The Effects of Time-Varying Blood Flow on Diffusional Resistance to Oxygen Transfer in the Pulmonary Capillaries

The effects of the persistence of pulsatile blood flow in the pulmonary capillaries on the over-all diffusing capacity and alveolar-arterial oxygen tension gradient were studied. A mathematical analysis was made of the oxygen transfer process using an undamped cardiac flow pulse in the capillaries and taking into account the finite rate of reaction of oxygen with hemoglobin.

In five cases of both normal and low oxygen atmospheres, combined with varying degree of exercise, it was found that the alveolar-arterial oxygen tension gradients were not affected by the time-varying blood flow, while in cases of breathing air the over-all diffusing capacity of the lung increased 10-15% over the diffusing capacity obtained with constant blood flow rate in the pulmonary capillaries.

     

Oxygen diffusive shunts under conditions of heterogeneous oxygen delivery

Oxygen transport to a given site of tissue from capillaries closest to this site and from more distant capillaries is analyzed under conditions of heterogeneous flow. The analysis is based on a more general solution of the capillary-tissue oxygen transport problem obtained by the author (Popel, 1978). The results of calculations indicate that the oxygen tension in a region poorly supplied by the closest capillaries can be significantly increased due to oxygen diffusion from more distant capillaries.     

A model study of intracellular oxygen gradients in a myoglobin-containing skeletal muscle fiber.

A theoretical two-dimensional model is used to investigate oxygen gradients in a red skeletal muscle fiber. The model describes the steady state, free and myoglobin-facilitated diffusion of oxygen into a respiring cylindrical muscle fiber cross section. The oxygen tension at the sarcolemma is assumed to vary along the sarcolemma as an approximation to the discrete capillary oxygen supply around the fiber. Maximal oxygen gradients are studied by considering parameters relevant to a maximally-respiring red muscle fiber. The model predicts that angular variations in the oxygen tension imposed at the sarcolemma due to the discrete capillary sources do not penetrate deeply into the fiber over a range of physiological values for myoglobin concentration, diffusion coefficients, number of surrounding capillaries, and oxygen tension level at the sarcolemma. Also, the oxygen tension in the core of the fiber is determined by the average oxygen tension at the sarcolemma. The drop in oxygen tension from fiber periphery to core, however, does depend significantly on the myoglobin concentration, the oxygen tension level at the sarcolemma, and the oxygen and myoglobin diffusivities. This dependence is summarized by calculating the minimum average sarcolemmal oxygen tension for maximal respiration without the development of an intracellular anoxic region. For a myoglobin-rich muscle fiber (0.5 mM myoglobin), the model predicts that maximal oxygen consumption can proceed with a relatively flat (less than 5 mm Hg) oxygen tension drop from fiber periphery to core over a large range for diffusion coefficients.     

Physiological analysis of the possible causes of hypoxemia under conditions of weightlessness

It was found that the partial oxygen tension in the capillary blood in astronauts during a space flight was 12–30% lower than that before the space flight. Analysis of the possible causes and mechanisms of hypoxemia was performed, which made it possible to conclude that an increase in the venous blood flow that passes through the lungs and does not undergo complete gas exchange in the pulmonary capillaries is most likely to be the main cause of the decrease in the oxygen tension in the blood in astronauts under conditions of weightlessness.     

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.     

Longitudinal oxygen gradients in cerebra micro vessels in acute anaemia in rats

Using a fine-tip oxygen microelectrodes the longitudinal gradients of oxygen tension (pO2) have been studied in small arterioles (with lumen diameter in control of 5 +/- 20 microm) and in capillaries of the rat brain cortex during stepwise decrease of the blood haemoglobin concentration [Hb] from control [Hb]--14.4 +/- 0.3 g/dl to 10.1 +/- 0.2 g/dl (step 1), 7.0 +/- 0.2 g/dl (step 2) and 3.7 +/- 0.2 g/dl (step 3). All data are presented as "mean +/- standard error". Oxygen tension was measured in arteriolar segments in two locations distanced deltaL = 265 +/- 34 microm, n = 30. Mean diameter of studied arterioles was 10.7 +/- 0.5 microm, n = 71. Length of studied capillary segments was about deltaL = 201 +/- 45 Mm, n = 18. The measured longitudinal pO2 gradient (deltapO2/deltaL) in arterioles amounted 0.03 +/- 0.01 mmHg/microm, n = 15 in control; 0.06 +/- 0.01 mmHg/microm, n = 16 (step 1); 0.07 +/- +/- 0.01 mmHg/microm, n = 14 (step 2); 0.1 +/- 0.01 mmHg/microm, n = 30 (step 3). In the capillaries, the deltapO2/deltaL amounted to: 0.07 +/- 0.01 mmHg/microm, n = 17 (control); 0.09 +/- 0.02 mmHg/microm, n = 16 (step 1); 0.08 +/- 0.01 mmHg/microm, n = 15 (step 2); 0.1 +/- 0.02 mmHg/microm, n = 18 (step 3). An over threefold decrease in the system blood oxygen capacity did not result in significant changes (p > 0.05) of the deltapO2/deltaL in capillaries that might result in relatively homogeneous oxygen flux from blood to tissue in acute anaemia. The longitudinal gradients of blood O2 saturation (deltaSO2/deltaL) in studied arterioles and capillaries were obtained using oxygen dissociation curve (ODC) of haemoglobin in the system blood. The gradients deltaSO2/deltaL in capillaries was shown to be threefold higher than the corresponding gradients in arterioles. The data show that anatomic capillaries are the main source of oxygen to brain tissue as in control and in hypoxic conditions. Sufficient oxygen delivery to brain tissue in acute anaemia is maintained by compensatory mechanisms of cardiovascular and respiratory systems. The data presented are the first measurements of the longitudinal pO, gradients in capillaries and minute cortical arterioles at acute anaemia.     

Effect of increased alveolar surface tension on segmental pulmonary vascular resistance

The site of change in pulmonary vascular resistance (PVR) after surfactant displacement with the detergent diocytl sodium sulfosuccinate (OT) was studied in the isolated canine left lower lobe preparation. Changes in PVR were assessed using the arterial and venous occlusion technique and the vascular pressure-flow relationship. Changes in alveolar surface tension were confirmed from measurements of pulmonary compliance as well as from measurements of surface tension of extracts from lung homogenates. After surfactant depletion (the perfusion rate constant) the total pressure gradient (delta PT) across the lobe increased from 13.4 +/- 1 to 17.1 +/- 0.8 mmHg. This increase in delta PT was associated with a significant increase in the arterial and venous gradients (3.7 +/- 0.3 to 4.9 +/- 0.4 and 5.7 +/- 0.5 to 9.4 +/- 0.6 mmHg, respectively) and a decrease in middle pressure gradient (4.1 +/- 0.8 to 2.9 +/- 0.6 mmHg). The vascular pressure-flow relationship supported these findings and showed that the mean slope increased by 52% (P less than 0.05), whereas the pressure intercept decreased slightly but not significantly (3.7 +/- 0.7 to 3.2 +/- 0.8 mmHg). These results suggest that the resistance of arteries and veins increases, whereas the resistance of the middle segment decreases after surfactant depletion. These effects were apparently due to surface tension that acts directly on the capillary wall. Direct visualization of subpleural capillaries supported the notion that capillaries become distended and recruited as alveolar surface tension increases. In the normal lung (perfused at constant-flow rate) changes in alveolar pressure (Palv) were transmitted fully to the capillaries as suggested by equal changes in pulmonary arterial pressure.(ABSTRACT TRUNCATED AT 250 WORDS)     

A compartmental model for oxygen transport in brain microcirculation in the presence of blood substitutes

A compartmental model is developed for oxygen (O(2)) transport in brain microcirculation in the presence of blood substitutes (hemoglobin-based oxygen carriers). The cerebrovascular bed is represented as a series of vascular compartments, on the basis of diameters, surrounded by a tissue compartment. A mixture of red blood cells (RBC) and plasma/extracellular hemoglobin solution flows through the vascular bed from the arterioles through the capillaries to the venules. Oxygen is transported by convection in the vascular compartments and by diffusion in the surrounding tissue where it is utilized. Intravascular resistance and the diffusive loss of oxygen from the arterioles to the tissue are incorporated in the model. The model predicts that most of the O(2) transport occurs at the level of capillaries. Results computed from the present model in the presence of hemoglobin-based oxygen carriers are consistent with those obtained from the earlier validated model (Sharan et al., 1989, 1998a) on oxygen transport in brain circulation in the absence of extracellular hemoglobin. We have found that: (a) precapillary PO(2) gradients increase as PO(2) in the arterial blood increases, P(50 p) (oxygen tension at 50% saturation of hemoglobin with O(2) in plasma) decreases, i.e. O(2) affinity of the extracellular hemoglobin is increased, the flow rate of the mixture decreases, hematocrit decreases at constant flow, metabolic rate increases, and intravascular transport resistance in the arterioles is neglected; (b) precapillary PO(2) gradients are not sensitive to (i) intracapillary transport resistance, (ii) cooperativity (n(p)) of hemoglobin with oxygen in plasma, (iii) hemoglobin concentration in the plasma and (iv) hematocrit when accounting for viscosity variation in the flow; (c) tissue PO(2) is not sensitive to the variation of intravascular transport resistance in the arterioles. We also found that tissue PO(2) is a non-monotonic function of the Hill coefficient n(p) for the extracellular hemoglobin with a maximum occurring when n(p) equals the blood Hill coefficient. The results of the computations give estimates of the magnitudes of the increases in tissue PO(2) as arterial PO(2) increases,P(50 p) increases, flow rate increases, hematocrit increases, hemoglobin concentration in the plasma increases, metabolic rate decreases, the capillary mass transfer coefficient increases or the intracapillary transport resistance decreases.     

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.     

Circulation changes depending on manifestations in soft tissue tensioning in the leg lengthening process

Surgical intervention was found to intensify circulation in the limb and redistribute the blood flow. Leg lengthening led to arterial inflow limitation due to the magisterial artery strain. The changes were accompanied both by increase of functioning capillaries in number and increase of venous outflow dependence on blood inflow. The decreased after surgery oxygen tension in m. gastrocnemius did not change throughout distraction. The increase of functioning capillaries in number in resting contributed to maintenance of tissue oxygenation in the initial period of distraction, and in case of maximal tissue tensioning hydrostatic pressure increased in the capillaries due to arterial pressure rise. Restoration of the circulation parameters in the fixation period started with an increase of circulation volumetric rate in vessels with preservation of the rest mechanisms of the tissue oxygenation maintenance.     

Oxygen diffusion in large single-celled organisms

The functional relationship between the oxygen uptake rate of a spherical, single cell organism and the external oxygen tension is shown to be related to the dependence of the specific oxygen consumption rate, that is, the consumption rate of an infinitesimal volume element of cellular material, on the external oxygen tension. Analytical solutions of the governing steady state diffusion equation are obtained by dividing the system into three regions, an inner region of the sphere in which oxygen consumption rate depends upon oxygen tension, an outer region of the sphere in which oxygen consumption rate is constant (independent of oxygen tension), a nonconsuming membrane over the sphere that offers only resistance to oxygen diffusion, and an infinite region outside the sphere and membrane supplying oxygen to the system. The solutions show the oxygen tension as a function of position inside the spherical cell for a variety of system parameters.     

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.     

The flow of sickle-cell blood in the capillaries.

Oxygen tension levels and red cell velocities for the flow of sickle-cell blood in the capillaries are determined by using the Krogh model for oxygen transport and lubrication theory for the cell motion. The coupling and interaction between these arises from the red cell compliance, which is assumed to vary with the oxygen concentration. Microsieving data is used to establish an upper bound for this relationship. Calculations are carried out for a range of capillary sizes, taking into account the rightward shift of the oxyhemoglobin dissociation curve and the reduced hematocrit of sickle-cell blood, and are compared to, as a base case, the flow of normal blood under normal pressure gradient. The results indicate that under normal pressure gradients the oxygen tensions and cell velocities for sickle blood are considerably higher than for normal blood, thus acting against the tendency for cells to sickle, or significantly change their rheological properties, in the capillaries. Under reduced pressure gradients, however, the concentrations and velocities drop dramatically, adding to the likelihood of such shape or flow property changes.     

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)     

Oxygen tension distribution in postcapillary venules in resting skeletal muscle

We tested the hypothesis that blood flow is distributed among capillary networks in resting skeletal muscle in such a manner as to maintain uniform end-capillary PO2. Oxygen tension in venules draining two to five capillaries was obtained by using the phosphorescence decay methodology in rat spinotrapezius muscle. For 64 postcapillary venules among 18 networks in 10 animals, the mean PO2 was 30.1 Torr (range, 9.7-43.5 Torr) with a coefficient of variation (CV; standard deviation/mean) of 0.26. Oxygen levels of postcapillary venules within a single network or single animal, however, displayed a much smaller CV (0.064 and 0.094, respectively). By comparison, the CV of blood flow in 57 postcapillary venules of 17 networks in 9 animals was 1.27 with a mean flow of 0.011 +/- 0.014 nl/s and a range of 3.7 x 10(-4) to 6.5 x 10(-2) nl/s. Blood flow of postcapillary venules within single networks displayed a lower CV (mean, 0.51), whereas that in individual animals was 0.78. Results indicate that among venular networks, heterogeneity of oxygen tension is less than that of blood flow and within venular networks the heterogeneity of oxygen tension is much less than that of blood flow. In addition, postcapillary PO2 was independent of flow among venules in which both were measured. Results of this study may be attributable to three factors: 1) O2 diffusion between adjacent capillaries and venules, 2) structural remodeling in regions of lower PO2, and 3) O2-dependent local control mechanisms.     

Angiogenesis in the hypertensive lung: response to ambient oxygen tension

The present study further analyzes the growth and reorganization of the vessels adjacent to capillaries in the hyperoxia-adapted lung in response to a lower ambient oxygen tension. The aim of the study was to determine the source of the new smooth muscle cells known to develop in these segments on return to breathing air. To accomplish this we determined the reorganization of vessel walls by quantitative light-microscopy techniques, and vascular cell phenotype(s) by high-resolution microscopy, in the lungs of rats that breathed a high oxygen tension (87% O2 for 4 weeks), followed by weaning to a lower oxygen tension (87-20% O2 over 1 week) and return to breathing air (for 1, 2 or 4 weeks). Return to breathing air initially triggered wall growth in a subset of vessels and wall thinning in others before wall thinning predominated throughout the vessel population. Interstitial fibroblasts were identified as the source of new perivascular cells. The recruitment of these cells was accompanied by loss of elastic laminae from vessel walls. Subsequently, most perivascular cells expressed a smooth muscle phenotype and elastic laminae were restored. Arteriography demonstrated an increase in the number of patent vessels on return to air, and light- and high-resolution microscopy restitution of the capillary network. We propose that in the hyperoxia-adapted lung return to breathing air represents a relative hypoxia that triggers differential patterns of vessel and capillary growth to meet new functional demands set by the lower ambient oxygen tension.     

Thermoacclimatory changes in blood oxygen binding properties and gill secondary lamellar structure ofSalmo gairdneri

Summary The blood oxygen binding properties and gill secondary lamellar structure of rainbow trout acclimated to several temperatures were studied. The blood oxygen carrying capacity decreased as acclimation temperature increased from 2 to 15 °C; the decrease was probably caused by an increase in plasma volume. Also the blood oxygen affinity decreased as the acclimation temperature increased from 2 to 15 °C. This change had no effect on the oxygen loading in gills, since the efferent arterial oxygen tension was adequate for approximately 100% erythrocytic O₂ saturation at all acclimation temperatures, but facilitated the oxygen unloading in tissues. At the highest acclimation temperature (18 °C) the oxygen loading in gills was facilitated by the changes in the secondary lamellar structure; the proportion of erythrocytes in the secondary lamellar capillaries was higher than at the other acclimation temperatures (2 and 10 °C).     

Pulmonary hemodynamics in fetal lambs during development at normal and increased oxygen tension.

During the latter third of gestation, the number of resistance vessels in the lungs of the fetal sheep increases by 10-fold even after correction for lung growth. We measured pulmonary arterial pressure and blood flow directly and calculated total pulmonary resistance (pressure divided by flow) in intrauterine fetal lambs at 93-95 days and at 136 days of gestation (term is 145-148 days). In addition, we used a hyperbaric chamber to increase oxygen tension in the fetuses and measured the effect on the pulmonary circulation. When corrected for wet weight of the lungs, pulmonary blood flow did not change with advancing gestation (139 +/- 42 to 103 +/- 45 ml.100 g-1.min-1). Pulmonary arterial pressure increased (42 +/- 5 to 49 +/- 3 mmHg); thus total pulmonary resistance increased with advancing gestation from 0.32 +/- 0.12 to 0.55 +/- 0.21 mmHg.100 g.min.ml-1. If the blood flow is corrected for dry weight of the lungs, neither pulmonary blood flow nor total pulmonary resistance changed with advancing gestation. Increasing oxygen tension increased pulmonary blood flow 10-fold in the more mature fetuses but only 0.2-fold in the less mature fetuses. At the normal low oxygen tension of the fetus, pulmonary blood flow does not increase between these two points of gestation in the fetal lamb despite the increase in vessel density in the lungs. However, during elevated oxygen tension, pulmonary blood flow does increase in proportion to the increase in vessel density.     

Oxygen tension in cerebral microvessels in acute anaemia in rats

Using polarographic oxygen microelectrodes, distribution of oxygen tension (pO2) in the rat cerebral arterioles (with a lumen diameter of 8-80 microm) and venules (with a lumen diameter of 8-120 microm) has been studied in acute reduction of haemoglobin concentration in the blood. Isovolumic haemodilution with 5 % albumin solution has been performed stepwise from 14 g/dl (control) to 10 g/dl (step 1), 7 g/dl (step 2) and to 4.6 g/dl (step 3). It was shown that step 1 of haemodilution led to no impairment of oxygen supply to the brain cortex. Step 2 resulted in moderate increase of pO2 in arterioles, whereas in venules oxygen tension fell down substantially (on the average, to 32 mm Hg). Step 3 resulted insignificant increase of pO2 in arterioles. A further fall of pO2 (to 27 mm Hg) in studied venules was recorded. The portion of venules with low pO2 grew to 31% (only 3 % in control). Microregions with a near-to-zero pO2 were recorded in some capillaries. This indicates presence of hypoxic zones in brain tissue. Hypoxic and anoxic microregions originate at this stage of anemia in locations with relatively low and/or impaired blood supply.     

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.