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

Although initial studies date back to the 1960s,1-3 interest was recently reignited by multiple pub-lications reporting significant sparing of normal tissue while maintaining bioeffect i

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,kStewart Mein, PhD, *,y,z,xIvana Dokic, PhD, *,y,z,x

Thomas Haberer, PhD,{ Ju¨rgen 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 effec-tively 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

(DFG-KFO214), Deutsche Krebshilfe, Germany (Max-Eder 108876), and

intra-mural 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

Healthcare GmbH, Merck KGaA, Solution Akademie GmbH, Ergomed PLC Surrey Research Park, Quintiles GmbH, Pharmaceutecal Research Associates GmbH, Boehringer Ingelheim Pharma GmbH Co, PTW-Freiburg 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.

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

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 VER-Satile 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-dose-rate radiation compared with conventional means underlines the importance of robust quantification of biophysical charac-teristics 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 bio-physical 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

pub-lications reporting significant sparing of normal tissue

while maintaining bioeffect in the tumor with application of

high dose levels at high dose rates compared with

con-ventional 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 cells6and zebrafish embryos4to

neurocognitive functionality of mice after whole-brain

irradiation7-9 and tail necrosis in mice.10 Furthermore,

in-stitutions have applied differing radiation sources such as

102 keV x-rays,8 10 MeV electrons,6,10 and 224 MeV

protons.11Sparing effects have been reported at doses

be-tween 10 and 50 to 75 Gy, and applying dose rates fromw

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,6and

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

be-tween 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.1,4Based on this hypothesis and/or other dose-rateedependent radiochem-ical mechanisms, such as radradiochem-ical recombination, models have recently been established to describe bioeffects at FLASH dose rate.14-16 Nonetheless, quantitative bench-marks 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 mecha-nistic model for predicting response of biological systems to ionizing radiation through consideration of several key conditions.17-19In this work, time-dependent processing of radiation-induced DNA damage,20,21oxygen depletion, and reoxygenation mechanisms14 are implemented toward ac-curate 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 conduc-tion of much needed foundaconduc-tional 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

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,22can be calculated using a

cell-line independent DSB yield of aDSBZ 5 

103DSB⁄ ððMbp  GyÞ Þ.23 , 24 Assuming this yield to be

constant over the clinically applied dose range, the

ex-pected total number of DSB (hNtDSBi) can be expressed as:

hNtDSBi ZaDSB D  DNAc ð1Þ

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.25To account for this change in effectiveness,

the DSB yield aDSB may be modified by a relative

bio-logical effectiveness factor (RBEDSB)

In the mechanistic view of UNIVERSE, a certain type of

chromatin substructure, so-called giant loops of about 2

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

associ-ated with an increased lethality for the cell due to the high

risk of chromatin loss.31Classifying giant loops containing

exactly 1 lesion as isolated DSB (iDSB) and 2 or more

lesions as complex DSB (cDSB) can accurately predict

populations of swiftly and slowly repairing lesions in

rejoining studies.32,33UNIVERSE shares this classification

of lesions with other models.34,35The total number of giant

loops (Ngl) having a DNA content of DNAgl is given by:

NglZDNAc

Following a Monte Carlo approach, the actual total

number of DSB induced in the nucleus (NtDSB) is sampled

for> 104iterations 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 1 DSB (NiDSB) or 2 and more

DSB (NcDSB) are counted The lethality parameters KiDSB

and KcDSBdescribe 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:

SZ ð1  KiDSBÞN iDSB,ð1  KcDSBÞN cDSB: ð3Þ

The average value of S over all iterations is used to

predict the surviving fraction of the cell population The

cell-line dependent parameters KiDSBand KcDSBare 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 hypoxia reduction factor (HRFO2

DSB), which resembles the classical oxygen enhancement ratio (OER), while the lethality parameters are assumed to be invariant.17-19 The reduced DSB yield,aO 2

DSB; can be expressed by:

aO 2

DSBZ aDSB HRFO2

DSB

ð4Þ

If both hypoxic and normoxic data are available, HRFO2

DSB can be determined by fitting the model to both datasets, while KiDSB and KcDSB are kept constant If only normoxic or hypoxic datasets are available, HRFO2

DSB for a given oxygen concentration ½O2 is estimated using an empirical parametrization:

HRFO2

DSBZm$K þ ½O2

introduced in an earlier publication17following previous works.36,37Due 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 mZ 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

KZ 0.41 The effect of the chosen values of m and K on the DSB yield as function of½O2 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 irradi-ation time (Trad) is divided into several sequential time-steps (Nt Z 100) The relationship between applied dose rate ( _D), total applied dose (D) and total irradiation time is given by:

TradZD_

The damage pattern induced by the partial dose applied

at a given time-step, DpartZ D

N t; is computed analogously to the static UNIVERSE described earlier However, to ac-count for possible oxygen depletion and reoxygenation occurring during irradiation, the oxygen level at the current time-step OðtÞ is determined using14:

OðtÞ Z Oenv

 l

g _Dþlþ



1 l

g _Dþl



eðg _Dþl Þt

 ð7Þ where t is the time passed since the start of the irradiation,

Oenvis the environmental oxygen level ([O2]) at tZ 0; g is the depletion rate constant, and l is the reoxygenation constant Values from Petersson et al14for in vitro analysis,

gZ 0:053 Gy1 and lZ 1 s1; were adopted The time-dependent oxygen concentration OðtÞ was used to calcu-late the current hypoxia reduction factor HRFO2 ðtÞ

following equation 5, effectively modifying the oxygen

dependent radiosensitivity of the cells in real-time Using

equations4and1, 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 inFigure 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

distribution based on repair half-life times T1=2

iDSBand T1=2

cDSB; respectively These half-life times can be obtained either

from literature (eg, biexponential fits to DSB repair

ki-netics32) 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

based on T1=2

cDSB: 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 KcDSBfor 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 Equation3

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

post-irradiation 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

pre-dict 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 1 Vrad

Vctrl; where Vrad is the volume of the tumor measured 15 days postirradiation, while Vctrlis the volume of

untreated tumors after the same period.39In this work, we

describe this value as the relative tumor volume suppression

(RTVS), and heuristically approximate the ratio Vrad

Vctrl to be given by the survival fraction of the cell population within the

irradiated tumor leading to the assumption RTVSZ 1  S:

For approximation of ND50and LD50, the dose at which

50% of mouse tails show radionecrosis as reported by

Hendry et al10and mice that died within 4 days after

whole-body irradiation as reported by Hornsey et al,40,41

respec-tively, we assumed both to be equal to the dose at 50%

survival fraction

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 con-ditions and parameters considered in the model on pre-dicted trend of the dose-rate effect, survival fraction was computed over a range of dose rates (0.01 Gy/s to 104Gy/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 suf-ficient 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 dose levels T1=2

iDSBZ 30 minutes, T1 =2

cDSBZ 5 hours, and [O2]

Z 2.5 % were chosen as fixed values A general trend of increased cell killing up to dose rates of about 1 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 2 lowest dose levels (2 and 8 Gy)

Environmental oxygen level

Figure 1B depicts the effect of different oxygen levels ([O2]) on survival prediction with the following fixed set-tings: total dose of 16 Gy, T1=2

iDSBZ 30 minutes and T1 =2

5 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

16 Gy and [O2] of 2.5% With variable T1=2

iDSB; T1 =2 cDSBwas set

to 5 hours, whereas for variable T1=2

cDSB; T1 =2 iDSBwas set to 30 minutes.Figure 1C makes evident that the effect of T1=2 is

Table 1 Model parameters of UNIVERSE applied in this work

Abbreviations: CHO Z Chinese hamster ovary.

Dose Rate [Gy/s]

Dose Rate [Gy/s]

Dose Rate [Gy/s]

32 Gy

8 Gy

16 Gy

Dose Rate [Gy/s]

pO2 0.01 % pO2 01 % pO2 1 %

pO2 2.5% pO2 7.5% pO2 20%

T1/2 iDSB 5 mins T1/2 iDSB 15 mins T1/2 iDSB 30 mins T1/2 iDSB 45 mins T1/2 iDSB 60 mins

T1/2 cDSB 1 hour T1/2 cDSB 2 hours T1/2 cDSB 5 hours

Fig 1 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 8 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 abovew1 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

highest underw1 Gy/s In this region, a shorter T1 =2

iDSBleads

to increasing slopes in survival for decreasing dose rates At

dose rates higher than w10 Gy/s, the effect of T1 =2

iDSB

diminishes In contrast, T1=2

cDSB 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 inTable 1

Survival of Chinese hamster ovary cells under various

radiation qualities and in split dose experiments

Figure 2A shows Chinese Hamster Ovary (CHO) cell

sur-vival after irradiation with a Co-60 source (0.01 Gy/s),

single 3 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 2 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

evolu-tion of survival An RBEDSBof 1.2 was set for the 280 kVp

x-rays.43 Using the repair half-life times of CHO cells found in the literature,20 the number of isolated and com-plex 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 2 fitted free parameters (both lethality parameters), 2 globally set parameters (HRFO2

DSB parametrization), and 3 parameters taken from literature (both repair half-life times and the RBEDSB) for the predictions of this dataset The R2values (coefficient of determination) for the prediction of the

Co-60, 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 ef-fect, an increased bioeffect for 280 kVp radiation is clearly visible The mean relative difference between measured and predicted survival (excluding the timepoint at

0 minutes) for the split doses of electrons (Fig 2B) and x-rays (Fig 2C) were 3.5% and 10%, respectively

Survival of HeLa cells after irradiation with single 3ns electron pulses under different oxygen levels

Figure 3 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

10 0

10 -1

10 -2

10 -3

Model Co-60 Model 3 ns e-Pulses Model 280 kVp Data Co-60 0.01 Gy/s Data 3 ns e Pulses Data Xrays 280 kVp 0.033 Gy/s

10 -4

10 -1

10 -3

10 -4

10 -2

10 -1

10 -2

10 -3

10 -4

0.0 2.5 5.0 7.5 10.0

12.5 15.0 17.5 0 20 40 60 80 100 120 140

Time [min]

Split Dose, 280 kVp X-Rays Split Dose, 3ns e-Pulses

5.0 Gy + 5.0 Gy

5.85 Gy + 5.85 Gy

6.9 Gy + 6.9 Gy

7.2 Gy + 7.2 Gy

Model Data

5.5 Gy + 5.5 Gy

6 Gy + 6 Gy

0 20 40 60 80 100 120 140

C

Fig 2 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 3 ns pulses ofw450 keV electrons42 and 280 kVp x-rays (0.033 Gy/s),43with 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 2 fractions ofw450 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 att Z 0:

predictions Furthermore, to illustrate the effect of oxygen

depletion (OD) and reoxygenation (RO) kinetics, an

addi-tional prediction is shown with both mechanisms

deacti-vated The repair half-life times were taken from the

literature44and 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

cur-ve_fit command of the scipy library for Python This results

in 4 free parameters (if we add the 2 HRFO2

DSB parameters that deviate from the global parametrization of the other

datasets to the fitted lethality parameters) and 2 parameters

taken from literature (both repair half-life times) for the

predictions of this dataset The resulting mean R2value for

the data inFigure 3was 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

sur-vival was observed for these mechanisms under hypoxic

conditions The sparing effect becomes visible atw10 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

post-irradiation 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

half-life 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

sur-vival data with the curve_fit command of the scipy library

for Python Thus, for the predictions for this dataset, we

have 2 fitted free parameters (both lethality parameters), 2

globally set parameters (HRFO2

DSB parametrization), and 2 parameters taken from literature (both repair half-life time)

The R2value 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 2

dose rates are essentially indistinguishable up tow10 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

parame-ters as described earlier The bounds of the UNIVERSE

predictions correspond to the lowest and highest

experi-mentally 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

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 ap-pears slightly underestimated by UNIVERSE at interme-diate [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 5 to 6 MeV electrons at conventional dose rates (0.1 Gy/s) and at high dose rates (between 125 Gy/s and single pulse of 1.8ms) from Bourhis et al,39with 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 5 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 3 free parameters (both lethality parameters and the repair half-life time of the isolated lesions), 2 globally set parameters (HRFO2

DSB

parametrization), and 2 parameters set according to litera-ture (oxygen tension and repair half-life time of complex lesions) for the predictions of this dataset R2for 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 betweenw10 and w30 Gy

ND50of 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 inFigure 5B

In one case, the system is oxygenated, whereas in the other, the mouse tail was under an anoxic atmosphere and clam-ped to minimize blood flow Following the arguments described earlier, the repair half-life time for the complex DSB was set to 5 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 appro-priately describe trends within a reasonable range.10,47For the predictions of this dataset, we used 4 free parameters (both lethality parameters, the repair half-life time of the isolated lesions and the oxygen tension) and 2 parameters set based on the literature (repair half-life time of the

complex lesions and RBEDSB) The mean relative

differ-ences 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:

dose-rate dependence

LD50(dose at which 50% of the subjects have died after a

given period of time; here t Z 4 days) is shown in

Figure 5C for whole body irradiation of mice withw8MeV electron and 250kVp x-ray sources (as above: RBEDSBZ 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 5 hours Again, both lethality parameters and the repair half-life time of the isolated lesions were determined based on thec2value of the predictions as K Z 10 4, K Z 0.065 and

Data

Model with OD/RO Model no OD/RO

O2 = 21%

Dose [Gy]

O2 = 0.91%

Dose [Gy]

O2 = 0.77%

Dose [Gy]

O2 = 0.59%

Dose [Gy]

Dose [Gy]

Dose [Gy]

Fig 3 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 abovew10

Gy for hypoxic cases (B-E), whereas normoxic (A) and anoxic (F) scenarios are evidently not affected by the oxygen depletion mechanism

iDSBZ 6 minutes, respectively An oxygen tension of 3%

was found to describe data best, fitting the expected O2

level range.46,47 Thus, we used 4 free parameters (both

lethality parameters, the repair half-life time of the isolated

lesions and the oxygen tension) and 2 parameters set based

on literature (repair half-life time of the complex lesions

and RBE ) The mean relative differences between the

measured and predicted LD50for the electron source were determined to be 4.3%

Discussion

An extension of the mechanistic biomodeling framework UNIVERSE is introduced, implementing time-dependent

10 -1

101

10 0

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101

10 0

10 -2

10-3

10 -4

10 -5

Dose [Gy]

10 -1

10 0

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10-5

Dose [Gy]

Model 0.23 Gy/s Model 600 Gy/s Data 0.23 Gy/s Data 600 Gy/s

Model 0.23 Gy/s Model 600 Gy/s Data 0.23 Gy/s Data 600 Gy/s

Model 0.23 Gy/s Model 600 Gy/s Data 0.23 Gy/s Data 600 Gy/s

O2 concentration [%]

Fig 4 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

100

80

60

40

20

0

90

80

70

60

50

40

30

RTVS of U87 Xenografts in Mice

Model 0.1 Gy/s Model 125 Gy/s Data 0.1 Gy/s Data 125 Gy/s

10-1 100 101 102 10-3 10-2 10-1 100 101 102

ND50 Mice Tail Necrosis LD50 of Mice Whole-Body-Irradiation

20

18

16

14

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10

8

6

Model Air Model Clamping + N2 Data Air Data Clamping + N2

Model electrons Model x-rays Data electrons Hornsey & Alper 1966 Data electrons Hornsey & Bewley 1971 Data x-rays Hornsey & Alper 1966

Fig 5 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 5 to 6 MeV electrons at conventional dose-rates (red: 0.1 Gy/s) and ultrahigh dose-rates (black: between 125 Gy/s and 1 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 electrons10in an oxygenated (blue) and anoxic environment (green: N2þ clamping of tail) with corresponding descriptions by UNIVERSE (C) LD50after whole-body-irradiation of mice with either 250kV x-rays (purple) orw8 MeV electrons (orange) over a range of dose-rates40,41and respective predictions by UNIVERSE For consistency in defining and interpreting the investigated endpoint (with tLD50Z 4 days), the data for LD50(tLD50Z 5 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 athttps://doi.org/10.1016/j.ijrobp.2020.12.048.)

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

ultrahigh-rate 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

de-pendencies and context for discussion of UNIVERSE

development and validation

Evolution of survival with dose rate exhibited by most

curves inFigure 1can be explained by 2 mechanisms: (1)

an initial survival decrease at lower dose rates is driven by

the reduced repair of DSB taking place during the

short-ening 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

Sur-vival 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 doses10 Gy

and dose rates greater than w40 Gy/s.4 , 5 The observed

dose-rate region of the survival increase is also in

agree-ment 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

pre-diction 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

pre-dicted by existing quantitative oxygen depletion effect

models.14,15Absence 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

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 2 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 evi-dence However, to further demonstrate validity of UNI-VERSE, 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 inFigure 2A does not exhibit a sparing effect under HDR radiation (3ns electron pulses) Further-more, this dataset highlights the importance of considering potential differences in biological effectiveness between radiation sources (eg, increased effectivity of 280-kVp x-rays) 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 inFigure 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), UNI-VERSE provides satisfactory description in both cases, adding validity to the implementation of the time-dependent repair processes However, survival is slightly overestimated at higher split times for the 2 higher doses of electron pulses and lowest dose of x-rays For the other 3 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 parame-ters,20which is supported by known discrepancies observed between values obtained from dose-rate and split-dose ex-periments, potentially caused by temperature fluctuations during split dose experiments.20,52

Modeling survival of HeLa cells (Fig 3) primarily ex-emplifies the capabilities of UNIVERSE in the lower hypoxic range (<1% oxygen) (Fig, 2, B-E) and visualizes the effect of the oxygen depletion and reoxygenation mechanism on survival The chosen HRFO2