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.

Simultaneous sampling of tissue oxygenation and oxygen consumption in skeletal muscle.

Under physiologic conditions, microvascular oxygen delivery appears to be well matched to oxygen consumption in respiring tissues. We present a technique to measure interstitial oxygen tension (PISFO2) and oxygen consumption (VO2) under steady-state conditions, as well as during the transitions from rest to activity and back. Phosphorescence Quenching Microscopy (PQM) was employed with pneumatic compression cycling to achieve 1 to 10 Hz sampling rates of interstitial PO2 and simultaneous recurrent sampling of VO2 (3/min) in the exteriorized rat spinotrapezius muscle. The compression pressure was optimized to 120-130 mmHg without adverse effect on the tissue preparation. A cycle of 5s compression followed by 15s recovery yielded a resting VO2 of 0.98 ± 0.03 ml O2/100 cm(3)min while preserving microvascular oxygen delivery. The measurement system was then used to assess VO2 dependence on PISFO2 at rest and further tested under conditions of isometric muscle contraction to demonstrate a robust ability to monitor the on-kinetics of tissue respiration and the compensatory changes in PISFO2 during contraction and recovery. The temporal and spatial resolution of this approach is well suited to studies seeking to characterize microvascular oxygen supply and demand in thin tissues.

Muscle contraction increases interstitial nitric oxide as predicted by a new model of local blood flow regulation.

The prevailing metabolic theory of local blood flow regulation suggests the dilatation of arterioles in response to tissue hypoxia via the emission of multiple metabolic vasodilators by parenchymal cells. We have proposed a mechanism of regulation, built from well-known components, which assumes that arterioles are normally dilated in metabolically active tissues, due to the emission of NO by the endothelium of microvessels. Regulation of local blood flow aims at preventing an excessive supply of oxygen (O2) and glucose to the tissue and thus provides an adequate supply, in contrast to the metabolic regulation theory which requires permanent hypoxia to generate the metabolic vasodilators. The mediator of the restrictive signal is superoxide anion (O2(-)) released by membrane NAD(P)H oxidases into the interstitial space, where it neutralizes NO at a diffusion-limited rate. This model predicts that the onset of muscle contraction will lead to the cessation of O2(-) production, which will cause an elevation of interstitial NO concentration and an increase in fluorescence of the NO probe DAF-FM after its conversion to DAF-T. The time course of DAF-T fluorescence in contracting muscle is predicted by also considering the washout from the muscle of the interstitially loaded NO indicator. Experiments using pulse fluorimetry confirmed an increase in the interstitial concentration of NO available for reaction with DAF-FM during bouts of muscle contraction. The sharp increase in interstitial [NO] is consistent with the hypothesis that the termination of the neutralizing superoxide flow into the interstitium is associated with the activation of mitochondria and a reduction of the interstitial oxygen tension. The advantage of the new model is its ability to explain the interaction of metabolic activity and local blood flow through the adequate delivery of glucose and oxygen.

Effects of non-leukocyte-reduced and leukocyte-reduced packed red blood cell transfusions on oxygenation of rat spinotrapezius muscle.

Leukoreduction of blood used for transfusion alleviates febrile transfusion reactions, graft versus host disease and alloimmunization to leukocyte antigen. However, the actual clinical benefit of leukoreduction in terms of microcirculatory tissue O2 delivery after packed red blood cell (pRBC) transfusion has not been investigated. As such, the aim of this study was to determine the effects of non-leukoreduced (NLR) and leukoreduced (LR) fresh pRBC transfusion on interstitial oxygenation in anesthetized male Sprague-Dawley rats. Interstitial fluid PO2 and arteriolar diameters in spinotrapezius muscle preparations were monitored before and after transfusion with NLR- or LR-pRBCs. The major findings were that (1) transfusion of NLR-pRBCs significantly decreased interstitial oxygenation whereas transfusion of LR-pRBCs did not, and (2) transfusion with LR-pRBCs elicited a substantially greater increase in arterial blood pressure (ABP) than did transfusion with NLR-pRBCs. These changes in PO2 and ABP were not associated with changes in the diameters of resistance arterioles in the spinotrapezius muscle. These data suggest that transfusion of fresh NLR-pRBCs may negatively affect tissue oxygenation via enhanced leukocyte influx and decreased O2 delivery. They also suggest that leukocytes diminish the capability of transfused pRBCs to increase cardiac output. As such, transfusion of LR-pRBCs may be less deleterious on tissue PO2 levels than NLR-pRBCs although a concomitantly greater increase in ABP may accompany transfusion of LR-pRBCs.

Effects of a hemoglobin-based oxygen carrier (HBOC-201) and derivatives with altered oxygen affinity and viscosity on systemic and microcirculatory variables in a top-load rat model.

The effects of a polymerized bovine hemoglobin-based oxygen carrier (HBOC) and two derivatives on arteriolar vasoactivity and tissue oxygen tension were explored by administering HBOC in a dose-response fashion to normovolemic rats. The effect of oxygen affinity (P50) and viscosity was also explored, where the P50 and viscosity of the parent compound (HBOC-201) and its modifications (MP50 and LP50A) were as follows: 40mmHg and 3.0cP (HBOC-20l); 18mmHg and 4.4cP (MP50); and 17mmHg and 12.1cP (LP50A). Anesthetized male Sprague-Dawley rats (N=32) were randomized to receive one of the HBOC solutions, and were administered four infusions that increased in concentration for each dose (2, 22, 230 and 780mg/kg, IV). Data were compared to rats receiving an equivalent volume for each of the four infusions (0.4, 0.4, 3.8, 13.1ml/kg, IV) of iso-oncotic 5.9% human serum albumin (HSA). Increasing doses of either HBOC solutions or HSA were associated with increasing MAP. Doses 3 and 4 of HBOC-201, MP50 and HSA produced significant increases in MAP, whereas similar increases began at a lower dose (Dose 2) with LP50A. There were no significant changes in arteriolar diameters at any dose for any group. Interstitial partial pressure of oxygen (ISF PO2) remained unchanged for HBOC-201, MP50 and HSA, but LP50A caused a significant decrease in ISF PO2 compared to baseline after Doses 3 and 4. In conclusion, there was no evidence that HBOC-201 would perform better with increased oxygen affinity (40 to 18mmHg) or viscosity (3.0 to 4.4cP).

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.

Bang-bang model for regulation of local blood flow.

The classical model of metabolic regulation of blood flow in muscle tissue implies the maintenance of basal tone in arterioles of resting muscle and their dilation in response to exercise and/or tissue hypoxia via the evoked production of vasodilator metabolites by myocytes. A century-long effort to identify specific metabolites responsible for explaining active and reactive hyperemia has not been successful. Furthermore, the metabolic theory is not compatible with new knowledge on the role of physiological radicals (e.g., nitric oxide, NO, and superoxide anion, O2 (-) ) in the regulation of microvascular tone. We propose a model of regulation in which muscle contraction and active hyperemia are considered the physiologically normal state. We employ the "bang-bang" or "on/off" regulatory model which makes use of a threshold and hysteresis; a float valve to control the water level in a tank is a common example of this type of regulation. Active bang-bang regulation comes into effect when the supply of oxygen and glucose exceeds the demand, leading to activation of membrane NADPH oxidase, release of O2 (-) into the interstitial space and subsequent neutralization of the interstitial NO. Switching arterioles on/off when local blood flow crosses the threshold is realized by a local cell circuit with the properties of a bang-bang controller, determined by its threshold, hysteresis, and dead-band. This model provides a clear and unambiguous interpretation of the mechanism to balance tissue demand with a sufficient supply of nutrients and oxygen.

Dynamics of PO2 and VO2 in resting and contracting rat spinotrapezius muscle.

This study examined changes in interstitial PO2, which allowed calculation of VO2 during periods of rest, muscle contraction and recovery using an in situ rat spinotrapezius muscle preparation. The PO2 was measured using phosphorescence quenching microscopy and the muscle VO2 was calculated as the rate of O2 disappearance during brief periods of muscle compression to stop blood flow with a supra-systolic pressure. The PO2 and VO2 measurements were made during "5 s compression and 15 s recovery" (CR) cycles. With all three stimulation frequencies, 1, 2 and 4 Hz, the fall in interstitial PO2 and rise in VO2 from resting values occurred within the first 20 s of contraction. The PO2 during contraction became lower as stimulation frequency increased from 1 to 4 Hz. VO2 was higher at 2 Hz than at 1 Hz contraction. With cessation of stimulation, PO2 began increasing exponentially towards baseline values. After 1 and 2 Hz contraction, the fall in muscle VO2 was delayed by one CR cycle and then exponentially decreased towards resting values. After 4 Hz stimulation, VO2 increased for 2 cycles and then decreased. The post-contraction transients of PO2 and VO2 were not synchronous and had different time constants. With further analysis two distinct functional responses were identified across all stimulation frequencies having PO2 during contraction above or below 30 mmHg. The corresponding VO2 responses were different - for "high" PO2, muscle VO2 reached high levels, while for the "low" PO2 data set muscle VO2 remained low. Recovery patterns were similar to those described above. In summary, local microscopic PO2 and VO2 were measured in resting and contracting muscle in situ and the post-contraction transients of PO2 and VO2 were all much slower than the onset transients.

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.

Effect of Hypoxic Blood Infusion on Pulmonary Physiology.

The ability to store red blood cells (RBCs) and other components for extended periods of time has expanded the availability and use of transfusion as a life-saving therapy. However, conventional RBC storage has a limited window of effective preservation and is accompanied by the progressive accumulation of a series of biochemical and morphological modifications, collectively referred to as "storage lesions." These lesions have been associated with negative clinical outcomes (i.e., postoperative complications as well as reduced short-term and long-term survival) in patients transfused with conventionally stored blood with older and deteriorated transfused red cells. Hence, there is an increased unmet need for improved RBC storage. Hypoxic storage of blood entails the removal of large amounts of oxygen to low levels prior to refrigeration and maintenance of hypoxic levels through the entirety of storage. As opposed to conventionally stored blood, hypoxic storage can lead to a reduction of oxidative damage to slow storage lesion development and create a storage condition expected to result in enhanced efficacy of stored RBCs without an effect on oxygen exchange in the lung. Hypoxic blood transfusions appear to offer minimal safety concerns, even in patients with hypoxemia. This review describes the physiology of hypoxically stored blood, how it differs from conventionally stored blood, and its use in potential clinical application, such as massively transfused and critically ill patients with oxygenation/ventilation impairments.

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.

The rate of O2 loss from mesenteric arterioles is not unusually high.

The O(2) disappearance curve (ODC) recorded in an arteriole after the rapid arrest of blood flow reflects the complex interaction among the dissociation of O(2) from hemoglobin, O(2) diffusivity, and rate of respiration in the vascular wall and surrounding tissue. In this study, the analysis of experimental ODCs allowed the estimation of parameters of O(2) transport and O(2) consumption in the microcirculation of the mesentery. We collected ODCs from rapidly arrested blood inside rat mesenteric arterioles using scanning phosphorescence quenching microscopy (PQM). The technique was used to prevent the artifact of accumulated O(2) photoconsumption in stationary media. The observed ODC signatures were close to linear, in contrast to the reported exponential decline of intra-arteriolar Po(2). The rate of Po(2) decrease was 0.43 mmHg/s in 20-µm-diameter arterioles. The duration of the ODC was 290 s, much longer than the 12.8 s reported by other investigators. The arterioles associated with lymphatic microvessels had a higher O(2) disappearance rate of 0.73 mmHg/s. The O(2) flux from arterioles, calculated from the average O(2) disappearance rate, was 0.21 nl O(2)·cm(-2)·s(-1), two orders of magnitude lower than reported in the literature. The physical upper limit of the O(2) consumption rate by the arteriolar wall, calculated from the condition that all O(2) is consumed by the wall, was 452 nl O(2)·cm(-3)·s(-1). From consideration of the microvascular tissue volume fraction in the rat mesentery of 6%, the estimated respiration rate of the vessel wall was ∼30 nl O(2)·cm(-3)·s(-1). This result was three orders of magnitude lower than the respiration rate in rat mesenteric arterioles reported by other investigators. Our results demonstrate that O(2) loss from mesenteric arterioles is small and that the O(2) consumption by the arteriolar wall is not unusually large.

Skeletal muscle arteriolar function following myocardial infarction: Analysis of branch-order effects.

Diminished bioavailability of nitric oxide (NO) may impair skeletal muscle arteriolar function after myocardial infarction (MI). We tested the hypotheses that chronic MI induced would diminish 1) endothelial function in large (resting diameter ~75µm) feed arterioles, and 2) functional dilation in feed arterioles, but not smaller arcade (~25µm) or transverse (~15µm) arterioles, in the spinotrapezius muscle of female Sprague-Dawley rats. Additionally, we hypothesized that blockade of NO production with N(G)-nitro-l-arginine methyl ester (l-NAME; 30mg/kg i.v.) would have a greater blunting effect on control rats than MI rats. Endothelial function of the feed arterioles was assessed with an infusion of acetylcholine (1.5µg i.v.) after pretreatment with indomethacin (5mg/kgi.p.). MI blunted the response to acetylcholine in feed arterioles (p=0.037), but did not affect resting or post-contraction diameter at any branching order. l-NAME had similar effects on MI and SHAM rats; the response to acetylcholine was blunted in feed arterioles (p=0.003), resting diameter was diminished in arcade arterioles (p=0.003), and post-contraction diameter was diminished in both arcade arterioles (p=0.03) and transverse arterioles (p=0.05). In conclusion, despite endothelial dysfunction in feed arterioles, functional dilation was not affected by MI in any branching order studied. l-NAME had similar effects on MI and SHAM rats that were branch order-dependent. These branch-order effects should be considered in future studies of the control of blood flow.

Measurement of oxygen in the microcirculation using phosphorescence quenching microscopy.

According to the classical concept of Krogh, O(2) is delivered to the tissues solely by capillaries and intra-capillary resistance to O(2) diffusion is negligible. Over the past three decades longitudinal PO(2) and SO(2) gradients in arterioles have been observed with a transmural PO(2) gradient in small arterioles of only 1-2 mmHg. Application of phosphorescence quenching microscopy to measurements of PO(2) in arterioles of the rat mesentery by Tsai et al. (1998) found a large transmural PO(2) in these arterioles. That led to the provocative conclusion that the arteriolar wall is the major sink for O(2) in the microcirculation. Our studies indicate that many of these results can be explained by photo-activated O(2) consumption following phosphor excitation, combined with a large excitation area and high frequency of flash excitation. We have developed the basic principles for phosphorescence quenching microscopy including the need to use a small excitation area, a low excitation frequency and a scanning excitation for stationary samples.

Hemorrhagic shock and nitric oxide release from erythrocytic nitric oxide synthase: a quantitative analysis.

A large loss of blood during hemorrhage can result in profound shock, a state of hypotension associated with hemodynamic abnormalities. One of the hypotheses to account for this collapse of homeostasis is that the production of nitric oxide (NO), a gas molecule that dilates blood vessels, is significantly impaired during hemorrhage, resulting in a mismatch between O(2) delivery and the metabolic activity in the tissues. NO can be released from multiple sources in the vasculature. Recent studies have shown that erythrocytes express functional endothelial nitric oxide synthase (NOS3), which potentially serves as an intraluminal NO source. NO delivery from this source is complex: erythrocytes are not only NO producers but also act as potent sinks because of the high affinity of NO for hemoglobin. To test our hypothesis that the loss of erythrocytic NOS3 during hemorrhage contributes to NO deficiency-related shock, we have constructed a multicellular computational model that simulates NO production and transport to allow us to quantify the loss of NO under different hemorrhagic conditions. Our model shows that: (1) during mild hemorrhage and subsequent hemodilution (hematocrit >30%), NO from this intraluminal source is only slightly decreased in the vascular smooth muscle, but the NO level is significantly reduced under severe hemorrhagic conditions (hematocrit <30%); (2) whether a significant amount of NO from this source can be delivered to vascular smooth muscle is strongly dependent on the existence of a protective mechanism for NO delivery; (3) if the expression level of NOS3 on erythrocytes is similar to that on endothelial cells, we estimate approximately 13 pM NO at the vascular smooth muscle from this source when such a protective mechanism is involved. This study provides a basis for detailed studies to characterize the impairment of NO release pathways during hemorrhage and yield important insights for the development of resuscitation methods.

Measurement of hemoglobin oxygen saturation using Raman microspectroscopy and 532-nm excitation.

The resonant Raman enhancement of hemoglobin (Hb) in the Q band region allows simultaneous identification of oxy- and deoxy-Hb. The heme vibrational bands are well known at 532 nm, but the technique has never been used to determine microvascular Hb oxygen saturation (So(2)) in vivo. We implemented a system for in vivo noninvasive measurements of So(2). A laser light was focused onto areas of 15-30 microm in diameter. Using a microscope coupled to a spectrometer and a cooled detector, Raman spectra were obtained in backscattering geometry. Calibration was performed in vitro using blood at several Hb concentrations, equilibrated at various oxygen tensions. So(2) was estimated by measuring the intensity of Raman signals (peaks) in the 1,355- to 1,380-cm(-1) range (oxidation state marker band nu(4)), as well as from the nu(19) and nu(10) bands (1,500- to 1,650-cm(-1) range). In vivo observations were made in microvessels of anesthetized rats. Glass capillary path length and Hb concentration did not affect So(2) estimations from Raman spectra. The Hb Raman peaks observed in blood were consistent with earlier Raman studies using Hb solutions and isolated cells. The correlation between Raman-based So(2) estimations and So(2) measured by CO-oximetry was highly significant for nu(4), nu(10), and nu(19) bands. The method allowed So(2) determinations in all microvessel types, while diameter and erythrocyte velocity could be measured in the same vessels. Raman microspectroscopy has advantages over other techniques by providing noninvasive and reliable in vivo So(2) determinations in thin tissues, as well as in solid organs and tissues in which transillumination is not possible.

Oxygen dependence of respiration in rat spinotrapezius muscle contracting at 0.5-8 twitches per second.

The oxygen dependence of respiration was obtained in situ in microscopic regions of rat spinotrapezius muscle for different levels of metabolic activity produced by electrical stimulation at rates from 0.5 to 8 Hz. The rate of O2 consumption (V̇o2) was measured with phosphorescence quenching microscopy (PQM) as the rate of O2 disappearance in a muscle with rapid flow arrest. The phosphorescent oxygen probe was loaded into the interstitial space of the muscle to give O2 tension (Po2) in the interstitium. A set of sigmoid curves relating the Po2 dependence of V̇o2 was obtained with a Po2-dependent region below a characteristic Po2 (~30 mmHg) and a Po2-independent region above this Po2. The V̇o2(Po2) plots were fit by the Hill equation containing O2 demand (rest to 8 Hz: 216 ± 26 to 636 ± 77 nl O2/cm3 s) and the Po2 value corresponding to O2 demand/2 (rest to 8 Hz: 22 ± 4 to 11 ± 1 mmHg). The initial Po2 and V̇o2 pairs of values measured at the moment of flow arrest formed a straight line, determining the rate of oxygen supply. This line had a negative slope, equal to the oxygen conductance for the O2 supply chain. For each level of tissue blood flow the set of possible values of Po2 and V̇o2 consists of the intersection points between this O2 supply line and the set of V̇o2 curves. An electrical analogy for the intraorgan O2 supply and consumption is an inverting transistor amplifier, which allows the use of graphic analysis methods for prediction of the behavior of the oxygen processing system in organs. NEW & NOTEWORTHY The sigmoidal shape of curves describing oxygen dependence of muscle respiration varies from basal to maximal workload and characterizes the oxidative metabolism of muscle. The rate of O2 supply depends on extracellular O2 tension and is determined by the overall oxygen conductance in the muscle. The dynamics of oxygen consumption is determined by the supply line that intersects the oxygen demand curves. An electrical analogy for the oxygen supply/consumption system is an inverting transistor amplifier.

Vascular smooth muscle NO exposure from intraerythrocytic SNOHb: a mathematical model.

We previously constructed computational models based on the biochemical pathway analysis of different nitric oxide (NO) synthase isoforms and found a large discrepancy between our predictions and perivascular NO measurements, suggesting the existence of nonenzymatic sources of NO. S-nitrosohemoglobin (SNOHb) has been suggested as a major source to release NO in the arteriolar lumen and induce hypoxic vasodilation. In the present study, we formulated a multicellular computational model to quantify NO exposure in arteriolar smooth muscle when the NO released by intraerythrocytic SNOHb is the sole NO source in the vasculature. Our calculations show an NO exposure of approximately 0.25-6 pM in the smooth muscle region. This amount does not account for the large discrepancy we encountered regarding perivascular NO levels. We also found that the amount of NO delivered by SNOHb to smooth muscle strongly depends on the SNOHb concentration and half-life, which further determine the rate of NO release, as well as on the membrane permeability of red blood cells (RBCs) to NO. In conclusion, our mathematical model predicts that picomolar amounts of NO can be delivered to the vascular smooth muscle by intraerythrocytic SNOHb; this amount of NO alone appears not sufficient to induce the hypoxic vasodilation.