Oxygen Diffusion Model Research Articles

Breath-hold calibrated fMRI mapping of absolute cerebral metabolic rate of oxygen metabolism (CMRO2): An assessment of the accuracy and repeatability in a healthy adult population

Abstract We previously introduced a calibrated fMRI framework that utilises respiratory modulation with only a single gas (CO2) to map the grey matter (GM) cerebral metabolic rate of oxygen consumption (CMRO2). The method decouples and estimates the cerebral blood volume (CBV) and the oxygen extraction fraction (OEF) from a single measure of the maximum BOLD modulation. The method links the two parameters of interest with a model of oxygen diffusion from capillaries to mitochondria which incorporates the cerebral blood flow (CBF). Here, we apply this framework to gas-free breath-hold calibrated fMRI (bhc-fMRI), where simultaneous BOLD and ASL acquisitions are combined with modulation of arterial CO2 through repeated breath-holding. The accuracy and repeatability of the method is assessed in 33 healthy volunteers at rest and during continuous visual stimulation. Average GM OEF estimated from bhc-fMRI was 0.37 ± 0.04, indicating a small bias of 0.04 (with limits of agreement from -0.11 to 0.12) compared to the whole brain OEF of 0.32 ± 0.07 estimated from sagittal sinus using T2 Relaxation Under Spin Tagging (TRUST). The within-session repeatability of GM estimates were moderate to good for OEF, with ICC = 0.75 (0.56–0.87) and good to excellent for CMRO2, with ICC = 0.88 (0.74–0.94). An ROI analysis in the visual cortex found an average CBF increase of 16%, a CMRO2 increase of 12%, and an OEF decrease of 3% during the visual stimulation. The bhc-fMRI measurement of CMRO2 is simple to implement, has comparable accuracy and repeatability to existing gas-based methods, and is sensitive to modulations in metabolism during functional hyperaemia.

Study on the interstitial oxygen diffusion to understand the reduction of cryogenic RF loss for the superconducting radio-frequency niobium cavities

Abstract Medium-temperature baking (Mid-T baking) is an innovative method employed to enhance the unloaded quality factor Q0 of superconducting radio-frequency (SRF) niobium (Nb) cavities at cryogenic temperatures. This study presents an interstitial oxygen diffusion model based on the decomposition of the natural oxide to clarify the improved performance of the Nb cavities after undergoing Mid-T baking. Additionally, the correlation between the interstitial oxygen within the RF penetration depth and the surface resistance of the Nb cavities has been explored. The parameter for the oxide decomposition was determined using in-situ X-ray photoelectron spectroscopy (XPS), where the thickness of the oxide/carbide layer was calculated from the peak fitting of Nb 3d spectra and the attenuation law of the photoelectron beam. The interstitial oxygen diffusion model, validated by the semi-quantitative distribution along the depth determined by Time of Flight Secondary Ion Mass Spectrometry (ToF-SIMS), quantifies the oxygen atomic concentration within the RF penetration depth in Mid-T baked Nb material. In the baking temperature range of 300~400 ℃, the calculated oxygen concentration from the interstitial oxygen diffusion model demonstrates a more pronounced dependence on the baking temperature than the baking time. This suggests that more precise control of the interstitial oxygen concentration can be achieved by adjusting the baking temperature. Furthermore, it has been observed that maintaining a uniform and moderate oxygen concentration throughout the depth is essential for optimal BCS resistance. This study paves the way for more efficient processing optimization and enhancing understanding of the mechanism behind RF loss in Nb cavities.

Cross-Scale Prediction Model of Oxygen Diffusion in Concrete Under Dry Conditions

Cross-Scale Prediction Model of Oxygen Diffusion in Concrete Under Dry Conditions

Two-dimensional oxygen-diffusion modelling for FLASH proton therapy with pencil beam scanning—Impact of diffusive tissue properties, dose, dose rate and scan patterns

Objective. Oxygen depletion is generally believed to play an important role in the FLASH effect—a differential reduction of the radiosensitivity of healthy tissues, relative to that of the tumour under ultra-high dose-rate (UHDR) irradiation conditions. In proton therapy (PT) with pencil-beam scanning (PBS), the deposition of dose, and, hence, the degree of (radiolytic) oxygen depletion varies both spatially and temporally. Therefore, the resulting oxygen concentration and the healthy-tissue sparing effect through radiation-induced hypoxia varies both spatially and temporally as well. Approach. We propose and numerically solve a physical oxygen diffusion model to study these effects and their dependence on tissue parameters and the scan pattern in pencil-beam delivery. Since current clinical FLASH PT (FLASH-PT) is based on 250 MeV shoot-through (transmission) beams, for which dose and dose rate (DR) hardly vary with depth compared to the variation transverse to the beam axis, we focus on the two-dimensional case. We numerically integrate the model to obtain the oxygen concentration in each voxel as a function of time and extract voxel-based and spatially and temporarily integrated metrics for oxygen (FLASH) enhanced dose. Furthermore, we evaluate the impact on oxygen enhancement of standard pencil-beam delivery patterns and patterns that were optimised on dose-rate. Our model can contribute to the identification of tissue properties and pencil-beam delivery parameters that are critical for FLASH-PT and it may be used for the optimisation of FLASH-PT treatment plans and their delivery. Main results. (i) the diffusive properties of oxygen are critical for the steady state concentration and therefore the FLASH effect, even more so in two dimensions when compared to one dimension. (ii) The FLASH effect through oxygen depletion depends primarily on dose and less on other parameters. (iii) At a fixed fraction dose there is a slight dependence on DR. (iv) Scan patterns optimised on DR slightly increase the oxygen induced FLASH effect. Significance. To our best knowledge, this is the first study assessing the impact of scan-pattern optimization (SPO) in FLASH-PT with PBS on a biological FLASH model. While the observed impact of SPO is relatively small, a larger effect is expected for larger target volumes. A better understanding of the FLASH effect and the role of oxygen (depletion) therein is essential for the further development of FLASH-PT with PBS, and SPO.

Quantitative Volumetric Analysis of Retinal Ischemia with an Oxygen Diffusion Model and OCT Angiography

PurposeRetinal ischemia is a major feature of diabetic retinopathy (DR). Traditional nonperfused areas measured by optical coherence tomography angiography (OCTA) measure blood supply but not ischemia. We propose a novel 3-dimensional (3D) quantitative method to derive ischemia measurements from OCTA data. DesignCross-sectional study. ParticipantsWe acquired 223 macular OCTA volumes from 33 healthy eyes, 33 diabetic eyes without retinopathy, 7 eyes with non-referable DR, 17 eyes with referable but non-vision-threatening DR, and 133 eyes with vision-threatening DR. MethodsEach eye was scanned using a spectral-domain OCTA system (Avanti RTVue-XR, Visionix/Optovue, Inc) with 1.6 mm scan depth in a 3 × 3-mm region (640 × 304 × 304 voxels) centered on the fovea. For each scanned OCTA volume, a custom algorithm removed flow projection artifacts. We then enhanced, binarized, and skeletonized the vasculature in each OCTA volume and generated a 3D oxygen tension map using a zero-order kinetics oxygen diffusion model. Each volume was scaled to the average retina thickness in healthy controls after foveal registration and flattening of the Bruch membrane. Finally, we extracted 3D ischemia maps by comparison with a reference map established from scans of healthy eyes using the same processing. To assess the ability of the ischemia maps to grade DR severity, we constructed receiver-operating characteristic (ROC) curves for diagnosing diabetes, referable DR, and vision-threatening DR. Main outcome measuresSpearman correlation coefficient and area under ROC curve (AUC) were used to quantify the ability of the ischemia maps to DR. ResultsThe ischemia maps showed that the ischemic tissues were at or near pathologically non-perfused areas, but not the normally non-vascular tissue, such as the foveal avascular zone. We found multiple novel metrics, including inferred 3D-oxygen tension, ischemia index, and ischemic volume ratio, were strongly correlated with DR severity. The AUCs of ischemia index measured were 0.95 for diabetes, 0.89 for DR, 0.88 for referable DR, and 0.85 for vision threatening DR. ConclusionsA quantitative method to infer 3D oxygen tension and ischemia using OCTA in diabetic eyes can identify ischemic tissue that are more specific to pathologic changes in DR.

A New Robust Iterative Scheme Applied in Solving a Fractional Diffusion Model for Oxygen Delivery via a Capillary of Tissues

In this paper, we constructed a new and robust fixed point iterative scheme called the UO iterative scheme for the approximation of a contraction mapping. The scheme converges strongly to the fixed point of a contraction mapping. A rate of convergence result is shown with an example, and our scheme, when compared, converges faster than some existing iterative schemes in the literature. Furthermore, the stability and data dependence results are shown. Our new scheme is applied in the approximation of the solution to the oxygen diffusion model. Finally, our results are applied in the approximation of the solution to the boundary value problems using Green’s functions with an example.

Increased Retinal Metabolism Induced by Flicker in the Isolated Mouse Retina.

Both the retina and brain exhibit neurovascular coupling, increased blood flow during increased neural activity. In the retina increased blood flow can be evoked by flickering light, but the magnitude of the metabolic change that underlies this is not known. Local changes in oxygen consumption (QO2) are difficult to measure in vivo when both supply and demand are changing. Here we isolated the C57BL/6J mouse retina and supplied it with oxygen from both sides of the tissue. Microelectrode recordings of PO2 were made in darkness and during 20 s of high scotopic flickering light at 1 Hz. Flicker led to a PO2 increase in the outer retina and a decrease in the inner retina, indicating that outer retinal QO2 (QOR) decreased and inner retinal QO2 (QIR) increased. A four-layer oxygen diffusion model was fitted to PO2 values obtained in darkness and at the end of flicker to determine the values of QOR and QIR. QOR in flicker was 76 ± 14% (mean and SD, n = 10) of QOR in darkness. The increase in QIR was smaller, 6.4 ± 5.0%. These metabolic changes are likely smaller than the maximum changes, because with no regeneration of pigment in the isolated retina, we limited the illumination. Further modeling indicated that at high illumination, QIR could increase by up to 45%, which is comparable to the magnitude of flow changes. This suggests that the blood flow increase is at least roughly matched to the increased metabolic demands of activity in the retina.

High-temperature oxidation characteristics of 20CrMnTi electroplated with copper

During high-temperature forming and phase change heat treatment, the steel surface is susceptible to oxidation. This can negatively affect the surface quality of steel parts. The production of antioxidant coatings on the surface of steel parts is important for high-temperature precision forming and heat treatment. In this paper, the high-temperature oxidation tests of 20CrMnTi steel, copper, and 20CrMnTi electroplated with copper are conducted. The 20CrMnTi samples showed varying degrees of mass gain above 900 °C; the copper samples showed varying degrees of mass gain above 700 °C; and the process of mass gain for copper-plated 20CrMnTi followed the same trend as for copper during heating and holding. For heated samples of 20CrMnTi plated with copper, the copper coating was oxidized and residual copper was observed in the oxide layer. The distance between the residual copper and the surface of the sample is greater than between the residual copper and the junction of the plating layer and the substrate. Oxygen diffuses through internal defects in the material at a higher rate than copper oxidation. In this study, an oxygen diffusion model and an antioxidant protective layer model at high temperatures were suggested. The protective layer against oxidation recommended in this research is a dense coating consisting of single crystals or fine grains free of porosities and cracks.

Mathematical model of oxygen, nutrient, and drug transport in tuberculosis granulomas.

Physiological abnormalities in pulmonary granulomas-pathological hallmarks of tuberculosis (TB)-compromise the transport of oxygen, nutrients, and drugs. In prior studies, we demonstrated mathematically and experimentally that hypoxia and necrosis emerge in the granuloma microenvironment (GME) as a direct result of limited oxygen availability. Building on our initial model of avascular oxygen diffusion, here we explore additional aspects of oxygen transport, including the roles of granuloma vasculature, transcapillary transport, plasma dilution, and interstitial convection, followed by cellular metabolism. Approximate analytical solutions are provided for oxygen and glucose concentration, interstitial fluid velocity, interstitial fluid pressure, and the thickness of the convective zone. These predictions are in agreement with prior experimental results from rabbit TB granulomas and from rat carcinoma models, which share similar transport limitations. Additional drug delivery predictions for anti-TB-agents (rifampicin and clofazimine) strikingly match recent spatially-resolved experimental results from a mouse model of TB. Finally, an approach to improve molecular transport in granulomas by modulating interstitial hydraulic conductivity is tested in silico.

Mathematical Modeling of Oxygen Diffusion from Capillary to Tissues during Hypoxia through Multiple Points Using Fractional Balance Equations with Memory.

The diffusion of oxygen through capillary to surrounding tissues through multiple points along the length has been addressed in many clinical studies, largely motivated by disorders including hypoxia. However relatively few analytical or numerical studies have been communicated. In this paper, as a compliment to physiological investigations, a novel mathematical model is developed which incorporates the multiple point diffusion of oxygen from different locations in the capillary to tissues, in the form of a fractional dynamical system of equations using the concept of system of balance equations with memory. Stability analysis of the model has been conducted using the well known Routh-Hurwitz stability criterion. Comprehensive analytical solutions for the differntial equation problem in the new proposed model are obtained using Henkel transformations. Both spatial and temporal variation of concentration of oxygen is visualized graphically for different control parameters. Close correlation with simpler models is achieved. Diffusion is shown to arise from different points of the capillary in decreasing order along the length of the capillary i.e. for the different values of z. The concentration magnitudes at low capillary length far exceed those further along the capillary. Furthermore with progrssive distance along the capillary, the radial distance of diffusion decreases, such that oxygen diffuses only effectively in very close proximity to tissues. The simulations provide a useful benchmark for more generalized mass diffusion computations with commercial finite element and finite volume software including ANSYS FLUENT.

Oxygen profiles and oxygen consumption in the isolated mouse retina

The retina has a large demand for oxygen, but there is only limited information on differences between oxygen utilization (QO2) in the inner and outer retina, and limited data on mouse, which has become a prevalent animal model. This study utilized the isolated mouse retina, which allowed more detailed spatial analysis of QO2 than other methods. Oxygen sensitive microelectrodes were used to obtain profiles of oxygen tension across the isolated mouse retina, and mathematical models of retinal oxygen diffusion with four and five layers were fitted to the data to obtain values for QO2 of the outer retina (QOR) and inner retina (QIR). The boundaries between layers were free parameters in these models. The five-layer model resulted in lower error between the model and data, and agreed better with known anatomy. The three layers for the outer retina occupied half of the retina, as in prior work on rat, cat, and monkey, and the inner half of the retina could be divided into two layers, in which the one closer to the vitreous (layer 5) had much lower QO2 than the more distal inner retina (layer 4). QIR in darkness was 3.9 ml O2-100 g−1-min−1, similar to the value for intact cat retina, and did not change during light. QOR in darkness was 2.4 ml O2-100 g−1-min−1, lower than previous values in cat and rat, possibly because of damage to photoreceptors during isolation. There was a tendency for QOR to be lower in light, but it was not significant in this preparation.

Elucidating the relationship between gaseous O2 and redox potential in a soil aquifer treatment system using data driven approaches and an oxygen diffusion model

Knowledge concerning the redox potential (Eh) conditions in the vadose zone of a soil aquifer treatment (SAT) system constitutes valuable information for assessing water quality and operational efficiency. The complex nature of Eh conditions in SAT limits the ability to predict and quantify them using detailed models. Alternatively, data-driven models can be used for predictions and relationship analysis. Hourly measurements of Eh, volumetric water content (θ), soil temperature (T), and gaseous oxygen (O2) were obtained at multiple depths of a SAT vadose zone. A correlation analysis showed that O2 correlated with Eh for most temporal components. Only the monthly component of T and the daily component of θ were correlated with Eh. A detailed multiple linear regression (MLR) analysis illustrated that the gaseous O2, at shallow depths, can explain the majority (above 80%) of the Eh variability. The MLR curve demonstrated breakpoints in the Eh response to O2 at shallow depths, which were identified using a piecewise regression. These breakpoints explain, in part, the different stages of microbial activity throughout the SAT wetting and drying cycles. Combining an oxygen transport analytical model with the piecewise regression enabled the Eh prediction through easy-to-acquire T and θ measurements. At deeper depths, the Eh–O2 relationship demonstrates a step-function characteristic, which indicates that the changes in Eh occur due to the arrival of a low-Eh solution. Thus, the Eh dynamic in the SAT vadose zone is mostly controlled by aerobic conditions.

Biological processes of nitrogen removal and modeling oxygen diffusion in flocculent sludge and in granular sequencing batch reactors

AbstractBACKGROUNDSimultaneous nitrification‐denitrification (SND) in biological wastewater treatment occurs under aerobic conditions in flocs and granules, exhibiting aerobic and internal anoxic zones; SND depends on dissolved oxygen concentration. Aerobic denitrification (AD) is an advantageous process because control of aeration is not required. In the present study, the effects of anoxic/aerobic conditions and size of microbial aggregates on the AD process were evaluated using sequencing batch reactors (SBR) with activated sludge (anoxic/aerobic SBRAS) or aerobic granules (SBRAG).RESULTSNitrogen mass balances were used to estimate nitrogen assimilation, nitrification and denitrification. An oxygen diffusion model was proposed to evaluate oxygen profiles in the microbial aggregates determining the contribution of AD on nitrogen removal. At COD:N ratio = 100:10, fully aerobic biomass was predicted for all flocs in SBRAS and for 82% of the granules in SBRAG. In SBRAS, intracellular carbon storage was favored in the anoxic phase; nitrification was followed by AD, achieving 67% inorganic nitrogen (Ni) removal. In SBRAG, SND was 55% and Ni removal 51%. For SBRAG, genomic analysis described microbial community and nitrogen metabolic pathways were proposed. Heterotrophic nitrification‐aerobic denitrification (HNAD) was proposed as the main nitrogen removal process. At COD:N = 100:15, 80% of the granules developed internal anoxic zones; anoxic denitrification predominated, allowing treatment of a higher nitrogen load with similar Ni removal.CONCLUSIONSBiological processes without oxygen control are simpler to operate. For anoxic/aerobic SBR, high Ni removal efficiency was achieved even with 3.5–5.4 mg O2 L−1 at the center of the flocs, as predicted by the diffusion model. In aerobic granular systems, SND carried out by HNAD bacteria constitutes a promising approach for nitrogen removal. © 2022 Society of Chemical Industry (SCI).

Single-Pipe Model of Oxygen Diffusion in Unsaturated Cement Pastes: Comprehensive Analysis of Surface, Knudsen, Bulk, Transition, and Water-Curtain Diffusion

Single-Pipe Model of Oxygen Diffusion in Unsaturated Cement Pastes: Comprehensive Analysis of Surface, Knudsen, Bulk, Transition, and Water-Curtain Diffusion

Energy-Efficient H2O2 Electro-production Based on an Integrated Natural Air-Diffusion Cathode and Its Application

Given the low oxygen mass transfer rate and high aeration energy consumption, the traditional two-electron oxygen reduction reaction (ORR) is restricted. In this study, the integrated natural air diffusion cathode (INAC) and a reactor configuration with the horizontal scale facing to air (FTA) demonstrated highly selective H2O2 production for the removal of organic contaminants. Simply synthesized by shaping the mixture of carbon black and polytetrafluoroethylene, the INAC exhibited not only massive pores in all directions for sufficient mass transfer but also the integrated configuration for low charge transfer resistance. Based on the oxygen mass transfer models, for the ORR reaction kinetics, the interface oxygen concentration index was higher than 40, contributing to the high current efficiency of H2O2 production (>90%). The oxygen diffusion model can provide the quantitative description of H2O2 synthesis for porous electrode optimized design. Combining the INAC with the reactor configuration with the FTA mode for free additional O2/air source supply, the electrical efficiency per order was lower than 0.14 kWh m–3, and the removal rate of sulfonamides per unit current could reach 11 mg min–1 A–1, reaching the best reports. This ultraefficient process equipped with the INAC and the FTA mode provides a meaningful practical application prospect for wastewater treatment.

Modeling the Effect of Hyperoxia on the Spin-Lattice Relaxation Rate R1 of Tissues.

PurposeInducing hyperoxia in tissues is common practice in several areas of research, including oxygen‐enhanced MRI (OE‐MRI), which attempts to use the resulting signal changes to detect regions of tumor hypoxia or pulmonary disease. The linear relationship between PO2 and R1 has been reproduced in phantom solutions and body fluids such as vitreous fluid; however, in tissue and blood experiments, factors such as changes in deoxyhemoglobin levels can also affect the ΔR1.Theory and MethodsThis manuscript proposes a three‐compartment model for estimating the hyperoxia‐induced changes in R1 of tissues depending on B0, SO2, blood volume, hematocrit, oxygen extraction fraction, and changes in blood and tissue PO2. The model contains two blood compartments (arterial and venous) and a tissue compartment. This model has been designed to be easy for researchers to tailor to their tissue of interest by substituting their preferred model for tissue oxygen diffusion and consumption. A specific application of the model is demonstrated by calculating the resulting ΔR1 expected in healthy, hypoxic and necrotic tumor tissues. In addition, the effect of sex‐based hematocrit differences on ΔR1 is assessed.ResultsThe ΔR1 values predicted by the model are consistent with reported literature OE‐MRI results: with larger positive changes in the vascular periphery than hypoxic and necrotic regions. The observed sex‐based differences in ΔR1 agree with findings by Kindvall et al. suggesting that differences in hematocrit levels may sometimes be a confounding factor in ΔR1.ConclusionThis model can be used to estimate the expected tissue ΔR1 in oxygen‐enhanced MRI experiments.

Electrically‐Driven Oxygen Vacancy Aggregation and Displacement in YBa2Cu3O7−δ Films

AbstractCombining direct visualization of current‐induced oxygen migration through optical microscopy and finite element modeling of driven oxygen diffusion, it is possible to estimate the average activation energy of oxygen motion in the crystallographic ab‐plane of c‐axis oriented polycrystalline YBa2Cu3O7−δ films. Experiments and modeling are compared side‐by‐side for the case of constant current electromigration as well as for a train of current pulses of varying amplitude. The simulations reproduce the induced resistance changes after electromigration and confirm a high degree of spatial inhomogeneity in the stoichiometry. Assuming a temperature and oxygen concentration dependent resistivity, the authors are able to capture the change of superconducting critical temperature, normal state resistance, and the development of multistep transitions as a function of the electromigration history. The simulations are further applied to scrutinize the influence of activation energy, disorder in oxygen content, and initial oxygen concentration on the electromigration process. These results shed new light on the non‐local modifications produced by the electromigration process on oxide conductors.

A moving boundary model for oxygen diffusion in a sick cell

In this paper we use an approximate analytical method for numerical solution of one dimensional moving boundary problem. We consider the oxygen diffusion problem where the oxygen is allowed to diffuse into a sick cell which absorbs and immobilizes oxygen at a constant rate. Our main problem consists in tracking the moving boundary that represents the oxygen penetration depth inside the sick cell. We can find an accurate solution which is obtained by a polynomial of third and fourth degree and we show some mistakes in the paper published by Seval Çatal in (App.Math.Comput 145:361–369, 2003).

The Better-of-Two Strategy for Active versus Passive Management: The Option Value of Active through Time

<h3>Abstract</h3> The placenta is a temporary and complex organ critical for fetal development through its subtle but convoluted harmonization of endocrine, vascular, haemodynamic and exchange adaptations. Yet, due to experimental, technological and ethical constraints, this unique organ remains poorly understood. <i>In silico</i> tools are emerging as a powerful means to overcome these challenges and have the potential to actualize novel breakthroughs. Here, we present an interdisciplinary framework combining <i>in vitro</i> experiments used to develop an elegant and scalable <i>in silico</i> model of oxygen diffusion. We then use <i>in utero</i> imaging of placental perfusion and oxygenation in both control and growth-restricted rodent placentas for validation of our <i>in silico</i> model. Our framework revealed the structure-function relationship in the feto-placental vasculature; oxygen diffusion is impaired in growth-restricted placentas, due to the diminished arborization of growth-restricted feto-placental vasculature and the lack of decelerated flow for adequate oxygen diffusion and exchange. We highlight the mechanisms of impairment in a rat model of growth restriction, underpinned by placental vascular impairment. Our framework reports and validates the prediction of blood flow deceleration impairment in growth restricted placentas with the placenta’s oxygen transfer capability being significantly impaired, both globally and locally.

Oxygen Depletion in Proton Spot Scanning: A Tool for Exploring the Conditions Needed for FLASH

FLASH radiotherapy is a rapidly developing field which promises improved normal tissue protection compared to conventional irradiation and no compromise on tumour control. The transient hypoxic state induced by the depletion of oxygen at high dose rates provides one possible explanation. However, studies have mostly focused on uniform fields of dose and there is a lack of investigation into the spatial and temporal variation of dose from proton pencil-beam scanning (PBS). A model of oxygen reaction and diffusion in tissue has been extended to simulate proton PBS delivery and its impact on oxygen levels. This provides a tool to predict oxygen effects from various PBS treatments, and explore potential delivery strategies. Here we present a number of case applications to demonstrate the use of this tool for FLASH-related investigations. We show that levels of oxygen depletion could vary significantly across a large parameter space for PBS treatments, and highlight the need for in silico models such as this to aid in the development and optimisation of FLASH radiotherapy.