Mathematical analysis of FLASH effect models based on theoretical hypotheses

Objective.Clinical applications of FLASH radiotherapy require formulas to describe how the FLASH radiation features and other related factors determine the FLASH effect. Mathematical analysis of the models can connect the theoretical hypotheses with the radiobiological effect, which provides the foundation for establishing clinical application models. Moreover, experimental and clinical data can be used to explore the key factors through mathematical analysis.Approach.We abstract the complex models of the oxygen depletion hypothesis and radical recombination-antioxidants hypothesis into concise mathematical equations. The equations are solved to analyze how the radiation features and other factors influence the FLASH effect. Then we propose methodologies for determining the parameters in the models and utilizing the models to predict the FLASH effect.Main results.The formulas linking the physical, chemical and biological factors to the FLASH effect are obtained through mathematical derivation of the equation. The analysis indicates that the initial oxygen concentration, radiolytic oxygen consumption and oxygen recovery are key factors for the oxygen depletion hypothesis and that the level of antioxidants is the key factor for the radical recombination-antioxidants hypothesis. According to the model derivations and analysis, the methodologies for determining parameters and predicting the FLASH effect are proposed: (1) the criteria for data filtration, (2) the strategy of hybrid FLASH and conventional dose rate (CONV) irradiation to ensure the acquisition of effective experimental data across a wide dose range, (3) the pipelines of fitting parameters and predicting the FLASH effect.Significance.This study establishes the quantitative relationship between the FLASH effect and key factors. The derived formulas can be used to calculate the FLASH effect in future clinical FLASH radiotherapy. The proposed methodologies guide to obtain sufficient high-quality datasets and utilize them to predict the FLASH effect. Furthermore, this study indicates the key factors of the FLASH effect and offers clues to further explore the FLASH mechanism.

Computational model of radiation oxygen effect with Monte Carlo simulation: effects of antioxidants and peroxyl radicals

PURPOSE

Oxygen plays a crucial role in radiation biology. Antioxidants and peroxyl radicals affect the oxygen effect greatly. This study aims to establish a computational model of the oxygen effect and explore the effect attributed to antioxidants and peroxyl radicals.

MATERIALS AND METHODS

Oxygen-related reactions are added to our track-structure Monte Carlo code NASIC, including oxygen fixation, chemical repair by antioxidants and damage migration from base-derived peroxyl radicals. Then the code is used to simulate the DNA damage under various oxygen, antioxidant and damage migration rate conditions. The oxygen enhancement ratio(OER) is calculated quantifying by the number of double-strand breaks for each condition. The roles of antioxidants and peroxyl radicals are examined by manipulating the relevant parameters.

RESULTS AND CONCLUSIONS

Our results indicate that antioxidants are capable of rapidly restoring DNA radicals through chemical reactions, which compete with natural and oxygen fixation processes. Additionally, antioxidants can react with peroxyl radicals derived from bases, thereby preventing the damage from migrating to DNA strands. By quantitatively accounting for the impact of peroxyl radicals and antioxidants on the OER curves, our study establishes a more precise and comprehensive model of the radiation oxygen effect.

Using oxygen dose histograms to quantify voxelised ultra-high dose rate (FLASH) effects in multiple radiation modalities

Purpose.To introduce a methodology to predict tissue sparing effects in pulsed ultra-high dose rate radiation exposures which could be included in a dose-effect prediction system or treatment planning system and to illustrate it by using three published experiments.Methods and materials.The proposed system formalises the variability of oxygen levels as an oxygen dose histogram (ODH), which provides an instantaneous oxygen level at a delivered dose. The histogram concept alleviates the need for a mechanistic approach. At each given oxygen level the oxygen fixation concept is used to calculate the change in DNA-damage induction compared to the fully hypoxic case. Using the ODH concept it is possible to estimate the effect even in the case of multiple pulses, partial oxygen depletion, and spatial oxygen depletion. The system is illustrated by applying it to the seminal results by Town (Nat. 1967) on cell cultures and the pre-clinical experiment on cognitive effects by Montay-Gruelet al(2017Radiother. Oncol.124365-9).Results.The proposed system predicts that a possible FLASH-effect depends on the initial oxygenation level in tissue, the total dose delivered, pulse length and pulse repetition rate. The magnitude of the FLASH-effect is the result of a redundant system, in that it will have the same specific value for a different combination of these dependencies. The cell culture data are well represented, while a correlation between the pre-clinical experiments and the calculated values is highly significant (p < 0.01).Conclusions. A system based only on oxygen related effects is able to quantify most of the effects currently observed in FLASH-radiation.

Oxygen Monitoring in Model Solutions and In Vivo in Mice During Proton Irradiation at conventional and FLASH Dose Rates

FLASH is a high-dose-rate form of radiation therapy that has the reported ability, compared with conventional dose rates, to spare normal tissues while being equipotent in tumor control, thereby increasing the therapeutic ratio. The mechanism underlying this normal tissue sparing effect is currently unknown, however one possibility is radiochemical oxygen depletion (ROD) during dose delivery in tissue at FLASH dose rates. In order to investigate this possibility, we used the phosphorescence quenching method to measure oxygen partial pressure before, during and after proton radiation delivery in model solutions and in normal muscle and sarcoma tumors in mice, at both conventional (Conv) (∼0.5 Gy/s) and FLASH (∼100 Gy/s) dose rates. Radiation dosimetry was determined by Advanced Markus Chamber and EBT-XL film. For solutions contained in sealed glass vials, phosphorescent probe Oxyphor PtG4 (1 μM) was dissolved in a buffer (10 mM HEPES) containing glycerol (1 M), glucose (5 mM) and glutathione (5 mM), designed to mimic the reducing and free radical-scavenging nature of the intracellular environment. In vivo oxygen measurements were performed 24 h after injection of PtG4 into the interstitial space of either normal thigh muscle or intra-muscular sarcoma tumors in mice. The "g-value" for ROD is reported in mmHg/Gy, which represents a slight modification of the more standard chemical definition (μM/Gy). In solutions, proton irradiation at conventional dose rates resulted in a g-value for ROD of up to 0.55 mmHg/Gy, consistent with earlier studies using X or gamma rays. At FLASH dose rates, the g-value for ROD was ∼25% lower, 0.37 mmHg/Gy. pO2 levels were stable after each dose delivery. For normal muscle in vivo, oxygen depletion during irradiation was counterbalanced by resupply from the vasculature. This process was fast enough to maintain tissue pO2 virtually unchanged at Conv dose rates. However, during FLASH irradiation there was a stepwise decrease in pO2 (g-value ∼0.28 mmHg/Gy), followed by a rebound to the initial level after ∼8 s. The g-values were smaller and recovery times longer in tumor tissue when compared to muscle and may be related to the lower initial endogenous pO2 levels in the former. Considering that the FLASH effect is seen in vivo even at doses as low as 10 Gy, it is difficult to reconcile the amount of protection seen by oxygen depletion alone. However, the phosphorescence probe in our experiments was confined to the extracellular space, and it remains possible that intracellular oxygen depletion was greater than observed herein. In cell-mimicking solutions the oxygen depletion g-vales were indeed significantly higher than observed in vivo.

May oxygen depletion explain the FLASH effect? A chemical track structure analysis

BACKGROUND AND PURPOSE

Recent observations in animal models show that ultra-high dose rate ("FLASH") radiation treatment significantly reduces normal tissue toxicity maintaining an equivalent tumor control. The dependence of this "FLASH" effect on target oxygenation has led to the assumption that oxygen "depletion" could be its major driving force.

MATERIALS AND METHODS

In a bottom-up approach starting from the chemical track evolution of 1 MeV electrons in oxygenated water simulated with the TRAX-CHEM Monte Carlo code, we determine the oxygen consumption and radiolytic reactive oxygen species production following a short radiation pulse. Based on these values, the effective dose weighted by oxygen enhancement ratio (OER) or the in vitro cell survival under dynamic oxygen pressure is calculated and compared to that of conventional exposures, at constant OER.

RESULTS

We find an excellent agreement of our Monte Carlo predictions with the experimental value for radiolytic oxygen removal from oxygenated water. However, the application of the present model to published radiobiological experiment conditions shows that oxygen depletion can only have a negligible impact on radiosensitivity through oxygen enhancement, especially at typical experimental oxygenations where a FLASH effect has been observed.

CONCLUSION

We show that the magnitude and dependence of the "oxygen depletion" hypothesis are not consistent with the observed biological effects of FLASH irradiation. While oxygenation plays an undoubted role in mediating the FLASH effect, we conclude that state-of-the-art radiation chemistry models do not support oxygen depletion and radiation-induced transient hypoxia as the main mechanism.

Approaches to combat hypoxia in cancer therapy and the potential for in silico models in their evaluation

AIM

The negative impact of tumour hypoxia on cancer treatment outcome has been long-known, yet there has been little success combating it. This paper investigates the potential role of in silico modelling to help test emerging hypoxia-targeting treatments in cancer therapy.

METHODS

A Medline search was undertaken on the current landscape of in silico models that simulate cancer therapy and evaluate their ability to test hypoxia-targeting treatments. Techniques and treatments to combat tumour hypoxia and their current challenges are also presented.

RESULTS

Hypoxia-targeting treatments include tumour reoxygenation, hypoxic cell radiosensitization with nitroimidazoles, hypoxia-activated prodrugs and molecular targeting. Their main challenges are toxicity and not achieving adequate delivery to hypoxic regions of the tumour. There is promising research toward combining two or more of these techniques. Different types of in silico therapy models have been developed ranging from temporal to spatial and from stochastic to deterministic models. Numerous models have compared the effectiveness of different radiotherapy fractionation schedules for controlling hypoxic tumours. Similarly, models could help identify and optimize new treatments for overcoming hypoxia that utilize novel hypoxia-targeting technology.

CONCLUSION

Current therapy models should attempt to incorporate more sophisticated modelling of tumour angiogenesis/vasculature and vessel perfusion in order to become more useful for testing hypoxia-targeting treatments, which typically rely upon the tumour vasculature for delivery of additional oxygen, (pro)drugs and nanoparticles.

Effects of irradiation conditions on the radiation sensitivity of microorganisms in the presence of OH-radical scavengers

PURPOSE

The purpose of the paper was to investigate the protective effect of some scavengers of OH radicals (hydroxyl radicals) on the radiation sensitivity of bacteria (in some cases also yeast) under normoxic (in air) or hypoxic (suboxic) conditions and to compare the obtained results with those published earlier for the yeast, all in a wide interval of irradiation conditions. Another aim was to investigate a possible impact of the reaction order of the reaction between the scavengers and the OH radicals on the protection of the cells.

MATERIALS AND METHODS

In order to study the protective effect of OH scavengers we used various concentrations of methanol and potassium formate (in some cases also ethanol) in isotonic salt solutions. These solutions containing living bacteria (Escherichia coli) or yeast (Saccharomyces cerevisiae) were irradiated with ⁶⁰Co radiation using various doses and dose rates. Irradiation was performed in air, in some cases under the hypoxic conditions. The number of surviving cells was determined prior to and after irradiation in suspension with and without scavengers. The surviving fractions after irradiation with and without scavenger were evaluated.

RESULTS

The surviving fraction of bacterial cells increases linearly with increasing concentration of both scavengers. The fraction of surviving cells does not increase with increasing concentration of the scavengers under suboxic conditions. The protective effect Ϭ increases linearly with increasing scavenging efficiency and this dependence is much sharper under normoxic conditions than under suboxic ones. The specific protection k is much higher for the methanol than for the potassium formate.

CONCLUSIONS

The basic characteristics of the impact of scavengers of OH radicals on radiation sensitivity of both bacteria and yeast are the same in a wide interval of doses and dose rates. The specific protection effect is much higher under the normoxic conditions. This protective effect is inversely proportional to the rate constant of the reaction between the scavenger and the OH radicals. It seems to be obvious that the presence of oxygen during irradiation is a necessary condition for the protective action of the scavengers which may be partially controlled by some transport processes and may be connected with the radiation sensitivity of the cells. On the other hand, the change of the reaction order of the reaction of the scavenger with the OH radicals has turned out to be unimportant.

Monte Carlo Simulation of the Oxygen Effect in DNA Damage Induction by Ionizing Radiation

DNA damage induced by ionizing radiation exposure is enhanced in the presence of oxygen (the "oxygen effect"). Despite its practical importance in radiotherapy, the oxygen effect has largely been excluded from models that predict DNA damage from radiation tracks. A Monte Carlo-based algorithm was developed in MATLAB software to predict DNA damage from physical and chemical tracks through a cell nucleus simulated in Geant4-DNA, taking into account the effects of cellular oxygenation (pO₂) on DNA radical chemistry processes. An initial spatial distribution of DNA base and sugar radicals was determined by spatially clustering direct events (that deposited at least 10.79 eV) and hydroxyl radical (^•OH) interactions. The oxygen effect was modeled by increasing the efficiency with which sugar radicals from direct-type effects were converted to strand breaks from 0.6 to 1, the efficiency with which sugar radicals from the indirect effect were converted to strand breaks from 0.28 to 1 and the efficiency of base-to-sugar radical transfer from ^•OH-mediated base radicals from 0 to 0.03 with increasing pO₂ from 0 to 760 mmHg. The DNA damage induction algorithm was applied to tracks from electrons, protons and alphas with LET values from 0.2 to 150 keV/μm under different pO₂ conditions. The oxygen enhancement ratio for double-strand break induction was 3.0 for low-LET radiation up to approximately 15 keV/μm, after which it gradually decreased to a value of 1.3 at 150 keV/μm. These values were consistent with a range of experimental data published in the literature. The DNA damage yields were verified using experimental data in the literature and results from other theoretical models. The spatial clustering approach developed in this work has low memory requirements and may be suitable for particle tracking simulations with a large number of cells.

Nitroimidazoles as hypoxic cell radiosensitizers and hypoxia probes: misonidazole, myths and mistakes

Nitroimidazoles have been extensively explored as hypoxic cell radiosensitizers but have had limited clinical success, with efficacy restricted by toxicity. However, they have proven clinically useful as probes for tumour hypoxia. Both applications, and probably much of the dose-limiting toxicities, reflect the dominant chemical property of electron affinity or ease of reduction, associated with the nitro substituent in an aromatic structure. This single dominant property affords unusual, indeed extraordinary flexibility in drug or probe design, suggesting further development is possible in spite of earlier limitations, in particular building on the benefit of hindsight and an appreciation of errors made in earlier studies. The most notable errors were: the delay in viewing cellular thiol depletion as a likely common artefact in testing in vitro; slow recognition of pH-driven concentration gradients when compounds were weak acids and bases; and a failure to explore the possible involvement of pH and ascorbate in influencing hypoxia probe binding. The experience points to the need to involve a wider range of expertise than that historically involved in many laboratories when studying the effects of chemicals on radiation response or using diagnostic probes.