Capillary structures and O2 supply to tissue

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.

Increased muscle blood supply and transendothelial nutrient and insulin transport induced by food intake and exercise: effect of obesity and ageing

This review concludes that a sedentary lifestyle, obesity and ageing impair the vasodilator response of the muscle microvasculature to insulin, exercise and VEGF-A and reduce microvascular density. Both impairments contribute to the development of insulin resistance, obesity and chronic age-related diseases. A physically active lifestyle keeps both the vasodilator response and microvascular density high. Intravital microscopy has shown that microvascular units (MVUs) are the smallest functional elements to adjust blood flow in response to physiological signals and metabolic demands on muscle fibres. The luminal diameter of a common terminal arteriole (TA) controls blood flow through up to 20 capillaries belonging to a single MVU. Increases in plasma insulin and exercise/muscle contraction lead to recruitment of additional MVUs. Insulin also increases arteriolar vasomotion. Both mechanisms increase the endothelial surface area and therefore transendothelial transport of glucose, fatty acids (FAs) and insulin by specific transporters, present in high concentrations in the capillary endothelium. Future studies should quantify transporter concentration differences between healthy and at risk populations as they may limit nutrient supply and oxidation in muscle and impair glucose and lipid homeostasis. An important recent discovery is that VEGF-B produced by skeletal muscle controls the expression of FA transporter proteins in the capillary endothelium and thus links endothelial FA uptake to the oxidative capacity of skeletal muscle, potentially preventing lipotoxic FA accumulation, the dominant cause of insulin resistance in muscle fibres.

Computer modeling of relationship between critical PvO2, VO2max and blood supply of skeletal muscle at working with a right-shifted blood O2 dissociation curve

Investigations were performed on a computer model of O2 delivery and O2 consumption in the one working muscle. At working with increasing power and achieving the critical value of VO2 (VO2crit), the muscle VO2 began to lag behind the oxygen demand qO2. The model permits to find critical pO2 in effluent venous blood Pvcrit at VO2crit as well as to calculate VO2max and PvO2 at VO2max under exercise with changing muscle blood flow F and blood pH.Pvcrit was computed from the condition VO2crit = 0.9qO2, and VO2max- from the condition (dVO2/dqO2) = 0.1. VO2max, Pv at VO2max, Pvcrit, and VO2crit were calculated for: 40 < or = F < or = 120 ml/min/100 g; 6.8 < or = pH < or = 7.4. It was shown that the faster is F and the lesser is blood pH, the greater were the Pvcrit and VO2max values. With decreasing F and blood pH, the influence of F on Pvcrit and VO2max increases, whereas the influence of blood pH on these values decreases. With increasing F and, hence, an increasing VO2max, the blood supply efficiency decreases due to the important limiting factor--tissue oxygen diffusion.

Nonlinear model for capillary-tissue oxygen transport and metabolism

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

Significance of the Bohr effect for tissue oxygenation in a model with counter-current blood flow

Counter-current arrangement of afferent and efferent blood flow in tissues is commonly considered to be detrimental to tissue oxygenation, since O2 diffusion would shunt O2 away from the tissue. We have investigated the combined effects of counter-current CO2 and O2 exchange in a simple model, paying particular attention to the Bohr effect. We have obtained the following main results. (1) Back-diffusion of CO2 leads to increasing CO2 partial pressure (PCO2) and CO2 content along the afferent vessel. This is enhanced when fixed acid is released by the tissue into the venous blood, e.g. during hypoxia, which leads to a further PCO2 increase therein. (2) The increasing PCO2, with concomitant decrease in pH, in the afferent blood leads to a decrease in blood O2 affinity (Bohr effect) and thus results in increased PO2. (3) The resulting O2 diffusion shunt diminishes the O2 content in afferent blood, but for most conditions its PO2 remains higher than without the Bohr effect. (4) During hypoxia, both the PO2 in blood reaching the tissue (Pta) as well as in that leaving it (Ptv) are significantly elevated above the level without the Bohr effect. Moreover, with fixed acid release both Pta and Ptv for O2 can be higher than the arterial PO2 value. (5) During hyperoxia, O2 diffusion shunt prevents the tissue PO2 levels from increasing to levels that might be regarded as toxic. It is concluded that a diffusion shunt in tissues stabilizes the O2 partial pressure at the tissue when it varies in arterial blood (hypoxia or hyperoxia).

Effect of intracapillary resistance to oxygen transport on the diffusional shunting between capillaries

The effect of intracapillary resistance to oxygen transport on distribution of oxygen tension in the tissue and along the capillary was investigated by means of a mathematical model. In some cases resistance significantly affects the diffusive interaction between neighbouring capillaries thus aggravating the deficiency of oxygen supply around capillaries with low oxygen tension.

Myocardial capillary flow pattern as determined by the method of coloured microspheres

In summary, it can be said that in spite of possible limitations, this technique provides previously unattainable data on capillary flow pattern in the myocardium. Qualitative and quantitative results indicate that the following anatomical and physiological concepts should be incorporated in any further modelling of oxygen transport to myocardium: (1) Concurrent flow pattern (2) Presence of short capillary loops (3) Presence of capillary bundles (4) Staggered arrangements of arteriolar inflow to capillary network.

Diffusional shunting of oxygen in saline-perfused isolated rabbit heart is negligible

Diffusional shunting of oxygen in the saline-perfused heart was studied by comparing the time course of the coronary venous concentrations of oxygen and an intravascular indicator following a simultaneous step-like change in their arterial concentrations. To this end 7 rabbit hearts were perfused according to Langendorff with Tyrode solution at a perfusion flow rate of 3.8 +/- 1.4 ml.min-1.g-1 (wet weight) at 37 degrees C. In the reference situation arterial (Pao2) and venous oxygen tensions (Pvo2) were about 610 and 290 mmHg, respectively. Step changes in Pao2 were made to a 60 mmHg lower level and back. Simultaneously the arterial concentration of albumin-bound indocyanine green, an intravascular indicator, was changed. No deflection in PvO2 was detected before the venous dye concentration changed. The venous dye concentration crossed 5% of its step amplitude 4 s after the arterial change, on average 2.3 s before Pvo2 crossed its 5% level. We conclude that shunt diffusion of oxygen from arterioles to venules and from arterial to venous ends of the capillary bed is negligible in saline-perfused hearts and thus cannot explain the high value of Pvo2 in these preparations.

Effect of Heterogeneous Oxygen Delivery on the Oxygen Distribution in Skeletal Muscle

Calculations of the oxygen distribution in resting and contracting skeletal muscle are presented, based on a mathematical model and experimental data obtained on the hamster cremaster muscle [Klitzman et al., Microvasc. Res. 25:108-131 (1983)]. The model considers a slab of tissue penetrated by a regular square array of capillaries with concurrent flow. The intracapillary resistance to oxygen transport is neglected. The capillary red blood cell flux and capillary inlet oxygen tension are assumed random variables following certain probability distributions. The sensitivity of the tissue and intracapillary PO2 to variations of these probability distributions are investigated. The mean tissue PO2 decreases as the dispersion of the random variables increases, provided that their mean values remain constant. Hypoxic regions appear gradually, especially in the case of contracting muscle, as the dispersion increases. The effect of the number of capillaries in the sample on the resultant distribution of oxygen is studied systematically. The calculated tissue PO2 histograms are compared with previously reported PO2 distributions obtained experimentally for resting and contracting skeletal muscle.

Dual role of diffusion in tissue gas exchange: blood-tissue equilibration and diffusion shunt

The role of diffusion in tissue gas exchange is investigated using a simple mathematical model which incorporates both tissue-blood equilibration and gas transfer between arterial and venous vessels with counter-current flow, leading to 'diffusion shunt'. Both increasing the diffusion coefficient of the gas considered or decreasing the blood flow results in two antagonistic effects: (i) improvement of blood/tissue equilibration, (ii) increase in extent of diffusion shunt. The diffusion shunt retards inert gas wash-out (local tissue clearance) and leads thus, if not taken into account, to an underestimation of capillary blood flow calculated from the wash-out rate constant. For O2 (and CO2) the diffusion shunt reduces the efficacy of blood/tissue transfer, but its extent is expected to be only moderate because of the chemical combination of these gases in blood.

Muscle O2 gradients from hemoglobin to cytochrome: new concepts, new complexities

The capillary is the principal barrier at high Vo2. Mathematical modelling indicates that at high flow and Vo2 the time required for release of O2 is greater than red cell transit time in some capillaries. This convective shunting appears to be particularly important in the myocardium. The Mb acts to buffer Po2 below 5 Torr during muscle contraction. This greatly increases the transcapillary O2 gradient and promotes O2 delivery. During voluntary movements, Mb should act as a major O2 source in parallel with capillaries. The Kroghian model of the capillary as a "low-resistance" point source of O2 supplying a spatially uniform sink appears to be the reverse of the actual geometry of O2 supply to working red muscle.

Diffusion-perfusion relationships in skeletal muscle: models and experimental evidence from inert gas washout

In order to study the dependence of blood-tissue gas exchange upon diffusion, the simultaneous washout of two inert gases of differing diffusivity was investigated in isolated-perfused dog gastrocnemius preparations. The muscles were equilibrated with CH4 and SF6 via arterial blood. The washout kinetics were determined from venous blood samples analyzed by gas chromatography. The results revealed the following features: The washout of the test gases was pronouncedly multi-exponential, and could be described by three exponential components when analyzed to 5% of the initial value. The non-exponential washout was attributed to unequal distribution of capillary blood flow to tissue volume. The mean ratio of washout rate constants CH4/SF6 was within 1.10-1.25 and was even smaller than the ratio expected for pure perfusion limitation (1.46). Therefore, no evidence for effective tissue-blood diffusion limitation was obtained. The observed washout rate constant ratio could be explained by a model with veno-arterial back diffusion which more strongly retards washout kinetics of the better diffusible gas (CH4) as compared to the less diffusible gas (SF6).

Oxygen transport in resting and contracting hamster cremaster muscles: experimental and theoretical microvascular studies

Intravital microscopy of the superfused cremaster muscle was used to measure the density, diameter, length, hematocrit, red cell velocity, and red cell flux in capillaries of the pentobarbital-anesthetized hamster. Oxygen microelectrodes were used to measure oxygen tension (Po2) at a position 75-100 micrometers deep in the muscle between the venous ends of capillaries and, very importantly, at the superfusate-muscle interface. These parameters were measured in resting and contracting muscles and under three values of superfusate Po2: low (8mm Hg), medium (40 mm Hg), and high (75 mm Hg). These data were complete enough to be useful input parameters in a recently developed mathematical model of oxygen transport in exposed tissue (A. S. Popel, 1981, Math. Biosci. 55, 231-246). The model indicated that with high superfusate Po2, oxygen was supplied to the resting muscle almost exclusively from the superfusate because of the vasoconstriction and reduced blood flow. Oxygen consumption of the resting muscle was estimated to be 0.4 ml O2/100 ml tissue X min, assuming muscle oxygen consumption was uniform and independent of Po2 above 1 mm Hg. The estimated rise in oxygen consumption with exercise was four to eight times resting muscle values, which agrees with previously published data. Also, the model predicted an inlet capillary Po2 of 27 mm Hg with a low superfusate Po2, which is consistent with the few available direct measurements. The model emphasized that with measurement of the Po2 at the superfusate-tissue interface, the complex O2 transport effects of the superfusate can be accurately characterized. Measurement of this and other parameters of the model leads to a potentially useful prediction of the Po2 distribution within tissues under a variety of conditions.

Direct measurement of intracellular O2 gradients; role of convection and myoglobin

During steady phasic exercise in a red muscle the entire O2 gradient between capillary and mitochondria occurs as a step over less than 5 m. The magnitude of this step is determined by VO2 and capillary PO2, and is independent of distance from a capillary, or local capillary density. The above cannot be explained by ordinary and/or facilitated diffusion, according to a classical Krogh model. A step gradient can be produced by intracellular convection and Mb, acting in concert. A uniformly low cell PO2 maximizes the trans-capillary O2 gradient, and hence the O2 flux. Since the O2 affinity of Mb is about 50 times less than that cytochrome a, a3, mitochondria can respire maximally at tensions well below the Mb P50. It seems likely that the principal function of Mb during steady, phasic exercise is to compensate for short capillary transit times by accelerating O2 release from Hb.

Mathematical Modeling of Oxygen Transport Near a Tissue Surface: Effect of the Surface PO2

The effect of the surface oxygen tension on the oxygen-tension distribution in the tissue is considered. A mathematical formulation of the problem is presented, and the solutions are obtained numerically using a finite-element method. It is shown that the oxygen tension at the surface of the tissue may significantly affect the oxygen-tension distribution in layers of tissue situated within several intercapillary distances below the surface.

Design of the mammalian respiratory system. VI Distribution of mitochondria and capillaries in various muscles

The variability of structures supporting tissue oxygen transport (capillaries) and oxygen consumption (mitochondria) was analyzed in skeletal muscles of wildebeest and dik-dik. Regional differences in mitochondria and capillary densities within individual muscles were found for M. semitendinosus (twofold) but not for M. longissimus dorsi and diaphragm. Comparing 20 different muscles from both animals, the volume density of mitochondria in the muscle fibers [Vv(mt,f)] was significantly higher in diaphragm (10-12%) and varied considerably (1-6%) in the other muscles. The relation between Vv(mt,f) and the number of capillaries per cross-sectional fiber area NA(c,f) showed great variability. In glycolytic fibers Vv(mt,f) was typically low (1%) whereas in oxidative fibers it ranged from 5-15%. No systematic trend was found for the packing of cristae in subsarcolemmal and interfibrillar mitochondria from both types of fibers in large and small animals.

Design of the mammalian respiratory system. VIII Capillaries in skeletal muscles

The relationship between capillary density and mitochondrial volume density in skeletal muscle tissue is investigated on 25 African mammals ranging in body mass from 0.4 to 251 kg. As a general trend higher capillary densities, NA (c,f) are found in muscles with higher volume densities of mitochondria, Vv(mt,f). The individual data however show considerable scatter. Part of this scatter can be explained by the fact that NA (c,f) alone is not a sufficient parameter to account for functional properties of the vascular supply. The regional variability of the capillary network from arterial to venous end also contributes to the data spread. A number of physiological variables of the vascular compartment may also influence the relationship of capillary counts to the mitochondrial densities of muscle fibers. This relationship therefore cannot be expected to be a simple one.

Comparison between hydrogen clearance and microsphere technique for rCBF measurement

Regional cerebral blood flow was measured repeatedly in anesthetized and immobilized cats under various experimental conditions by recording the clearance of inhaled hydrogen with inserted platinum electrodes and by recording the distribution of 15 mu microspheres labeled with 3 different radioisotopes. The values for both methods in normal cortical tissue were comparable (75.7 +/- 23.5 ml/100 g min for H2-clearance; 67.6 +/- 26.2 ml/100 g min for microsphere technique), but were below those recorded in awake cats. With both methods the values could be reliably reproduced (correlation coefficient between measurements: 0.903 for H2-clearance, 0.754 for microsphere technique). During ischemia induced by temporary occlusion of the middle cerebral artery the microsphere technique usually yielded higher flow values than the H2-clearance, and did not indicate severe ischemia in 6 out of 20 instances. After restoration of flow, hyperperfusion was observed by the microsphere technique in 2 cases only while H2-clearance indicated hyperemia in 6 instances. This limited comparability between the 2 methods was also expressed in a low correlation coefficient (0.486) calculated from 139 flow values obtained simultaneously with both methods. The discrepancy between the methods under pathological conditions might be due mainly to the different recording volumes: while Pt-electrodes record H2-clearance from a few mm3 or less, tissue samples of 300-700 mg were necessary for the microsphere technique and inhomogeneities of flow may thereby escape detection. The technique for measuring cerebral blood flow in an experimental setup should be selected according to the requirements of the study and according to the limitations of the various methods.

Oxygen Diffusion from Capillary Layers with Concurrent Flow

Oxygen transport from capillary layers with concurrent flow is considered for symmetric and asymmetric distributions of oxygen concentration between the layers. The analysis is based on the solution previously obtained by the author [1]. Solutions for the symmetric case are shown to be very close to the corresponding solutions of the Krogh cylinder model. Asymmetry in oxygen distribution is introduced systematically by considering different velocities of blood in the alternate capillary layers, different inlet capillary oxygen tensions, and different capillary hematocrits. It is shown that increase of the degree of asymmetry leads to diminution of the mean oxygen tension.

Analysis of Capillary-Tissue Diffusion in Multicapillary Systems

The diffusive transport of a substance between a parallel capillary network and the surrounding tissue is investigated. The consumption/production rate of the substance in the tissue is assumed to be constant (zero-order chemical kinetics). The solution of the diffusion problem which describes the distribution of the substance in the tissue and along the capillary network is found in an analytical form. A rather general assumption regarding the symmetry of capillary network makes it possible to formulate a Neumann-type boundary-value problem in a rectangular domain. The solution of the diffusion problem in the rectangle allows the capillary-tissue fluxes to be expressed linearly in terms of the concentrations in the capillaries, and hence leads to ordinary differential equations for those concentrations. Several examples are considered with different network geometry and concurrent or countercurrent flow conditions. The solution makes it possible to investigate the effect of capillary interaction on mass transfer in various microcirculatory units.

Distribution of the myocardial tissue PO2 in the rat and the inhomogeneity of the coronary bed

The structural inhomogeneity of the myocardial capillary bed is stimulated by microcirculatory units (MCU's) in a diffusion model. This stimulation is based on MCU's in which the arrangement of the capillary ends (concurrent structure, partial and total countercurrent (structure, helical structure) as well as the structure and supply parameters are varied. The variation of these parameters is based on own measurements of the intracapillary HbO2 saturation as well as on the following parameters from the literature: frequency distribution of capillary distance and capillary radius, mean capillary length or capillary section length respectively, arterial and mean venous PO2, mean coronary blood flow, mean O2 consumption and diffusion conductivity. The analysis of O2 supply of the normoxic rat heart shows that an O2 diffusion shunt is obligatory except of MCU's with an extremely large capillary distance or with a concurrent capillary structure. Therefore the minimal tissue PO2 lies at the level of the capillary venous PO2 of a MCU. The maximum of the total PO2 frequency distribution in the normoxic rat myocardium lies at 25 +/- 5 mm Hg, i.e. above the mean venous PO2 (20 mm Hg). Tissue PO2 values between 0 and 5 mm Hg amount to 0.5% i.e. they are extremely rare. Tissue PO2 values of 0-1 mm Hg represent less than 0.2%.

Intracapillary HbO2 saturation in tumor tissue of DS-carcinosarcoma during normoxia

The measurements of the intravascular HbO2 saturation in tumor capillaries using the cryophotometric micromethod reveal that very low HbO2 saturation values predominate in malignant tumors. Under normoxic conditions only 8% of the measured values exceed 50% saturation. 53% of the intracapillary HbO2 saturation values are in the range of 0-10% HbO2 saturation. Great regional differences are seldom and can be found only in areas where a sufficient vascularization still exists. Taking into account the data of morphometric analysis of tumor vascularization and the parameters of respiratory gas exchange, the measured frequency distribution of HbO2 saturation values in tumor capillaries is simulated by means of different three-dimensional capillary structures; On the basis of these microcirculatory units, tissue pO2 values are computed in the intercapillary regions. As a result of these calculations it can be stated that the computed data derived from intracapillary HbO2 saturations are in sufficient agreement with pO2 values measured polarographically using gold- microelectrodes.