Temperature dependence of oxygen diffusion and consumption in mammalian striated muscle

The dependence of maximum oxygen uptake and utilization (V̇O2 max) on hemoglobin-oxygen affinity and altitude

Oxygen transport from the lungs to peripheral tissue is dependent on the affinity of hemoglobin for oxygen. Recent experimental data have suggested that the maximum human capacity for oxygen uptake and utilization (V̇O2 max) at sea level and altitude (~3000 m) is sensitive to alterations in hemoglobin-oxygen affinity. However, the effect of such alterations on V̇O2 max at extreme altitudes remains largely unknown due to the rarity of mutations affecting hemoglobin-oxygen affinity. This work uses a mathematical model that couples pulmonary oxygen uptake with systemic oxygen utilization under conditions of high metabolic demand to investigate the effect of hemoglobin-oxygen affinity on V̇O2 max as a function of altitude. The model includes the effects of both diffusive and convective limitations on oxygen transport. Pulmonary oxygen uptake is calculated using a spatially-distributed model that accounts for the effects of hematocrit and hemoglobin-oxygen affinity. Systemic oxygen utilization is calculated assuming Michaelis-Menten kinetics. The pulmonary and systemic model components are solved iteratively to compute predicted arterial and venous oxygen levels. Values of V̇O2 max are predicted for several values of hemoglobin-oxygen affinity and hemoglobin concentration based on data from humans with hemoglobin mutations. The model predicts that increased hemoglobin-oxygen affinity leads to increased V̇O2 max at altitudes above ~4500 m.

Hyperhydration of Cancers: A Characteristic Biophysical Trait Strongly Increasing O2, CO2, Glucose and Lactate Diffusivities, and Improving Thermophysical Properties of Solid Malignancies

Cancers are complex, heterogeneous, dynamic and aggressive diseases exhibiting a series of characteristic biophysical traits which complement the original biological hallmarks of cancers favouring progressive growth, metastasis, and contributing to immune evasion and treatment resistance. One of the prevalent differences between most solid tumors and their corresponding, healthy tissues is a significantly higher water content (hyperhydration) in cancers. As a consequence, cancers have distinctly higher (Fick's) diffusion coefficients D [cm2 s-1] for the respiratory gases O2 and CO2, the key substrate glucose, and for the oncometabolite lactate. In addition, cancers have (a) clearly increased specific heat capacities cp [J g-1 K-1], thus representing high-capacity-tissues upon therapeutic heating induced by electromagnetic irradiation, and (b) higher thermal conductivities k [W m-1 K-1], i.e., increased abilities to conduct heat. Therefore, in diffusion analyses (e.g., when describing critical O2 and glucose supplies or CO2 removal, and the development of hypoxic subvolumes) and for modeling temperature distributions in hyperthermia treatment planning, these specific cancer-related data must be considered in order to reliably reflect oncologic thermo-radiotherapy settings.

A two-layer continuously distributed capillary O2 transport model applied to blood flow regulation in resting skeletal muscle

The microcirculation is the site of direct oxygen transfer from blood to tissue, and also of oxygen delivery control via regulation of local blood flow. In addition, a number of diseases including type II diabetes mellitus (DMII) and sepsis are known to produce microcirculatory dysfunction in their early phases. Given the complexity of microvascular structure and physiology, and the difficulty of measuring tissue oxygenation at the micro-scale, mathematical modelling has been necessary for understanding the physiology and pathophysiology of O₂ transport in the microcirculation and for interpreting in vivo experiments. To advance this area, a model of blood-tissue O₂ transport in skeletal muscle was recently developed which uses continuously distributed capillaries and includes O₂ diffusion, convection, and consumption. The present work extends this model to two adjacent layers of skeletal muscle with different blood flow rates and applies it to study steady-state O₂ transport when flow regulation is stimulated using an O₂ exchange chamber. To generate a model which may be validated through in vivo experiments, an overlying O₂ permeable membrane is included. The model is solved using traditional methods including separation of variables and Fourier decomposition, and to ensure smooth profiles at the muscle-muscle and muscle-membrane interfaces matching conditions are developed. The study presents qualitative verification for the model, using visualizations of tissue PO₂ distributions for varying capillary density (CD), and presents capillary velocity response values in the near layer for varying chamber PO₂ under the assumption that outlet capillary O₂ saturation is equalized between adjacent layers. These compensatory velocity profiles, along with effective 'no-flux' chamber PO₂ values, are presented for varying CD and tissue O₂ consumption values. Insights gained from the two-layer model provide guidance for interpreting and planning future in-vivo experiments, and also provide motivation for further development of the model to improve understanding of the interaction between O₂ transport and blood flow regulation.

Signal Filtering Enabled by Spike Voltage-Dependent Plasticity in Metalloporphyrin-Based Memristors

Neural systems can selectively filter and memorize spatiotemporal information, thus enabling high-efficient information processing. Emulating such an exquisite biological process in electronic devices is of fundamental importance for developing neuromorphic architectures with efficient in situ edge/parallel computing, and probabilistic inference. Here a novel multifunctional memristor is proposed and demonstrated based on metalloporphyrin/oxide hybrid heterojunction, in which the metalloporphyrin layer allows for dual electronic/ionic transport. Benefiting from the coordination-assisted ionic diffusion, the device exhibits smooth, gradual conductive transitions. It is shown that the memristive characteristics of this hybrid system can be modulated by altering the metal center for desired metal-oxygen bonding energy and oxygen ions migration dynamics. The spike voltage-dependent plasticity stemming from the local/extended movement of oxygen ions under low/high voltage is identified, which permits potentiation and depression under unipolar different positive voltages. As a proof-of-concept demonstration, memristive arrays are further built to emulate the signal filtering function of the biological visual system. This work demonstrates the ionic intelligence feature of metalloporphyrin and paves the way for implementing efficient neural-signal analysis in neuromorphic hardware.

Metabolic Signaling in a Theoretical Model of the Human Retinal Microcirculation

Impaired blood flow and oxygenation contribute to many ocular pathologies, including glaucoma. Here, a mathematical model is presented that combines an image-based heterogeneous representation of retinal arterioles with a compartmental description of capillaries and venules. The arteriolar model of the human retina is extrapolated from a previous mouse model based on confocal microscopy images. Every terminal arteriole is connected in series to compartments for capillaries and venules, yielding a hybrid model for predicting blood flow and oxygenation throughout the retinal microcirculation. A metabolic wall signal is calculated in each vessel according to blood and tissue oxygen levels. As expected, a higher average metabolic signal is generated in pathways with a lower average oxygen level. The model also predicts a wide range of metabolic signals dependent on oxygen levels and specific network location. For example, for high oxygen demand, a threefold range in metabolic signal is predicted despite nearly identical PO2 levels. This whole-network approach, including a spatially nonuniform structure, is needed to describe the metabolic status of the retina. This model provides the geometric and hemodynamic framework necessary to predict ocular blood flow regulation and will ultimately facilitate early detection and treatment of ischemic and metabolic disorders of the eye.

Localized Oxygen Exchange Platform for Intravital Video Microscopy Investigations of Microvascular Oxygen Regulation

Intravital microscopy has proven to be a powerful tool for studying microvascular physiology. In this study, we propose a gas exchange system compatible with intravital microscopy that can be used to impose gas perturbations to small localized regions in skeletal muscles or other tissues that can be imaged using conventional inverted microscopes. We demonstrated the effectiveness of this system by locally manipulating oxygen concentrations in rat extensor digitorum longus muscle and measuring the resulting vascular responses. A computational model of oxygen transport was used to partially validate the localization of oxygen changes in the tissue, and oxygen saturation of red blood cells flowing through capillaries were measured as a surrogate for local tissue oxygenation. Overall, we have demonstrated that this approach can be used to study dynamic and spatial responses to local oxygen challenges to the microenvironment of skeletal muscle.

Simulation of oxygen transport and estimation of tissue perfusion in extensive microvascular networks: Application to cerebral cortex

Advanced imaging techniques have made available extensive three-dimensional microvascular network structures. Simulation of oxygen transport by such networks requires information on blood flow rates and oxygen levels in vessels crossing boundaries of the imaged region, which is difficult to obtain experimentally. Here, a computational method is presented for estimating blood flow rates, oxygen levels, tissue perfusion and oxygen extraction, based on incomplete boundary conditions. Flow rates in all segments are estimated using a previously published method. Vessels crossing the region boundary are classified as arterioles, capillaries or venules. Oxygen levels in inflowing capillaries are assigned based on values in outflowing capillaries, and similarly for venules. Convective and diffusive oxygen transport is simulated. Contributions of each vessel to perfusion are computed in proportion to the decline in oxygen concentration along that vessel. For a vascular network in the mouse cerebral cortex, predicted tissue oxygen levels show a broad distribution, with 99% of tissue in the range of 20 to 80 mmHg under reference conditions, and steep gradients near arterioles. Perfusion and extraction estimates are consistent with experimental values. A 30% reduction in perfusion or a 30% increase in oxygen demand, relative to reference levels, is predicted to result in tissue hypoxia.

Blood flow regulation and oxygen transport in a heterogeneous model of the mouse retina

Elevated intraocular pressure is the primary risk factor for glaucoma, yet vascular health and ocular hemodynamics have also been established as important risk factors for the disease. The precise physiological mechanisms and processes by which flow impairment and reduced tissue oxygenation relate to retinal ganglion cell death are not fully known. Mathematical modeling has emerged as a useful tool to help decipher the role of hemodynamic alterations in glaucoma. Several previous models of the retinal microvasculature and tissue have investigated the individual impact of spatial heterogeneity, flow regulation, and oxygen transport on the system. This study combines all three of these components into a heterogeneous mathematical model of retinal arterioles that includes oxygen transport and acute flow regulation in response to changes in pressure, shear stress, and oxygen demand. The metabolic signal (S_i) is implemented as a wall-derived signal that reflects the oxygen deficit along the network, and three cases of conduction are considered: no conduction, a constant signal, and a flow-weighted signal. The model shows that the heterogeneity of the downstream signal serves to regulate flow better than a constant conducted response. In fact, the increases in average tissue PO₂ due to a flow-weighted signal are often more significant than if the entire level of signal is increased. Such theoretical work supports the importance of the non-uniform structure of the retinal vasculature when assessing the capability and/or dysfunction of blood flow regulation in the retinal microcirculation.

August Krogh's theory of muscle microvascular control and oxygen delivery: a paradigm shift based on new data

August Krogh twice won the prestigious international Steegen Prize, for nitrogen metabolism (1906) and overturning the concept of active transport of gases across the pulmonary epithelium (1910). Despite this, at the beginning of 1920, the consummate experimentalist was relatively unknown worldwide and even among his own University of Copenhagen faculty. But, in early 1919, he had submitted three papers to Dr Langley, then editor of The Journal of Physiology in England. These papers coalesced anatomical observations of skeletal muscle capillary numbers with O₂ diffusion theory to propose a novel active role for capillaries that explained the prodigious increase in blood-muscle O₂ flux from rest to exercise. Despite his own appraisal of the first two papers as "rather dull" to his friend, the eminent Cambridge respiratory physiologist, Joseph Barcroft, Krogh believed that the third one, dealing with O₂ supply and capillary regulation, was"interesting". These papers, which won Krogh an unopposed Nobel Prize for Physiology or Medicine in 1920, form the foundation for this review. They single-handedly transformed the role of capillaries from passive conduit and exchange vessels, functioning at the mercy of their upstream arterioles, into independent contractile units that were predominantly closed at rest and opened actively during muscle contractions in a process he termed 'capillary recruitment'. Herein we examine Krogh's findings and some of the experimental difficulties he faced. In particular, the boundary conditions selected for his model (e.g. heavily anaesthetized animals, negligible intramyocyte O₂ partial pressure, binary open-closed capillary function) have not withstood the test of time. Subsequently, we update the reader with intervening discoveries that underpin our current understanding of muscle microcirculatory control and place a retrospectroscope on Krogh's discoveries. The perspective is presented that the imprimatur of the Nobel Prize, in this instance, may have led scientists to discount compelling evidence. Much as he and Marie Krogh demonstrated that active transport of gases across the blood-gas barrier was unnecessary in the lung, capillaries in skeletal muscle do not open and close spontaneously or actively, nor is this necessary to account for the increase in blood-muscle O₂ flux during exercise. Thus, a contemporary model of capillary function features most muscle capillaries supporting blood flow at rest, and, rather than capillaries actively vasodilating from rest to exercise, increased blood-myocyte O₂ flux occurs predominantly via elevating red blood cell and plasma flux in already flowing capillaries. Krogh is lauded for his brilliance as an experimentalist and for raising scientific questions that led to fertile avenues of investigation, including the study of microvascular function.

The mass transfer coefficient for oxygen transport from blood to tissue in cerebral cortex

The functioning of cerebral cortex depends on adequate tissue oxygenation. MRI-based techniques allow estimation of blood oxygen levels, tissue perfusion, and oxygen consumption rate (CMRO₂), but do not directly measure partial pressure of oxygen (PO₂) in tissue. To address the estimation of tissue PO₂, the oxygen mass transfer coefficient (KTO₂) is here defined as the CMRO₂ divided by the difference in spatially averaged PO₂ between blood and tissue, and is estimated by analyzing Krogh-cylinder type models. Resistance to radial diffusion of oxygen from microvessels to tissue is distributed within vessels and in the extravascular tissue. The value of KTO₂ is shown to depend strongly on vascular length density and also on microvessel tube hematocrits and diameters, but to be insensitive to blood flow rate and to transient changes in flow or oxygen consumption. Estimated values of KTO₂ are higher than implied by previous studies, implying smaller declines in PO₂ from blood to tissue. Average tissue PO₂ can be estimated from MRI-based measurements as average blood PO₂ minus the product of KTO₂ and CMRO₂. For oxygen consumption rates and vascular densities typical of mouse cortex, the predicted difference between average blood and tissue PO₂ is about 10 mmHg.

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.

Hypothermia Decreases O2 Cost for Ex Vivo Contraction in Mouse Skeletal Muscle

INTRODUCTION

Evidence suggests that the energy efficiency of key ATPases involved in skeletal muscle contractile activity is improved in a hypothermic condition. However, it is unclear how a decrease in temperature affects skeletal muscle O2 consumption (mVO2) induced by muscle contraction.

METHODS

Isolated mouse extensor digitorum longus (EDL) muscles were incubated in a temperature-controlled (37°C or 25°C) bath that included an O2 probe. EDL muscles from one limb were subjected to the measurement of resting mVO2, and the contralateral EDL muscles were used for the measurement of mVO2 with electrically stimulated contraction. For the resting protocol, muscles were suspended at resting tension for 15 min with continuous O2 recordings. For the contraction protocol, EDL muscles underwent 10 electrically stimulated isometric contractions with continuous O2 recordings for 15 min. The rate of O2 disappearance was quantified as micromoles of O2 per minute and normalized to the wet weight of the muscle.

RESULTS

Resting mVO2 was greater at 37°C than at 25°C, consistent with the idea that lower temperature reduces basal metabolic rate. Electrically stimulated contraction robustly increased mVO2 at both 37°C and 25°C, which was sustained for ~3 min postcontraction. During that period, mVO2 was elevated approximately fivefold at both 37°C and 25°C. Greater contraction-induced mVO2 at 37°C compared with 25°C occurred despite lower force generated at 37°C than at 25°C.

CONCLUSIONS

Together, O2 cost for muscle contraction (force-time integral per O2 consumed) was greater at 37°C than at 25°C. Levels of high-energy phosphates were consistent with greater energy demand at 37°C compared with 25°C. In conclusion, these results indicate that muscle contraction that occurs at subnormal temperature requires less O2 than at 37°C.

Insights on the impact of mitochondrial organisation on bioenergetics in high-resolution computational models of cardiac cell architecture

Recent electron microscopy data have revealed that cardiac mitochondria are not arranged in crystalline columns but are organised with several mitochondria aggregated into columns of varying sizes spanning the cell cross-section. This raises the question—how does the mitochondrial arrangement affect the metabolite distributions within cardiomyocytes and what is its impact on force dynamics? Here, we address this question by employing finite element modeling of cardiac bioenergetics on computational meshes derived from electron microscope images. Our results indicate that heterogeneous mitochondrial distributions can lead to significant spatial variation across the cell in concentrations of inorganic phosphate, creatine (Cr) and creatine phosphate (PCr). However, our model predicts that sufficient activity of the creatine kinase (CK) system, coupled with rapid diffusion of Cr and PCr, maintains near uniform ATP and ADP ratios across the cell cross sections. This homogenous distribution of ATP and ADP should also evenly distribute force production and twitch duration with contraction. These results suggest that the PCr shuttle and associated enzymatic reactions act to maintain uniform force dynamics in the cell despite the heterogeneous mitochondrial organization. However, our model also predicts that under hypoxia activity of mitochondrial CK enzymes and diffusion of high-energy phosphate compounds may be insufficient to sustain uniform ATP/ADP distribution and hence force generation.

Mammalian cardiomyocytes contain a high volume of mitochondria, which maintains the continuous and bulk supply of ATP to sustain normal heart function. Previously, cardiac mitochondria were understood to be distributed in a regular, crystalline pattern, which facilitated a steady supply of ATP at different workloads. Using electron microscopy images of cell cross sections, we recently found that they are not regularly distributed inside cardiomyocytes. We created new spatially accurate computational models of cardiac cell bioenergetics and tested whether this heterogeneous distribution of mitochondria causes non-uniform energy supply and contractile force production in the cardiomyocyte. We found that ATP and ADP concentrations remain uniform throughout the cell because of the activity of creatine kinase (CK) enzymes that convert ATP produced in the mitochondria into creatine phosphate. Creatine phosphate rapidly diffuses to the myofibril region where it can be converted back to ATP for the contraction cycle in a timely manner. This mechanism is called the phosphocreatine shuttle (PCr shuttle). The PCr shuttle ensures that different areas of the cell produce the same amount of force regardless of the mitochondrial distribution. However, our model also shows that when the cellular oxygen supply is limited—as can be the case in conditions such as heart failure—the PCr shuttle cannot maintain uniform ATP and ADP concentrations across the cell. This causes a non-uniform acto-myosin force distribution and non-uniform twitch duration across the cell cross section. Our study suggests that mechanisms other than the PCr shuttle may be necessary to maintain uniform supply of ATP in a hypoxic environment.

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.

Influence of Cholesterol on the Oxygen Permeability of Membranes: Insight from Atomistic Simulations

Cholesterol is widely known to alter the physical properties and permeability of membranes. Several prior works have implicated cell membrane cholesterol as a barrier to tissue oxygenation, yet a good deal remains to be explained with regard to the mechanism and magnitude of the effect. We use molecular dynamics simulations to provide atomic-resolution insight into the influence of cholesterol on oxygen diffusion across and within the membrane. Our simulations show strong overall agreement with published experimental data, reproducing the shapes of experimental oximetry curves with high accuracy. We calculate the upper-limit transmembrane oxygen permeability of a 1-palmitoyl,2-oleoylphosphatidylcholine phospholipid bilayer to be 52 ± 2 cm/s, close to the permeability of a water layer of the same thickness. With addition of cholesterol, the permeability decreases somewhat, reaching 40 ± 2 cm/s at the near-saturating level of 62.5 mol % cholesterol and 10 ± 2 cm/s in a 100% cholesterol mimic of the experimentally observed noncrystalline cholesterol bilayer domain. These reductions in permeability can only be biologically consequential in contexts where the diffusional path of oxygen is not water dominated. In our simulations, cholesterol reduces the overall solubility of oxygen within the membrane but enhances the oxygen transport parameter (solubility-diffusion product) near the membrane center. Given relatively low barriers to passing from membrane to membrane, our findings support hydrophobic channeling within membranes as a means of cellular and tissue-level oxygen transport. In such a membrane-dominated diffusional scheme, the influence of cholesterol on oxygen permeability is large enough to warrant further attention.

Theoretical analysis of the determinants of lung oxygen diffusing capacity

The process of pulmonary oxygen uptake is analyzed to obtain an explicit equation for lung oxygen diffusing capacity in terms of hematocrit and pulmonary capillary diameter. An axisymmetric model with discrete cylindrical erythrocytes is used to represent radial diffusion of oxygen from alveoli through the alveolar-capillary membrane into pulmonary capillaries, through the plasma, and into erythrocytes. Analysis of unsteady diffusion due to the passage of the erythrocytes shows that transport of oxygen through the alveolar-capillary membrane occurs mainly in the regions adjacent to erythrocytes, and that oxygen transport through regions adjacent to plasma gaps can be neglected. The model leads to an explicit formula for diffusing capacity as a function of geometric and oxygen transport parameters. For normal hematocrit and a capillary diameter of 6.75 μm, the predicted diffusing capacity is 102 ml O₂ min⁻¹ mmHg⁻¹. This value is 30-40% lower than values estimated previously by the morphometric method, which considers the total membrane area and the specific uptake rate of erythrocytes. Diffusing capacity is shown to increase with increasing hematocrit and decrease with increasing capillary diameter and increasing thickness of the membrane. Simulations of pulmonary oxygen uptake in humans under conditions of exercise or hypoxia based show closer agreement with experimental data than previous models, but still overestimate oxygen uptake. The remaining discrepancy may reflect effects of heterogeneity of perfusion and ventilation in the lung.

Oxygen transport in the microcirculation and its regulation

OBJECTIVE

Cells require energy to carry out their functions and they typically use oxidative phosphorylation to generate the needed ATP. Thus, cells have a continuous need for oxygen, which they receive by diffusion from the blood through the interstitial fluid. The circulatory system pumps oxygen-rich blood through a network of increasingly minute vessels, the microcirculation. The structure of the microcirculation is such that all cells have at least one nearby capillary for diffusive exchange of oxygen and red blood cells release the oxygen bound to hemoglobin as they traverse capillaries.

METHODS

This review focuses first on the historical development of techniques to measure oxygen at various sites in the microcirculation, including the blood, interstitium, and cells.

RESULTS

Next, approaches are described as to how these techniques have been employed to make discoveries about different aspects of oxygen transport. Finally, ways in which oxygen might participate in the regulation of blood flow toward matching oxygen supply to oxygen demand is discussed.

CONCLUSIONS

Overall, the transport of oxygen to the cells of the body is one of the most critical functions of the cardiovascular system and it is in the microcirculation where the final local determinants of oxygen supply, oxygen demand, and their regulation are decided.

A new method for measuring the oxygen diffusion constant and oxygen consumption rate of arteriolar walls

Oxygen transport is believed to primarily occur via capillaries and depends on the oxygen tension gradient between the vessels and tissues. As blood flows along branching arterioles, the O(2) saturation drops, indicating either consumption or diffusion. The blood flow rate, the O(2) concentration gradient, and Krogh's O(2) diffusion constant (K) of the vessel wall are parameters affecting O(2)delivery. We devised a method for evaluating K of arteriolar wall in vivo using phosphorescence quenching microscopy to measure the partial pressure of oxygen in two areas almost simultaneously. The K value of arteriolar wall (inner diameter, 63.5 ± 11.9 μm; wall thickness, 18.0 ± 1.2 μm) was found to be 6.0 ± 1.2 × 10(-11) (cm(2)/s)(ml O(2)·cm(-3) tissue·mmHg(-1)). The arteriolar wall O(2) consumption rate (M) was 1.5 ± 0.1 (ml O(2)·100 cm(-3) tissue·min(-1)), as calculated using Krogh's diffusion equation. These results suggest that the arteriolar wall consumes a considerable proportion of the O(2) that diffuses through it.

Impaired adaptability of in vivo mitochondrial energetics to acute oxidative insult in aged skeletal muscle

Periods of elevated reactive oxygen species (ROS) production are a normal part of mitochondrial physiology. However, little is known about age-related changes in the mitochondrial response to elevated ROS in vivo. Significantly, ROS-induced uncoupling of oxidative phosphorylation has received attention as a negative feedback mechanism to reduce mitochondrial superoxide production. Here we use a novel in vivo spectroscopy system to test the hypothesis that ROS-induced uncoupling is diminished in aged mitochondria. This system simultaneously acquires (31)P magnetic resonance and near-infrared optical spectra to non-invasively measure phosphometabolite and O(2) concentrations in mouse skeletal muscle. Using low dose paraquat to elevate intracellular ROS we assess in vivo mitochondrial function in young, middle aged, and old mice. Oxidative phosphorylation was uncoupled to the same degree in response to ROS at each age, but this uncoupling was associated with loss of phosphorylation capacity and total ATP in old mice only. Using mice lacking UCP3 we demonstrate that this in vivo uncoupling is independent of this putative uncoupler of skeletal muscle mitochondria. These data indicate that ROS-induced uncoupling persists throughout life, but that oxidative stress leads to mitochondrial deficits and loss of ATP in aged organisms that may contribute to impaired function and degeneration.

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.

Phosphorescence quenching microrespirometry of skeletal muscle in situ

We have developed an optical method for the evaluation of the oxygen consumption (Vo(2)) in microscopic volumes of spinotrapezius muscle. Using phosphorescence quenching microscopy (PQM) for the measurement of interstitial Po(2), together with rapid pneumatic compression of the organ, we recorded the oxygen disappearance curve (ODC) in the muscle of the anesthetized rats. A 0.6-mm diameter area in the tissue, preloaded with the phosphorescent oxygen probe, was excited once a second by a 532-nm Q-switched laser with pulse duration of 15 ns. Each of the evoked phosphorescence decays was analyzed to obtain a sequence of Po(2) values that constituted the ODC. Following flow arrest and tissue compression, the interstitial Po(2) decreased rapidly and the initial slope of the ODC was used to calculate the Vo(2). Special analysis of instrumental factors affecting the ODC was performed, and the resulting model was used for evaluation of Vo(2). The calculation was based on the observation of only a small amount of residual blood in the tissue after compression. The contribution of oxygen photoconsumption by PQM and oxygen inflow from external sources was evaluated in specially designed tests. The average oxygen consumption of the rat spinotrapezius muscle was Vo(2) = 123.4 ± 13.4 (SE) nl O(2)/cm(3) · s (N = 38, within 6 muscles) at a baseline interstitial Po(2) of 50.8 ± 2.9 mmHg. This technique has opened the opportunity for monitoring respiration rates in microscopic volumes of functioning skeletal muscle.

Myoglobin's old and new clothes: from molecular structure to function in living cells

Myoglobin, a mobile carrier of oxygen, is without a doubt an important player central to the physiological function of heart and skeletal muscle. Recently, researchers have surmounted technical challenges to measure Mb diffusion in the living cell. Their observations have stimulated a discussion about the relative contribution made by Mb-facilitated diffusion to the total oxygen flux. The calculation of the relative contribution, however, depends upon assumptions, the cell model and cell architecture, cell bioenergetics, oxygen supply and demand. The analysis suggests that important differences can be observed whether steady-state or transient conditions are considered. This article reviews the current evidence underlying the evaluation of the biophysical parameters of myoglobin-facilitated oxygen diffusion in cells, specifically the intracellular concentration of myoglobin, the intracellular diffusion coefficient of myoglobin and the intracellular myoglobin oxygen saturation. The review considers the role of myoglobin in oxygen transport in vertebrate heart and skeletal muscle, in the diving seal during apnea as well as the role of the analogous leghemoglobin of plants. The possible role of myoglobin in intracellular fatty acid transport is addressed. Finally, the recent measurements of myoglobin diffusion inside muscle cells are discussed in terms of their implications for cytoarchitecture and microviscosity in these cells and the identification of intracellular impediments to the diffusion of proteins inside cells. The recent experimental data then help to refine our understanding of Mb function and establish a basis for future investigation.

Mechanical ventilator for delivery of ¹⁷O₂ in brief pulses

The ¹⁷O nucleus has been used recently by several groups for magnetic resonance (MR) imaging of cerebral metabolism. Inhalational delivery of ¹⁷O₂ in very brief pulses could, in theory, have significant advantages for determination of the cerebral metabolic rate for oxygen (CMRO₂) with MR imaging. Mechanical ventilators, however, are not typically capable of creating step changes in gas concentration at the airway. We designed a ventilator for large animal and human studies that provides mechanical ventilation to a subject inside an MR scanner through 25 feet of small-bore connecting tubing, and tested its capabilities using helium as a surrogate for ¹⁷O₂. After switching the source gas from oxygen to helium, the 0-90% response time for helium concentration changes at the airway was 2.4 seconds. The capability for creating rapid step changes in gas concentration at the airway in large animal and human studies should facilitate the experimental testing of the delivery ¹⁷O₂ in brief pulses, and its potential use in imaging CMRO₂.

Microvascular transport model predicts oxygenation changes in the infarcted heart after treatment

Chronic heart failure is most commonly due to ischemic cardiomyopathy after a previous myocardial infarction (MI). Rebuilding lost myocardium to prevent heart failure mandates a neovasculature able to nourish new cardiomyocytes. Previously we have used a series of novel techniques to directly measure the ability of the scar neovasculature to deliver and exchange oxygen at 1–4 wk after MI in rats following left coronary artery ligation. In this study, we have developed a morphologically realistic mathematical model of oxygen transport in cardiac tissue to help in deciding what angiogenic strategies should be used to rebuild the vasculature. The model utilizes microvascular morphology of cardiac tissue based on available morphometric images and is used to simulate experimentally measured oxygen levels after MI. Model simulations of relative oxygenation match experimental measurements closely and can be used to simulate distributions of oxygen concentration in normal and infarcted rat hearts. Our findings indicate that both vascular density and vascular spatial distribution play important roles in cardiac tissue oxygenation after MI. Furthermore, the model can simulate relative changes in tissue oxygen levels in infarcted tissue treated with proangiogenic compounds such as losartan. From the minimum oxygen concentration myocytes need to maintain their normal function, we estimate that 2 wk after MI 29% of the myocardium is severely hypoxic and that the vascular density of the infarcted tissue should reach 75% of normal tissue to ensure that no areas of the myocardium are critically hypoxic.

Microstructural analysis of deformation-induced hypoxic damage in skeletal muscle

Deep pressure ulcers are caused by sustained mechanical loading and involve skeletal muscle tissue injury. The exact underlying mechanisms are unclear, and the prevalence is high. Our hypothesis is that the aetiology is dominated by cellular deformation (Bouten et al. in Ann Biomed Eng 29:153–63, 2001; Breuls et al. in Ann Biomed Eng 31:1357–364, 2003; Stekelenburg et al. in J App Physiol 100(6):1946–954, 2006) and deformation-induced ischaemia. The experimental observation that mechanical compression induced a pattern of interspersed healthy and dead cells in skeletal muscle (Stekelenburg et al. in J App Physiol 100(6):1946–954, 2006) strongly suggests to take into account the muscle microstructure in studying damage development. The present paper describes a computational model for deformation-induced hypoxic damage in skeletal muscle tissue. Dead cells stop consuming oxygen and are assumed to decrease in stiffness due to loss of structure. The questions addressed are if these two consequences of cell death influence the development of cell injury in the remaining cells. The results show that weakening of dead cells indeed affects the damage accumulation in other cells. Further, the fact that cells stop consuming oxygen after they have died, delays cell death of other cells.

Hemoglobin-based O2 carrier O2 affinity and capillary inlet pO2 are important factors that influence O2 transport in a capillary

Hemopure (Biopure; Cambridge, MA) and PolyHeme (Northfield Laboratories; Evanston, IL) are two acellular hemoglobin-based O2 carriers (HBOCs) currently in phase III clinical trials for use as red blood cell substitutes. The most common adverse side effect that these HBOCs exhibit is increased vasoconstriction. Autoregulatory theory has been presented as a possible explanation for this physiological effect, where it is hypothesized that low-affinity HBOCs over-deliver O2 to tissues surrounding arterioles, thereby eliciting vasoconstriction. In this paper, we wanted to investigate HBOC oxygenation of tissue surrounding a capillary, which is the smallest element of the circulatory system. An a priori model has been developed in which the performance of mixtures of acellular HBOCs (synthesized by our group and others) and human red blood cells (hRBCs) has been simulated using a Krogh tissue cylinder model (KTCM) comprising a capillary surrounded by a capillary membrane and skeletal muscle tissue in cylindrical coordinates with specified tissue O2 consumption rates and Michaelis-Menten kinetics. In this study, the total hemoglobin (hRBCs and HBOCs) concentration was kept constant. The HBOCs studied possessed O2 affinities that were higher and lower compared to hRBCs (P50's spanned 5-55 mmHg), and the equilibrium binding/release of oxygen to/from the HBOCs was modeled using the Adair equation. At normoxic inlet pO2's, there was no correlation between O2 flux out of the capillary and the O2 affinity of the HBOC. However, a correlation was found between the average pO2 tension in the capillary and the O2 affinity of the HBOC. Additionally, we studied the change in the O2 equilibrium curve of HBOCs with different O2 affinities over a wide range of inlet pO2's and found that changing the inlet pO2 greatly affected which HBOC, having a unique O2 affinity, best delivered O2 to the surrounding tissue. The analysis of oxygen transport presented could lead to a better prediction of which acellular HBOC is best suited for a specific transfusion application that many times depends on the capillary inlet pO2 tension.

A computational model of oxygen delivery by hemoglobin-based oxygen carriers in three-dimensional microvascular networks

A detailed computational model is developed to simulate oxygen transport from a three-dimensional (3D) microvascular network to the surrounding tissue in the presence of hemoglobin-based oxygen carriers. The model accounts for nonlinear O(2) consumption, myoglobin-facilitated diffusion and nonlinear oxyhemoglobin dissociation in the RBCs and plasma. It also includes a detailed description of intravascular resistance to O(2) transport and is capable of incorporating realistic 3D microvascular network geometries. Simulations in this study were performed using a computer-generated microvascular architecture that mimics morphometric parameters for the hamster cheek pouch retractor muscle. Theoretical results are presented next to corresponding experimental data. Phosphorescence quenching microscopy provided PO(2) measurements at the arteriolar and venular ends of capillaries in the hamster retractor muscle before and after isovolemic hemodilution with three different hemodilutents: a non-oxygen-carrying plasma expander and two hemoglobin solutions with different oxygen affinities. Sample results in a microvascular network show an enhancement of diffusive shunting between arterioles, venules and capillaries and a decrease in hemoglobin's effectiveness for tissue oxygenation when its affinity for O(2) is decreased. Model simulations suggest that microvascular network anatomy can affect the optimal hemoglobin affinity for reducing tissue hypoxia. O(2) transport simulations in realistic representations of microvascular networks should provide a theoretical framework for choosing optimal parameter values in the development of hemoglobin-based blood substitutes.

Anisotropy and temperature dependence of myoglobin translational diffusion in myocardium: implication for oxygen transport and cellular architecture

Pulsed field gradient NMR methods have determined the temperature-dependent diffusion of myoglobin (Mb) in perfused rat myocardium. Mb diffuses with an averaged translational diffusion coefficient (DMb) of 4.24-8.37x10(-7)cm2/s from 22 degrees C to 40 degrees C and shows no orientation preference over a root mean-square displacement of 2.5-3.5 microm. The DMb agrees with the value predicted by rotational diffusion measurements. Based on the DMb, the equipoise diffusion PO2, the PO2 in which Mb-facilitated and free O2 diffusion contribute equally to the O2 flux, varies from 2.72 to 0.15 in myocardium and from 7.27 to 4.24 mmHg in skeletal muscle. Given the basal PO2 of approximately 10 mmHg, the Mb contribution to O2 transport appears insignificant in myocardium. In skeletal muscle, Mb-facilitated diffusion begins to contribute significantly only when the PO2 approaches the P50. In marine mammals, the high Mb concentration confers a predominant role for Mb in intracellular O2 transport under all physiological conditions. The Q10 of the DMb ranges from 1.3 to 1.6. The Mb diffusion data indicate that the postulated gel network in the cell must have a minimum percolation cutoff size exceeding 17.5 A and does not impose tortuosity within the diffusion root mean-square displacement. Moreover, the similar Q10 for the DMb of solution versus cell Mb suggests that any temperature-dependent alteration of the postulated cell matrix does not significantly affect protein mobility.

Myoglobin translational diffusion in rat myocardium and its implication on intracellular oxygen transport

Current theory of respiratory control invokes a role of myoglobin (Mb)-facilitated O2 diffusion in regulating the intracellular O2 flux, provided Mb diffusion can compete effectively with free O2 diffusion. Pulsed-field gradient NMR methods have now followed gradient-dependent changes in the distinct 1H NMR gamma CH3 Val E11 signal of MbO2 in perfused rat myocardium to obtain the endogenous Mb translational diffusion coefficient (D(Mb)) of 4.24 x 10(-7) cm2 s(-1) at 22 degrees C. The D(Mb) matches precisely the value predicted by in vivo NMR rotational diffusion measurements of Mb and shows no orientation preference. Given values in the literature for the Krogh's free O2 diffusion coefficient (K0), myocardial Mb concentration and a partial pressure of O2 that half saturates Mb (P50), the analysis yields an equipoise diffusion P(O2) of 1.77 mmHg, where Mb and free O2 contribute equally to the O2 flux. In the myocardium, Mb-facilitated O2 diffusion contributes increasingly more than free O2 diffusion when the P(O2) falls below 1.77 mmHg. In skeletal muscle, the P(O2) must fall below 5.72 mmHg. Altering the Mb P50 induces modest change. Mb-facilitated diffusion has a higher poise in skeletal muscle than in myocardium. Because the basal P(O2) hovers around 10 mmHg, Mb does not have a predominant role in facilitating O2 transport in myocardium but contributes significantly only when cellular oxygen falls below the equipoise diffusion P(O2).

Mitochondrial coupling in vivo in mouse skeletal muscle

The coupling of mitochondrial ATP synthesis and oxygen consumption (ratio of ATP and oxygen fluxes, P/O) plays a central role in cellular bioenergetics. Reduced P/O values are associated with mitochondrial pathologies that can lead to reduced capacity for ATP synthesis and tissue degeneration. Previous work found a wide range of values for P/O in normal mitochondria. To measure mitochondrial coupling under physiological conditions, we have developed a procedure for determining the P/O of skeletal muscle in vivo. This technique measures ATPase and oxygen consumption rates during ischemia with31P magnetic resonance and optical spectroscopy, respectively. This novel approach allows the independent quantitative measurement of ATPase and oxygen flux rates in intact tissue. The quantitative measurement of oxygen consumption is made possible by our ability to independently measure the saturations of hemoglobin (Hb) and myoglobin (Mb) from optical spectra. Our results indicate that the P/O in skeletal muscle of the mouse hindlimb measured in vivo is 2.16 ± 0.24. The theoretical P/O for resting muscle is 2.33. Systemic treatment with 2,4-dinitrophenol to partially uncouple mitochondria does not affect the ATPase rate in the mouse hindlimb but nearly doubles the rate of oxygen consumption, reducing in vivo P/O to 1.37 ± 0.22. These results indicate that only a small fraction of the oxygen consumption in resting mouse skeletal muscle is nonphosphorylating under physiological conditions, suggesting that mitochondria are more tightly coupled than previously thought.

The dichotomous oxyregulatory behaviour of the planktonic crustaceanDaphnia magna

The dual function of appendage movement (food acquisition, ventilation)proved to be the key to explaining the peculiar oxyregulatory repertoire of the planktonic filter feeder Daphnia magna. Short-term hypoxic exposure experiments with normoxia-acclimated animals under varying food concentrations revealed a dichotomous response pattern with a compensatory tachycardia under food-free conditions and a ventilatory compensation prevailing under food-rich conditions. Food-free, normoxic conditions resulted in maximum appendage beating rates (fa) and half-maximum heart rates (fh), which restricted the scope for oxyregulation to the circulatory system. Food-rich conditions (105algal cells ml-1), on the contrary, had a depressing effect on fa whereas fh increased to 83% of the maximum. In this physiological state, D. magna was able to respond to progressive hypoxia with a compensatory increase in ventilation. A conceptual and mathematical model was developed to analyse the efficiency of ventilatory and circulatory adjustments in improving oxygen transport to tissue. Model predictions showed that an increase in perfusion rate was most effective under both food-free and food-rich conditions in reducing the critical ambient oxygen tension (PO2crit) at which oxygen supply to the tissue started to become impeded. By contrast, a hypothetical increase in ventilation rate had almost no effect on PO2crit under food-free conditions, indicating that appendage movement is driven by nutritive rather than respiratory requirements. However, the model predicted a moderate reduction of PO2crit by hyperventilation under food-rich conditions. Since the regulatory scope for an adjustment in fh was found to be limited in D. magna under these conditions, the increase in ventilation rate is the means of choice for a fed animal to cope with short-term, moderate reductions in ambient oxygen availability. Under long-term and more severe hypoxic conditions, however, the increase in the concentration and oxygen affinity of haemoglobin represents the one and only measure for improving the transport of oxygen from environment to cells.

Estimation of capillary density in human skeletal muscle based on maximal oxygen consumption rates

A previously developed Krogh-type theoretical model was used to estimate capillary density in human skeletal muscle based on published measurements of oxygen consumption, arterial partial pressure of oxygen, and blood flow during maximal exercise. The model assumes that oxygen consumption in maximal exercise is limited by the ability of capillaries to deliver oxygen to tissue and is therefore strongly dependent on capillary density, defined as the number of capillaries per unit cross-sectional area of muscle. Based on an analysis of oxygen transport processes occurring at the microvascular level, the model allows estimation of the minimum number of straight, evenly spaced capillaries required to achieve a given oxygen consumption rate. Estimated capillary density values were determined from measurements of maximal oxygen consumption during knee extensor exercise and during whole body cycling, and they range from 459 to 1,468 capillaries/mm2. Measured capillary densities, obtained with either histochemical staining techniques or electron microscopy on quadriceps muscle biopsies from healthy subjects, are generally lower, ranging from 123 to 515 capillaries/mm2. This discrepancy is partly accounted for by the fact that capillary density decreases with muscle contraction and muscle biopsy samples typically are strongly contracted. The results imply that estimates of maximal oxygen transport rates based on capillary density values obtained from biopsy samples do not fully reflect the oxygen transport capacity of the capillaries in skeletal muscle.

Myocardial oxygenation in isolated hearts predicted by an anatomically realistic microvascular transport model

An anatomically realistic model for oxygen transport in cardiac tissue is introduced for analyzing data measured from isolated perfused guinea pig hearts. The model is constructed to match the microvascular anatomy of cardiac tissue based on available morphometric data. Transport in the three-dimensional system (divided into distinct microvascular, interstitial, and parenchymal spaces) is simulated. The model is used to interpret experimental data on mean cardiac tissue myoglobin saturation and to reveal differences in tissue oxygenation between buffer-perfused and red blood cell-perfused isolated hearts. Interpretation of measured mean myoglobin saturation is strongly dependent on the oxygen content of the perfusate (e.g., red blood cell-containing vs. cell-free perfusate). Model calculations match experimental values of mean tissue myoglobin saturation, measured mean myoglobin, and venous oxygen tension and can be used to predict distributions of intracellular oxygen tension. Calculations reveal that approximately 20% of the tissue is hypoxic with an oxygen tension of <0.5 mmHg when the buffer is equilibrated with 95% oxygen to give an arterial oxygen tension of over 600 mmHg. The addition of red blood cells to give a hematocrit of only 5% prevents tissue hypoxia. It is incorrect to assume that the usual buffer-perfused Langendorff heart preparation is adequately oxygenated for flows in the range of < or =10 ml. min-1. ml tissue-1.

Oxygen delivery to skeletal muscle fibers: effects of microvascular unit structure and control mechanisms

The number of perfused capillaries in skeletal muscle varies with muscle activation. With increasing activation, muscle fibers are recruited as motor units consisting of widely dispersed fibers, whereas capillaries are recruited as groups called microvascular units (MVUs) that supply several adjacent fibers. In this study, a theoretical model was used to examine the consequences of this spatial mismatch between the functional units of muscle activation and capillary perfusion. Diffusive oxygen transport was simulated in cross sections of skeletal muscle, including several MVUs and fibers from several motor units. Four alternative hypothetical mechanisms controlling capillary perfusion were considered. First, all capillaries adjacent to active fibers are perfused. Second, all MVUs containing capillaries adjacent to active fibers are perfused. Third, each MVU is perfused whenever oxygen levels at its feed arteriole fall below a threshold value. Fourth, each MVU is perfused whenever the average oxygen level at its capillaries falls below a threshold value. For each mechanism, the dependence of the fraction of perfused capillaries on the level of muscle activation was predicted. Comparison of the results led to the following conclusions. Control of perfusion by MVUs increases the fraction of perfused capillaries relative to control by individual capillaries. Control by arteriolar oxygen sensing leads to poor control of tissue oxygenation at high levels of muscle activation. Control of MVU perfusion by capillary oxygen sensing permits adequate tissue oxygenation over the full range of activation without resulting in perfusion of all MVUs containing capillaries adjacent to active fibers.

Oxygen diffusion and consumption of aortic valve cusps

To maintain tissue oxygenation, normal aortic valves contain a vascular bed where tissue thickness is greatest. Avascular "living" tissue-engineered heart valves have been proposed, yet little information exists regarding the magnitude of valve tissue metabolic activity or oxygen requirements. We therefore set out to measure the oxygen diffusivity (DO(2)) and oxygen consumption (VO(2)) of seven porcine aortic valve cusps in vitro at 37 degrees C using a chamber with a Clark oxygen sensor. Mean DO(2) and VO(2) were 1.06 x 10(-5) cm(2)/s and 3.05 x 10(-5) x ml O(2). ml tissue(-1) x s(-1), respectively. When modeled as a three-layered structure by using these values and a boundary condition of 100 mmHg at both surfaces, the average aortic cusp predicted a central mean PO(2) of 27 mmHg (range of 0-50 mmHg). The DO(2) value obtained was similar to that found for other vascular structures, but because our studies were carried out in vitro, the VO(2) measurements may be lower than that required by the functioning valves. These values provide an initial understanding of the oxygen supply possible from the cusp surfaces and the oxygen needs of the tissue.

A theoretical model for oxygen transport in skeletal muscle under conditions of high oxygen demand

Oxygen transport from capillaries to exercising skeletal muscle is studied by use of a Krogh-type cylinder model. The goal is to predict oxygen consumption under conditions of high demand, on the basis of a consideration of transport processes occurring at the microvascular level. Effects of the decline in oxygen content of blood flowing along capillaries, intravascular resistance to oxygen diffusion, and myoglobin-facilitated diffusion are included. Parameter values are based on human skeletal muscle. The dependence of oxygen consumption on oxygen demand, perfusion, and capillary density are examined. When demand is moderate, the tissue is well oxygenated and consumption is slightly less than demand. When demand is high, capillary oxygen content declines rapidly with axial distance and radial oxygen transport is limited by diffusion resistance within the capillary and the tissue. Under these conditions, much of the tissue is hypoxic, consumption is substantially less than demand, and consumption is strongly dependent on capillary density. Predicted consumption rates are comparable with experimentally observed maximal rates of oxygen consumption.

Motor nerve topology reflects myocyte morphology in hamster retractor and epitrochlearis muscles

Neuromuscular activation is a primary determinant of metabolic demand and oxygen transport. The m. retractor and m. epitrochlearis are model systems for studying metabolic control and oxygen transport; however, the organization of muscle fibers and motor nerves in these muscles is unknown. We tested whether the topology of motor innervation was related to the morphology of muscle fibers in m. retractor and m. epitrochlearis of male hamsters ( approximately 100 g). Respective muscles averaged 47 and 12 mm in length 100 and 35 mg in mass. Staining for acetylcholinesterase revealed neuromuscular junctions arranged in clusters throughout m. retractor and as a central band across m. epitrochlearis, suggesting differences in fiber morphology. For both muscles, complete cross-sections contained approximately 1,700 fibers. Fiber cross-sectional areas were distributed nearly normal in m. epitrochlearis (mean = 1,559 +/- 17 microm(2)) and skewed left (P < 0.05) in m. retractor (mean = 973 +/- 15 microm(2)). Single fiber length (Lf) spanned muscle length (Lm) in m. epitrochlearis, while fibers tapered to terminate within m. retractor (Lf/Lm = 0.43 +/- 0. 02). With myelin staining, a single branch of ulnar nerve projected axons across the midregion of m. epitrochlearis. For m. retractor, the spinal accessory nerve branched to give rise to proximal and distal regions of innervation, with intermingling of axons between nerve branches. Nerve bundle cross-sections stained for acetylcholinesterase indicate that each motor axon projects to an average of 65 muscle fibers in m. epitrochlearis and 100 in m. retractor. Differences in fiber morphology, innervation topology, and neuromuscular organization may contribute to the heterogeneity of metabolic demand and oxygen supply in skeletal muscle.

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.

Protein diffusion in living skeletal muscle fibers: dependence on protein size, fiber type, and contraction

Sarcoplasmic protein diffusion was studied under different conditions, using microinjection in combination with microspectrophotometry. Six globular proteins with molecular masses between 12 and 3700 kDa, with diameters from 3 to 30 nm, were used for the experiments. Proteins were injected into single, intact skeletal muscle fibers taken from either soleus or extensor digitorum longus (edl) muscle of adult rats. No correlation was found between sarcomere spacing and the sarcoplasmic diffusion coefficient (D) for all proteins studied. D of the smaller proteins cytochrome c (diameter 3.1 nm), myoglobin (diameter 3.5 nm), and hemoglobin (diameter 5.5 nm) amounted to only approximately 1/10 of their value in water and was not increased by auxotonic fiber contractions. D for cytochrome c and myoglobin was significantly higher in fibers from edl (mainly type II fibers) compared to fibers from soleus (mainly type I fibers). Measurements of D for myoglobin at 37 degrees C in addition to 22 degrees C led to a Q(10) of 1.46 for this temperature range. For the larger proteins catalase (diameter 10.5 nm) and ferritin (diameter 12.2 nm), a decrease in D to approximately 1/20 and approximately 1/50 of that in water was observed, whereas no diffusive flux at all of earthworm hemoglobin (diameter 30 nm) along the fiber axis could be detected. We conclude that 1) sarcoplasmic protein diffusion is strongly impaired by the presence of the myofilamental lattice, which also gives rise to differences in diffusivity between different fiber types; 2) contractions do not cause significant convection in sarcoplasm and do not lead to increased diffusional transport; and 3) in addition to the steric hindrance that slows down the diffusion of smaller proteins, diffusion of large proteins is further hindered when their dimensions approach the interfilament distances. This molecular sieve property progressively reduces intracellular diffusion of proteins when the molecular diameter increases to more than approximately 10 nm.

Diffusion of myoglobin in skeletal muscle cells--dependence on fibre type, contraction and temperature

We measured the diffusion coefficient of myoglobin (DMb) inside mammalian skeletal muscle cells with a microinjection technique. A small bolus of horse Mb was injected into a single muscle fibre and the subsequent time-dependent changes of the Mb profiles along the fibre axis were measured with a microscope-photometer. For fibres of the rat soleus muscle at 22 degrees C, a DMb of 1.3.10(-7) cm2/s was found, confirming a result obtained previously by us for rat diaphragm muscle with a photo-oxidation technique. In the extensor digitorum longus muscle of the rat, a higher value of 1.9.10(-7) cm2/s was measured. Auxotonic muscle contractions did not change the apparent DMb. For the temperature range between 22 degrees C and 37 degrees C, a temperature coefficient. Q10, of 1.5 was calculated. The implication of this result for the role of Mb in the facilitation of oxygen transport was examined. Model calculations show that with this relatively low DMb value, the intracellular oxygen supply can be improved only slightly.

Diffusivity of myoglobin in intact skeletal muscle cells

We report a method that allows us to determine the diffusion coefficient of native myoglobin in intact and mechanically unaffected red muscle fibers. The method is based on an optical recording of intracellular diffusion of metmyoglobin, which is produced inside the cells by photooxidation of oxymyoglobin with a UV light pulse. We find a myoglobin diffusivity of 1.2 x 10(-7) cm2/s (22 degrees C), which is only 1/10th of the value measured in very dilute myoglobin solutions and 1/5th of the value obtained from measurements in solutions of myoglobin at 18 g/dl. The latter value often has been used in model calculations of oxygen transport to tissue incorporating myoglobin-facilitated oxygen diffusion. Recalculating facilitated diffusion with the value obtained by us implies that its contribution to total intracellular oxygen transport is of minor importance. Furthermore, it shows that sterical hindrance to myoglobin diffusion is dominated by the muscle-cell architecture rather than by the overall protein concentration of the muscle fiber.