Deciphering time dependent DNA damage complexity, repair, and oxygen tension a mechanistic model for FLASH dose rate radiation therapy

www.redjournal.org Physics Contribution Deciphering Time-Dependent DNA Damage Complexity, Repair, and Oxygen Tension: A Mechanistic Model for FLASH-Dose-Rate Radiation Therapy Hans Liew, MSc,*,y,z,x,k Stewart Mein, PhD,*,y,z,x Ivana Dokic, PhD,*,y,z,x Thomas Haberer, PhD,{ Juărgen Debus, MD, PhD,z,x,k,{,# Amir Abdollahi, MD, PhD,*,y,z,x and Andrea Mairani, PhD#,** *Clinical Cooperation Unit Translational Radiation Oncology, National Center for Tumor Diseases (NCT), Heidelberg University Hospital (UKHD) and German Cancer Research Center (DKFZ), Heidelberg, Germany; yDivision of Molecular and Translational Radiation Oncology, Department of Radiation Oncology, Heidelberg Faculty of Medicine (MFHD) and Heidelberg University Hospital (UKHD), Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg, Germany; zGerman Cancer Consortium (DKTK) Core-Center Heidelberg, German Cancer Research Center (DKFZ), Heidelberg, Germany; xClinical Cooperation Unit Radiation Oncology, Heidelberg Institute of Radiation Oncology (HIRO), National Center for Radiation Oncology (NCRO), Heidelberg University and German Cancer Research Center (DKFZ), Heidelberg, Germany; kFaculty of Physics and Astronomy, Heidelberg University, Heidelberg, Germany; {Heidelberg Ion-Beam Therapy Center (HIT), Department of Radiation Oncology, Heidelberg University Hospital, Heidelberg, Germany;#National Center for Tumor diseases (NCT), Heidelberg, Germany; and **National Center of Oncological Hadrontherapy (CNAO), Medical Physics, Pavia, Italy Received Aug 13, 2020, and in revised form Dec 4, 2020 Accepted for publication Dec 28, 2020 Purpose: Irradiation with ultrahigh dose rates (FLASH) has reemerged as a promising radiation therapy approach to effectively lower potential damage burden on normal tissue without sacrificing tumor control However, the large number of recent FLASH studies have been conducted under vastly different experimental conditions and circumstances (ie, investigated Corresponding author: Andrea Mairani, PhD; E-mail: Andrea Mairani@med.uni-heidelberg.de This work was supported by the German Research Council (DFGKFO214), Deutsche Krebshilfe, Germany (Max-Eder 108876), and intramural funds from the National Center for Tumor Diseases (NCT3.0_2015.21/22 NCT-PRO and Biodose programs), as well as a PhD stipend from the Helmholtz International Graduate School for Cancer Research in Heidelberg (to H.L.), The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript Disclosures: JD reports grants from CRIeThe Clinical Research Institute GmbH, View Ray Inc, Accuray International Sarl, Accuray Incorporated, RaySearch Laboratories AB, Vision RT Limited, Merck Serono GmbH, Astellas Pharma GmbH, Astra Zeneca GmbH, Siemens Int J Radiation Oncol Biol Phys, Vol -, No -, pp 1e13, 2021 0360-3016/$ - see front matter Ó 2021 Elsevier Inc All rights reserved https://doi.org/10.1016/j.ijrobp.2020.12.048 Healthcare GmbH, Merck KGaA, Solution Akademie GmbH, Ergomed PLC Surrey Research Park, Quintiles GmbH, Pharmaceutecal Research Associates GmbH, Boehringer Ingelheim Pharma GmbH Co, PTWFreiburg Dr Pychlau GmbH, and Nanobiotix AA, outside the submitted work AA reports grants and other support from Merck, EMD, Fibrogen, BMS, BioMedX, and Roche, outside the submitted work Data Sharing: Research data are stored in an institutional repository and will be shared upon request to the corresponding author Supplementary material for this article can be found at https://doi.org/ 10.1016/j.ijrobp.2020.12.048 AcknowledgmentsdWe thank Dr Kristoffer Petersson and Dr Gabriel Adrian for sharing the raw cell survival data as a function of oxygen concentration 2 Liew et al International Journal of Radiation Oncology  Biology  Physics biological endpoint, radiation quality, and environmental oxygen level), with unverified biological mechanisms of action and unexplored interplay effect of the main dependencies To facilitate radiobiological investigation of FLASH phenomena and assessment of clinical applicability, we present an extension of the mechanistic radiobiological model “UNified and VERSatile bio response Engine” (UNIVERSE) Methods and Materials: The dynamic (time-dependent) extension of UNIVERSE was developed incorporating fundamental temporal mechanisms necessary for dose-rate effect prediction, ie, DNA damage repair kinetics [DDRK], oxygen depletion and reoxygenation during irradiation Model performance in various experimental conditions is validated based on a large panel of in vitro and in vivo data from the literature The effect of dose, dose rate, oxygen tension, tissue-type, beam quality and DDRK is analyzed Results: UNIVERSE adequately reproduces dose-, dose-ratee and oxygen tensionedependent influence on cell killing For the studied systems, results indicate that the extent of cell/tissue sparing effect, if present at all, strongly depends on DDRK and beam quality used for reference conventional irradiation A validated mechanistic framework for predicting clinically relevant endpoints comparing conventional and FLASH high-dose-rate effect has been successfully established, relying on time-dependent processing of radiation-induced damage classes taking variable oxygen tension into account Conclusions: Highlighted by UNIVERSE itself, the multidimensional nature of this relative sparing effect using high-doserate radiation compared with conventional means underlines the importance of robust quantification of biophysical characteristics and consistent, well-documented experimental conditions both in vitro and in vivo before clinical translation To further elucidate underlying mechanisms and appraise clinical viability, UNIVERSE can provide reliable prediction for biophysical investigations of radiation therapy using ultrahigh dose rate Ó 2021 Elsevier Inc All rights reserved Introduction Irradiation with ultrahigh dose rates (>>10 Gy/s) has reemerged as a promising therapeutic tool affording clinical conditions where elevated normal tissue radio-resistances are observed Although initial studies date back to the 1960s,1-3 interest was recently reignited by multiple publications reporting significant sparing of normal tissue while maintaining bioeffect in the tumor with application of high dose levels at high dose rates compared with conventional radiation therapy using low dose rate, known as the FLASH effect.4,5 Experimental data in the literature, however, entail highly diverse biological endpoints ranging from in vitro cell survival with human cells6 and zebrafish embryos4 to neurocognitive functionality of mice after whole-brain irradiation7-9 and tail necrosis in mice.10 Furthermore, institutions have applied differing radiation sources such as 102 keV x-rays,8 10 MeV electrons,6,10 and 224 MeV protons.11 Sparing effects have been reported at doses between 10 and 50 to 75 Gy, and applying dose rates from w 106 Gy/s down to w10 Gy/s.7-10 Moreover, conventional radiation sources used a reference range from a Cs-137 source with a dose rate of 0.03 Gy/s12 up to a 10 MeV electron source with a dose rate of 0.23 Gy/s,6 and oxygenation readings of radiobiological setups are often unreliable In short, experimental conditions of reported data on the FLASH effect are subject to great variability, and it is therefore challenging to unravel the underlying dependencies and define explicit clinical parameters The mechanisms that induce differential sparing between normal tissue and tumors remain highly debated.13 However, the radiochemical depletion of oxygen via high dose-rate delivery and resulting transient hypoxia causing radio-resistance (oxygen depletion effect) is commonly considered to explain sparing in general.1,4 Based on this hypothesis and/or other dose-rateedependent radiochemical mechanisms, such as radical recombination, models have recently been established to describe bioeffects at FLASH dose rate.14-16 Nonetheless, quantitative benchmarks of these models are limited or lacking completely In essence, experimental results regarding the FLASH effect describe differing biological endpoints obtained under vastly different settings To date, there is an absence of cohesive and extensively benchmarked approaches to model all relevant conditions of biological systems when exposed to FLASH dose rates, crucial for facilitating assessment of the underlying mechanisms To this end, the “UNIfied and VERSatile bio response Engine” (UNIVERSE) is a mechanistic model for predicting response of biological systems to ionizing radiation through consideration of several key conditions.17-19 In this work, time-dependent processing of radiation-induced DNA damage,20,21 oxygen depletion, and reoxygenation mechanisms14 are implemented toward accurate prediction of biological response over a broad range of conventional and ultrahigh (FLASH) dose rates Moreover, UNIVERSE is benchmarked against in vitro and in vivo data from the literature, obtained under various experimental conditions Physical, biological, and clinical implications of the UNIVERSE to support consistent planning and conduction of much needed foundational experimental studies of FLASH bioeffect are explored Methods and Materials UNIVERSE is a mechanistic model for biological response to ionizing radiation based on interaction with biological Volume -  Number -  2021 substructure and cell functionality The time dependent, or “dynamic,” version of UNIVERSE is introduced in this work, extended from its time-independent, or “static,” predecessor presented in previous publications,17-19 which we will briefly recall as follows: In the case of sparsely ionizing radiation (eg, x-rays, gamma rays, electrons), the dose deposition throughout the cell nucleus is assumed to be homogeneous The number of DNA double strand breaks (DSB), considered the most impactful type of DNA lesion,22 can be calculated using a cell-line independent DSB yield of aDSB Z  10À3 DSB⁄ ððMbp  GyÞ Þ.23,24 Assuming this yield to be constant over the clinically applied dose range, the expected total number of DSB (hNtDSB i) can be expressed as: ð1Þ hNtDSB i Z aDSB  D  DNAc where DNAc is the DNA content of a cell (w6000 mega base pairs [Mbp]) and D the applied dose in units of Gy Low-energy photon radiation sources have been found to induce a larger amount of DSBs for the same physical dose applied, compared with photon radiation sources with higher energy.25 To account for this change in effectiveness, the DSB yield aDSB may be modified by a relative biological effectiveness factor (RBEDSB ) In the mechanistic view of UNIVERSE, a certain type of chromatin substructure, so-called giant loops of about Mbp of DNA,26-28 play a central role in classifying local distributions of DSBs Multiple DSBs inside such giant loops are repaired significantly slower29,30 and are associated with an increased lethality for the cell due to the high risk of chromatin loss.31 Classifying giant loops containing exactly lesion as isolated DSB (iDSB) and or more lesions as complex DSB (cDSB) can accurately predict populations of swiftly and slowly repairing lesions in rejoining studies.32,33 UNIVERSE shares this classification of lesions with other models.34,35 The total number of giant loops (Ngl ) having a DNA content of DNAgl is given by: DNAc Ngl Z ð2Þ DNAgl Following a Monte Carlo approach, the actual total number of DSB induced in the nucleus (NtDSB ) is sampled for > 104 iterations based on a Poisson distribution with the expectation value from Equation (1) For each iteration, the sampled amount of DSBs is then distributed randomly over the giant loops contained in the nucleus Thereafter, the number of giant loops with DSB (NiDSB ) or and more DSB (NcDSB ) are counted The lethality parameters KiDSB and KcDSB describe the probabilities of one isolated DSB or complex DSB lead to cell inactivation, respectively The ultimate probability of a cell surviving the irradiation (S) is then given by18,31: N N S Z ð1 À KiDSB Þ iDSB ,ð1 À KcDSB Þ cDSB : ð3Þ The average value of S over all iterations is used to predict the surviving fraction of the cell population The FLASH-dose-rate radiation therapy in the dynamic UNIVERSE cell-line dependent parameters KiDSB and KcDSB are derived by fitting the model to data of cell survival In the static UNIVERSE, a change in the oxygen level can be accounted for by solely reducing the DSB yield by a O2 hypoxia reduction factor (HRFDSB ), which resembles the classical oxygen enhancement ratio (OER), while the lethality parameters are assumed to be invariant.17-19 The reduced DSB yield, aO DSB ; can be expressed by: aODSB Z aDSB O2 HRFDSB ð4Þ If both hypoxic and normoxic data are available, O2 HRFDSB can be determined by fitting the model to both datasets, while KiDSB and KcDSB are kept constant If only O2 normoxic or hypoxic datasets are available, HRFDSB for a given oxygen concentration ½O2 Š is estimated using an empirical parametrization: m$K ỵ ẵO2 O2 : 5ị HRFDSB Z K ỵ ẵO2 introduced in an earlier publication17 following previous works.36,37 Due to the variety of endpoints included in the study and the distinct approaches to their analysis, an automized global fitting of the parameters m and K was not feasible in the scope of this work Instead, the values derived in a previous publication17 were adapted and the values m Z 3.1 and K Z 0.27 were found to be suitable for the investigated datasets However, the dataset of Epp et al38 was best described with the values m Z 3.4 and K Z 0.41 The effect of the chosen values of m and K on the DSB yield as function of ½O2 Š is shown in Figure E1 The paragraphs above described the time-independent (static) version of UNIVERSE From here forward, the temporal extension of UNIVERSE will be described In the resulting dynamic version of UNIVERSE, the total irradiation time (Trad ) is divided into several sequential timesteps (Nt Z 100) The relationship between applied dose _ total applied dose (D) and total irradiation time is rate (D), given by: D Trad Z ð6Þ D_ The damage pattern induced by the partial dose applied at a given time-step, Dpart Z NDt ; is computed analogously to the static UNIVERSE described earlier However, to account for possible oxygen depletion and reoxygenation occurring during irradiation, the oxygen level at the current time-step OðtÞ is determined using14:     l l _ OðtÞ Z Oenv ỵ egDỵlịt 7ị gD_ ỵ l gD_ ỵ l where t is the time passed since the start of the irradiation, Oenv is the environmental oxygen level ([O2]) at tZ 0; g is the depletion rate constant, and l is the reoxygenation constant Values from Petersson et al14 for in vitro analysis, gZ 0:053 GyÀ1 and lZ sÀ1 ; were adopted The timedependent oxygen concentration OðtÞ was used to calcuO2 late the current hypoxia reduction factor HRFDSB ðtÞ Liew et al following equation 5, effectively modifying the oxygen dependent radiosensitivity of the cells in real-time Using equations and 1, one can compute the reduced number of DSBs to be distributed at each time-step The resulting trend of DSB yield as a function of irradiation time is depicted in Figure E1 To model the time-dependent repair process of induced damage in the cell nucleus, each iDSB and cDSB is attributed a random lifetime drawn from an exponential 1=2 1=2 distribution based on repair half-life times TiDSB and TcDSB ; respectively These half-life times can be obtained either from literature (eg, biexponential fits to DSB repair kinetics32) or fitted to available data If by the application of a partial dose at a given time-step, any number of DSB is added to a giant loop that harbors exactly one DSB (iDSB), it is reclassified as a cDSB and a new lifetime is drawn 1=2 based on TcDSB : At every time-step, any damage that has exceeded its lifetime is removed from the damage pattern However, when such a repair event takes place, there is a probability equal to the values of KiDSB for isolated DSB and KcDSB for cDSB to trigger a “misrepair” event that sets the survival probability of this cell (or rather Monte Carlo iteration) to zero This approach ensures the consistency of the model when repair processes are considered over a large period of time Key concepts of the implementation described here had been introduced and validated in works by Herr et al.20,21 In our implementation, if by the end of the irradiation time no lethal event was triggered due to the failure of a repair process, the survival probability of the given Monte Carlo iteration is calculated using Equation Again, the survival fraction of the population is determined by the mean value of the survival probabilities determined by each Monte Carlo iteration A fully mechanistic prediction of in vivo effects postirradiation would pose a considerable jump in complexity from the already challenging description of cell populations in vitro However, to explore the principle possibilities of UNIVERSE to provide estimates on higher level systems, major simplifications and assumptions were made to predict in vivo endpoints, without explicit mechanistic description of the transition from in vitro to in vivo Bhouris et al have reported the effect of different dose rates of radiation on the growth delay of tumors with the expression À VVrad ; where Vrad is the volume of the tumor ctrl measured 15 days postirradiation, while Vctrl is the volume of untreated tumors after the same period.39 In this work, we describe this value as the relative tumor volume suppression (RTVS), and heuristically approximate the ratio VVrad to be ctrl given by the survival fraction of the cell population within the irradiated tumor leading to the assumption RTVS Z À S: For approximation of ND50 and LD50, the dose at which 50% of mouse tails show radionecrosis as reported by Hendry et al10 and mice that died within days after wholebody irradiation as reported by Hornsey et al,40,41 respectively, we assumed both to be equal to the dose at 50% survival fraction International Journal of Radiation Oncology  Biology  Physics For in vivo data, lethality parameters remain as free parameters for each endpoint but can be reinterpreted as the probability of each damage class to ultimately trigger radio-necrosis or death of the mouse, respectively Results Survival over dose rate To investigate and survey general effect of different conditions and parameters considered in the model on predicted trend of the dose-rate effect, survival fraction was computed over a range of dose rates (0.01 Gy/s to 104 Gy/s) with several representative inputs for a given model parameter, while all other parameters are fixed to certain values These fixed values were chosen such that trends of interest are clearly visible (eg, enough dose to induce sufficient oxygen depletion) while remaining within the range of experimentally relevant values During analysis, lethality parameters were set for demonstrative purposes to values found for the DU145 cell-line obtained from Adrian et al6 (Table 1) Total dose Figure 1A displays predictions for various total applied 1=2 1=2 dose levels TiDSB Z 30 minutes, TcDSB Z hours, and [O2] Z 2.5 % were chosen as fixed values A general trend of increased cell killing up to dose rates of about Gy/s was observed before survival increases up to roughly hundreds of Gy/s after which survival plateaus for the given settings However, this trend is progressively pronounced with increasing total delivered dose and not observable for the lowest dose levels (2 and Gy) Environmental oxygen level Figure 1B depicts the effect of different oxygen levels ([O2]) on survival prediction with the following fixed set1=2 1=2 tings: total dose of 16 Gy, TiDSB Z 30 minutes and TcDSB Z hours Results indicate that [O2] substantially influences sparing effects at higher dose rates Given the settings, significant survival increase (beginning at w1 Gy/s) was observed only for intermediate [O2] at 7.5%, 2.5%, and 1% For normoxia (20%) and severe hypoxia (0.1%) and anoxia (0.01%), no significant sparing at higher dose rates was observed with the selected parameters Moreover, increasing [O2] increased the slope of the initial decrease of survival at lower dose rates Repair half-life times In Figure 1, C and D, predictions are shown for different repair half-life times of isolated and complex DSB, respectively, with the following fixed settings: total dose of 1=2 1=2 16 Gy and [O2] of 2.5% With variable TiDSB ; TcDSB was set 1=2 1=2 to hours, whereas for variable TcDSB ; TiDSB was set to 30 1=2 minutes Figure 1C makes evident that the effect of TiDSB is Volume -  Number -  2021 Table FLASH-dose-rate radiation therapy in the dynamic UNIVERSE Model parameters of UNIVERSE applied in this work K iDSB K cDSB T 1=2 iDSB [min] 1=2 T cDSB [min] m K 5.9E-3 6.7E-3 5.9E-3 0.9E-3 0.17E-3 0.1E-3 0.19 0.21 0.17 0.095 0.006 0.065 80.22 14 60 60 300 130 100 300 300 300 3.1 3.4 3.1 3.1 3.1 3.1 0.27 0.41 0.27 0.27 0.27 0.27 Endpoint 42,43 In vitro survival (CHO) In vitro survival (HeLa)38 In vitro survival (DU145)6 RTVS (U87 xenograft)39 Mice tail radionecrosis10 LD50 whole-body irradiation mice40,41 Abbreviations: CHO Z Chinese hamster ovary A B 10-1 10-1 Survival Survival 10-3 10-5 10-3 10-5 10-7 Gy Gy 16 Gy 10-9 10-2 10-1 100 101 102 Dose Rate [Gy/s] 24 Gy 32 Gy 10-7 103 104 C pO2 2.5% pO2 7.5% pO2 20% pO2 0.01 % pO2 01 % pO2 % 10-2 10-1 100 101 102 Dose Rate [Gy/s] 103 104 D 10-2 Survival Survival 10-2 T1/2 iDSB mins T1/2 iDSB 15 mins T1/2 iDSB 30 mins T1/2 iDSB 45 mins T1/2 iDSB 60 mins 10-3 10-2 10-1 100 101 102 Dose Rate [Gy/s] 103 104 T1/2 cDSB hour T1/2 cDSB hours T1/2 cDSB hours 10-3 10-2 10-1 100 101 102 Dose Rate [Gy/s] 103 104 Fig Effect of different model parameters: dose (A), environmental oxygen level (B), repair halftimes for isolated double strand breaks (iDSB) (C), and complex double strand breaks (cDSB) (D) (A) Initial decrease of the survival fraction is followed by onset of a sparing effect No such effect is observed for lower doses (2 and Gy) (B) Onset of significant sparing is only visible at intermediate oxygen levels (7.5%, 2.5%, and 1%) (C) Effect is larger with lower dose-rates, with shorter half-lives increasing the survival No effect is seen above w1 Gy/s for the applied values (D) Half-lives of cDSB have no effect on survival in the given dose-rate range for the chosen values 6 International Journal of Radiation Oncology  Biology  Physics Liew et al 1=2 highest under w1 Gy/s In this region, a shorter TiDSB leads to increasing slopes in survival for decreasing dose rates At 1=2 dose rates higher than w10 Gy/s, the effect of TiDSB 1=2 diminishes In contrast, TcDSB does not seem to affect survival for the dose rates and parameters comparable to those used in this study Benchmark against in vitro data Numerical values of applied model parameters for the following datasets are presented in Table Survival of Chinese hamster ovary cells under various radiation qualities and in split dose experiments Figure 2A shows Chinese Hamster Ovary (CHO) cell survival after irradiation with a Co-60 source (0.01 Gy/s), single ns pulses of w450 keV electrons, and 280 kVp x-rays (0.033 Gy/s) collected from Michaels et al42 with corresponding model predictions Figure 2, B and C, display CHO cell survival after irradiation with fractions of the same pulsed electron source and x-ray source at various doses with different separation times43 against model prediction, which are normalized (at t Z 0) to account for statistical deviation and highlight time evolution of survival An RBEDSB of 1.2 was set for the 280 kVp A x-rays.43 Using the repair half-life times of CHO cells found in the literature,20 the number of isolated and complex DSB were simulated for 3ns pulses over the analyzed dose range Based on these values, the lethality parameters were fit to the measured survival data using the curve_fit routine of the scipy library for Python This makes fitted free parameters (both lethality parameters), globally set O2 parameters (HRFDSB parametrization), and parameters taken from literature (both repair half-life times and the RBEDSB ) for the predictions of this dataset The R2 values (coefficient of determination) for the prediction of the Co60, electrons and x-ray survival data (Figure 2A) were determined to be 0.98, 0.98, and 0.99, respectively While Co-60 and the 3ns electron pulses show near identical effect, an increased bioeffect for 280 kVp radiation is clearly visible The mean relative difference between measured and predicted survival (excluding the timepoint at minutes) for the split doses of electrons (Fig 2B) and xrays (Fig 2C) were 3.5% and 10%, respectively Survival of HeLa cells after irradiation with single 3ns electron pulses under different oxygen levels Figure presents survival of HeLa cells postirradiation with single 3ns pulses of w350 keV electrons at various [O2] taken from Epp et al38 and respective model B Split Dose, 3ns e-Pulses 10-1 100 5.85 Gy + 5.85 Gy -2 10 Survival 6.9 Gy + 6.9 Gy 10-1 7.2 Gy + 7.2 Gy 10-3 Model Data -4 Survival 10 10-2 20 40 60 80 100 120 140 Time [min] C Split Dose, 280 kVp X-Rays 10-1 5.0 Gy + 5.0 Gy Survival 10-2 10-3 Model Co-60 Model ns e-Pulses Model 280 kVp Data Co-60 0.01 Gy/s Data ns e Pulses Data Xrays 280 kVp 0.033 Gy/s 10-4 0.0 2.5 5.0 7.5 10.0 Dose [Gy] 12.5 5.5 Gy + 5.5 Gy 10-3 Gy + Gy 15.0 17.5 10-4 20 40 60 80 100 120 140 Time [min] Fig Effect of radiation quality ad repair kinetics in split dose experiments (A) Chinese hamster ovary (CHO) cells survival after irradiation with a Co-60 source (0.01 Gy/s), single ns pulses of w450 keV electrons42 and 280 kVp x-rays (0.033 Gy/s),43 with respective simulations by UNIVERSE RBEDSB of 1.2 was applied to the x-ray simulation (B and C) Survival of CHO cells after irradiation with fractions of w450 keV electrons (3 ns pulses) and 280 kVp x-rays (0.033 Gy/s) with different split doses and various times in between,43 with respective simulations by UNIVERSE The simulations by UNIVERSE were normalized to the data point at t Z 0: Volume -  Number -  2021 predictions Furthermore, to illustrate the effect of oxygen depletion (OD) and reoxygenation (RO) kinetics, an additional prediction is shown with both mechanisms deactivated The repair half-life times were taken from the literature44 and used to calculate the number of iDSB and cDSB under normoxic conditions within the analyzed dose range Using these values, both lethality parameters were fit to the normoxic survival data (Fig 3A) applying the curve_fit command of the scipy library for Python This results O2 in free parameters (if we add the HRFDSB parameters that deviate from the global parametrization of the other datasets to the fitted lethality parameters) and parameters taken from literature (both repair half-life times) for the predictions of this dataset The resulting mean R2 value for the data in Figure was determined to be 0.73 Although no effect of the OD and RO mechanisms are visible for the normoxic and anoxic cases, a significant elevation in survival was observed for these mechanisms under hypoxic conditions The sparing effect becomes visible at w10 Gy and subsequently increases for higher dose levels Survival of DU145 cells under distinct dose rates and oxygen levels Figures 4, A and B, depict DU145 cell survival postirradiation with low (0.23 Gy/s) and high (600 Gy/s) dose rates of 10 MeV electron radiation gathered from Adrian et al6 alongside UNIVERSE predictions under normoxia (20% oxygen) and hypoxia (1.6% oxygen) The repair halflife times for DU145 cells were taken from the literature45 and used to predict the number of iDBS and cDSB for the high dose rate and normoxic situation These values were used to fit both lethality parameters to the measured survival data with the curve_fit command of the scipy library for Python Thus, for the predictions for this dataset, we have fitted free parameters (both lethality parameters), O2 globally set parameters (HRFDSB parametrization), and parameters taken from literature (both repair half-life time) The R2 value of the model prediction was found to be 0.99 for the low and high dose rate under normoxia (Fig 4A), as well as under hypoxia (Fig 4B) Predicted survival for the dose rates are essentially indistinguishable up to w10 Gy At higher doses, UNIVERSE correctly reproduces higher survival for high dose rate under hypoxia as observed in the data On the contrary, in normoxia, a slight increase in survival for the lower dose rate is predicted at higher applied doses However, this effect lies within the error margins of the data, which largely overlap for both dose rates In Figure 4C, DU145 survival measurement and prediction are presented under different [O2] levels after irradiation with 18 Gy using the same beams and parameters as described earlier The bounds of the UNIVERSE predictions correspond to the lowest and highest experimentally measured doses of each dose rate (low dose rate: 18.0-18.2 Gy; high dose rate: 17.0-19.0 Gy [personal communication, Petersson, April 2020]) A sparing effect is predicted at intermediate [O2] levels, whereas at upper and lower boundaries, both dose rates converge The data of the FLASH-dose-rate radiation therapy in the dynamic UNIVERSE low dose-rate radiation are predicted well for hypoxic [O2] levels, whereas the normoxic data point appears to be overestimated In contrast, survival of high dose rate appears slightly underestimated by UNIVERSE at intermediate [O2] levels However, predictions lie within the large error margins of the corresponding data Benchmark against in vivo data Relative tumor growth supression of U87 xenografts in mice Figure 5A shows measured RTVS of tumors based on U87 human glioblastoma cells engrafted subcutaneously in mice postirradiation with to MeV electrons at conventional dose rates (0.1 Gy/s) and at high dose rates (between 125 Gy/s and single pulse of 1.8 ms) from Bourhis et al,39 with respective UNIVERSE simulations Findings (Fig 1D) suggest the negligible effect of the chosen repair half-life times of complex damages on the overall effect, thus we set its value to hours in cases in which no literature values were available, simplifying the determination of the remaining parameters.20 Both lethality parameters and the repair half-life time of the isolated lesions were determined simultaneously based on the analysis of c2 values, comparing the predictions against the low dose-rate data A [O2] of 1% was assumed based on literature values for xenografts.46 Ultimately, we have free parameters (both lethality parameters and the repair half-life time of the O2 isolated lesions), globally set parameters (HRFDSB parametrization), and parameters set according to literature (oxygen tension and repair half-life time of complex lesions) for the predictions of this dataset R2 for the model predictions of the RTVS was determined to be 0.99 and 0.96 under low- and high-dose-rate conditions, respectively A slight sparing effect for the higher dose rate is visible between w10 and w30 Gy ND50 of mouse tail radionecrosis: dose-rate dependence ND50 (dose required to produce necrosis in half of the cohort) of mouse tail radionecrosis over the dose rate of 10 MeV electrons, as measured by Hendry et al10 and respective UNIVERSE predictions are shown in Figure 5B In one case, the system is oxygenated, whereas in the other, the mouse tail was under an anoxic atmosphere and clamped to minimize blood flow Following the arguments described earlier, the repair half-life time for the complex DSB was set to hours Both lethality parameters and the repair half-life time of the isolated DSB were determined as described in the supplementary material (Fig 3E) Exact values of the oxygen status in both cases were unknown, but oxygen levels of 0.4% and 0.12% for the oxygenated and clamped situation, respectively, were found to appropriately describe trends within a reasonable range.10,47 For the predictions of this dataset, we used free parameters (both lethality parameters, the repair half-life time of the isolated lesions and the oxygen tension) and parameters set based on the literature (repair half-life time of the International Journal of Radiation Oncology  Biology  Physics Liew et al A B 101 Model with OD/RO Model no OD/RO 100 100 10-1 10-1 Survival Survival 101 Data 10-2 10-2 10-3 10-3 O2 = 21% 10-4 10 20 30 40 Dose [Gy] 101 D 101 100 100 10-1 10-1 10-2 30 40 30 40 30 40 10-3 O2 = 0.77% 10-4 10 O2 = 0.59% 10-4 20 30 40 Dose [Gy] 20 Dose [Gy] F 101 10 101 100 100 10-1 10-1 Survival Survival 20 Dose [Gy] 10-2 10-3 E 10 Survival Survival C O2 = 0.91% 10-4 10-2 10-2 10-3 10-3 O2 = 0.26% 10-4 10 O2 = 0% 10-4 20 30 Dose [Gy] 40 10 20 Dose [Gy] Fig Effect of environmental oxygen status and the oxygen depletion/reoxygenation mechanism (A-F) HeLa survival after irradiation with single 3ns pulses of w350 keV electrons38 at various environmental oxygen levels and respective simulations by UNIVERSE (solid line) To illustrate the effect of implementing the oxygen depletion/reoxygenation mechanism, the dotted line shows the simulation results with both mechanisms deactivated An effect is visible above w10 Gy for hypoxic cases (B-E), whereas normoxic (A) and anoxic (F) scenarios are evidently not affected by the oxygen depletion mechanism complex lesions and RBEDSB ) The mean relative differences between the measured and predicted ND50 were determined to be 6.2% and 0.3% for the oxygenated and clamped situation, respectively LD50 (4 days) of whole-body irradiation of mice: doserate dependence LD50 (dose at which 50% of the subjects have died after a given period of time; here t Z days) is shown in Figure 5C for whole body irradiation of mice with w8MeV electron and 250kVp x-ray sources (as above: RBEDSB Z 1.2) measured by Hornsey et al40,41 over a range of dose rates with respective UNIVERSE prediction Following the same reasoning as described above, the repair half-life time for the complex lesions was set to hours Again, both lethality parameters and the repair half-life time of the isolated lesions were determined based on the c2 value of the predictions as KiDSB Z 10 À4, KcDSB Z 0.065 and Volume -  Number -  2021 A B DU 145, Normoxia 101 10-1 -2 Survival 10-1 Survival Survival DU 145, variable O2 100 Model 0.23 Gy/s Model 600 Gy/s Data 0.23 Gy/s Data 600 Gy/s 100 10-1 10 C DU 145, Hypoxia (1.6 %) 101 Model 0.23 Gy/s Model 600 Gy/s Data 0.23 Gy/s Data 600 Gy/s 100 FLASH-dose-rate radiation therapy in the dynamic UNIVERSE -2 10 10-2 10-3 10-3 10-3 10-4 10-4 10-5 0 10 10-5 25 20 15 Dose [Gy] 10-4 30 10 20 15 Dose [Gy] 25 30 10-5 10-3 Model 0.23 Gy/s Model 600 Gy/s Data 0.23 Gy/s Data 600 Gy/s 10-2 10-1 100 O2 concentration [%] 101 Fig Sparing effects in hypoxic conditions DU145 survival after irradiation with conventional (0.23 Gy/s) and high dose rate (600 Gy/s) of 10 MeV electron radiation under normoxia (20% [O2]) (A), hypoxia (1.6% [O2]) (B) and different oxygen levels after irradiation with 18 Gy (C),6 with corresponding predictions by UNIVERSE Upper and lower bounds in (C) represent range of measured doses A B RTVS of U87 Xenografts in Mice C ND50 Mice Tail Necrosis 90 20 100 LD50 of Mice Whole-Body-Irradiation 18 80 16 80 60 14 LD50 [Gy] ND50 [Gy] RTVS [%] 70 60 12 10 40 50 Model 0.1 Gy/s Model 125 Gy/s Data 0.1 Gy/s Data 125 Gy/s 20 0 10 15 20 25 Dose [Gy] 30 35 Model Air Model Clamping + N2 Data Air Data Clamping + N2 40 30 10-1 100 101 Dose-rate[Gy/s] 102 10-3 Model electrons Model x-rays Data electrons Hornsey & Alper 1966 Data electrons Hornsey & Bewley 1971 Data x-rays Hornsey & Alper 1966 10-2 10-1 100 Dose-rate[Gy/s] 101 102 Fig Effect of dose rate on in vivo endpoints (A) relative tumor volume suppression (RTVS) measured in U87 human glioblastoma engrafted subcutaneously in mice, after irradiation with to MeV electrons at conventional dose-rates (red: 0.1 Gy/s) and ultrahigh dose-rates (black: between 125 Gy/s and pulse of 1.8 ms),39 with respective simulations by UNIVERSE An oxygen level of 1% was assumed in the xenograft (B) ND50 of mice tail necrosis with different dose rates of 10 MeV electrons10 in an oxygenated (blue) and anoxic environment (green: N2 ỵ clamping of tail) with corresponding descriptions by UNIVERSE (C) LD50 after whole-body-irradiation of mice with either 250kV x-rays (purple) or w8 MeV electrons (orange) over a range of dose-rates40,41 and respective predictions by UNIVERSE For consistency in defining and interpreting the investigated endpoint (with tLD50 Z days), the data for LD50 (tLD50 Z days) reported by Hornsey and Bewley41 (square) has been normalized to the corresponding LD50 at the same dose-rate (A color version of this figure is available at https://doi.org/10.1016/j.ijrobp.2020.12.048.) 1=2 TiDSB Z minutes, respectively An oxygen tension of 3% was found to describe data best, fitting the expected O2 level range.46,47 Thus, we used free parameters (both lethality parameters, the repair half-life time of the isolated lesions and the oxygen tension) and parameters set based on literature (repair half-life time of the complex lesions and RBEDSB ) The mean relative differences between the measured and predicted LD50 for the electron source were determined to be 4.3% Discussion An extension of the mechanistic biomodeling framework UNIVERSE is introduced, implementing time-dependent 10 Liew et al repair of DSB lesions and oxygen depletion as well as reoxygenation mechanisms, expanding the capabilities of UNIVERSE to predict the dose-rate-dependent bioeffect from lower conventional (clinical) settings up to ultrahighrate delivery The effect of different parameters on general survival trends as a function of dose rate are presented and discussed first, providing an overview of FLASH dependencies and context for discussion of UNIVERSE development and validation Evolution of survival with dose rate exhibited by most curves in Figure can be explained by mechanisms: (1) an initial survival decrease at lower dose rates is driven by the reduced repair of DSB taking place during the shortening irradiation times (“classical” dose-rate effect48) and (2) a subsequent survival increase can be attributed to the onset of the oxygen depletion effect As for the latter, to trigger this effect a sufficiently high dose rate is needed to deplete oxygen quicker than it is replenished in the system Furthermore, even without reoxygenation mechanisms, a specific dose level (ie, dose-threshold) is necessary to deplete enough oxygen to induce a sparing effect.14 Survival plateaus because irradiation times become virtually instantaneous, allowing no intraradiation repair and limiting the ability of elevated dose rates to deplete more oxygen The dose-rate range in which we find the survival increasing (w5-100 Gy/s) and the doses needed to observe substantial sparing (8-16 Gy) in Figure 1A fit well with observations made in in vivo experiments: significant sparing effects have been mostly reported at doses !10 Gy and dose rates greater than w40 Gy/s.4,5 The observed dose-rate region of the survival increase is also in agreement with a dimensional analysis by Zhou et al,49 which predicts the order of magnitude of the minimum dose rate to observe a sparing effect in the range of 10 to 100 Gy/s However, even for less complex cases of in vitro effects, one cannot give a precise and simultaneously general prediction concerning dose and dose-rate thresholds and whether a sparing effect in comparison to conventional dose rates can be observed Not only are thresholds highly dependent on assumed oxygen kinetics,14 but a sparing effect relative to conventional dose rates is dependent on several parameters One of the major parameters is the [O2] level (Fig 1B) The observation of no significant oxygen depletion effect at normoxic and anoxic environments in this work is further supported by experimental data in the literature, reporting no sparing effects in systems with known normoxic4,6,41,50 and anoxic50 conditions Furthermore, this effect is predicted by existing quantitative oxygen depletion effect models.14,15 Absence of a sparing effect at normoxia can be explained by the large doses required to deplete enough oxygen to observe significant radioprotection, whereas at the lowest oxygen concentrations, the absolute amount of possible depletion is insufficient to observe any change in radiosensitivity.4,5,14 Another possible influence is the selected dose-rate level of the reference radiation More specifically, one could International Journal of Radiation Oncology  Biology  Physics argue that the lower the reference dose rate, the less likely a relative sparing at higher dose rates would be observed (and potentially even the inverse effect may appear due to the “classical” dose-rate effect) This effect is modified by the assumed repair half-life of the DSB classes, in which a shorter half-life leads to increased survival at lower dose rates For the dose-rate range, and thus irradiation times, considered in this work, this is especially relevant for the shorter repair half-life times of the isolated DSB (w5-60 minutes), whereas the significantly longer repair half-life times of the complex DSB (several hours) have little effect (Fig 1, C and D) DSB repair half-life times could also explain in part the potential tissue-specificity of a sparing effect discussed in the literature.51 Taken together, generalized UNIVERSE predictions over the range of dose rates and dependencies with relevant parameters are consistent with existing experimental evidence However, to further demonstrate validity of UNIVERSE, quantitative benchmarking was performed based on datasets from the literature, which were acquired under diverse combinations of radiation sources, cell-lines, and [O2] levels Furthermore, many of the discussed features are visibly reflected in these datasets In line with prior discussion, under normoxic conditions, CHO cell survival in Figure 2A does not exhibit a sparing effect under HDR radiation (3ns electron pulses) Furthermore, this dataset highlights the importance of considering potential differences in biological effectiveness between radiation sources (eg, increased effectivity of 280-kVp xrays) The predicted survival curves of the Co-60 and x-rays for their respective dose rates would be virtually the same in the given dose range, as illustrated in Figure 1A, if the RBEDSB of the x-ray source is not taken into account However, including the RBEDSB reported by the literature for the given x-ray energy leads to a convincing match between data and prediction If such information is neglected, severe misinterpretations of dose-rate effects may arise Although repair half-life times taken from the literature were applied to both the survival curves (Fig 2A) and the split dose experiments (Fig 2, B and C), UNIVERSE provides satisfactory description in both cases, adding validity to the implementation of the timedependent repair processes However, survival is slightly overestimated at higher split times for the higher doses of electron pulses and lowest dose of x-rays For the other datasets, survival is somewhat underestimated for lower split times One may achieve improved descriptions of the split dose experiments by using a separate set of parameters,20 which is supported by known discrepancies observed between values obtained from dose-rate and split-dose experiments, potentially caused by temperature fluctuations during split dose experiments.20,52 Modeling survival of HeLa cells (Fig 3) primarily exemplifies the capabilities of UNIVERSE in the lower hypoxic range (