Radiation biophysical modeling of the FLASH effect: from mechanistic understanding towards clinical endpoint prediction

Background Ultra-High Dose Rate (UHDR) or, commonly, FLASH irradiation is a novel dose-delivery technique based on fast beam release, with typically a total irradiation time < 100 ms and a total mean dose rate > 40 Gy/s for a single dose, usually higher than 10 Gy. Experimentally, compared to conventional dose rate (Conv) irradiation (typically, 0.03–0.1 Gy/s), the UHDR irradiation allows to obtain reduced side effects for normal tissue, for example, with reported evidence of a decrease in memory loss or less intestine necrosis, and, at the same time, the same effectiveness on tumor control, e.g., an indistinguishable tumor response for HBCx-12A xenografts. This FLASH sparing effect has also been confirmed in animals, e.g., no severe fibrotic lesions on mini pig skin. UHDR electron irradiation was successfully tested in a first patient with cutaneous lymphoma. Furthermore, the first clinical trial with proton-FLASH irradiation is ongoing. In addition to that, the FLASH effect has been observed across different radiation qualities, namely, particle types, energies, and linear energy transfer (LET). In particular, it has been demonstrated using electron LINACs, showed for UHDR irradiation a significant sparing of animals from cognitive deficits in learning and memory. The FLASH effect has been seen using proton beams, where the loss of proliferating cells in intestinal crypts or the acute skin damage and radiation-induced fibrosis was reduced at FLASH regime with respect to Conv, for the same tumor control. Lastly, this effect has been confirmed with ions, in particular with helium and carbon beams, both in-vitro and in-vivo. Despite a plethora of experiments supporting the FLASH effect, the biological mechanism underpinning it is still unclear and highly debated after 10 years from its discovery. Different possible explanations have been proposed, such as (i) transient hypoxia due to O2 depletion, (ii) organic radical recombination, (iii) inter-track effects, or (iv) the immune system-driven effect. However, some of these have been discredited by further experiments. Based on these mechanisms, several mathematical models have been proposed. However, most of these have been based on a single driving mechanism and have failed to fully explain the FLASH effect or to reproduce a significant part of the experimental data. For these reasons, this study is devoted to the development of a novel mechanistic approach to investigate the biological mechanism behind the FLASH effect. At the core of the mathematical model development is the hypothesis that the FLASH effect is due to a complex interplay of various spatio-temporal scales of the radiation damage action. Development of a multiscale radiation biophysical model for ultra-high dose rate (UHDR) investigations The first part of this study focused on the conception, realization, implementation, and validation of a multiscale stochastic radiobiological model for the study of the FLASH effect, based on beam irradiation at UHDR. From the experimental effort, an established consensus is arising in the community that the concurrent involvement of multiple scales of radiation damage is involved. In particular, the crucial role of the chemical environment and the redox system is underlined. For these reasons, we developed the MultiScale Generalized Stochastic Microdosimetric Model (MS-GSM2) [Battestini et al., 2023, Battestini et al., 2025a], a multi-stage extension of the Generalized Stochastic Microdosimetric Model (GSM2) [Cordoni et al., 2021, Cordoni et al., 2022b, Cordoni et al., 2022a, Bordieri et al., 2024]. The GSM2 is a probabilistic model that describes the time evolution of DNA lesions in a cell nucleus according to microdosimetric principles, without considering the Poissonian assumption to describe the number of radiation-induced DNA damage. The MS-GSM2 can investigate the combined effects of several chemical species and the formation and time evolution of DNA damage at the UHDR regime, incorporating the complex interplay between different levels of spatio-temporal stochasticity in physics, chemistry, and biology. In particular, our model includes the physical stage, allowing the description of the energy deposition by each single particle of a beam in a microscopic volume, which mimics the cell nucleus. The absorbed dose of every energy deposition event is distributed on the transverse plane of the cell nucleus using an Amorphous Track (AT) model, a parametrization of the radial dose distribution for a particle track hitting the target. The MS-GSM2 is capable of describing any dose-delivery time structures and radiation qualities, for particle, electron, and X-ray beams. Our model considers the homogeneous chemical stage, which consists of an optimized chemical reaction network of a pre-existing reaction kinetics model [Labarbe et al., 2020], described by five ODEs. The system involves reactions between chemical species derived from the water radiolysis and organic molecules, for example, radicals of nucleotides, proteins, and lipids, scavengers, such as vitamin E, thiols, and their derivatives, and those between organic species alone. The early pre-chemical and heterogeneous chemical stages are assumed to be instantaneous, and their final effect is incorporated in the model input. In particular, these two stages are described by the G-values, i.e., the number of chemical species produced per 100 eV of energy absorbed by the medium, of the production terms of chemical species in the ODEs’ system. The G-values were tabulated using a Monte Carlo particle track structure code. The MS-GSM2 takes into account the bio-chemical stage, which describes the connection between the energy deposited by ionizing radiation, the chemical environment of the cell, and the yield of biological damage. Since the oxygen is among the considered species in the chemical network, we include the impact of the oxygenation levels on the formation of DNA damage. We explicitly incorporate the reduction of radiation-induced DNA damage due to lower oxygen concentration. Starting from [Labarbe et al., 2020], we assume that UHDR irradiation modifies the chemical environment of the cell, reducing the accumulation in time of organic peroxyl radicals ROO•, and thus the cell toxicity. In fact, the persistence of ROO• in the cellular environment leads to biological damage [Labarbe et al., 2020]. For this reason, we link the different time evolution of the organic peroxyl radical concentration [ROO•](t) after Conv and UHDR irradiation with the number of indirect damage created, which implies a reduction in the indirect DNA damage yield only at UHDR regime. Thus, the indirect DNA damage yield decreases as the oxygenation level decreases and the dose rate increases. Lastly, the model includes the biological stage, which considers the possible repair of the radiation-induced DNA damages (the sub-lethal lesions), and the plausible presence of irreparable damages (the lethal lesions), at time t. In particular, the sub-lethal damage can go through three possible biological pathways: it can be left unrepaired and lead to cell inactivation, at rate a, it can interact with another sub-lethal lesion becoming a lethal one, at rate b, or it can be repaired, at rate r. The final biological endpoint predicted by the MS-GSM2 is the surviving probability of the cell, allowing a direct comparison of our model predictions with the experimental data. Comparison of the MS-GSM2 predictions with UHDR experiments and proposal of a new mechanism behind the FLASH effect We studied the impact of different physical parameters (radiation quality, dose, dose rate, and beam structure) on the emergence of the FLASH biological effect. The study was performed at the chemical level, analyzing the different time evolution of the organic peroxyl radical ROO• between conventional and UHDR irradiation; at bio-chemical level, studying the relative reduction in indirect damage per unit Gy between conventional and UHDR irradiation; at biological level, predicting the cell survival probability for both conventional and UHDR irradiation. We investigated the biological effect of different physical irradiation parameters, i.e., dose-delivery time structures and scanning pathways, for UHDR irradiation, calculating a look-up table in dose, dose rate, LET, antioxidant rate, and oxygenation level, through the MS-GSM2. We compared the MS-GSM2 predictions with all the main in-vitro experimental results at UHDR regime (DU145 cell line at 10 MeV electrons irradiation [Adrian et al., 2020], A549 cell line at 4.5 keV/µm helium ions irradiation [Tessonnier et al., 2021], CHO-K1 cell line at 13 keV/µm carbon ions irradiation [Tinganelli et al., 2022]), for different radiation quality, and oxygenation level. All the irradiation parameters (oxygenation, time structure, dose rates, doses, radiation quality, etc.) have been set as reported in the original publication. The three biological parameters (a, b, r) of the MS-GSM2 have been calibrated on the experimental data points at standard conditions, namely, conventional dose rate and normoxia (i.e., 21% oxygenation), while all the other points at different oxygenation levels and dose rates have been completely predicted. Thus, we showed remarkable accuracy through a wide range of radiation quality and oxygen concentration. FLASH irradiation, in a clinical perspective, would have a great impact, because it can be selective on healthy tissue and not on the tumor. However, no theory at the moment can fully explain this. In particular, one of the initially most accredited hypotheses (oxygen depletion) has now been largely discredited. For this reason, we proposed a new consistent mechanism for the FLASH differential effect observed in normal tissues and tumors, highlighting the crucial role of the redox environment. In particular, we analyzed the combined action of oxygenation and antioxidant environment on the emergence of the FLASH effect. From this analysis, we observed how, for a given oxygenation, the FLASH effect decreases for increasing antioxidant rate. Since tumors typically have higher antioxidant levels than healthy tissues, our hypothesis would justify the emergence of the FLASH effect only on normal tissues. Therefore, from our in-silico analysis, we underlined the fundamental role of combined effect of the environmental oxygenation level and the redox balance on the appearance of the FLASH effect. Thus, correlating tissue specificities to the onset and the severity of the effect. Therefore, the developed MS-GSM2 can consistently describe multiple aspects of the FLASH effect, reproducing the main evidence from the in-vitro experimental data. Development of a mechanistic-driven model for predicting healthy tissue complications and tumor control at Conv and UHDR regime. In the second part of this thesis, to target more clinically relevant endpoints, we focused on the conception, realization, implementation, and first validation of a mechanistic-driven Normal Tissue Complication Probability (NTCP) model and Tumor Control Probability (TCP) model for both Conv and UHDR irradiations. This study aims to extend the MS-GSM2 to clinically relevant biological endpoints, integrating the radiation biophysical model MS-GSM2 into the Relative Seriality Model [Källman et al., 1992] for NTCP and TCP predictions, allowing a comprehensive investigation of healthy tissue complications for conventional and UHDR irradiations. The MS-GSM2-driven NTCP model [Battestini et al., 2025b] considers single-cell resolution, allowing it to describe heterogeneity at the cell and tissue levels, considering different geometric and functional arrangements of cells, and gradients of oxygen concentration, but also effects due to different radiation quality. Moreover, the developed NTCP model can also account for different fractionation schemes of dose delivery. We investigated the impact of physical parameters (e.g., radiation quality, total dose, fractionation, partial irradiation), the chemical environment (e.g., oxygenation level), and the biological characteristics of the tissue (e.g., cell line, tissue architecture) on the emergence of possible complications in normal tissue for Conv irradiation. We applied our NTCP model to several experimental scenarios across various particles, in particular, protons, helium, and carbon ions, at both Conv, for example [Saager et al., 2018, Hintz et al., 2022, Karger et al., 2006], and UHDR regimes, such as [Sørensen et al., 2022]. The MS-GSM2-driven NTCP model described different dose-delivery fractionation schemes, e.g., for the rat spinal cord during Conv irradiation. Furthermore, it can reproduce the UHDR experiment with protons for mouse skin injury. Therefore, the developed NTCP model provide a mechanistic approach to calculate clinically relevant endpoints for both Conv and UHDR irradiation. Towards FLASH biological treatment planning. The final part of this work focused on possible extensions and improvements of the developed models to enable the clinical translation of FLASH radiotherapy from a computational point of view. The developed radiobiological model is fast, but, at the moment, it does not allow to optimize clinical plans because this would still require too much time. Since FLASH radiation therapy is very innovative and different from a conventional dose delivery approach, predictive models that are able to calculate the biological effect are needed to optimize FLASH treatment plans. Furthermore, compared to a conventional approach, it is not only the dose that counts but also the dose rate, and therefore it is necessary to predict the biological impact of the scanning pattern for the dose-delivery. So we need fast and efficient models that predict the FLASH effect to figure out the best treatment plan for UHDR irradiation. A fully mechanistic approach, while fundamental for basic understanding, is computationally expensive and, as a result, is currently impractical for biological optimization of treatment plans at FLASH dose rates. Indeed, a traditional optimization approach requires predicting biological outcomes for a huge number of parameters across various doses, dose rates, LET values, and oxygenation levels. Furthermore, even with fixed parameters, calculating the biological effect on a clinical treatment plan is too expensive. Thus, in our opinion, the first step towards enabling UHDR biological treatment planning is enhancing the mechanistic model using artificial intelligence (AI). Therefore, we developed an AI-enhanced mechanistic model, i.e., a surrogate model of the MS-GSM2, for a fast study of the FLASH effect in preclinical and clinical scenarios. We trained a neural network to replicate the biological outcome predicted by MSGSM2. This enables a rapid and comprehensive exploration of physical and physiological parameters related to the emergence of the FLASH effect. We combined the speed and predictive capability of AI with the robustness of a mechanistic-driven approach to overcome the previously calculated look-up table, by MS-GSM2, of biological outcomes across a wide range of physical, chemical, and biological parameters. So, this AI-enhanced MSGSM2, coupled with the previously proposed NTCP model, allows fast prediction of possible healthy tissue complications. Moreover, it allows us to study how different scanning patterns of dose delivery affect the dose rate and the resulting biological effect, considering various environmental conditions of the irradiated tissue. Therefore, the AI-enhanced MS-GSM2 can unleash significant breakthroughs in the clinical use of UHDR radiation. Conclusions and future perspectives. The current version of the MS-GSM2 accounts for DNA-damage-related death pathways, which probably play the main role in in-vitro biological systems. However, due to the great complexity of in-vivo biological systems, death pathways not mediated by DNA, such as ferroptosis, are known to contribute to the FLASH effect. For this reason, future effort is devoted to the inclusion of lipid peroxidation, which could influence the redox balance of a macroscopic biological system, thus contributing to the emergence of the FLASH effect. Regarding the clinical translation of FLASH radiotherapy, we are working on the development of a biologically-driven optimizer for UHDR treatment planning. We use the AI-enhanced MS-GSM2 to investigate the biological effect of different physical parameters, taking into account possible gradients in oxygen concentration. In summary, in this work, we developed a multiscale radiation biophysical model, i.e., the MS-GSM2, for in-vitro UHDR investigations. We integrated the MS-GSM2 into NTCP and TCP models for mechanistic-driven predictions of possible healthy tissue complications and tumor control probability at Conv and UHDR regimes. We enhanced the MS-GSM2 using AI for a fast and comprehensive investigation of the impact of physical, chemical, and biological parameters on the emergence of the FLASH effect. Thus, we proposed a consistent picture to get insight into the mechanism underpinning the FLASH effect. Further ongoing work focuses on the inclusion in the MS-GSM2 of alternative pathways to DNA damage and on the biological optimization of FLASH treatment plans.