Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta

To investigate the effects of both non-Newtonian behavior and the pulsation of blood flow on the distributions of luminal surface LDL concentration and oxygen flux along the wall of the human aorta, we numerically compared a non-Newtonian model with the Newtonian one under both steady flow and in vivo pulsatile flow conditions using a human aorta model constructed from MRI images. The results showed that under steady flow conditions, although the shear thinning non-Newtonian nature of blood could elevate wall shear stress (WSS) in most regions of the aorta, especially areas with low WSS, it had little effect on luminal surface LDL concentration (c(w)) in most regions of the aorta. Nevertheless, it could significantly enhance c(w) in areas with high luminal surface LDL concentration through the shear dependent diffusivity of LDLs. For oxygen transport, the shear thinning non-Newtonian nature of blood could slightly reduce oxygen flux in most regions of the aorta, but this effect became much more apparent in areas with already low oxygen flux. The pulsation of blood flow could significantly reduce c(w) and enhance oxygen flux in these disturbed places. In most other regions of the aorta, the oxygen flux was also significantly higher than that for the steady flow simulation. In conclusion, the shear shining non-Newtonian nature of blood has little effect on LDL and oxygen transport in most regions of the aorta, but in the atherogenic-prone areas where luminal surface LDL concentration is high and oxygen flux is low, its effect is apparent. Similar is for the effect of pulsatile flow on the transport of LDLs. But, the pulsation of blood flow can apparently affect oxygen flux in the aorta, especially in areas with low oxygen flux.     

Determination of oxygen saturation and hematocrit of flowing human blood using two different spectrally resolving sensors.

The blood parameters oxygen saturation and hematocrit were determined by two different spectral sensors using reflectance spectra from 550 to 900 nm and partial transmission spectra centered at 660 nm. The spectra were analyzed by the method of partial least squares. One sensor consists of a miniature integrating sphere, while the other was fiber-guided. The results show that the geometry of the sensors and different blood flows do not influence the spectral analysis significantly. Independent of the sensor geometry, both hematocrit and oxygen saturation could be determined with an absolute predicted root mean square error of less than 3%. Furthermore, the analysis showed that hematocrit prediction requires eight wavelength regions and oxygen saturation prediction requires four wavelength regions using reflectance spectroscopy. This implies that if the measurement is restricted to reflectance, a spectrometer is indispensable for determining both blood parameters. Hematocrit determination could be improved using reflectance measurements in combination with transmission.     

Analysis of oxygen transport from pulsatile, viscous blood flow to diseased coronary arteries of man

Oxygen transport to multiple “non-obstructive” plaque regions in main coronary arteries of man was examined by numerically solving the oxygen transport equation for convective and diffusive processes in the lumen for actual variations of blood flow rate and the velocity field during the cardiac cycle. Oxygen transport to the wall varied significantly along the arterial section, was strongly dependent upon the various flow regions that occurred, and varied considerably during the cardiac cycle. A drastic reduction in oxygen transport to the arterial wall occurred at the incipient separation location on the back side of a plaque where it is believed that the lumen side resistance to oxygen transport is at least an order of magnitude greater than the inner avascular wall resistance, and therefore the availability of oxygen for cellular respiration is essentially boundary layer controlled. In vivo measurements with oxygen microelectrodes in animals are needed to learn more about variations of oxygen transport in plaque regions, in particular on the back side of plaques where hypoxia may occur.     

Evidence against significant resting alpha-adrenergic coronary vasoconstrictor tone

The importance of sympathetically mediated coronary vasoconstrictor tone as a determinant of resting coronary blood flow was assessed in the conscious dog by comparing blood flow and oxygen extraction in a normally innervated (I) and a previously sympathectomized (Sx) region of the same left ventricle. The regional ventricular sympathectomy was achieved by the topical application of phenol. The animals were well acclimated to the laboratory environment before regional myocardial blood flow was measured with microspheres or regional myocardial oxygen extraction was determined on blood sampled from chronically implanted coronary venous catheters. Results indicated that blood flow and oxygen extraction were not significantly different in I and Sx regions under these conditions. Regional blood flow data obtained after beta-adrenergic blockade or combined alpha- and beta-adrenergic blockade were not significantly different from control data. Thus we were unable to confirm previous evidence in the literature of significant resting sympathetic coronary vasoconstrictor tone in the conscious animal.     

Regional differences in blood flow and oxygen consumption in resting muscle and their relationship during recovery from exhaustive exercise.

This investigation evaluated regional differences in blood flow and oxygen consumption and their relationship in exercised muscle during recovery from exhaustive exercise. Five healthy men performed exhaustive one-legged cycling exercise. Positron emission tomography was used to measure blood flow, oxygen uptake, and oxygen extraction in the quadriceps femoris muscle before and after exercise. Regions of interest included five areas of the muscle (two proximal, one central, and two distal), which were evenly spaced across the muscle. Before exercise, blood flow and oxygen consumption decreased significantly (P < 0.05) in the direction from the proximal to the distal portions; blood flow declined from 2.0 +/- 0.5 to 1.4 +/- 0.3 ml x 100 g-1 x min-1, and oxygen consumption decreased from 0.21 +/- 0.04 to 0.17 +/- 0.02 ml.100 g-1x min-1. In contrast, these gradients in blood flow and oxygen consumption diminished during recovery after exercise. Consequently, there was a positive relationship between changes in blood flow and oxygen consumption in an exercised muscle during recovery after exercise (r = 0.963, P < 0.01). These changes became larger in the direction from proximal to distal portions: blood flow increased from 2.9 +/- 0.7 to 3.9 +/- 0.8 and oxygen consumption from 1.4 +/- 0.1 to 1.8 +/- 0.4 times resting values. These results suggest that hemodynamic variables are heterogeneous within a muscle both at rest and during recovery from exercise and that there is a systematic difference in these variables in the direction from proximal to distal regions within the quadriceps femoris muscle.     

Biochemical characterization of human S-nitrosohemoglobin. Effects on oxygen binding and transnitrosation.

S-Nitrosation of cysteine beta93 in hemoglobin (S-nitrosohemoglobin (SNO-Hb)) occurs in vivo, and transnitrosation reactions of deoxygenated SNO-Hb are proposed as a mechanism leading to release of NO and control of blood flow. However, little is known of the oxygen binding properties of SNO-Hb or the effects of oxygen on transnitrosation between SNO-Hb and the dominant low molecular weight thiol in the red blood cell, GSH. These data are important as they would provide a biochemical framework to assess the physiological function of SNO-Hb. Our results demonstrate that SNO-Hb has a higher affinity for oxygen than native Hb. This implies that NO transfer from SNO-Hb in vivo would be limited to regions of extremely low oxygen tension if this were to occur from deoxygenated SNO-Hb. Furthermore, the kinetics of the transnitrosation reactions between GSH and SNO-Hb are relatively slow, making transfer of NO+ from SNO-Hb to GSH less likely as a mechanism to elicit vessel relaxation under conditions of low oxygen tension and over the circulatory lifetime of a given red blood cell. These data suggest that the reported oxygen-dependent promotion of S-nitrosation from SNO-Hb involves biochemical mechanisms that are not intrinsic to the Hb molecule.     

A computational study of the effect of vasomotion on oxygen transport from capillary networks

The objective of this study was to investigate the effect of arteriolar vasomotion on oxygen transport from capillary networks. A computational model was used to calculate blood flow and oxygen transport from a simulated network of striated muscle capillaries. For varying tissue oxygen consumption rates, the importance of the frequency and amplitude of vasomotion-induced blood flow oscillations was studied. The effect of myoglobin on oxygen delivery during vasomotion was also examined. In the absence of myoglobin, it was found that when consumption is high enough to produce regions of hypoxia under steady flow conditions, vasomotion-induced flow oscillations can significantly increase tissue oxygenation and decrease oxygen transport heterogeneity. The largest effect was seen for low-frequency, high-amplitude oscillations (1.5-3 cycles min(-1), 90% of steady-state velocity). By contrast, at physiological tissue myoglobin concentrations, vasomotion did not improve tissue oxygenation. This unexpected finding is due to the buffering effect of myoglobin, suggesting that in highly aerobic muscles short-term storage of oxygen is more important than the possibility of increasing transport through vasomotion.     

Modeling the influence of superoxide dismutase on superoxide and nitric oxide interactions,including reversible inhibition of oxygen consumption

A mathematical mass transport model was constructed in cylindrical geometry to follow coupled biochemical reactions and diffusion of oxygen, nitric oxide, superoxide, peroxynitrite, hydrogen peroxide, nitrite, and nitrate around a blood vessel. Computer simulations were performed for a 50 microm internal diameter arteriole to characterize mass transport in five concentric regions (blood, plasma layer, endothelium, vascular wall, perivascular tissue). Steady state gradients in nitric oxide, oxygen partial pressure, superoxide, and peroxynitrite, and associated production of hydrogen peroxide, nitrite, and nitrate were predicted for varying superoxide production rates, superoxide dismutase concentrations, and other physiological conditions. The model quantifies how competition between superoxide scavenging by nitric oxide and superoxide dismutase catalyzed removal varies spatially. Reversible inhibition of oxygen consumption by nitric oxide, which causes increased tissue oxygenation at deeper locations, was also included in the model. The mass transport model provides insight into complex interactions between reactive oxygen and nitrogen species in blood and tissue, and provides an objective way to evaluate the relative influence of different biochemical pathways on these interactions.     

Quantification of hypoxic regions distant from occlusions in cerebral penetrating arteriole trees

The microvasculature plays a key role in oxygen transport in the mammalian brain. Despite the close coupling between cerebral vascular geometry and local oxygen demand, recent experiments have reported that microvascular occlusions can lead to unexpected distant tissue hypoxia and infarction. To better understand the spatial correlation between the hypoxic regions and the occlusion sites, we used both in vivo experiments and in silico simulations to investigate the effects of occlusions in cerebral penetrating arteriole trees on tissue hypoxia. In a rat model of microembolisation, 25 μm microspheres were injected through the carotid artery to occlude penetrating arterioles. In representative models of human cortical columns, the penetrating arterioles were occluded by simulating the transport of microspheres of the same size and the oxygen transport was simulated using a Green’s function method. The locations of microspheres and hypoxic regions were segmented, and two novel distance analyses were implemented to study their spatial correlation. The distant hypoxic regions were found to be present in both experiments and simulations, and mainly due to the hypoperfusion in the region downstream of the occlusion site. Furthermore, a reasonable agreement for the spatial correlation between hypoxic regions and occlusion sites is shown between experiments and simulations, which indicates the good applicability of in silico models in understanding the response of cerebral blood flow and oxygen transport to microemboli.     

Increasing blood oxygen increases an index of 5-HT synthesis in human brain as measured using alpha-[(11)C]methyl-L-tryptophan and positron emission tomography

The main objective of this investigation was to test the hypothesis that brain serotonin (5-HT) synthesis, as measured by trapping of alpha-[(11)C]methyl-L-tryptophan (alpha-MTrp) using positron emission tomography (PET), can be modulated by changes in blood oxygen. The study involved six healthy participants (three male and three female), who breathed a 15% or 60% oxygen mixture starting 15 min before the injection of tracer and continuing during the entire acquisition period. Participants were injected with up to 12m Ci of alpha-MTrp. Two sets of PET images were acquired while the participants were breathing each of the oxygen mixtures and, after reconstruction, all images were converted into brain functional images illustrating the brain trapping constant K(*) (microL/g/min). The K(*) values were obtained for 12 regions of interest outlined on the magnetic resonance images. The K(*) values obtained at high and low blood oxygen content were compared by paired statistics using Tukey's post hoc correction. As there were no difference in plasma tryptophan concentrations, these K(*) values are directly related to regional 5-HT synthesis. The results showed highly significant increases (50% on average) in brain serotonin synthesis (K(*) values) at high (mean value of 223+/-41 mmHg) relative to low (mean value 77.1+/-7.7 mmHg) blood oxygen levels. This suggests that tryptophan hydroxylase is not saturated with oxygen in the living human brain and that increases in blood oxygen can elevate brain serotonin synthesis.     

Myocardial O2 consumption in porcine left ventricle is heterogeneously distributed in parallel to heterogeneous O2 delivery

Myocardial blood flow is unevenly distributed, but the cause of this heterogeneity is unknown. Heterogeneous blood flow may reflect heterogeneity of oxygen demand. The aim of the present study was to assess the relation between oxygen consumption and blood flow in small tissue regions in porcine left ventricle. In seven male, anesthetized, open-chest pigs, local oxygen consumption was quantitated by computational model analysis of the incorporation of 13C in glutamate via the tricarboxylic acid cycle during timed infusion of [13C]acetate into the left anterior descending coronary artery. Blood flow was measured with radioactive microspheres before and during acetate infusion. High-resolution nuclear magnetic resonance 13C spectra were obtained from extracts of tissue samples (159 mg mean dry wt) taken at the end of the acetate infusion. Mean regional myocardial blood flow was stable [5.0 +/- 1.6 (SD) and 5.0 +/- 1.4 ml.min(-1).g dry wt(-1) before and after 30 min of acetate infusion, respectively]. Mean left ventricular oxygen consumption measured with the NMR method was 18.6 +/- 7.7 micromol.min(-1).g dry wt(-1) and correlated well (r = 0.85, P = 0.02, n = 7) with oxygen consumption calculated from blood flow, hemoglobin, and blood gas measurements (mean 22.8 +/- 4.7 micromol.min(-1).g dry wt(-1)). Local blood flow and oxygen consumption were significantly correlated (r = 0.63 for pooled normalized data, P < 0.0001, n = 60). We calculate that, in the heart at normal workload, the variance of left ventricular oxygen delivery at submilliliter resolution is explained for 43% by heterogeneity in oxygen demand.     

Cerebral blood flow in the fetal guinea-pig

To measure brain blood flow in the fetal guinea-pig, radioactive microspheres were injected in the lateral saphenous vein whilst a reference sample of blood was withdrawn from the right axillary artery. Measurements were made near term of pregnancy, on the 60th-66th day, during anaesthesia with pentobarbitone and diazepam. Fetal blood pressure was 4.25 +/- 0.12 kPa and fetal heart rate was 250 +/- 7 beats per min. The arterial oxygen content varied between 1.9-5.1 mmol 1(-1). Blood flow to the whole brain (mean 1.13 +/- 0.14 ml min-1 g-1) was significantly correlated to the reciprocal of arterial oxygen content (r = 0.84). Four regions of the brain were examined: the cerebral hemispheres, the cerebellum, the thalamus and midbrain, and the pons and medulla. In each region blood flow was inversely related to arterial oxygen content (r = 0.80-0.83) but the rate of perfusion of the brain stem was greater than that of the cerebral hemispheres or cerebellum.     

Interactions between ion and gas transfer in freshwater teleost fish

Carbonic anhydrase and proton ATPase are co-distributed, being restricted to the apical regions of the gill epithelium of freshwater teleosts. Carbonic anhydrase supplies protons to the apical proton ATPase. Carbonic anhydrase is absent from the basal regions of the gill epithelium. Plasma flowing through the gills has no available carbonic anhydrase activity and plasma CO2/bicarbonate reactions are uncatalyzed. Thus, bicarbonate dehydration in plasma is negligible, and catalyzed bicarbonate dehydration occurs in erythrocytes in blood flowing through the gills. This results in tight coupling of carbon dioxide excretion to oxygen uptake and the evolution of hemoglobins with large Haldane effects but low buffering capacities, typical of many freshwater teleosts. Tight coupling of carbon dioxide and oxygen transfer in these fish also ensures that the Root shift does not impair oxygen uptake at the gills. Under these conditions, there is a selective advantage for hemoglobins with a Root shift. The presence of a Root shift augments oxygen transfer to the tissues in general and the eye and swimbladder in particular.     

Embryonic mouse blood flow and oxygen correlate with early pancreatic differentiation

The mammalian embryo represents a fundamental paradox in biology. Its location within the uterus, especially early during development when embryonic cardiovascular development and placental blood flow are not well-established, leads to an obligate hypoxic environment. Despite this hypoxia, the embryonic cells are able to undergo remarkable growth, morphogenesis, and differentiation. Recent evidence suggests that embryonic organ differentiation, including pancreatic β-cells, is tightly regulated by oxygen levels. Since a major determinant of oxygen tension in mammalian embryos after implantation is embryonic blood flow, here we used a novel survivable in utero intracardiac injection technique to deliver a vascular tracer to living mouse embryos. Once injected, the embryonic heart could be visualized to continue contracting normally, thereby distributing the tracer specifically only to those regions where embryonic blood was flowing. We found that the embryonic pancreas early in development shows a remarkable paucity of blood flow and that the presence of blood flow correlates with the differentiation state of the developing pancreatic epithelial cells in the region of the blood flow.     

Stress-mediated progression of solid tumors: effect of mechanical stress on tissue oxygenation,cancer cell proliferation,and drug delivery

Oxygen supply plays a central role in cancer cell proliferation. While vascular density increases at the early stages of carcinogenesis, mechanical solid stresses developed during growth compress tumor blood vessels and, thus, drastically reduce not only the supply of oxygen, but also the delivery of drugs at inner tumor regions. Among other effects, hypoxia and reduced drug delivery compromise the efficacy of radiation and chemo/nanotherapy, respectively. In the present study, we developed a mathematical model of tumor growth to investigate the interconnections among tumor oxygenation that supports cancer cell proliferation, the heterogeneous accumulation of mechanical stresses owing to tumor growth, the non-uniform compression of intratumoral blood vessels due to the mechanical stresses, and the insufficient delivery of oxygen and therapeutic agents because of vessel compression. We found that the high vascular density and increased cancer cell proliferation often observed in the periphery compared to the interior of a tumor can be attributed to heterogeneous solid stress accumulation. Highly vascularized peripheral regions are also associated with greater oxygenation compared with the compressed, less vascularized inner regions. We also modeled the delivery of drugs of two distinct sizes, namely chemotherapy and nanomedicine. Model predictions suggest that drug delivery is affected negatively by vessel compression independently of the size of the therapeutic agent. Finally, we demonstrated the applicability of our model to actual geometries, employing a breast tumor model derived from MR images.     

Metabolic changes during carcinogenesis: potential impact on invasiveness

Successful adaptation to varying microenvironmental constraints plays a crucial role during carcinogenesis. We develop a hybrid cellular automation approach to investigate the cell-microenvironmental interactions that mediate somatic evolution of cancer cells. This allows investigation of the hypothesis that regions of premalignant lesions develop a substrate-limited environment as proliferation carries cells away from blood vessels which remain separated by the intact basement membrane. We find that selective forces in tumoural regions furthest from the blood supply act to favour cells whose metabolism is best suited to respond to local changes in oxygen, glucose and pH levels. The model predicts three phases of somatic evolution. Initially, cell survival and proliferation is limited due to diminished oxygen levels. This promotes adaptation to a second phase of growth dominated by cells with constitutively up-regulated glycolysis, less reliant on oxygen for ATP production. Increased glycolysis induces acidification of the local environment, limiting proliferation and inducing cell death through necrosis and apoptosis. This promotes a third phase of cellular evolution, with emergence of phenotypes resistant to acid-induced toxicity. This emergent cellular phenotype has a significant proliferative advantage because it will consistently acidify the local environment in a way that is toxic to its competitors but harmless to itself. The model's results suggest this sequence is essential in the transition from self-limited premalignant growth to invasive cancer, and, therefore, that this transition may be delayed or prevented through novel strategies directed towards interrupting the hypoxia-glycolysis-acidosis cycle.     

Cerebral blood flow regulation in REM sleep: a model for flow-metabolism coupling.

The pattern of metabolic and circulatory changes occurring during REM sleep in the whole brain is also observed at a regional level in different instances of functional activation. This pattern is characterized by an increase in metabolic rate, blood flow, glucose and oxygen uptake, the increase in glucose uptake generally exceeding oxygen uptake. A model of interpretation is presented, based on the assumption that substantial limitation to oxygen diffusion exists in the brain. According to the model, microregions lying at mid-distance between capillaries may become hypoxic, depending on metabolic rate and blood-cell PO2 difference. At increasing metabolic rates, O2 consumption in pericapillary microregions increases and the PO2 drop becomes steeper. As a consequence, in microregions far from capillaries a decrease in O2 availability occurs, in concomitance with the increase in metabolic rate, so that non-oxidative glucose metabolism develops locally. A similar spatial PO2 pattern forms in the case of arterial hypoxia, when capillary PO2, and then blood-cell PO2 difference, is reduced. The hypoxic microregions are the source of vasodilatatory messages, the consequent vasodilatation increasing average capillary PO2 and then favoring O2 diffusion to the tissue. Oxygen thus appears to be a better candidate than glucose as a mediator of blood flow-metabolism coupling. This is supported by its higher extraction fraction and by the fact that, in physiologic conditions, arterial hypoxia (and not hypoglycemia) acts on cerebral blood flow. Moreover, the diffusion capacity of glucose in the brain is higher than that of oxygen, so that diffusion limitation is more likely to occur for oxygen. The present model allows consistent organization of the stereotyped changes in cerebral blood flow and glucose and oxygen uptake occurring both in REM sleep and in other instances of brain activation.     

Methodology for predicting oxygen transport on an intravenous membrane oxygenator combining computational and analytical models

A computational methodology for accurately predicting flow and oxygen-transport characteristics and performance of an intravenous membrane oxygenator (IMO) device is developed, tested, and validated. This methodology uses extensive numerical simulations of three-dimensional computational models to determine flow-mixing characteristics and oxygen-transfer performance, and analytical models to indirectly validate numerical predictions with experimental data, using both blood and water as working fluids. Direct numerical simulations for IMO stationary and pulsating balloons predict flow field and oxygen transport performance in response to changes in the device length, number of and balloon pulsation frequency. Multifiber models are used to investigate interfiber interference and length effects for a stationary balloon whereas a single fiber model is used to analyze the effect of balloon pulsations on velocity and oxygen concentration fields and to evaluate oxygen transfer rates. An analytical lumped model is developed and validated by comparing its numerical predictions with experimental data. Numerical results demonstrate that oxygen transfer rates for a stationary balloon regime decrease with increasing number of fibers, independent of the fluid type. The oxygen transfer rate ratio obtained with blood and water is approximately two. Balloon pulsations show an effective and enhanced flow mixing, with time-dependent recirculating flows around the fibers regions which induce higher oxygen transfer rates. The mass transfer rates increase approximately 100% and 80%, with water and blood, respectively, compared with stationary balloon operation. Calculations with combinations of frequency, number of fibers, fiber length and diameter, and inlet volumetric flow rates, agree well with the reported experimental results, and provide a solid comparative base for analysis, predictions, and comparisons with numerical and experimental data.     

Effect of nitric oxide on the transport and release of oxygen in fetal blood

It is well known that nitric oxide (NO), the most important vasodilator agent, plays an important role in lowering vascular resistance in the human umbilical-placental circulation and that its deficiency is related to the pathogenesis of pre-eclamptic disorder. Besides it has recently been demonstrated that human hemoglobin (HbA) is able to transport nitric oxide, as S-nitrosohemoglobin (SNO-Hb), from the arterial to the venous blood. In the present study we examine the functional properties of the adult and fetal nitrosated hemoglobins to see if the double transport of oxygen and NO may influence the fetal oxygenation and the relation between maternal and fetal blood. Our results show that S-nitrosation significantly increases the oxygen affinity of the adult Hb (HbA) with respect to native protein (no-nitrosated) while the functional properties of HbF are less influenced. The oxygen affinity modification, found for SNO-HbA, was ascribed to the nitrosation of cysteine beta 93: really, the same residue is also present in the gamma chains of fetal hemoglobin, while the increase of affinity is less evidenced; hence, it is probable that the 39 aminoacidic substitutions between beta and gamma chains allay the effects of S-nitrosation. As regards the physiological modulators (protons, chloride ions, 2,3-diphosphoglyceric acid, and temperature), they influence the oxygen affinity of the two hemoglobins S-nitrosated, in equal mode with respect to the native forms determining the same variation on the oxygen affinity. Hence, our results evidence the fact that the NO release by SNO-HbA "in vivo" would be limited to regions of extremely low oxygen tension (such as hypoxic regions), while in fetus, SNO-HbF would unload nitric oxide and oxygen at pressure values close to normal.     

Oxygen dependence of respiration in rat spinotrapezius muscle in situ

The oxygen dependence of respiration in striated muscle in situ was studied by measuring the rate of decrease of interstitial Po(2) [oxygen disappearance curve (ODC)] following rapid arrest of blood flow by pneumatic tissue compression, which ejected red blood cells from the muscle vessels and made the ODC independent from oxygen bound to hemoglobin. After the contribution of photo-consumption of oxygen by the method was evaluated and accounted for, the corrected ODCs were converted into the Po(2) dependence of oxygen consumption, Vo(2), proportional to the rate of Po(2) decrease. Fitting equations obtained from a model of heterogeneous intracellular Po(2) were applied to recover the parameters describing respiration in muscle fibers, with a predicted sigmoidal shape for the dependence of Vo(2) on Po(2). This curve consists of two regions connected by the point for critical Po(2) of the cell (i.e., Po(2) at the sarcolemma when the center of the cell becomes anoxic). The critical Po(2) was below the Po(2) for half-maximal respiratory rate (P(50)) for the cells. In six muscles at rest, the rate of oxygen consumption was 139 ± 6 nl O(2)/cm(3)·s and mitochondrial P(50) was k = 10.5 ± 0.8 mmHg. The range of Po(2) values inside the muscle fibers was found to be 4-5 mmHg at the critical Po(2). The oxygen dependence of respiration can be studied in thin muscles under different experimental conditions. In resting muscle, the critical Po(2) was substantially lower than the interstitial Po(2) of 53 ± 2 mmHg, a finding that indicates that Vo(2) under this circumstance is independent of oxygen supply and is discordant with the conventional hypothesis of metabolic regulation of the oxygen supply to tissue.