depending on the spatial radionuclide distribution and the activity distribution per cell. TCP of 1 was always obtained with an APC larger than 0.534 mBq when a uniform tumoral distribution of radionuclides was considered, and for APC larger than 0.801 mBq with a lognormal distribution. However, below these activities, TCP could strongly depend on the radionuclide distributions up to a factor of 9.5 with a uniform distribution and 1.5 for a lognormal one. CONCLUSIONS:According to these findings, a precise modeling of alpha-emitter intracellular distributions may be required for small micro-metastases or tumors presenting regions with relatively low radionuclide concentration in order to limit the prediction uncertainties on biological outputs. Intratumoral fluctuations of APC were also found to be a critical parameter to consider for therapeutic efficacy prediction in TAT.

Respiratory-induced organ motion is a technical challenge to radiation therapy for lung cancer. Breathing is controlled by two independent muscles: the thorax and diaphragm muscles. The modeling of their action constitutes an important step for the respiratory motion model. The amplitude of the diaphragm forces and ribs displacement are patient-specific and depends on geometrical and physiological characteristics of the patient. This article presents a patient-specific bio-mechanical model (PSBM) of the diaphragm, as well as ribs kinematics. To determine the appropriate values of specific diaphragm forces for each patient, during a whole respiratory cycle, inverse finite element (FE) analysis methodology has been implemented to match the experimental results to the FE simulation results. Ribs kinematics extracted and calculated directly from 4D Computed Tomography (CT) scan images. We have investigated the effect of element type, finite deformation and elasticity on the accuracy and computation time. The results demonstrate that the proposed FE model including ribs kinematics can accurately predict the diaphragm motion with an average surface error in diaphragm/lungs contact region less than 2.2 +/- 2.1mm. This constitutes first steps for biomechanical patient-specific of the respiratory system modeling to pilot lungs and lung tumor motion for External Beam Radiation Therapy (EBRT).

Proton therapy enables precise dose delivery to tumors while sparing healthy tissues, offering significant advantages over conventional radiotherapy. Accurate prediction of biological doses requires detailed knowledge of radiation interactions with biological targets, especially DNA, a key site of radiation-induced damage. While most biophysical models (LEM, mMKM, NanOx) rely on water as a surrogate, this simplification neglects the complexity of real biomolecules. In this work, we calculate the stopping power and range of protons in liquid water, dry DNA, and hydrated DNA using semi-empirical cross sections for ionization, electronic excitation, electron capture, and electron loss by protons and neutral hydrogen in the 10 keV–100 MeV energy range. Additionally, ionization cross sections for uracil are computed to explore potential differences between DNA and RNA damage. Our results show excellent agreement with experimental and ab initio data, highlighting significant deviations in stopping power and range between water and DNA. Notably, the stopping power of DNA exceeds that of water at most energies, reducing proton ranges in dry and hydrated DNA by up to 20% and 26%, respectively. These findings provide improved input for Monte Carlo simulations and biophysical models, enhancing RBE predictions and dose accuracy in hadrontherapy.

Chromosome aberrations, a biomarker of space radiation-induced carcinogenesis, are a direct consequence of DNA double-strand break (DSB) misrepair and play an important role in the fate of irradiated cells. Their formation is a function of different physical and biological factors including the 3D DNA architecture. At the nanometric scale, the DNA is wrapped around histone proteins to form nucleosomes, which fold together to form the chromatin fiber. Different levels of DNA density exist, namely the less compact euchromatin (EC) and the denser heterochromatin (HC). Recent studies showed that EC is more prone to DNA damage than HC at the same dose, suggesting that DNA compaction might influence chromosome aberration formation. In this work, we investigated how DNA compaction at the nucleosome level influences the formation of DSBs and total exchanges for exposure to high charge and energy ions (HZE) with linear energy transfer (LET) in the range 0.4 - 235 keV/μm. The radiation transport tool RITRACKS and DNA damage and chromosome aberration model RITCARD allow the transport of HZE ions in cell nuclei and evaluate the yield of DNA damage and chromosome aberrations but does not provide detailed geometries of the DNA with different compaction levels. In contrast, Geant4-DNA provide atomic scale models of HC or EC DNA and can be used to evaluate DNA damage. We combined Geant4-DNA and RITCARD to model radiation transport, DNA damage and DNA repair in fibroblast cell nuclei filled with EC or HC and compared the results to those obtained by RITRACKS/RITCARD. For all cell nuclei, the 3D distribution of the DNA was obtained with the tool G-NOME using experimental chromosome conformation capture (Hi-C) data. Large differences were obtained for the yield of DSB between RITRACKS/RITCARD and Geant4 DNA (-25% - 125% for HC nuclei), reflecting major differences in how the two models score DNA damage, which were responsible for large differences (-50% - 150% for HC nuclei) in the yield of total exchanges. For Geant4-DNA, we found that DNA decompaction increased the yield of DNA DSB by 4-8%, depending on the ion LET. The effect was more pronounced for total exchanges, with an increased yield of 50-75% for EC nuclei compared to HC nuclei. This larger total exchange yield was attributed mainly to differences in DNA distribution across the cell nucleus and, to a lesser extent, the increased DSB yield. Euchromatin nuclei presented chromosome domains that were more spread out, likely favoring inter-chromosomal proximity at the periphery of chromosome territories and, therefore, chromosome rearrangements. These findings provide further evidence that DNA compaction could be a factor of cell radiosensitivity.

BACKGROUND:In cancer research, clonogenic assays are often performed as a means to determine the response of a given cell line to radiation exposure. The resulting cell survival fractions as a function of absorbed dose are usually fitted to a linear-quadratic (LQ) expression involving two coefficients, α $\alpha$ and β $\beta$ , describing the cell's radiosensitivity. However, β $\beta$ is particularly hard to compute with accuracy. On the other hand, biophysical models are developed for predicting the enhanced biological efficiency of heavy ions compared to photons. These models provide a more mechanistic description of the biological effects induced by ionizing radiation, while allowing the estimation of the α $\alpha$ and β $\beta$ coefficients. PURPOSE:In this work, we propose an analytical expression for the fast computation of the β $\beta$ coefficient for ions with energies ranging from ∼ $\sim$ 1 to ∼ $\sim$ 25 MeV/n. METHODS:The analytical expression for β $\beta$ was derived starting from the formalism of the NanOx biophysical model and introducing a set of approximations. The latter consider that the irradiation is carried out under track-segment conditions (as is the case in hadrontherapy) and with doses inducing a low number of impacts (i.e., of the order of some Gy). Moreover, it is assumed that the radiation tracks are narrow with respect to the sensitive volume (the cell nucleus) and that the fluctuations between radiation tracks remain small enough to work with the average values of the specific energy and the number of lethal events. Calculations of β $\beta$ were performed for three cell lines (HSG, CHO-K1, and V79) irradiated with hydrogen, helium and carbon ions. The values of β $\beta$ predicted with the analytical expression were compared with the results of a more time-consuming approach involving the computation of cell survival fractions with NanOx followed by a LQ fit. Our results were also compared with available experimental data and with the predictions of other biophysical models. RESULTS:We obtained an analytical expression for β $\beta$ as a function of α $\alpha$ , the linear energy transfer (LET), the β $\beta$ coefficient for reference radiation (photons) and the ratio of the chemical yields of hydroxyl radicals ( OH • ${\rm OH}^{\bullet }$ ) for the ion of interest and photons. We found that NanOx predicts a decrease in β $\beta$ with increasing LET, showing a similar trend to some other models described in the literature. Moreover, the values of β $\beta$ calculated with the analytical expression were in close agreement with the results obtained by applying a LQ fit to the cell survival fractions predicted with NanOx for the energy range in which the approximations underpinning the analytical approach hold. CONCLUSIONS:We derived in this work an analytical expression for the fast calculation of the β $\beta$ coefficient for ion irradiations. Although the analytical expression resulted from the NanOx model, it can be also applied to any model used to compute α $\alpha$ . Overall, the approach presented in this work may provide a reasonable description of the behavior of β $\beta$ with LET despite the large spread observed in experimental data.

BACKGROUND:Targeted radiotherapies with low-energy ions show interesting possibilities for the selective irradiation of tumor cells, a strategy particularly appropriate for the treatment of disseminated cancer. Two promising examples are boron neutron capture therapy (BNCT) and targeted radionuclide therapy with α $\alpha$ -particle emitters (TAT). The successful clinical translation of these radiotherapies requires the implementation of accurate radiation dosimetry approaches able to take into account the impact on treatments of the biological effectiveness of ions and the heterogeneity in the therapeutic agent distribution inside the tumor cells. To this end, biophysical models can be applied to translate the interactions of radiations with matter into biological endpoints, such as cell survival. PURPOSE:The NanOx model was initially developed for predicting the cell survival fractions resulting from irradiations with the high-energy ion beams encountered in hadrontherapy. We present in this work a new implementation of the model that extends its application to irradiations with low-energy ions, as the ones found in TAT and BNCT. METHODS:The NanOx model was adapted to consider the energy loss of primary ions within the sensitive volume (i.e., the cell nucleus). Additional assumptions were introduced to simplify the practical implementation of the model and reduce computation time. In particular, for low-energy ions the narrow-track approximation allowed to neglect the energy deposited by secondary electrons outside the sensitive volume, increasing significantly the performance of simulations. Calculations were performed to compare the original hadrontherapy implementation of the NanOx model with the present one in terms of the inactivation cross sections of human salivary gland cells as a function of the kinetic energy of incident α $\alpha$ -particles. RESULTS:The predictions of the previous and current versions of NanOx agreed for incident energies higher than 1 MeV/n. For lower energies, the new NanOx implementation predicted a decrease in the inactivation cross sections that depended on the length of the sensitive volume. CONCLUSIONS:We reported in this work an extension of the NanOx biophysical model to consider irradiations with low-energy ions, such as the ones found in TAT and BNCT. The excellent agreement observed at intermediate and high energies between the original hadrontherapy implementation and the present one showed that NanOx offers a consistent, self-integrated framework for describing the biological effects induced by ion irradiations. Future work will focus on the application of the latest version of NanOx to cases closer to the clinical setting.

This work aims at investigating the impact of DNA geometry, compaction and calculation chain on DNA break and chromosome aberration predictions for high charge and energy (HZE) ions, using the Monte Carlo codes Geant4-DNA, RITRACKS and RITCARD. To ensure consistency of ion transport of both codes, we first compared microdosimetry and nanodosimetry spectra for different ions of interest in hadrontherapy and space research. The Rudd model was used for the transport of ions in both models. Developments were made in Geant4 (v11.2) to include periodic boundary conditions (PBC) to account for electron equilibrium in small targets. Excellent agreements were found for both microdosimetric and nanodosimetric spectra for all ion types, with and without PBC. Some discrepancies remain for low-energy deposition events, likely due to differences in electron interaction models. The latest results obtained using the newly available Geant4 example “dsbandrepair” will be presented and compared to DNA break predictions obtained with RITCARD.

Introduction: NanOx is a theoretical framework developed to predict cell survival to ionizing radiation in the context of radiotherapy. Based on statistical physics, NanOx takes the stochastic nature of radiation at different spatial scales fully into account. It extends concepts from microdosimetry to nanodosimetry, and considers as well the primary oxidative stress. This article presents in detail the general formalism behind NanOx.Methods: Cell death induction in NanOx is modeled through two types of biological events: the local lethal events, modeled by the inactivation of nanometric sensitive targets, and the global events, represented by the toxic accumulation of oxidative stress and sublethal lesions. The model is structured into general premises and postulates, the theoretical bases compliant with radiation physics and chemistry, and into simplifications and approximations, which are required for its practical implementation.Results: Calculations performed with NanOx showed that the energy deposited in the penumbra of ion tracks may be neglected for the low-energy ions encountered in some radiotherapy techniques, such as targeted radionuclide therapy. On the other hand, the hydroxyl radical concentration induced by ions was shown to be larger for low-LET ions and to decrease faster with time compared to photons. Starting from the general formalism of the NanOx model, an expression was derived for the cell survival to local lethal events in the track-segment approximation.Discussion: The NanOx model combines premises of existing biophysical models with fully innovative features to consider the stochastic effects of radiation at all levels in order to estimate cell survival and the relative biological effectiveness of ions. The details about the NanOx model formalism given in this paper allow anyone to implement the model and modify it by introducing different approximations and simplifications to improve it, or even adapt it to other medical applications.

For the evaluation of the biological effects, Monte Carlo toolkits were used to provide an RBE-weighted dose using databases of survival fraction coefficients predicted through biophysical models. Biophysics models, such as the mMKM and NanOx models, have previously been developed to estimate a biological dose. Using the mMKM model, we calculated the saturation corrected dose mean specific energy z1D* (Gy) and the dose at 10% D10 for human salivary gland (HSG) cells using Monte Carlo Track Structure codes LPCHEM and Geant4-DNA, and compared these with data from the literature for monoenergetic ions. These two models were used to create databases of survival fraction coefficients for several ion types (hydrogen, carbon, helium and oxygen) and for energies ranging from 0.1 to 400 MeV/n. We calculated α values as a function of LET with the mMKM and the NanOx models, and compared these with the literature. In order to estimate the biological dose for SOBPs, these databases were used with a Monte Carlo toolkit. We considered GATE, an open-source software based on the GEANT4 Monte Carlo toolkit. We implemented a tool, the BioDoseActor, in GATE, using the mMKM and NanOx databases of cell survival predictions as input, to estimate, at a voxel scale, biological outcomes when treating a patient. We modeled the HIBMC 320 MeV/u carbon-ion beam line. We then tested the BioDoseActor for the estimation of biological dose, the relative biological effectiveness (RBE) and the cell survival fraction for the irradiation of the HSG cell line. We then tested the implementation for the prediction of cell survival fraction, RBE and biological dose for the HIBMC 320 MeV/u carbon-ion beamline. For the cell survival fraction, we obtained satisfying results. Concerning the prediction of the biological dose, a 10% relative difference between mMKM and NanOx was reported.

Biophysical models are useful tools for predicting the biological effects of ionizing radiation. From a practical point of view, these models can help clinicians to optimize the radiation absorbed dose delivered to patients in particle therapy. The biophysical model NanOx was recently developed to predict cell survival fractions in the context of radiotherapy. The model takes into account the stochastic nature of radiation at different levels and considers as well the accumulation of radio-induced oxidative stress in cells caused by reactive chemical species. We show in this work how the general formalism of NanOx is adapted to hadrontherapy applications. We then use NanOx to compute the cell survival fractions for three cell lines (V79, CHO-K1 and HSG) in response to carbon ions of different energies, and benchmark the predictions against experimental data. The results attest that NanOx provides a good description of both the overkill effect and the evolution of the shoulders of cell survival curves with linear energy transfer.

We present a simple theoretical model to calculate multiple-ionization cross sections (MICS) of Ne and Ne-like molecules (molecules with ten electrons as H2O, CH4, NH3, and HF) for proton and light-ion impact, taking into account both direct and postcollisional emissions. In this paper, we tackle the case of water molecules, relevant to investigate the radiobiological effects of ion impact on living matter. The theory is developed in the framework of the independent electron model (IEM). To keep the model as simple as possible, we describe the impact parameter dependence of the single-particle ionization probabilities required by the IEM through decreasing exponential functions for each target orbital. We obtain the parameters of the exponential functions from the total net-ionization cross sections for each orbital by applying either the continuum distorted wave-eikonal initial-state (CDW-EIS) approximation or Rudd's model. We then calculate the contribution of Auger postcollisional electron emission to MICS by using the Ne postcollisional emission probabilities. This postcollisional treatment offers a very simple alternative to the much more complex molecular evaluation of postcollisional relaxation and provides results in close agreement with experimental data for proton and other light ions. We also demonstrate the relevance of considering postcollisional emission for water molecules after the 2a(1) (2s Ne-like) orbital direct ionization.

Purpose In hadrontherapy, biophysical models can be used to predict the biological effect received by cancerous tissues and organs at risk. The input data of these models generally consist of information on nano/micro dosimetric quantities and, concerning some models, reactive species produced in water radiolysis. In order to fully account for the radiation stochastic effects, these input data have to be provided by Monte Carlo track structure (MCTS) codes allowing to estimate physical, physico-chemical, and chemical effects of radiation at the molecular scale. The objective of this study is to benchmark two MCTS codes, Geant4-DNA and LPCHEM, that are useful codes for estimating the biological effects of ions during radiation therapy treatments. Material and methods In this study we considered the simulation of specific energy spectra for monoenergetic proton beams (10 MeV) as well as radiolysis species production for both electron (1 MeV) and proton (10 MeV) beams with Geant4-DNA and LPCHEM codes. Options 2, 4, and 6 of the Geant4-DNA physics lists have been benchmarked against LPCHEM. We compared probability distributions of energy transfer points in cylindrical nanometric targets (10 nm) positioned in a liquid water box. Then, radiochemical species (center dot OH, eaq-${\rm{e}}_{{\rm{aq}}}<^> - $, H3O+,H2O2${{\rm{H}}_3}{{\rm{O}}<^> + },{\rm{\;}}{{\rm{H}}_2}{{\rm{O}}_2}$, H-2, and OH-)${\rm{O}}{{\rm{H}}<^> - }){\rm{\;}}$yields simulated between 10(-12) and 10(-6) s after irradiation are compared. Results Overall, the specific energy spectra and the chemical yields obtained by the two codes are in good agreement considering the uncertainties on experimental data used to calibrate the parameters of the MCTS codes. For 10 MeV proton beams, ionization and excitation processes are the major contributors to the specific energy deposition (larger than 90%) while attachment, solvation, and vibration processes are minor contributors. LPCHEM simulates tracks with slightly more concentrated energy depositions than Geant4-DNA which translates into slightly faster recombination than Geant4-DNA. Relative deviations (C-EV) with respect to the average of evolution rates of the radical yields between 10(-12) and 10(-6) s remain below 10%. When comparing execution times between the codes, we showed that LPCHEM is faster than Geant4-DNA by a factor of about four for 1000 primary particles in all simulation stages (physical, physico-chemical, and chemical). In multi-thread mode (four threads), Geant4-DNA computing times are reduced but remain slower than LPCHEM by similar to 20% up to similar to 50%. Conclusions For the first time, the entire physical, physico-chemical, and chemical models of two track structure Monte Carlo codes have been benchmarked along with an extensive analysis on the effects on the water radiolysis simulation. This study opens up new perspectives in using specific energy distributions and radiolytic species yields from monoenergetic ions in biophysical models integrated to Monte Carlo software.