Diffusion of oxygen in plasma and blood

Relating Macroscopic PET Radiomics Features to Microscopic Tumor Phenotypes Using a Stochastic Mathematical Model of Cellular Metabolism and Proliferation

Cancers can manifest large variations in tumor phenotypes due to genetic and microenvironmental factors, which has motivated the development of quantitative radiomics-based image analysis with the aim to robustly classify tumor phenotypes in vivo. Positron emission tomography (PET) imaging can be particularly helpful in elucidating the metabolic profiles of tumors. However, the relatively low resolution, high noise, and limited PET data availability make it difficult to study the relationship between the microenvironment properties and metabolic tumor phenotype as seen on the images. Most of previously proposed digital PET phantoms of tumors are static, have an over-simplified morphology, and lack the link to cellular biology that ultimately governs the tumor evolution. In this work, we propose a novel method to investigate the relationship between microscopic tumor parameters and PET image characteristics based on the computational simulation of tumor growth. We use a hybrid, multiscale, stochastic mathematical model of cellular metabolism and proliferation to generate simulated cross-sections of tumors in vascularized normal tissue on a microscopic level. The generated longitudinal tumor growth sequences are converted to PET images with realistic resolution and noise. By changing the biological parameters of the model, such as the blood vessel density and conditions for necrosis, distinct tumor phenotypes can be obtained. The simulated cellular maps were compared to real histology slides of SiHa and WiDr xenografts imaged with Hoechst 33342 and pimonidazole. As an example application of the proposed method, we simulated six tumor phenotypes that contain various amounts of hypoxic and necrotic regions induced by a lack of oxygen and glucose, including phenotypes that are distinct on the microscopic level but visually similar in PET images. We computed 22 standardized Haralick texture features for each phenotype, and identified the features that could best discriminate the phenotypes with varying image noise levels. We demonstrated that "cluster shade" and "difference entropy" are the most effective and noise-resilient features for microscopic phenotype discrimination. Longitudinal analysis of the simulated tumor growth showed that radiomics analysis can be beneficial even in small lesions with a diameter of 3.5-4 resolution units, corresponding to 8.7-10.0 mm in modern PET scanners. Certain radiomics features were shown to change non-monotonically with tumor growth, which has implications for feature selection for tracking disease progression and therapy response.

Metabolic collaboration between cells in the tumor microenvironment has a negligible effect on tumor growth

The tumor microenvironment is composed of a complex mixture of different cell types interacting under conditions of nutrient deprivation, but the metabolism therein is not fully understood due to difficulties in measuring metabolic fluxes and exchange of metabolites between different cell types in vivo. Genome-scale metabolic modeling enables estimation of such exchange fluxes as well as an opportunity to gain insight into the metabolic behavior of individual cell types. Here, we estimated the availability of nutrients and oxygen within the tumor microenvironment using concentration measurements from blood together with a metabolite diffusion model. In addition, we developed an approach to efficiently apply enzyme usage constraints in a comprehensive metabolic model of human cells. The combined modeling reproduced severe hypoxic conditions and the Warburg effect, and we found that limitations in enzymatic capacity contribute to cancer cells' preferential use of glutamine as a substrate to the citric acid cycle. Furthermore, we investigated the common hypothesis that some stromal cells are exploited by cancer cells to produce metabolites useful for the cancer cells. We identified over 200 potential metabolites that could support collaboration between cancer cells and cancer-associated fibroblasts, but when limiting to metabolites previously identified to participate in such collaboration, no growth advantage was observed. Our work highlights the importance of enzymatic capacity limitations for cell behaviors and exemplifies the utility of enzyme-constrained models for accurate prediction of metabolism in cells and tumor microenvironments.

Microfluidic design for in-vitro liver zonation-a numerical analysis using COMSOL Multiphysics

The liver is one of the most important organs, with a complex physiology. Current in-vitro approaches are not accurate for disease modeling and drug toxicity research. One of those features is liver zonation, where cells display different physiological states due to different levels of oxygen and nutrient supplements. Organ-on-a-chip technology employs microfluidic platforms that enable a controlled environment for in-vitro cell culture. In this study, we propose a microfluidic design embedding a gas channel (of ambient air), creating an oxygen gradient. We numerically simulate different flow rates and cell densities with the COMSOL Multiphysics package considering cell-specific consumption rates of oxygen and glucose. We establish the cell density and flow rate for optimum oxygen and glucose distribution in the cell culture chamber. Furthermore, we show that a physiologically relevant concentration of oxygen and glucose in the chip is reached after 24 h and 30 min, respectively. The proposed microfluidic design and optimal parameters we identify in this paper provide a tool for in-vitro liver zonation studies. However, the microfluidic design is not exclusively for liver cell experiments but is foreseen to be applicable in cell studies where different gas concentration gradients are critical, e.g., studying hypoxia or toxic gas impact.

The aerotaxis of Dictyostelium discoideum is independent of mitochondria, nitric oxide and oxidative stress

Spatial and temporal variations of oxygen environments affect the behaviors of various cells and are involved in physiological and pathological events. Our previous studies with Dictyostelium discoideum as a model of cell motility have demonstrated that aerotaxis toward an oxygen-rich region occurs below 2% O₂. However, while the aerotaxis of Dictyostelium seems to be an effective strategy to search for what is essential for survival, the mechanism underlying this phenomenon is still largely unclear. One hypothesis is that an oxygen concentration gradient generates a secondary oxidative stress gradient that would direct cell migration towards higher oxygen concentration. Such mechanism was inferred but not fully demonstrated to explain the aerotaxis of human tumor cells. Here, we investigated the role on aerotaxis of flavohemoglobins, proteins that can both act as potential oxygen sensors and modulators of nitric oxide and oxidative stress. The migratory behaviors of Dictyostelium cells were observed under both self-generated and imposed oxygen gradients. Furthermore, their changes by chemicals generating or preventing oxidative stress were tested. The trajectories of the cells were then analyzed through time-lapse phase-contrast microscopic images. The results indicate that both oxidative and nitrosative stresses are not involved in the aerotaxis of Dictyostelium but cause cytotoxic effects that are enhanced upon hypoxia.

Rapid Formation of Methemoglobin via Nitric Oxide Delivery for Potential Use as an MRI Contrast Agent

Contrast-enhanced magnetic resonance angiography is a vital tool for evaluating vascular pathology. However, concerns about the limitations and safety of gadolinium-based contrast agents have led to an interest in alternative agents. Methemoglobin (metHb) increases the T1-weighted signal intensity of the magnetic resonance image of blood and could provide a safe and effective alternative. MetHb can be produced by the reaction of nitric oxide (NO) gas with oxyhemoglobin followed by natural conversion back to hemoglobin by cytochrome b5 reductase. Since rapid production of metHb via NO has not been studied, the effectiveness of producing metHb via NO delivery to blood was evaluated using a hollow-fiber module. MetHb production began immediately and > 90% conversion was achieved within 10 min. MetHb remained stable for at least 90 min when NO delivery was removed following metHb formation. Comparison of experimental data for metHb formation with model predictions showed that only a fraction of the NO delivered was utilized for metHb production, suggesting an additional fast reaction of NO with other blood constituents. Directly delivering NO to blood for the rapid formation of metHb provides a potential platform for producing metHb as an alternative contrast agent.

Computational Modeling and Imaging of the Intracellular Oxygen Gradient

Computational modeling can provide a mechanistic and quantitative framework for describing intracellular spatial heterogeneity of solutes such as oxygen partial pressure (pO₂). This study develops and evaluates a finite-element model of oxygen-consuming mitochondrial bioenergetics using the COMSOL Multiphysics program. The model derives steady-state oxygen (O₂) distributions from Fickian diffusion and Michaelis–Menten consumption kinetics in the mitochondria and cytoplasm. Intrinsic model parameters such as diffusivity and maximum consumption rate were estimated from previously published values for isolated and intact mitochondria. The model was compared with experimental data collected for the intracellular and mitochondrial pO₂ levels in human cervical cancer cells (HeLa) in different respiratory states and under different levels of imposed pO₂. Experimental pO₂ gradients were measured using lifetime imaging of a Förster resonance energy transfer (FRET)-based O₂ sensor, Myoglobin-mCherry, which offers in situ real-time and noninvasive measurements of subcellular pO₂ in living cells. On the basis of these results, the model qualitatively predicted (1) the integrated experimental data from mitochondria under diverse experimental conditions, and (2) the impact of changes in one or more mitochondrial processes on overall bioenergetics.

In silico analyses of blood flow and oxygen transport in human micro-veins and valves

BACKGROUND

Almost 95% of the venous valves are micron scale found in veins smaller than 300μm diameter. The fluid dynamics of blood flow and transport through these micro venous valves and their contribution to thrombosis is not yet well understood or characterized due to difficulty in making direct measurements in murine models.

OBJECTIVE

The unique flow patterns that may arise in physiological and pathological non-actuating micro venous valves are predicted.

METHODS

Computational fluid and transport simulations are used to model blood flow and oxygen gradients in a microfluidic vein.

RESULTS

The model successfully recreates the typical non-Newtonian vortical flow within the valve cusps seen in preclinical experimental models and in clinic. The analysis further reveals variation in the vortex strengths due to temporal changes in blood flow. The cusp oxygen is typically low from the main lumen, and it is regulated by systemic venous flow.

CONCLUSIONS

The analysis leads to a clinically-relevant hypothesis that micro venous valves may not create a hypoxic environment needed for endothelial inflammation, which is one of the main causes of thrombosis. However, incompetent micro venous valves are still locations for complex fluid dynamics of blood leading to low shear regions that may contribute to thrombosis through other pathways.

Attenuated Microcirculation in Small Metastatic Tumors in Murine Liver

Metastatic cancer disease is the major cause of death in cancer patients. Because those small secondary tumors are clinically hardly detectable in their early stages, little is known about drug biodistribution and permeation into those metastatic tumors potentially contributing to insufficient clinical success against metastatic disease. Our recent studies indicated that breast cancer liver metastases may have compromised perfusion of intratumoral capillaries hindering the delivery of therapeutics for yet unknown reasons. To understand the microcirculation of small liver metastases, we have utilized computational simulations to study perfusion and oxygen concentration fields in and around the metastases smaller than 700 µm in size at the locations of portal vessels, central vein, and liver lobule acinus. Despite tumor vascularization, the results show that blood flow in those tumors can be substantially reduced indicating the presence of inadequate blood pressure gradients across tumors. A low blood pressure may contribute to the collapsed intratumoral capillary lumen limiting tumor perfusion that phenomenologically corroborates with our previously published in vivo studies. Tumors that are smaller than the liver lobule size and originating at different lobule locations may possess a different microcirculation environment and tumor perfusion. The acinus and portal vessel locations in the lobule were found to be the most beneficial to tumor growth based on tumor access to blood flow and intratumoral oxygen. These findings suggest that microcirculation states of small metastatic tumors can potentially contribute to physiological barriers preventing efficient delivery of therapeutic substances into small tumors.

What are appropriate values of relative krogh diffusion Constant of NO against CO and of theta-NO in alveolar septa?

OBJECTIVES

To propose new physical constants for NO and CO (Krogh diffusion constant ratio (KD_NO/CO) and specific blood conductance for NO (θ_NO)) for calculating DMCO and Vc, according to Roughton-Forster's equation (Roughton and Forster, J. Appl. Physiol. 11: 290-302, 1957) from simultaneous DLNO and DLCO measurements.

RESULTS AND CONCLUSIONS

(1) The Graham's law is unacceptable for determining KD_NO/CO because CO does not fulfil all the conditions of an "ideal" gas. We have re-estimated KD_NO/CO in a new way based on difference in molar volumes of two gases (molar volume theory). The KD_NO/CO thus decided is 2.34. (2) θ_NO measured with rapid-reaction, constant-flow method by Carlsen and Comroe (J. Gen. Physiol. 42: 83-107, 1958) may be underestimated by about 40 % due to unstirred water layer surrounding the erythrocyte. (3) Erythrocyte θ_O2 can be harvested from O₂ release kinetics in presence of high concentration of dithionite, which effectively removes the unstirred water layer-elicited effect. Multiplication of erythrocyte θ_O2 by erythrocyte KD_NO/O2 equals erythrocyte θ_NO, the value of which is 6.2 mL/min/mmHg/(mL⋅blood). According to the concepts of Kang et al. (RESPNB. 241: 62-71, 2017) and Borland et al. (RESPNB. 241: 58-61, 2017), in vitro θ_NO decided from rapid-mixing experiments may mirror bulk absorption of NO by erythrocytes. (4) In pulmonary capillaries, NO uptake takes place predominantly in the surface rim of the erythrocyte. This surface absorption of NO increases the θ_NO 10-fold versus bulk absorption of NO to about 60 mL/min/mmHg/(mL⋅blood).

Computational fluid dynamic analysis of bioprinted self-supporting perfused tissue models

Natural tissues are incorporated with vasculature, which is further integrated with a cardiovascular system responsible for driving perfusion of nutrient‐rich oxygenated blood through the vasculature to support cell metabolism within most cell‐dense tissues. Since scaffold‐free biofabricated tissues being developed into clinical implants, research models, and pharmaceutical testing platforms should similarly exhibit perfused tissue‐like structures, we generated a generalizable biofabrication method resulting in self‐supporting perfused (SSuPer) tissue constructs incorporated with perfusible microchannels and integrated with the modular FABRICA perfusion bioreactor. As proof of concept, we perfused an MLO‐A5 osteoblast‐based SSuPer tissue in the FABRICA. Although our resulting SSuPer tissue replicated vascularization and perfusion observed in situ, supported its own weight, and stained positively for mineral using Von Kossa staining, our in vitro results indicated that computational fluid dynamics (CFD) should be used to drive future construct design and flow application before further tissue biofabrication and perfusion. We built a CFD model of the SSuPer tissue integrated in the FABRICA and analyzed flow characteristics (net force, pressure distribution, shear stress, and oxygen distribution) through five SSuPer tissue microchannel patterns in two flow directions and at increasing flow rates. Important flow parameters include flow direction, fully developed flow, and tissue microchannel diameters matched and aligned with bioreactor flow channels. We observed that the SSuPer tissue platform is capable of providing direct perfusion to tissue constructs and proper culture conditions (oxygenation, with controllable shear and flow rates), indicating that our approach can be used to biofabricate tissue representing primary tissues and that we can model the system in silico.

Oxygen consumption in human, tissue-engineered myobundles during basal and electrical stimulation conditions

During three-dimensional culture of skeletal muscle in vitro, electrical stimulation provides an important cue to enhance skeletal muscle mimicry of the in vivo structure and function. However, increased respiration can cause oxygen transport limitations in these avascular three-dimensional constructs, leading to a hypoxic, necrotic core, or nonuniform cell distributions in larger constructs. To enhance oxygen transport with convection, oxygen concentrations were measured using an optical sensor at the inlet and outlet of an 80 μl fluid volume microphysiological system (MPS) flow chamber containing three-dimensional human skeletal muscle myobundles. Finite element model simulations of convection around myobundles and oxygen metabolism by the myobundles in the 80 μl MPS flow chamber agreed well with the oxygen consumption rate (OCR) at different flow rates, suggesting that under basal conditions, mass transfer limitations were negligible for flow rates above 1.5 μl s^-1. To accommodate electrodes for electrical stimulation, a modified 450 μl chamber was constructed. Electrical stimulation for 30 min increased the measured rate of oxygen consumption by the myobundles to slightly over 2 times the basal OCR. Model simulations indicate that mass transfer limitations were significant during electrical stimulation and, in the absence of mass transfer limitations, electrical stimulation induced about a 20-fold increase in the maximum rate of oxygen consumption. The results indicate that simulated exercise conditions increase respiration of skeletal muscle and mass transfer limitations reduce the measured levels of oxygen uptake, which may affect previous studies that model exercise with engineered muscle.

A Mechanistic Analysis of Possible Blood Transfusion Failure to Increase Circulatory Oxygen Delivery in Anemic Patients

The effects of changing hematocrit (Hct) on the rate of circulatory oxygen ([Formula: see text]) delivery were modeled analytically to describe transfusion of 0.5-3.0 units of packed red blood cells (pRBC, 300 mL/unit, 60% Hct) to anemic patients. In our model, Hct affects [Formula: see text] delivery to the microcirculation by changing blood [Formula: see text] carrying capacity and blood viscosity, which in turn affects blood flow velocity and, therefore, [Formula: see text] delivery. Changing blood velocity impacts the [Formula: see text] delivery by affecting the oxygen diffusive losses as blood transits through the arteriolar vasculature. An increase in Hct has two opposite effects: it increases the blood [Formula: see text] carrying capacity and decreases the flow velocity. This suggests the existence of an optimal Hct that maximizes [Formula: see text] delivery. Our results show that maximal [Formula: see text] delivery occurs in the anemic range, where [Formula: see text]%. Optimal blood management is associated with transfusing enough units up to reaching maximal [Formula: see text] delivery. Although somewhat complex to implement, this practice would result in both substantial blood savings and improved [Formula: see text] delivery.

The Relation Between Capillary Transit Times and Hemoglobin Saturation Heterogeneity. Part 1: Theoretical Models

Capillary dysfunction impairs oxygen supply to parenchymal cells and often occurs in Alzheimer's disease, diabetes and aging. Disturbed capillary flow patterns have been shown to limit the efficacy of oxygen extraction and can be quantified using capillary transit time heterogeneity (CTH). However, the transit time of red blood cells (RBCs) through the microvasculature is not a direct measure of their capacity for oxygen delivery. Here we examine the relation between CTH and capillary outflow saturation heterogeneity (COSH), which is the heterogeneity of blood oxygen content at the venous end of capillaries. Models for the evolution of hemoglobin saturation heterogeneity (HSH) in capillary networks were developed and validated using a computational model with moving RBCs. Two representative situations were selected: a Krogh cylinder geometry with heterogeneous hemoglobin saturation (HS) at the inflow, and a parallel array of four capillaries. The heterogeneity of HS after converging capillary bifurcations was found to exponentially decrease with a time scale of 0.15-0.21 s due to diffusive interaction between RBCs. Similarly, the HS difference between parallel capillaries also drops exponentially with a time scale of 0.12-0.19 s. These decay times are substantially smaller than measured RBC transit times and only weakly depend on the distance between microvessels. This work shows that diffusive interaction strongly reduces COSH on a small spatial scale. Therefore, we conclude that CTH influences COSH yet does not determine it. The second part of this study will focus on simulations in microvascular networks from the rodent cerebral cortex. Actual estimates of COSH and CTH will then be given.

Simultaneous measurement of pulmonary diffusing capacity for carbon monoxide and nitric oxide

In Europe and America, the newly-developed, simultaneous measurement of diffusing capacity for CO (D_LCO) and NO (D_LNO) has replaced the classic D_LCO measurement for detecting the pathophysiological abnormalities in the acinar regions. However, simultaneous measurement of D_LCO and D_LNO is currently not used by Japanese physicians. To encourage the use of D_LNO in Japan, the authors reviewed aspects of simultaneously-estimated D_LCO and D_LNO from previously published manuscripts. The simultaneous D_LCO-D_LNO technique identifies the alveolocapillary membrane-related diffusing capacity (membrane component, D_M) and the blood volume in pulmonary microcirculation (V_C); V_C is the principal factor constituting the blood component of diffusing capacity (D_B,D_B=θ·V_C where θ is the specific gas conductance for CO or NO in the blood). As the association velocity of NO with hemoglobin (Hb) is fast and the affinity of NO with Hb is high in comparison with those of CO, θ_NO can be taken as an invariable simply determined by diffusion limitation inside the erythrocyte. This means that θ_NO is independent of the partial pressure of oxygen (PO₂). However, θ_CO involves the limitations by diffusion and chemical reaction elicited by the erythrocyte, resulting in θ_CO to be a PO₂-dependent variable. Furthermore, D_LCO is determined primarily by D_B (∼77%), while D_LNO is determined equally by D_M (∼55%) and D_B (∼45%). This suggests that D_LCO is more sensitive for detecting microvascular diseases, while D_LNO can equally identify alveolocapillary membrane and microcirculatory abnormalities.

Limitations of oxygen delivery to cells in culture: An underappreciated problem in basic and translational research

Molecular oxygen is one of the most important variables in modern cell culture systems. Fluctuations in its concentration can affect cell growth, differentiation, signaling, and free radical production. In order to maintain culture viability, experimental validity, and reproducibility, it is imperative that oxygen levels be consistently maintained within physiological "normoxic" limits. Use of the term normoxia, however, is not consistent among scientists who experiment in cell culture. It is typically used to describe the atmospheric conditions of a standard incubator, not the true microenvironment to which the cells are exposed. This error may lead to the situation where cells grown in a standard "normoxic" oxygen concentration may actually be experiencing a wide range of conditions ranging from hyperoxia to near-anoxic conditions at the cellular level. This apparent paradox is created by oxygen's sluggish rate of diffusion through aqueous medium, and the generally underappreciated effects that cell density, media volume, and barometric pressure can have on pericellular oxygen concentration in a cell culture system. This review aims to provide an overview of this phenomenon we have termed "consumptive oxygen depletion" (COD), and includes a basic review of the physics, potential consequences, and alternative culture methods currently available to help circumvent this largely unrecognized problem.

A multiscale model of placental oxygen exchange: The effect of villous tree structure on exchange efficiency

The placenta is critical to fetal health during pregnancy as it supplies oxygen and nutrients to maintain life. It has a complex structure, and alterations to this structure across spatial scales are associated with several pregnancy complications, including intrauterine growth restriction (IUGR). The relationship between placental structure and its efficiency as an oxygen exchanger is not well understood in normal or pathological pregnancies. Here we present a computational framework that predicts oxygen transport in the placenta which accounts for blood and oxygen transport in the space around a placental functional unit (the villous tree). The model includes the well-defined branching structure of the largest villous tree branches, as well as a smoothed representation of the small terminal villi that comprise the placenta's gas exchange interfaces. The model demonstrates that oxygen exchange is sensitive to villous tree geometry, including the villous branch length and volume, which are seen to change in IUGR. This is because, to be an efficient exchanger, the architecture of the villous tree must provide a balance between maximising the surface area available for exchange, and the opposing condition of allowing sufficient maternal blood flow to penetrate into the space surrounding the tree. The model also predicts an optimum oxygen exchange when the branch angle is 24 °, as villous branches and TBs are spread out sufficiently to channel maternal blood flow deep into the placental tissue for oxygen exchange without being shunted directly into the DVs. Without concurrent change in the branch length and angles, the model predicts that the number of branching generations has a small influence on oxygen exchange. The modelling framework is presented in 2D for simplicity but is extendible to 3D or to incorporate the high-resolution imaging data that is currently evolving to better quantify placental structure.

Reproducing the Hemoglobin Saturation Profile, a Marker of the Blood Oxygenation Level Dependent (BOLD) fMRI Effect, at the Microscopic Level

The advent of functional MRI in the mid-1990s has catalyzed progress pertaining to scientific discoveries in neuroscience. With the prospect of elucidating the physiological aspect of the Blood Oxygenation Level Dependent (BOLD) effect we present a computational capillary-tissue system capable of mapping venous hemoglobin saturation— a marker of the BOLD hemodynamic response. Free and facilitated diffusion and convection for hemoglobin and oxygen are considered in the radial and axial directions. Hemoglobin reaction kinetics are governed by the oxyhemoglobin dissociation curve. Brain activation, mimicked by dynamic transitions in cerebral blood velocity (CBv) and oxidative metabolism (CMR_O2), is simulated by normalized changes in m = (ΔCBv/CBv)/(ΔCMR_O2/CMR_O2) of values 2, 3 and 4. Venous hemoglobin saturation profiles and peak oxygenation results, for m = 2, based upon a 50% and a 25% increase in CBv and CMR_O2, respectively, lie within physiological limits exhibiting excellent correlation with the BOLD signal, for short-duration stimuli. Our analysis suggests basal CBv and CMR_O2 values of 0.6 mm/s and 200 μmol/100g/min. Coupled CBv and CMR_O2 responses, for m = 3 and m = 4, overestimate peak hemoglobin saturation, confirming the system’s responsiveness to changes in hematocrit, CBv and CMR_O2. Finally, factoring in neurovascular effects, we show that no initial dip will be observed unless there is a time delay in the onset of increased CBv relative to CMR_O2.

Regulation of cellular gas exchange, oxygen sensing, and metabolic control

Cells must continuously monitor and couple their metabolic requirements for ATP utilization with their ability to take up O2 for mitochondrial respiration. When O2 uptake and delivery move out of homeostasis, cells have elaborate and diverse sensing and response systems to compensate. In this review, we explore the biophysics of O2 and gas diffusion in the cell, how intracellular O2 is regulated, how intracellular O2 levels are sensed and how sensing systems impact mitochondrial respiration and shifts in metabolic pathways. Particular attention is paid to how O2 affects the redox state of the cell, as well as the NO, H2S, and CO concentrations. We also explore how these agents can affect various aspects of gas exchange and activate acute signaling pathways that promote survival. Two kinds of challenges to gas exchange are also discussed in detail: when insufficient O2 is available for respiration (hypoxia) and when metabolic requirements test the limits of gas exchange (exercising skeletal muscle). This review also focuses on responses to acute hypoxia in the context of the original "unifying theory of hypoxia tolerance" as expressed by Hochachka and colleagues. It includes discourse on the regulation of mitochondrial electron transport, metabolic suppression, shifts in metabolic pathways, and recruitment of cell survival pathways preventing collapse of membrane potential and nuclear apoptosis. Regarding exercise, the issues discussed relate to the O2 sensitivity of metabolic rate, O2 kinetics in exercise, and influences of available O2 on glycolysis and lactate production.

Contribution of membrane permeability and unstirred layer diffusion to nitric oxide-red blood cell interaction

Nitric oxide (NO) consumption by red blood cell (RBC) hemoglobin (Hb) in vasculature is critical in regulating the vascular tone. The paradox of NO production at endothelium in close proximity of an effective NO scavenger Hb in RBCs is mitigated by lower NO consumption by RBCs compared to that of free Hb due to transport resistances including membrane resistance, extra- and intra-cellular resistances for NO biotransport to the RBC. Relative contribution of each transport resistance on NO-RBC interactions is still not clear. We developed a mathematical model of NO transport to a single RBC to quantify the contributions from individual transport barriers by analyzing the effect of RBC membrane permeability (P(m)), hematocrit (Hct) and NO-Hb reaction rate constants on NO-RBC interactions. Our results indicated that intracellular diffusion of NO was not a rate limiting step for NO-RBC interactions. The extracellular diffusion contributed 70-90% of total transport resistance for P(m)>1 cm s(-1) whereas membrane resistance accounts for 50-75% of total transport resistance for P(m)<0.1 cm s(-1). We propose a narrow P(m) range of 0.21-0.44 cm s(-1) for 10-45% Hct, respectively, below which membrane resistance is more significant and above which extracellular diffusion is a dominating transport resistance for NO-RBC interactions.

Predicted oxygenation efficacy of a thoracic artificial lung

A thoracic artificial lung (TAL) provides respiratory support for lung disease. How well a TAL improves blood oxygenation for a specific pathology depends on how the TAL is attached to the pulmonary circulation: in series with the natural lungs (NLs), in parallel, or in a hybrid series/parallel combination. A computational model, including hemodynamic and O(2) and CO(2) exchange components, predicts TAL effects on blood flow rates and gas transport in pulmonary disease states modeled by elevated pulmonary vascular resistance (PVR) or reduced oxygen diffusivity in the NLs. In most cases, parallel and series TAL attachment provide comparable, maximal oxygenation. Series, with passage of total cardiac output (CO) through the NLs, is preferred for its filtration of emboli. Hybrid TAL attachment is more complicated, requiring a third graft, yet oxygenates less well than parallel and series. With extreme elevations of PVR, as in primary pulmonary hypertension, parallel TAL attachment provides an oxygenating shunt around the high resistance of the NLs, thus unloading the right ventricle, normalizing CO, and maximizing oxygenation.

Outer retinal oxygen consumption of rat by phosphorescence lifetime imaging

PURPOSE

Since the metabolic function of the retinal tissue is altered due to physiologic changes or disease, measurements of outer retinal oxygen consumption (Q(OR)) may be beneficial in assessment of retinal status. The purpose of this study was to report measurements of Q(OR) in rats using a phosphorescence lifetime imaging technique.

METHODS

Phosphorescence lifetime imaging was performed and retinal PO(2) maps were generated in 10 rats under a light-adapted condition. Depth-resolved retinal PO(2) profiles were derived from the PO(2) maps. From the profiles, the maximum outer retina PO(2) (P(max)O(2)) was obtained and Q(OR) was calculated using a one-dimensional oxygen diffusion model. Repeatability, inter-location variability, and inter-subject variability of P(max)O(2) and Q(OR) measurements were established.

RESULTS

Intraclass correlation coefficients of repeated measurements of P(max)O(2) and Q(OR) were 0.89 and 0.70, respectively (P < 0.001). Inter-location variability of P(max)O(2) and Q(OR) measurements at superior to inferior contiguous locations on the retina were on average 9 mmHg and 0.22 ml O(2)/100 g-tissue-min, respectively. Mean and standard deviation of P(max)O(2) and Q(OR) measurements averaged over all rats were 60 ± 16 mmHg and 0.73 ± 0.28 ml O(2)/100 g-tissue-min, respectively. Inter-subject variability of P(max)O(2) and Q(OR) measurements was on average 2.3 and 1.5 times inter-location variability, respectively.

CONCLUSIONS

Measurements of outer retinal oxygen consumption can be made by phosphorescence lifetime imaging and may be of potential value for detecting changes in retinal oxygen metabolic activity due to altered physiological and pathological conditions over multiple locations and time points.

Three-dimensional numerical modeling and computational fluid dynamics simulations to analyze and improve oxygen availability in the AMC bioartificial liver

A numerical model to investigate fluid flow and oxygen (O(2)) transport and consumption in the AMC-Bioartificial Liver (AMC-BAL) was developed and applied to two representative micro models of the AMC-BAL with two different gas capillary patterns, each combined with two proposed hepatocyte distributions. Parameter studies were performed on each configuration to gain insight in fluid flow, shear stress distribution and oxygen availability in the AMC-BAL. We assessed the function of the internal oxygenator, the effect of changes in hepatocyte oxygen consumption parameters in time and the effect of the change from an experimental to a clinical setting. In addition, different methodologies were studied to improve cellular oxygen availability, i.e. external oxygenation of culture medium, culture medium flow rate, culture gas oxygen content (pO(2)) and the number of oxygenation capillaries. Standard operating conditions did not adequately provide all hepatocytes in the AMC-BAL with sufficient oxygen to maintain O(2) consumption at minimally 90% of maximal uptake rate. Cellular oxygen availability was optimized by increasing the number of gas capillaries and pO(2) of the oxygenation gas by a factor two. Pressure drop over the AMC-BAL and maximal shear stresses were low and not considered to be harmful. This information can be used to increase cellular efficiency and may ultimately lead to a more productive AMC-BAL.

Diffusing capacity reexamined: relative roles of diffusion and chemical reaction in red cell uptake of O2, CO, CO2, and NO

This paper presents an analytical expression for the diffusing capacity (Θt) of the red blood cell (RBC) for any reactive gas in terms of size and shape of the RBC, thickness of the unstirred plasma layer surrounding the RBC, diffusivities and solubilities of the gas in RBC and boundary layer, hematocrit, and the slope of the dissociation curve. The expression for Θthas been derived by spatial averaging of the fundamental convection-diffusion-reaction equation for O2in the RBC and has been generalized to all cell shapes and for other reactive gases such as CO, NO, and CO2. The effects of size and shape of the RBC, thickness of the unstirred plasma layer, hemoglobin concentration, and hematocrit on Θthave been analyzed, and the analytically obtained expression for Θthas been validated by comparison with different sets of existing experimental data for O2and CO2. Our results indicate that the discoidal shape of the human RBC with average dimensions of 1.6-μm thickness and 8-μm diameter is close to optimal design for O2uptake and that the true reaction velocity in the RBC is suppressed significantly by the mass transfer resistance in the surrounding unstirred layer. In vitro measurements using rapid-mixing technique, which measures Θtin the presence of artificially created large boundary layers, substantially underpredicts the in vivo diffusing capacity of the RBC in the diffusion-controlled regime. Depending on the conditions in the RBC, uptake of less reactive gases (such as CO) undergoes transition from reaction-limited to diffusion-limited regime. For a constant set of morphological parameters, the theoretical expression for Θtpredicts that Θt,NO> Θt,CO2> Θt,O2> Θt,CO.

A model of nitric oxide capillary exchange

OBJECTIVE

Our aim was to develop a mathematical model that describes the nitric oxide (NO) transport in and around capillaries. The model is used to make quantitative predictions for (1) the contribution of capillary endothelium to the nitric oxide flux into the parenchymal tissue cells; (2) the scavenging of arteriolar endothelium-derived NO by capillaries in the surrounding tissue; and (3) the role of myoglobin in tissue cells and plasma-based hemoglobin on NO diffusion in and around capillaries.

METHODS

We used a finite element model of a capillary and surrounding tissue with discrete parachute-shape red blood cells (RBCs) moving inside the capillary to obtain the NO concentration distribution. An intravascular mass transfer coefficient is estimated as a function of RBC membrane permeability and capillary hematocrit. A continuum model of the capillary is also formulated, in which blood is treated as a homogeneous fluid; it uses the mass transfer coefficient and provides a closed-form analytic solution for the average exchange rate of NO in a capillary-perfused region.

RESULTS

The NO concentration in the parenchymal cells depends on parameters such as RBC membrane permeability and capillary hematocrit; the concentration is predicted for a wide range of parameters. In the absence of myoglobin or plasma-based hemoglobin, the average tissue concentration generally ranges between 20 and 300 nM. In the presence of myoglobin or after transfusion of a hemoglobin-based blood substitute, there is minimal NO penetration into the tissue from the capillary endothelium.

CONCLUSIONS

The model suggests that NO originating from the capillary wall can diffuse toward the parenchymal cells and potentially sustain physiologically significant concentrations. The model provides estimates of NO exchange and concentration level in capillary-perfused tissue, and it can be used in models of NO transport around arterioles or other NO sources.

Plasma oxygen permeability may be a factor in atherosclerosis

Plasma oxygen permeability measures how easily oxygen dissolves in and diffuses through blood plasma. There has long been evidence that artery wall hypoxia plays a role in atherogenesis. This paper reviews the influence that plasma oxygen permeability has on artery wall oxygenation and presents experimental evidence for a relationship between plasma oxygen permeability and clinically significant obstructive coronary artery disease. Thirty-eight inpatients referred for diagnostic cardiac catheterization were scored for active coronary artery disease, and their plasma oxygen permeabilities were measured. There was a statistically significant (p = 0.04) correlation between active coronary artery disease and plasma oxygen permeability. There were also statistically significant differences in mean plasma oxygen permeability both between patients who did and did not have actively progressing coronary artery disease (p = 0.01) and between patients who did and did not have clinically significant obstructive coronary artery disease, whether it was actively progressing or not (p = 0.02). These findings suggest that a decline in plasma oxygen permeability may be one of the many factors associated with progression of atherosclerosis and that substances which increase oxygen permeability might offer a useful adjunct to current therapeutic measures.

Erythrocyte consumption of nitric oxide in presence and absence of plasma-based hemoglobin

Experimental measurements have suggested a consumption rate of nitric oxide (NO) by red blood cells (RBCs) that is orders of magnitude smaller than that of an equivalent concentration of free hemoglobin in solution. This difference has been attributed to external diffusion limitations in the transport of NO from the plasma to the surface of the RBC or to resistance in the transport through the erythrocytic membrane. A detailed mathematical model is developed to quantify the resistance to NO transport around a single RBC and to predict the consumption rate in the presence and absence of extracellular hemoglobin. We provide a description for the NO consumption rate as a function of hematocrit, RBC radius, membrane permeability, and extracellular hemoglobin concentration. We predict a first-order rate constant for NO consumption in blood between 7.5 x 10(2) and 6.5 x 10(3) s(-1) at a hematocrit of 45% for membrane permeability values between 0.1 and 40 cm/s. Our results suggest that the difference in NO uptake by RBCs and free hemoglobin is smaller than previously reported and it is hematocrit dependent.

Calculations of oxygen transport by red blood cells and hemoglobin solutions in capillaries

A theoretical model is developed to investigate the influence of hemoglobin-based oxygen carriers (HBOCs) on oxygen transport in capillary-size vessels. A discrete cell model is presented with red blood cells (RBCs) represented in their realistic parachute shape flowing in a single file through a capillary. The model includes the free and Hb-facilitated transport of O2 and Hb-O2 kinetics in the RBC and plasma, diffusion of free O2 in the suspending phase, capillary wall, interstitium and tissue. A constant tissue consumption rate is specified that drives the simultaneous release of O2 from RBC and plasma as the cells traverse the capillary. The model mainly focuses on low capillary hematocrits and studies the effect of free hemoglobin affinity, cooperativity and concentration. The results are expressed in the form of cell and capillary mass transfer coefficients, or inverse transport resistances, that relate the spatially averaged flux of O2 coming out of the RBC and capillary to a driving force for O2 diffusion. The results show that HBOCs at a concentration of 7 g/dl reduce the intracapillary transport resistance by as much as 60% when capillary hematocrit is 0.2. HBOCs with high O2 affinity unload most O2 at the venular end, while those with low affinity supply O2 at the arteriolar end. A higher cooperativity did not favor O2 delivery due to the large variation in the mass transfer coefficient values during O2 unloading. The mass transfer coefficients obtained will be used in simulations of O2 transport in complex capillary networks.

Calculations of intracapillary oxygen tension distributions in muscle

Characterizing the resistances to O(2) transport from the erythrocyte to the mitochondrion is important to understanding potential transport limitations. A mathematical model is developed to accurately determine the effects of erythrocyte spacing (hematocrit), velocity, and capillary radius on the mass transfer coefficient. Parameters of the hamster cheek pouch retractor muscle are used in the calculations, since significant amounts of experimental physiological data and mathematical modeling are available for this muscle. Capillary hematocrit was found to have a large effect on the PO(2) distribution and the intracapillary mass transfer coefficient per unit capillary area, k(cap), increased by a factor of 3.7 from the lowest (H=0.25) to the highest (H=0.55) capillary hematocrits considered. Erythrocyte velocity had a relatively minor effect, with only a 2.7% increase in the mass transfer coefficient as the velocity was increased from 5 to 25 times the observed velocity in resting muscle. The capillary radius is varied by up to two standard deviations of the experimental measurements, resulting in variations in k(cap) that are <15% at the reference case. The magnitude of these changes increases with hematocrit. An equation to approximate the dependence of the mass transfer coefficient on hematocrit is developed for use in simulations of O(2) transport from a capillary network.

Nonlinear model for capillary-tissue oxygen transport and metabolism

Oxygen consumption in small tissue regions cannot be measured directly, but assessment of oxygen transport and metabolism at the regional level is possible with imaging techniques using tracer 15O-oxygen for positron emission tomography. On the premise that mathematical modeling of tracer kinetics is the key to the interpretation of regional concentration-time curves, an axially-distributed capillary-tissue model was developed that accounts for oxygen convection in red blood cells and plasma, nonlinear binding to hemoglobin and myoglobin, transmembrane transport among red blood cells, plasma, interstitial fluid and parenchymal cells, axial dispersion, transformation to water in the tissue, and carriage of the reaction product into venous effluent. Computational speed was maximized to make the model useful for routine analysis of experimental data. The steady-state solution of a parent model for nontracer oxygen governs the solutions for parallel-linked models for tracer oxygen and tracer water. The set of models provides estimates of oxygen consumption, extraction, and venous pO2 by fitting model solutions to experimental tracer curves of the regional tissue content or venous outflow. The estimated myocardial oxygen consumption for the whole heart was in good agreement with that measured directly by the Fick method and was relatively insensitive to noise. General features incorporated in the model make it widely applicable to estimating oxygen consumption in other organs from data obtained by external detection methods such as positron emission tomography.

Modeling [15O]oxygen tracer data for estimating oxygen consumption

The most direct measure of oxidative tissue metabolism is the conversion rate of oxygen to water via mitochondrial respiration. To calculate oxygen consumption from the analysis of tissue residue curves or outflow dilution curves after injection of labeled oxygen one needs realistic mathematical models that account for convection, diffusion, and transformation in the tissue. A linear, three-region, axially distributed model accounts for intravascular convection, penetration of capillary and parenchymal cell barriers (with the use of appropriate binding spaces to account for oxygen binding to hemoglobin and myoglobin), the metabolism to [15O]water in parenchymal cells, and [15O]water transport into the venous effluent. Model solutions fit residue and outflow dilution data obtained in an isolated, red blood cell-perfused rabbit heart preparation and give estimates of the rate of oxygen consumption similar to those obtained experimentally from the flow times the arteriovenous differences in oxygen contents. The proposed application is for the assessment of regional oxidative metabolism in vivo from tissue 15O-residue curves obtained by positron emission tomography.

Effects of red cell spacing and red cell movement upon oxygen release under conditions of maximally working skeletal muscle

RBC spacing in capillaries plays an important role in that it determines the total number of RBCs contained in a capillary and, therefore, the total O2 flux out of the capillary. The detrimental effects of increased RBC spacing upon capillary O2 release are in part compensated for by enhanced O2 release out of single RBCs due to improved diffusion geometry and RBC movement. Non-uniformity of O2 flux brought about by the particulate nature of blood is considerably smaller than calculations which do not consider RBC movement indicate. It creates oscillations in the O2 supply to the tissue, the periodicity of which is fast, however, compared to the time constant of the PO2 decay in a temporarily unsupplied tissue. We conclude that non-uniformity of O2 flux out of capillaries due to large inter-erythrocytic plasma gaps does not play an important role for tissue O2 supply as long as average RBC spacing is sufficiently small to guarantee an appropriate overall capillary O2 flux.

A model study of intracellular oxygen gradients in a myoglobin-containing skeletal muscle fiber

A theoretical two-dimensional model is used to investigate oxygen gradients in a red skeletal muscle fiber. The model describes the steady state, free and myoglobin-facilitated diffusion of oxygen into a respiring cylindrical muscle fiber cross section. The oxygen tension at the sarcolemma is assumed to vary along the sarcolemma as an approximation to the discrete capillary oxygen supply around the fiber. Maximal oxygen gradients are studied by considering parameters relevant to a maximally-respiring red muscle fiber. The model predicts that angular variations in the oxygen tension imposed at the sarcolemma due to the discrete capillary sources do not penetrate deeply into the fiber over a range of physiological values for myoglobin concentration, diffusion coefficients, number of surrounding capillaries, and oxygen tension level at the sarcolemma. Also, the oxygen tension in the core of the fiber is determined by the average oxygen tension at the sarcolemma. The drop in oxygen tension from fiber periphery to core, however, does depend significantly on the myoglobin concentration, the oxygen tension level at the sarcolemma, and the oxygen and myoglobin diffusivities. This dependence is summarized by calculating the minimum average sarcolemmal oxygen tension for maximal respiration without the development of an intracellular anoxic region. For a myoglobin-rich muscle fiber (0.5 mM myoglobin), the model predicts that maximal oxygen consumption can proceed with a relatively flat (less than 5 mm Hg) oxygen tension drop from fiber periphery to core over a large range for diffusion coefficients.

Analysis of intracellular oxygenation of isolated adult cardiac myocytes

The influence of cellular shape, cellular O2 consumption rate, and intracellular diffusion coefficient for O2 on the magnitude of intracellular O2 gradients during hypoxia was analyzed with the model of Boag (Curr. Top. Radiat. Res. 5: 141-195, 1969) to determine whether these parameters could account for the experimentally measured O2 dependence curves for myoglobin (Mb) oxygenation and cytochrome a + a3 oxidation in heart cells. The analysis shows that the intracellular diffusion coefficient for O2 must be below 4 X 10(-6) cm2/s for a substantial intracellular gradient to occur. The intracellular diffusion coefficient was calculated from the difference in half-maximal oxidation (P50) values for isolated Mb and intracellular Mb and was found to be 1.76 X 10(-6) cm2/s. Use of this value and appropriate geometric models satisfactorily described the O2 dependence of Mb oxygenation and cytochrome a + a3 oxidation in cells over an eightfold range of O2 consumption rates. However, the analysis does not account for the correspondence of intracellular P50 values of Mb oxygenation and cytochrome a + a3 oxidation. This implies that there exists an intracellular heterogeneity of either Mb distribution, mitochondrial distribution, or mitochondrial respiratory characteristics. Such heterogeneity would further contribute to diffusion limitation of O2 supply during hypoxia and could be a major factor underlying the cardiac myocyte structure-function relationship.

Theoretical analysis of oxygen supply to contracted skeletal muscle

Honig and collaborators reported striking contradictions in current understanding of O2 supply to working skeletal muscle. Therefore we re-examined the problem by means of a new composite computer simulation. As inclusion of erythrocytic O2 desaturation and oxygen transport and consumption inside the muscle cell into a single model would entail immense numerical difficulties, we broke up the whole process into its several components: O2 desaturation of erythrocytes O2 transport and consumption in muscle fiber capillary transit time characterizing the period of contact between red cell and muscle fiber. "Erythrocyte model" as well as "muscle fiber model" both consist of a central core cylinder surrounded by a concentric diffusion layer representing the extracellular resistance to O2 diffusion (Fig. 1). Resistance layers in both models are to be conceived of as one and the same anatomical structure--even though in each model their shape is adapted to the respective geometry. By means of this overlap region a spatial connexion between both is given, whereas temporal coherence governing O2 fluxes and red cell spacing is derived from capillary transit time. Analysis of individual components is outlined as follows: Assuming axial symmetry of the problem a numerical algorithm was employed to solve the parabolic system of partial differential equations describing red cell O2 desaturation. Hb-O2 reaction kinetics, free and facilitated O2 diffusion in axial and radial directions, and red cell movement in capillary were considered. Resulting time courses of desaturation, which are considerably faster than the ones computed by Honig et al., are given in the following table (see also Fig. 3). (Formula: see text) Furthermore, we studied the respective importance of the several processes included in our model: Omission of longitudinal diffusion increased desaturation time by 15% to 23%, whereas effects of reaction kinetics and axial movement were 5% and 2% respectively. For time courses see Fig. 2. Nature and magnitude of extra-erythrocytic resistance to O2 diffusion playing a prominent part in O2 desaturation are scarcely explored. Calculated desaturation times based upon our new estimates (line 3 of above table) correspond well, however, with findings by Sinha, who observed 1.75 to 4-fold prolongation in omental and mesenteric capillaries compared to desaturation through equivalent plasma layers. The 3-dimensional elliptic system of partial differential equations describing stationary O2 transport through resistance layer and subsequent free and facilitated O2 diffusion and O2 consumption in muscle fiber was solved analytically.(ABSTRACT TRUNCATED AT 400 WORDS)

Limitations of tracer oxygen uptake in the canine coronary circulation

Theoretical models of oxygen transport in the myocardium have failed to account for low average tissue pO2 relative to to coronary sinus pO2, measured with pO2 electrodes and myoglobin saturation, and for hypoxic contractile failure at relatively high coronary sinus pO2 levels. These findings could be explained by either arteriovenous diffusional shunting or a limiting rate of transfer of oxygen from blood to tissue, or both. To gain new insights, we performed multiple indicator dilution tracer experiments across the coronary circulation in the dog, with 18O2 as the oxygen tracer and 51Cr-labeled red cells as the reference tracer for oxygen. 125I-Albumin and 22Na+ were included to provide the relative plasma flow rate. The tracer oxygen outflow curve consisted of a large early peak related to its reference red cell curve. No tracer emerged before the labeled red cells. The downslope, which contains the returning component of the tracer curve, decreased less steeply when oxygen consumption was reduced by propranolol. Fitting the tracer oxygen outflow curve with a distributed model including irreversible sequestration behind a resistance gave a transfer rate constant which was relatively small, and a relatively large rate constant for sequestration. Relative oxygen consumption (estimated from the arteriovenous difference) correlated closely with the rate constant for sequestration. Estimated average tissue oxygen concentrations were of the order of one-third blood concentration. Dimensional analysis indicates that the low transfer rate constant derives from hemoglobin-oxygen binding; this decreases fractional tracer oxygen transfer in proportion to the ratio of plasma:red cell oxygen pools.

Significance of luminal plasma layer resistance in arterial wall oxygen supply

Previous analyses of the arterial wall oxygen supply system have assumed that a cell-free layer of plasma next to the endothelium is the major transport barrier in the lumen. Using a computer simulation, we have quantitatively tested this assumption. Our results show that oxygen diffusion gradients extend significantly into the flowing blood well beyond any plasma layer and that the major luminal transport resistance lies in the flowing blood and not in the plasma layer. The simulation was also employed to compute the effect of a reported 50% drop in plasma oxygen diffusivity. This rather large reduction did significantly lower oxygen levels within the arterial wall tissue. Whether such large reductions in diffusivity ever actually occur in human plasma is a subject of current controversy.

Oxygen diffusivity in tumor tissue (DS-carcinosarcoma) under temperature conditions within the range of 20--40 degrees C

The O2 diffusion constants D and K of tumor tissue (DS-Carcinosarcoma in the rat kidney) were determined at temperatures of 20, 30, 37, and 40 degrees C. The following mean values were obtained for the conditions of 37 degrees C: D = 1.75-10(-5) cm2/s and K = 1.9-10(-5) mlO2/cm-min-atm. Within the range of 20-40 degrees C, temperature variations in tumor tissue cause changes in the O2 diffusion coefficient D of 2.0-2.5%/C and in the Krogh O2 diffusion constant K of 0.5-1.5%/C. The measured O2 diffusion constants for tumor tissue correspond to values of normal tissue with similar water content. This indicates that the insufficient O2 supply in DS-Carcinosarcoma is due not to unfavorable O2 diffusivity of the tumor tissue but rather to a decreased convective O2 transport and to insufficient capillarization. An analysis of O2 diffusion in DS-Carcinosarcoma tissue using the determined O2 diffusion constants lead to the result that, under the conditions of arterial normoxia and normocapnia, critical O2 supply conditions are to be expected when the intercapillary distance exceeds approximately 120 micrometer.