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.     

Structure of the glomerular capillaries of the domestic chicken and desert quail

The glomerular capillary architecture of nephrons that include a loop of Henle (looped) and those that lack the loop (loopless) nephrons was examined qualitatively and quantitatively by electron microscopy in Gallus gallus and Callipepla gambelii. The glomerular capillaries of looped nephrons form a dichotomously branched network, while those of loopless nephrons are arranged loosely, and the majority are unbranched. There was no significant difference in the diameter of the glomerular capillaries between looped and loopless nephrons; however, in all cases the diameter of the afferent arteriole was significantly larger than that of the efferent arteriole. Based on size alone, the predicted blood flow rate in the efferent arteriole in 20% that of the afferent arteriole in G. gallus and 7% that of the afferent arteriole in C. gambelii. There was no significant difference in the volume density (Vv) of the glomerular capillaries between looped and loopless nephrons. However, the surface area density (Sv) of the glomerular capillaries in loopless nephrons of C. gambelii was significantly larger than for the looped nephrons, and for the loopless nephrons in G. gallus. This suggests that there may be a decrease in blood flow rate along the glomerular capillaries of the loopless nephrons in C. gambelii. Overall, the results indicate that the avian glomerular capillaries are less complex than those of mammals. Reasons may be that either avian blood is more viscous than that of mammals or that avian erythrocytes may be unable to fit physically through a tight intertwining network of capillaries due to the presence of a nucleus, which limits the tank-treading ability of avian erythrocytes. © 1995 Wiley-Liss, Inc.     

Three-dimensional reconstruction of the human capillary network and the intramyocardial micronecrosis

Three-dimensional reconstruction of the human heart was performed to define the structure of the intramyocardial microvasculature. A total of 200 consecutive serial sections of 6 μm each were prepared from the left ventricular tissue of an autopsied human heart with normal coronary arteries. The corresponding arteriole, venule, and all capillaries were reconstructed using three-dimensional software. The capillary network extended right and left along the cardiomyocyte with major and minor axes of about 130 and 120 μm, respectively. The capillary length from an arteriole to an adjacent venule was about 350 μm. Two types of sack-like structures, the precapillary sinus and the capillary sinus, were present in the capillary network, and many capillaries diverged from these sinuses. The cardiomyocytes were covered with reticular capillaries. In contrast, the precapillary and capillary sinuses were surrounded by many cardiomyocytes. The arterial and venous capillaries were positioned alternately, forming a lattice pattern. Intramyocardial microcirculatory units forming a capillary network from an arteriole to adjacent venules on both sides were present. The sizes of myocardial micronecroses corresponded to that of the intramyocardial microcirculatory unit. These results show that the capillary network is an ordered and anatomically regulated structure and that the microcirculatory unit and the precapillary and capillary sinuses may play an important role in maintaining the intramyocardial microcirculation during contraction and relaxation.     

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.     

Microcirculatory hematocrit and blood flow

Direct measurements from many laboratories indicate that the oxygen tension in skeletal muscle is significantly less than in the large veins draining these tissues. Harris (1986) has proposed that because of the parallel anatomic arrangement of large arterioles and venules in skeletal muscle, a counter-current exchange between these vessels can occur. He theorized that diffusion of O2 between arteriole and venule would lower the PO2 in the blood as it enters capillaries and result in a decreased tissue PO2 and an increase in large vein PO2. Calculations (Appendix) show that the amount of O2 transferred between arteriole and venule is inadequate to account for this difference in PO2 between tissue and veins due to the small surface area that is involved. It is well documented that the microcirculatory hematocrit ranges between 20 and 50% of that in the supply vessels. The reduced hematocrit lowers the oxygen content in these vessels and results in a low oxygen tension in the surrounding tissue. True arteriovenous shunts are not present in most skeletal muscles, but 15-20% of the microvessels represent thoroughfare or preferential flow channels. It is suggested that these vessels contain a greater than normal hematocrit to account for a conservation of red cell mass across the microcirculation. Furthermore, it is shown that the hematocrit in the preferential flow channels is an inverse function of the flow rate for any level of the microcirculatory hematocrit. The increased hematocrit raises the flow resistance in these vessels which reduces flow further and represents a positive feedback condition which may contribute to the intermittent and uneven flow patterns which are present within the microcirculation.(ABSTRACT TRUNCATED AT 250 WORDS)     

Control and Modulation of Fluid Flow in the Rat Kidney

We have developed a mathematical model of the rat’s renal hemodynamics in the nephron level, and used that model to study flow control and signal transduction in the rat kidney. The model represents an afferent arteriole, glomerular filtration, and a segment of a short-loop nephron. The model afferent arteriole is myogenically active and represents smooth muscle membrane potential and electrical coupling. The myogenic mechanism is based on the assumption that the activity of nonselective cation channels is shifted by changes in transmural pressure, such that elevation in pressure induces vasoconstriction, which increases resistance to blood flow. From the afferent arteriole’s fluid delivery output, glomerular filtration rate is computed, based on conservation of plasma and plasma protein. Chloride concentration is then computed along the renal tubule based on solute conservation that represents water reabsorption along the proximal tubule and the water-permeable segment of the descending limb, and chloride fluxes driven by passive diffusion and active transport. The model’s autoregulatory response is predicted to maintain stable renal blood flow within a physiologic range of blood pressure values. Power spectra associated with time series predicted by the model reveal a prominent fundamental peak at ～165 mHz arising from the afferent arteriole’s spontaneous vasomotion. Periodic external forcings interact with vasomotion to introduce heterodynes into the power spectra, significantly increasing their complexity.     

O2 transport in cerebral microregions (mathematical simulation)

The effects of the circulation rate in capillaries, the intensity of O2 consumption by nerve cells and the capillary network density on the O2 tension distribution in the cerebral cortex have been studied, utilizing a mathematical model simulating actual neuron-capillary relationships. The model has been written as a system of equations in partial derivatives, its solution obtained by the net-point method. Regulatory variations of the capillary circulation rate in certain cerebral microregions have been shown to ensure similar changes in oxygen supply throughout the region. A drop of the pO2 level in a cerebral microregion with a rising O2 consumption by nerve cells is shown to be due, by 75 percent, to the increase of O2 consumption and by 25 percent, to the lower pO2 in the capillaries. Conversely, an increase in pO2 in microregions resulting from a lower O2 consumption by neurons is due by 75 percent, to a pO2 rise in capillaries and by 25 percent, at the expense of an O2 consumption decrease. In cerebral regions differing in capillary network density by 20 percent, changes in the conditions for oxygen supply to tissue are due by 1/3 to pO2 variations in the capillaries and by 2/3 to alterations in the diffusion distances.     

A computational study of the effect of capillary network anastomoses and tortuosity on oxygen transport

The objective of this study was to investigate the effects of capillary network anastomoses and tortuosity on oxygen transport in skeletal muscle, as well as the importance of muscle fibers in determining the arrangement of parallel capillaries. Countercurrent flow and random capillary blockage (e.g. by white blood cells) were also studied. A general computational model was constructed to simulate oxygen transport from a network of blood vessels within a rectangular volume of tissue. A geometric model of the capillary network structure, based on hexagonally packed muscle fibers, was constructed to produce networks of straight unbranched capillaries, capillaries with anastomoses, and capillaries with tortuosity, in order to examine the effects of these geometric properties. Quantities examined included the tissue oxygen tension and the capillary oxyhemoglobin saturation. The computational model included a two-phase simulation of blood flow. Appropriate parameters were chosen for working hamster cheek-pouch retractor muscle. Our calculations showed that the muscle-fiber geometry was important in reducing oxygen transport heterogeneity, as was countercurrent flow. Tortuosity was found to increase tissue oxygenation, especially when combined with anastomoses. In the absence of tortuosity, anastomoses had little effect on oxygen transport under normal conditions, but significantly improved transport when vessel blockages were present.     

稳定同位素技术在植物水分利用研究中的应用

近20a稳定同位素技术在植物生态学研究中的应用得到了长足发展,使得对植物与水分关系也有了更深一步的了解。介绍稳定同位素性碳、氢、氧同位素在研究植物水分关系中的应用及进展,以期能为国内植物水分利用研究提供参考。由于植物根系从土壤中吸收水分时并不发生同位素分馏,对木质部水分同位素分析有助于对植物利用水分来源,生态系统中植物对水分的竞争和利用策略的研究,更好地了解生态系统结构与功能。稳定碳同位素作为植物水分利用效率的一个间接指标,在不同水分梯度环境中,及植物不同代谢产物与水分关系中有着广泛的应用。同位素在土壤-植被-大气连续体水分中的应用,有助于了解生态系统的水分平衡。随着稳定同位素方法的使用,植物与水分关系的研究将取得更大的进展。     

Remote arteriolar dilations in response to muscle contraction under capillaries

In hamster cremaster muscle, it has been shown previously that contraction of skeletal muscle fibers underlying small groups of capillaries (modules) induces dilations that are proportional to metabolic rate in the two arteriolar generations upstream of the stimulated capillaries (Berg BR, Cohen KD, and Sarelius IH. Am J Physiol Heart Circ Physiol 272: H2693-H2700, 1997). These remote dilations were hypothesized to be transmitted via gap junctions and not perivascular nerves. In the present study, halothane (0.07%) blocked dilation in the module inflow arteriole, and dilation in the second arteriolar generation upstream, the branch arteriole, was blocked by both 600 mosM sucrose and halothane but not tetrodotoxin (2 microM). Dilations in both arterioles were not blocked by the gap junction uncoupler 18-beta-glycyrrhetinic acid (40 microM), and 80 mM KCl did not block dilation of the module inflow arteriole. These data implicate a gap junctional-mediated pathway insensitive to 18-beta-glycyrrhetinic acid in dilating the two arterioles upstream of the capillary module during "remote" muscle contraction. Dilation in the branch arteriole, but not the module inflow arteriole, was attenuated by 100 microM N(omega)-nitro-L-arginine. Thus selective contraction of muscle fibers underneath capillaries results in dilations in the upstream arterioles that have characteristics consistent with a signal that is transmitted along the vessel wall through gap junctions, i.e., a conducted vasodilation. The observed insensitivities to 18-beta-glycyrrhetinic acid, to KCl, and to N(omega)-nitro-L-arginine suggest, however, that there are multiple signaling pathways by which remote dilations can be initiated in these microvessels.     

Study of glomerular vasculature in teleosts with the resin-replica method

Glomerular vasculature was investigated in the carpCyprinus carpio, the scorpionfishSebastiscus marmoratus, and the marine catfishPlotosus lineatus with the resin-replica method. An afferent arteriole was connected with a glomerulus in every fish. It was slender in the carp, whereas the scorpionfish and marine catfish possessed thick afferent arterioles. The glomerular capillaries were sinusoidal. The divergences, convergences, and windings of these capillaries were not well developed in any of the fish. The glomerular capillaries converged into an efferent arteriole in the carp and scorpionfish. In the marine catfish, on the other hand, most of the glomeruli had two efferent arterioles.     

A new method for assessing arteriolar diameter and hemodynamic resistance using image analysis of vessel lumen

To characterize the nonuniform diameter response in a blood vessel after a given stimulus (e.g., arteriolar conducted response), frequent serial diameter measurements along the vessel length are required. We used an advanced image analysis algorithm (the "discrete dynamic contour") to develop a quick, reliable method for serial luminal diameter measurements along the arteriole visualized by intravital video microscopy. With the use of digitized images of the arteriole and computer graphics, the method required an operator to mark the image of the two inner edges of the arteriole at several places along the arteriolar length. The algorithm then "filled in" these marks to generate two continuous contours that "hugged" these edges. A computer routine used these contours to determine luminal diameters every 20 microm. Based on these diameters and on Poiseuille's law, the routine also estimated the hemodynamic resistance of the blood vessel. To demonstrate the usefulness of the method, we examined the character of spatial decay of KCl-induced conducted constriction along approximately 500-microm-long arteriolar segments and the KCl-induced increase in hemodynamic resistance computed for these segments. The decay was only modestly fitted by a simple exponential, and the computed increase in resistance (i.e., 5- to 70-fold) was only modestly predicted by resistance increase based on our mathematical model involving measurements at two arteriolar sites (Tyml K, Wang X, Lidington D, and Oullette Y. Am J Physiol Heart Circ Physiol 281: H1397-H1406, 2001). We conclude that our method provides quick, reliable serial diameter measurements. Because the change in hemodynamic resistance could serve as a sensitive index of conducted response, use of this index in studies of conducted response may lead to new mechanistic insights on the response.     

Computational modeling of RBC and neutrophil transit through the pulmonary capillaries.

A computational model of the pulmonary microcirculation is developed and used to examine blood flow from arteriole to venule through a realistically complex alveolar capillary bed. Distributions of flow, hematocrit, and pressure are presented, showing the existence of preferential pathways through the system and of large segment-to-segment differences in all parameters, confirming and extending previous work. Red blood cell (RBC) and neutrophil transit are also analyzed, the latter drawing from previous studies of leukocyte aspiration into micropipettes. Transit time distributions are in good agreement with in vivo experiments, in particular showing that neutrophils are dramatically slowed relative to the flow of RBCs because of the need to contract and elongate to fit through narrower capillaries. Predicted neutrophil transit times depend on how the effective capillary diameter is defined. Transient blockage by a neutrophil can increase the local pressure drop across a segment by 100--300%, leading to temporal variations in flow and pressure as seen by videomicroscopy. All of these effects are modulated by changes in transpulmonary pressure and arteriolar pressure, although RBCs, neutrophils, and rigid microspheres all behave differently.     

Cortical microvasculature of the feline kidney

Scanning electron microscopy of corrosion casts was used to study the ultrastructural morphology of the microcirculation in the feline kidney. The technique used enabled us to examine the renal microvasculature by obtaining stable and consistent replicas of the vasculature. Corrosion casts were evaluated at three different levels, namely subcapsular, midcortical and the corticomedullary junction. The interlobular arteries, given off by the arcuate arteries, coursed through the cortex in a radial fashion and afferent arterioles were given off at varying intervals. Large afferent arterioles formed the glomerular capillary lobules which consisted of very tortuous capillaries. Smaller-diameter efferent arterioles were formed at the vascular pole and ran in the opposite direction to the afferent arteriole. The peritubular plexuses were seen as interconnecting capillaries at both the subcapsular, midcortical and corticomedullary junction. Numerous efferent arterioles, derived from the corticomedullary glomeruli, were seen as large, radiating vessels running towards the renal papilla.     

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

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

Effect of convection in capillaries on oxygen removal from arterioles in striated muscle

Based on experimental data that show the presence of significant oxygen saturation gradients in precapillary arterioles, it has been suggested that the in vivo permeability to oxygen of resting striated muscle may be significantly higher than the corresponding in vitro value obtained in unperfused tissue samples (Popel et al., 1989b, Adv. expl. Med. Biol. 247, 215). The present study performs two analyses to further compare theoretical predictions with experimental data obtained under control conditions and during hemodilution and hemoconcentration. First, it is shown that, in principle, a capillary-perfused tissue layer with a thickness of a few hundred microns is necessary to convectively carry the experimentally determined amount of oxygen released by precapillary arterioles under control and hemodiluted conditions. This capacity to convect oxygen depends strongly on the resting tissue oxygen tension. Second, a more general version of a previous model (Weerappuli & Popel, 1989, J. Biomech. Eng. 111, 24) is used to examine whether changes made in the model parameters within the physiological range of values can explain the experimentally measured flux. The results show that the theoretical predictions can be made compatible with experimental observations if the in vivo permeability of perfused tissue to oxygen is assumed to be one to two orders of magnitude higher than the in vitro value. Furthermore, the predicted in vivo permeability for perfused tissue surrounding an arteriole varies with the arteriolar luminal oxygen tension and flow. This may be due to simplifying approximations made in the model or possible experimental artifacts. Alternatively, it could also be speculated that this variability indicates the flow dependency of the permeability of perfused tissue to oxygen.     

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

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

Simulation of 3D Solid Tumour Angiogenesis Including Arteriole,Capillary and Venule

In this paper, a 3D mathematical model of tumour angiogenesis is developed, to generate a functional tumour vasculature for blood microcirculation. The model follows that of Anderson and Chaplain (1998) ^[1] with three exceptions: (a) extending the model from 2D to 3D, one arteriole and one venule is induced as two parent vessels to form an intact circulation network for blood flow; (b) generating networks able to penetrate into the tumour interior rather than the exterior only; (c) considering branching generations with different diameters, based on which three groups of vessels, such as arterioles, venules and capillaries are classified. The present study contains four steps: 1. Generation of 3D angiogenic vasculature induced from one arteriole and one venule, with branching generations considered. 2. Examination of vessel connectivity among each other to construct a functional network for blood circulation, investigation of sensitivity of network architectures to changes in some model parameters. 3. Simulation of blood flow in the developed vasculatures. 4. Comparisons of blood flow calculated on the networks induced from an arteriole-venule system and from a single parent vessel.
The networks from simulations could present basic geometric and morphological features of tumour vasculatures. The sensitivity analysis indicates the controllability of the created networks, which could construct architectures of some specific geometric features to suit different types of tumours. The comparisons of blood flow mentioned above demonstrate the validity of the present vasculature, which could be served as a more realistic network structure for research of microcirculation, drug delivery in solid tumors.