Michaelis-Menten kinetics model of oxygen consumption by rat brain slices following hypoxia

In the present study, we have measured partial pressure of oxygen (pO₂) profiles through rat brain slices before and after periods of hypoxia (5 and 10 min) to determine its effect on tissue oxygen demand. Tissue pO₂ profiles were measured through rat cerebral cortex slices superfused with phosphate buffer using oxygen (O₂)-sensitive microelectrodes at different times in controls [40% O₂ balance nitrogen (N₂)], and at different times before and after 5 or 10 min of hypoxia (100% N₂). A one-dimensional, steady-state model of ordinary diffusion with a Michaelis-Menten model of O₂ consumption where the maximal O₂ consumption (V_max) and the rate at half-maximal O₂ consumption (K_m) were allowed to vary was used to determine the kinetics of O₂ consumption. Actual pO₂ profiles through tissue were fitted to theoretical profiles by a least-squares method. V_max varied among penetrations in a control slice and among slices. V_max seemed to decrease after hypoxic insult, but the change was not statistically significant. The K_m value measured before hypoxia was lower than the first K_m value measured after the end of hypoxia, indicating that hypoxia induced a compensatory change in the metabolic state of the tissue. K_m increased immediately after both 5- and 10-min hypoxic insults and returned to normal after recovery for each case. It seems that during and immediately after short periods of hypoxia, K_m increases from near zero but returns to normal values within a few minutes.     

Oxygen Tension Imaging in the Mouse Retina

A newly developed microscope-based imaging system was used to measure the oxygen tension (PO₂) inside the retinal and choroidal vessels of mice and to generate in vivo maps of retinal PO₂. These maps were generated from the phosphorescence lifetimes of an injected palladium–porphyrin compound using a frequency-domain measurement. The system was fully calibrated and used to produce retinal PO₂ maps at different inspiratory oxygen fractions. PO₂ rose accordingly and predictably as inspiratory O₂ was stepped from hypoxic to hyperoxic conditions. Important experimental and acquisition parameters necessary for applying phosphorescence lifetime imaging to the mouse eye were investigated, including camera exposure and intensifier gain settings. Because of a need to limit light exposure to the retina, PO₂ map quality as measured by the coefficient of determination was investigated as a function of signal-to-noise and accumulated excitation energy deposition. With the development of this technology for use in mice, the potential for investigating the oxygen dynamics in genetically engineered mouse models of retinal disease, including diabetic retinopathy, glaucoma, and age-related macular degeneration, is advanced. © 2003 Biomedical Engineering Society. PAC2003: 4266Ew, 8763Lk, 8719Dd     

Oxygen and reactive oxygen species in articular cartilage: modulators of ionic homeostasis

Articular cartilage is an avascular tissue dependent on diffusion mainly from synovial fluid to service its metabolic requirements. Levels of oxygen (O₂) in the tissue are low, with estimates of between 1 and 6%. Metabolism is largely, if not entirely, glycolytic, with little capacity for oxidative phosphorylation. Notwithstanding, the tissue requires O₂ and consumes it, albeit at low rates. Changes in O₂ tension also have profound effects on chondrocytes affecting phenotype, gene expression, and morphology, as well as response to, and production of, cytokines. Although chondrocytes can survive prolonged anoxia, low O₂ levels have significant metabolic effects, inhibiting glycolysis (the negative Pasteur effect), and also notably matrix production. Why this tissue should respond so markedly to reduction in O₂ tension remains a paradox. Ion homeostasis in articular chondrocytes is also markedly affected by the extracellular matrix in which the cells reside. Recent work has shown that ion homeostasis also responds to changes in O₂ tension, in such a way as to produce significant effects on cell function. For this purpose, O₂ probably acts via alteration in levels of reactive oxygen species. We discuss the possibility that O₂ consumption by this tissue is required to maintain levels of ROS, which are then used physiologically as an intracellular signalling device. This postulate may go some way towards explaining why the tissue is dependent on O₂ and why its removal has such marked effects. Understanding the role of oxygen has implications for disease states in which O₂ or ROS levels may be perturbed.     

Mathematical evidence for flow-induced changes in myocardial oxygen consumption

The objective of this investigation was to aid in the determination of the mechanism by which oxygen consumption changes in proportion to coronary perfusion pressure or coronary blood flow. A mathematical model of oxygen transport and consumption in the isolated-perfused heart was developed, based on data from an autoregulating, cell-free perfused, externally paced, isovolumic feline heart preparation. The model features the unique combination of Michaelis-Menten kinetics, and one-dimensional (axial) diffusion in radially well-mixed tissue. An adaptive finite-difference integration routine was used to solve the resulting third order stiff two-point boundary value problem. A simplex minimization was employed to determine the parameter values that minimized the squared difference between the model and the experimental data in terms of tissue PO₂ distribution (histograms). Different cases of the model representing pressure-induced, flow-induced, and “magnified” flow effects were run. The flow-dependent oxygen consumption version of the model produced a histogram squared error 30% lower than the pressure-induced version and 5% lower than any other case. The model and a critical review of the literature indicate that a flow-related mechanism is responsible for this phenomenon. Evidence also demonstrates that the Michaelis-Menten kinetics constant is not constant for different oxygen tensions.     

Die Nierenmarkhypoxie: Ein Schlüssel zum Verständnis des akuten Nierenversagens?

Summary The ability to produce a concentrated urine is imposed by a uniquely low ambient oxygen pressure in the renal medulla due to shunt diffusion within the vascular bundles. As the thick ascending limb of Henle's loop (TAL-segment) is able to glycolyse anaerobically, a phase of oxygen deficiency may be bridgespanned. It allows an exceptionally high oxygen extraction of 80% in this area. If oxygen capacity is reduced systematically, which can be effected in the isolated kidney model by using cell free perfusate, a typical pattern of lesions occur in TAL-segments. Segments near vascular bundles remain intact, as they take advantage from a radial oxygen diffusion originating from vascular bundles. The extent of lesions is increasing directed to the inner medulla due to the reduction of oxygen pressure, whereas lesions are not present in the inner medulla itself. Cells of TAL-segments are swelling during oxygen deficiency, when transport work surpasses the available energy necessary due to the luminal fluid inflow. Lesions could be prevented, when oxygen capacity was enhanced by adding erythrocytes or when transport was blocked by furosemide. Swollen cells in TAL-segments however are able to aggravate medullary hypoxia by an outflow block in vivo.Secondly, it can be demonstrated, that oxygen shunt diffusion is not only present in renal medulla but also within renal cortex especially as a preglomerular diffusion shunt for blood gases. Thus PCO₂ has been measured to be 65 mmHg in the outermost cortical zone and thereby some 20 mmHg higher than renal venous blood. Our own measurements of the PO₂ at superficial glomeruli in vivo using MWF-rats demonstrate values as low as 42–46 mmHg at average and a simultaneously measured arterial PO₂ of 90 mmHg in systemic blood. This represents a markedly higher desaturation of hemoglobin than found in renal venous blood. This unexpected high preglomerular shuntdiffusion is likely localized within interlobular vessels, where thinwalled arteries and veins exhibiting the wall structure of capillaries are generally in close contact. Following this concept, PO₂ of the superficial cortical zone is low and the PO₂ of the juxtamedullary cortical zone is not far from arterial PO₂. Plasmaskimming may modify O₂-pressure as well as O₂-capacity within the different cortical zones. These results may explain, why proximal tubules within the renal cortex — which exhibit a low enzymatic activity to glycolyse anaerobically compared to TAL-segments — develop lesions very rapidly under ischemic or hypoxic conditions or when the demand of energy for transport work cannot be produced aerobically. This becomes evident especially within areas of oxygen deficiency at the outer stripe of outer medulla, where predominantly P₃-segments in the interbundle area are involved however much less TAL-segments. This may also explain, that the production of erythropoietin is localized within the renal cortex and outer stripe of outer medulla, as oxygen deficiency can be measured effectively in this area. The common error, that oxygen supply of the kidney is abundant, must be revised: it is at the brink of oxygen deficiency in the case of renal medulla and at shortage also for renal cortex.     

Modeling Advection and Diffusion of Oxygen in Complex Vascular Networks

A realistic geometric model for the three-dimensional capillary network geometry is used as a framework for studying the transport and consumption of oxygen in cardiac tissue. The nontree-like capillary network conforms to the available morphometric statistics and is supplied by a single arterial source and drains into a pair of venular sinks. We explore steady-state oxygen transport and consumption in the tissue using a mathematical model which accounts for advection in the vascular network, nonlinear binding of dissolved oxygen to hemoglobin and myoglobin, passive diffusion of freely dissolved and protein-bound oxygen, and Michaelis–Menten consumption in the parenchymal tissue. The advection velocity field is found by solving the hemodynamic problem for flow throughout the network. The resulting system is described by a set of coupled nonlinear elliptic equations, which are solved using a finite-difference numerical approximation. We find that coupled advection and diffusion in the three-dimensional system enhance the dispersion of oxygen in the tissue compared to the predictions of simplified axially distributed models, and that no lethal corner, or oxygen-deprived region occurs for physiologically reasonable values for flow and consumption. Concentrations of 0.5–1.0 mM myoglobin facilitate the transport of oxygen and thereby protect the tissue from hypoxia at levels near its p₅₀ that is, when local oxygen consumption rates are close to those of delivery by flow and myoglobin-facilitated diffusion, a fairly narrow range. © 2001 Biomedical Engineering Society. PAC01: 8719Tt, 0270Bf, 8710+e     

An Analysis of Hypoxia in Sheep Brain using a Mathematical Model

Cerebral blood flow (CBF) increases as arterial oxygen content falls with hypoxic (low PO₂), anemic (low hemoglobin) and carbon monoxide (CO) (high carboxyhemoglobin) hypoxia. Despite a higher arterial PO₂, CO hypoxia provokes a greater increase in CBF than hypoxic hypoxia. We analyzed published data using a compartmental mathematical model to test the hypothesis that differences in PO₂ in tissue, or a closely related vascular compartment, account for the greater response to CO hypoxia. Calculations showed that tissue, but not arteriolar, PO₂ was lower in CO hypoxia because of the increased oxyhemoglobin affinity with CO hypoxia. Analysis of studies in which oxyhemoglobin affinity was changed independently of CO supports the conclusion that changes in tissue PO₂ (or closely related capillary or venular PO₂) are predictive of alterations in CBF. We then sought to determine the role of tissue PO₂ in anemic hypoxia, with no change in arterial and little, if any, change in venous PO₂. Calculations predict a small fall in tissue PO₂ as hematocrit decreases from 55% to 20%. However, calculations show that changes in blood viscosity can account for the increase in CBF in anemic hypoxia over this range of hematocrits. © 1998 Biomedical Engineering Society. PAC98: 8710+e, 8722-q, 8745Ft     

Endothelin receptors in the detached retina of the pig

Endothelin-1 (ET-1) is a potent vasoconstrictor that causes hypoperfusion of the neurosensory retina. We investigated immunohistochemically the expression of the receptors for ET-1, ET(A) and ET(B), in control and locally detached retinas of the pig. Immunoreactivity for ET(A) was expressed in the innermost retinal layers and in the outer plexiform layer in control retinas, and was additionally strongly expressed by retinal blood vessels at 7 days after detachment of the sensory retina from the pigment epithelium. Immunoreactivity for ET(B) was expressed by the innermost retinal layers, by ganglion cell somata, and by Müller glial cells in the control tissue, and was not altered in its expression after detachment. The vascular expression of ET(A) may suggest a hypoperfusion of the retina after detachment.     

Urocortin 2 protects against retinal degeneration following bilateral common carotid artery occlusion in the rat

Urocortin 2 (Ucn 2) is corticotropin-releasing factor (CRF) paralog that preferentially activates CRF₂ receptors. Ucns exert CRF₂-mediated cytoprotective effects against ischemia-reperfusion injury in cardiomyocytes. However, little is known regarding potential retinoprotective effects of Ucns despite the known presence of CRF family peptides and their receptors (predominantly CRF_2α) in retina. Therefore, the present study investigated the effects of post-ischemic intravitreal Ucn 2 (2 nmol) administration on ischemia-induced retinal degeneration. Two-month-old rats were subjected to permanent bilateral common carotid artery occlusion, and their retinas were processed histologically after two weeks survival to determine the density of viable cells in the ganglion cell layer and the thickness of all retinal layers. In vehicle-treated subjects, carotid occlusion reduced retina thickness by approximately 60% as compared to sham-operated animals. In contrast, intraocular Ucn 2 treatment led to a marked amelioration of the retinal layers, and the thickness of all layers was significantly increased by 40% compared to ischemic vehicle-treated subjects. Ucn 2 treatment also increased the number of cells by 55% in the ganglion cell layer as compared to those from carotid-occluded retinas of vehicle-treated subjects. These findings suggest that intraocular Ucn 2 treatment may protect against ischemia-induced retinal degeneration, results with potential therapeutic implications for ophthalmic diseases.     

Ischemia-reperfusion alters the immunolocalization of glial aquaporins in rat retina

Glial cells control the retinal osmohomeostasis, in part via mediation of water fluxes through aquaporin (AQP) water channels. By using immunohistochemical staining, we investigated whether ischemia-reperfusion of the rat retina causes alterations in the distribution of AQP1 and AQP4 proteins. Transient ischemia was induced in retinas of Long–Evans rats by elevation of the intraocular pressure for 60 min. In control retinas, immunoreactive AQP1 was expressed in the outer retina and by distinct amacrine cells, and AQP4 was expressed by glial cells (Müller cells and astrocytes) predominantly in the inner retina. After ischemia, retinal glial cells in the nerve fiber/ganglion cell layers strongly expressed AQP1. The perivascular staining around the superficial vessels altered from AQP4 in control retinas to AQP1 in postischemic retinas. The data suggest that the glial cell-mediated water transport in the retina is altered after ischemia especially at the superficial vessel plexus.     

PO2-profiles in hippocampal slices of the guinea pig

Summary For a detailed analysis of the oxygen supply of hippocampal slices, tissue PO₂ (P_{t,o 2}) was recorded polarographically in the neural layers of thick and thin slice preparations from the guinea pig. The experiments showed that the P_t,o₂-gradients were extremely steep in the outer zones of vital slices. In an air equilibrated salt solution the surface PO₂ was reduced to less than 50% within ca. 25 m. Minimum values were measured at a depth of ca. 150 m. A rise of temperature lowered the oxygen supply in the deeper layers of the excised tissue. An elevation of the surface PO₂ hardly improved P_{t,o 2} in the deep structures, because the O₂-consumption of the hippocampal slices increased with rising PO₂.Supported by DFG (Sp 108/6)Dedicated to Professor Dr. H. Caspers on the occasion of his 60th birthday     

Spatial energy balance within a structural model of the left ventricle

A model describing the local instantaneous energetic needs within the left ventricle (LV) myocardium is presented. The model, which combines the myocardial oxygen consumption (MVO₂) with the mechanical activity of the cardiac muscle, is based on the theory of cross bridge kinetics between the actin and myosin fibers within the sarcomere. The microscale relationship between the stress, stress development, strain rate and basal metabolism demand is incorporated into the LV model which describes the mechanical activities of different layers within the myocardium. The model shows a significant increase in the oxygen consumption in the endocardial layers as compared with the epicardial layers. Integrating the spatial and temporal oxygen consumption distribution within the myocardium yields the total myocardial oxygen consumption. The quantitative relationships between the heat rate, stress, contractility and external work and the MVO₂ are in agreement with known data. The model thus offers a tool to assess the local instantaneous as well as the time averaged overall energy consumption, over a wide range of loading conditions of the LV.     

A Model of NO/O<Subscript>2</Subscript> Transport in Capillary-perfused Tissue Containing an Arteriole and Venule Pair

The goal of this study was to investigate the complex co-transport of nitric oxide (NO) and oxygen (O₂) in a paired arteriole–venule, surrounded by capillary-perfused tissue using a computer model. Blood flow was assumed to be steady in the arteriolar and venular lumens and to obey Darcy’s law in the tissue. NO consumption rate was assumed to be constant in the core of the arteriolar and venular lumen and to decrease linearly to the endothelium. Average NO consumption rate by capillary blood in a unit tissue volume was assumed proportional to the blood flux across the volume. Our results predict that: (1) the capillary bed, which connects the arteriole and venule, facilitates the release of O₂ from the vessel pair to the surrounding tissue; (2) decreasing the distance between arteriole and venule can result in a higher NO concentration in the venular wall than in the arteriolar wall; (3) in the absence of capillaries in the surrounding tissue, diffusion of NO from venule to arteriole contributes little to NO concentration in the arteriolar wall; and (4) when capillaries are added to the simulation, a significant increase of NO in the arteriolar wall is observed.     

Transmural Oxygen Tension Gradients in Rat Cerebral Cortex Arterioles

Modified needle oxygen microelectrodes and vital microscopy were used to measure transmural oxygen tension gradients (PO₂) in pial arterioles with lumen diameters of 20–90  μm. A relationship between the magnitude of the transmural PO₂ gradient and arteriole wall tone was found: in control conditions, PO₂ gradients were 1.17 ± 0.06 mmHg/μm (n  = 40), while in conditions of arteriolar wall dilation the transmural PO₂ gradient decreased to 0.68 ± 0.04 mmHg/μm (p  <  0.001, n  = 38). These data provide the first measurements of transmural PO₂ gradients in pial arterioles of different calibers at different levels of vascular tone and have fundamental importance for assessing the role of arterial microvessels in tissue oxygen supply processes. The results obtained here provide evidence that oxygen consumption by the vessel wall is within the range characteristic of enveloping tissues and that oxygen consumption by the endothelial cell layer probably has no significant effect on the magnitude of the transmural PO₂ gradient. Translated from Rossiiskii Fiziologicheskii Zhurnal imeni I. M. Sechenova, Vol. 94, No. 4, pp. 394–405, April, 2008.     

The effect of temperature on the basal metabolism of cardiac muscle

Using independent methods, measurements were made of the rate of oxygen consumption of quiescent rat ventricular tissue slices and of K⁺-arrested rabbit hearts at different temperatures. Experiments were designed such that the effect of temperature could be separated from the effect of time. The rate of oxygen consumption of both cardiac muscle preparations declined with time following cardiectomy. Likewise the rate of resting oxygen consumption of both preparations was relatively insensitive to temperature: Q₁₀=1.3. By contrast, the rate of oxygen consumption of rat liver slices showed a Q₁₀ of 2.6. The low Q₁₀ values of the cardiac preparations do not appear to be due to an inadequate supply of oxygen. The results are in close agreement with those of myothermic studies.A preliminary account of this research was presented to the Australasian Section of the International Society for Heart Research, Auckland, New Zealand, August 1982 (J Mol Cell Cardiol 14, suppl 2. p 10)     

The histone H3K36 demethylase Fbxl11 plays pivotal roles in the development of retinal late-born cell types

Histone methylation plays a vital role in retinal development. However, the role of histone H3K36 methylation in retinal development is not clear. We examined the role of H3K36 methylation by loss-of-function analysis of H3K36me1/2 demethylases, Fbxl10, and Fbxl11. We analyzed the effect of knockout of these genes in the developing and mature retina on retinal development. Knockout of Fbxl10 specifically in the developing retina did not result in gross developmental abnormalities. Although adult rod photoreceptor-specific knockout of Fbxl11 in mature retinas did not result in morphological abnormalities, Fbxl11 knockout in developing retinas increased apoptosis, suppressed the proliferation of retinal progenitor cells, and resulted in microphthalmia. Morphological analysis revealed perturbed differentiation of rod photoreceptor and bipolar cells. RNA-seq of retinas at P7 showed markedly decreased expression of genes characterizing rod photoreceptor and bipolar cells in Fbxl11-knockout retinas. In addition, perturbation of alternative splicing increased intron retention in Fbxl11-knockout retinas. Genome-wide evaluation of the H3K36 methylation status revealed that Fbxl11 knockout altered the distribution of H3K36me2/3 in genes important for rod photoreceptor development. Taken together, we show that Fbxl11 plays pivotal roles in the development of retinal late-born cell types and may contribute to tight control of H3K36 methylation during retinal development.     

Screen-printed transcutaneous oxygen sensor employing polymer electrolytes

A disposable, transcutaneous oxygen sensor has been designed and implemented using screen-printing technology for all fabrication stages. The sensor incorporates an integral heating element to promote transcutaneous diffusion of blood gases so that a reliable estimation of arterial blood gas concentration can be obtained. The oxygen sensing part of the device consists of a screen-printed Clark cell implemented as electrodes, electrolyte and membrane. A three-electrode configuration is employed with gold working and counter electrodes and a silver/silver chloride reference electrode. Several different polymer electrolyte and membrane materials were evaluated in the construction of the device, and their performances were compared. A fully automated gas testing rig was constructed to enable oxygen levels to be varied under computer control. Cyclic voltammetry and static analysis of the sensors were carried out at different oxygen concentration levels and in various test environments. Linear relationships were established with an averaged sensitivity level of 0.02 μA(mmHg)⁻¹ and high regression coefficients of 0.99. The prototype covered with a polytetrafluoroethylene membrane gave the experimental result of I (μA)=−0.025PO₂ (mmHg)−0.085. Several factors influenced the performance of the sensors. The investigations have greatly contributed towards an understanding of the suitability of the materials in achieving a viable, low-cost sensor.     

A compartmental model for oxygen transport in brain microcirculation

A compartmental model is formulated for oxygen transport in the cerebrovascular bed of the brain. The model considers the arteriolar, capillary and venular vessels. The vascular bed is represented as a series of compartments on the basis of blood vessel diameter. The formulation takes into account such parameters as hematocrit, vascular diameter, blood viscosity, blood flow, metabolic rate, the nonlinear oxygen dissociation curve, arterial PO₂, P₅₀ (oxygen tension at 50% hemoglobin saturation with O₂) and carbon monoxide concentration. The countercurrent diffusional exchange between paired arterioles and venules is incorporated into the model. The model predicts significant longitudinal PO₂ gradients in the precapillary vessels. However, gradients of hemoglobin saturation with oxygen remain fairly small. The longitudinal PO₂ gradients in the postcapillary vessels are found to be very small. The effect of the following variables on tissue PO₂ is studied: blood flow, PO₂ in the arterial blood, hematocrit, P₅₀, concentration of carbon monoxide, metabolic rate, arterial diameter, and the number of perfused capillaries. The qualitative features of PO₂ distrbution in the vascular network are not altered with moderate variation of these parameters. Finally, the various types of hypoxia, namely hypoxic, anemic and carbon monoxide hypoxia, are discussed in light of the above sensitivity analysis.     

The energy cost of walking and running with and without a backpack load

Summary The effect of a backpack load (20 kg) on oxygen consumption while walking and running at different speeds was investigated. Fifteen males walked and ran (with and without load) up a 5% sloped treadmill at 6.4, 7.2, 8.0, 9.6, and 11.2 km/h (4, 4.5, 5, 6, and 7 mph). While walking O₂ rose at a rate of 0.6 (l/min)/(km/h) and while running 0.3 (l/min)/(km/h). The mean oxygen consumption at the various speeds was 28.65, 33.78, 40.64, 46.84, 54.48 ml O₂/kg BW/min, respectively, for the whole group without load and 26.52, 32.26, 38.28, 44.26, 48.16, respectively, with load. The breaking point between walking and running was at about 8.2 km/h. Carrying the load increased O₂ at a constant rate, and induced a breaking point between walking and running at a significantly lower speed for the smaller subjects than for the more robust ones. The results indicate that for certain tasks involving endurance and heavy load carriage, people should be selected according to criteria which integrate aerobic capacity and anthropometrical features.     

In vivo diffusion tensor MRI of the mouse retina: a noninvasive visualization of tissue organization

Diffusion tensor MRI (DTI) is a method for the noninvasive assessment of cellular organization and integrity in vivo. In this study, in vivo DTI was performed to demonstrate its ability to reflect photoreceptor cell alignment in adult C57BL/6 wild‐type mice. Age‐matched retinal degeneration 1 (rd1) mice were employed as a negative control, i.e. loss of the photoreceptor cell layer. In wild‐type mice, DTI‐estimated cell alignment suggests that the MR‐detected outer retinal layer comprises cells aligning perpendicular to the retinal surface, consistent with the known organization of photoreceptor cells. The MR‐detected outer retinal layer exhibits a lower apparent diffusion coefficient and higher fractional anisotropy than the other two MR‐detected retinal layers (p < 0.05 for all comparisons). In rd1 mice, the remaining MR‐detected retinal layer exhibits different cell alignment, apparent diffusion coefficient and fractional anisotropy from that of the MR‐detected outer retinal layer in wild‐type mice (p < 0.05 for all comparisons), reflecting the degeneration of photoreceptor cells in rd1 mouse retina. Overall, our findings suggest that in vivo DTI assessment of mouse retina with normal physiology or degenerative pathology is feasible. Copyright © 2010 John Wiley & Sons, Ltd.