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Register a new userOxygen depletion hypothesis remains controversial: a mathematical model of oxygen depletion during FLASH radiation
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Background: Experiments have reported low normal tissue toxicities during FLASH radiation, but the mechanism has not been elaborated. Several hypotheses have been proposed to explain the mechanism. The oxygen depletion hypothesis has been introduced and mostly studied qualitatively. Methods: We present a computational model to describe the time-dependent change of oxygen concentration in the tissue. The kinetic equation of the model is solved numerically using the finite difference method. The model is used to analyze the FLASH effect with the oxygen depletion hypothesis, and the brain tissue is chosen as an example. Results: The oxygen distribution is determined by the oxygen consumption rate of the tissue and the distance between capillaries. The change of oxygen concentration with time after radiation has been found to follow a negative exponential function, and the time constant is determined by the distance between capillaries. When the dose rate is high enough, the same dose results in the same change of oxygen concentration regardless of dose rate. The analysis of FLASH effect in the brain tissue based on this model does not support the explanation of the oxygen depletion hypothesis. Conclusions: The oxygen depletion hypothesis remains controversial because oxygen in most normal tissues cannot be depleted by FLASH radiation according to the mathematical analysis with this model and experiments on the expression and distribution of the hypoxia-inducible factors.
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Purpose: Recent studies suggest ultra-high dose rate (FLASH) irradiation can spare normal tissues from radiotoxicity, while efficiently controlling the tumor, and this is known as the FLASH effect. This study performed theoretical analyses about the impact of radiolytic oxygen depletion (ROD) on the cellular responses after FLASH irradiation. Methods: Monte Carlo simulation was used to model the ROD process, determine the DNA damage, and calculate the amount of oxygen depleted (LROD) during FLASH exposure. A mathematical model was applied to analyze oxygen tension (pO2) distribution in human tissues and the recovery of pO2 after FLASH irradiation. DNA damage and cell survival fractions (SFs) after FLASH irradiation were calculated. The impact of initial cellular pO2, FLASH pulse number, pulse interval, and radiation quality of the source particles on ROD and subsequent cellular responses were systematically evaluated. Results: The simulated electron LROD range was 0.38-0.43 {mu}M/Gy when pO2 ranged from 7.5-160 mmHg. The calculated DNA damage and SFs show that radioprotective effect is only evident in cells with a lower pO2. Different irradiation setups alter the cellular responses by modifying the pO2. Single pulse delivery or multi-pulse delivery with pulse intervals shorter than 10-50 ms resulted in fewer DNA damages and higher SFs. Source particles with a low radiation quality have a higher capacity to deplete oxygen, and thus, lead to a more conspicuous radioprotective effect. Conclusions: The FLASH radioprotective effect due to ROD may only be observed in cells with a low pO2. Single pulse delivery or multi-pulse delivery with short pulse intervals are suggested for FLASH irradiation to avoid oxygen tension recovery during pulse intervals. Source particles with low radiation quality are preferred for their conspicuous radioprotective effects.
Radiotherapy can effectively kill malignant cells, but the doses required to cure cancer patients may inflict severe collateral damage to adjacent healthy tissues. Hyperthermia (HT) is a promising option to improve the outcome of radiation treatment (RT) and is increasingly applied in hospital. However, the synergistic effect of simultaneous thermoradiotherapy is not well understood yet, while its mathematical modelling is essential for treatment planning. To better understand this synergy, we propose a theoretical model in which the thermal enhancement ratio (TER) is explained by the fraction of cells being radiosensitised by the infliction of sublethal damage through mild HT. Further damage finally kills the cell or inhibits its proliferation in a non-reversible process. We suggest the TER to be proportional to the energy invested in the sensitisation, which is modelled as a simple rate process. Assuming protein denaturation as the main driver of HT-induced sublethal damage and considering the temperature dependence of the heat capacity of cellular proteins, the sensitisation rates were found to depend exponentially on temperature; in agreement with previous empirical observations. Our predictions well reproduce experimental data from in-vitro and in-vivo studies, explaining the thermal modulation of cellular radioresponse for simultaneous thermoradiotherapy.
Purpose: To investigate experimentally, if FLASH irradiation depletes oxygen within water for different radiation types such as photons, protons and carbon ions. Methods: This study presents measurements of the oxygen consumption in sealed, 3D printed water phantoms during irradiation with X-rays, protons and carbon ions at varying dose rates up to 340 Gy/s. The oxygen measurement was performed using an optical sensor allowing for non-invasive measurements. Results: Oxygen consumption in water only depends on dose, dose rate and linear energy transfer (LET) of the irradiation. The total amount of oxygen depleted per 10 Gy was found to be 0.04 - 0.18 % atm for 225 kV photons, 0.04 - 0.25 % atm for 224 MeV protons and 0.09 - 0.17 % atm for carbon ions. consumption depends on dose rate by an inverse power law and saturates for higher dose rates because of self-interactions of radicals. Higher dose rates yield lower oxygen consumption. No total depletion of oxygen was found for clinical doses. Conclusions: FLASH irradiation does consume oxygen, but not enough to deplete all the oxygen present. For higher dose rates, less oxygen was consumed than at standard radiotherapy dose rates. No total depletion was found for any of the analyzed radiation types for 10 Gy dose delivery using FLASH.
In this article, we present a multispecies reaction-advection-diffusion partial differential equation (PDE) coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma multiforme observed in magnetic resonance imaging (MRI) scans. These include enhancing and necrotic tumor structures, brain edema and the so called mass effect, that is, the deformation of brain tissue due to the presence of the tumor. The multispecies model accounts for proliferating, invasive and necrotic tumor cells as well as a simple model for nutrition consumption and tumor-induced brain edema. The coupling of the model with linear elasticity equations with variable coefficients allows us to capture the mechanical deformations due to the tumor growth on surrounding tissues. We present the overall formulation along with a novel operator-splitting scheme with components that include linearly-implicit preconditioned elliptic solvers, and semi-Lagrangian method for advection. Also, we present results showing simulated MRI images which highlight the capability of our method to capture the overall structure of glioblastomas in MRIs.
A mathematical model is presented for the Joule heating that occurs in a ceramic powder compact during the process of flash sintering. The ceramic is assumed to have an electrical conductivity that increases with temperature, and this leads to the possibility of runaway heating that could facilitate and explain the rapid sintering seen in experiments. We consider reduced models that are sufficiently simple to enable concrete conclusions to be drawn about the mathematical nature of their solutions. In particular we discuss how different local and non-local reaction terms, which arise from specified experimental conditions of fixed voltage and current, lead to thermal runaway or to stable conditions. We identify incipient thermal runaway as a necessary condition for the flash event, and hence identify the conditions under which this is likely to occur.
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