Metabolic models of microcirculatory regulation.

The functions and integrity of body tissues are critically dependent on an adequate oxygen supply. Because the transport of oxygen to the cells is intimately linked to the microcirculation, the concept of microcirculation-metabolism coupling has received much attention. In essence, the metabolic theory of intrinsic control of the microcirculation states that microvascular tone is locally modulated to maintain adequate oxygen levels in the parenchymal cells. We propose a two-component control system for the regulation of tissue O2 delivery in accordance with metabolic needs. A precapillary sphincter control mechanism maintains tissue PO2 by governing the number of perfused capillaries. Functional capillary density in turn determines surface area available for diffusion and capillary-to-cell diffusion distance. On the other hand, the arteriolar control system modulates local blood flow in accordance with parenchymal O2 utilization and thereby minimizes changes in capillary PO2 when the O2 availability/demand ratio is decreased. We propose that the precapillary sphincters are more sensitive to changes in tissue PO2 than are the flow-regulating arterioles. Consequently, for mild stresses, adequate tissue oxygenation is maintained mainly by precapillary sphincter control of diffusion parameters without the need for changes in blood flow. However, as metabolic stresses become greater, blood flow regulation becomes the dominant factor in the control of tissue O2 delivery. Thus, by working in concert, the local mechanisms regulating microvascular resistance and effective capillary density provide a wide margin of safety against the development of cellular hypoxia.     

A quantitative framework for the design of acellular hemoglobins as blood substitutes: implications of dynamic flow conditions

The delivery of oxygen to tissue by cell-free carriers eliminates intraluminal barriers associated with red blood cells. This is important in arterioles, since arteriolar tone controls capillary perfusion. We describe a mathematical model for O(2) transport by hemoglobin solutions and red blood cells flowing through arteriolar-sized tubes to optimize values of p50, Hill number, hemoglobin molecular diffusivity and concentration. Oxygen release is evaluated by including an extra-luminal resistance term to reflect tissue oxygen consumption. For low consumption (i.e., high resistance to O(2) release) a hemoglobin solution with p50=15 mmHg, n=1, D(HBO2)=3 x 10(-7) cm(2)/s delivers O(2) at a rate similar to that of red blood cells. For high consumption, the p50 must be decreased to 5 mmHg. The model predicts that regardless of size, hemoglobin solutions with higher p50 will present excess O(2) to arteriolar walls. Oversupply of O(2) to arteriolar walls may cause constriction and paradoxically reduced capillary perfusion.     

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)     

Comparison of PEG-modified albumin and hemoglobin in extreme hemodilution in the rat.

We have reported a new polyethylene glycol (PEG)-modified, hemoglobin-based O2 carrier (MP4) with novel properties, including a large molecular excluded volume and low PO2 necessary to obtain 50% O2 (approximately 6 Torr). To evaluate the ability of MP4 to transport O2, we compared it with PEG-modified albumin (MPA) using the identical chemistry of attachment of PEG chains. The resulting solutions were well matched with respect to all physical properties except that MP4 is an O2 carrier, whereas MPA is not. An additional solution, 10% pentastarch, was matched with the PEG-modified proteins with regard to oncotic activity and viscosity but does not contain PEG. The model used to evaluate O2 transport was continuous exchange transfusion in the rat until the hematocrit was virtually unmeasurable. Objective end points included survival and the onset of anaerobic metabolism, signaled by acid-base derangement and accumulation of lactic acid. Continuous exchange transfusion of 2.5 blood volumes in rats (n=5 in each treatment group) was carried out over 60 min, such that the final hematocrit was between 0 and 5% in all animals. Animals were observed for an additional 70 min, when survivors were killed. Overall survival for the MP4 animals was 100%; no animal that received either pentastarch or MPA survived. The hematocrit at which lactic acid began to rise was approximately 14.8% in both pentastarch and MPA animals and 7.4% in the animals that received MP4. In all groups, the total hemoglobin was approximately 5 g/dl at this point. We conclude that, despite its low PO2 necessary to obtain 50% O2, MP4 effectively substitutes for red blood cell hemoglobin in its ability to oxygenate tissues in extreme hemodilution.     

Numerical simulation of oxygen delivery to muscle tissue in the presence of hemoglobin-based oxygen carriers

This work represents a culmination of research on oxygen transport to muscle tissue, which takes into account oxygen transport due to convection, diffusion, and the kinetics of simultaneous reactions between oxygen and hemoglobin and myoglobin. The effect of adding hemoglobin-based oxygen carriers (HBOCs) to the plasma layer of blood in a single capillary surrounded by muscle tissue based on the geometry of the Krogh tissue cylinder is examined for a range of HBOC oxygen affinity, HBOC concentration, capillary inlet oxygen tension (pO(2)), and hematocrit. The full capillary length of the hamster retractor muscle was modeled under resting (V(max) = 1.57 x 10(-4) mLO(2) mL(-1) s(-1), cell velocity (v(c)) = 0.015 cm/s) and working (V(max) = 1.57 x 10(-3) mLO(2) mL(-1) s(-1), v(c) = 0.075 cm/s) conditions. Two spacings between the red blood cell (RBC) and the capillary wall were examined, corresponding to a capillary with and without an endothelial surface layer. Simulations led to the following conclusions, which lend physiological insight into oxygen transport to muscle tissue in the presence of HBOCs: (1) The reaction kinetics between oxygen and myoglobin in the tissue region, oxygen and HBOCs in the plasma, and oxygen and RBCs in the capillary lumen should not be neglected. (2) Simulation results yielded new insight into possible mechanisms of oxygen transport in the presence of HBOCs. (3) HBOCs may act as a source or sink for oxygen in the capillary and may compete with RBCs for oxygen. (4) HBOCs return oxygen delivery to muscle tissue to normal for varying degrees of hypoxia (inlet capillary pO(2) < 30 mmHg) and anemia (hematocrit < 46%) for the hamster model.     

Transmural gradients of oxygen tension on cerebral microvessels in rats

Using modified oxygen needle microelectrodes, vital microscopy with video-recording facilities, measurements of tissue oxygen tension (PO2) profiles near the cortical arterioles and transmural PO2 gradients on pial arterioles of the rat were performed. At control transmural PO2 gradient averaged 1.17 +/- 0.06 mm Hg/microm (mean +/- SEM, n = 40). Local dilatation of the arteriolar wall (microapplication of sodium nitroprusside approximately 2 x 10(-7) M) resulted in marked drop of the transmural PO2 gradient to 0.68 +/- 0.04 mm Hg/microm (p < 0.001, n = 38). The important finding of the study is the dependence of the transmural PO2 gradient on the vascular tone of pial arterioles. The data presented allow to conclude that O2 consumption of the arteriolar wall lies within the range for surrounding tissue and O2 consumption of the endothelial layer and, apparently, has no substantial impact on transmural PO2 gradient.     

Cerebrovascular response to decreased hematocrit: effect of cell-free hemoglobin,plasma viscosity,and CO2

The effect of transfusing a nonextravasating, zero-link polymer of cell-free hemoglobin on pial arteriolar diameter, cerebral blood flow (CBF), and O2 transport (CBF x arterial O2 content) was compared with that of transfusing an albumin solution at equivalent reductions in hematocrit (approximately 19%) in anesthetized cats. The influence of viscosity was assessed by coinfusion of a high-viscosity solution of polyvinylpyrrolidone (PVP), which increased plasma viscosity two- to threefold. Exchange transfusion of a 5% albumin solution resulted in pial arteriolar dilation, increased CBF, and unchanged O2 transport, whereas there were no significant changes over time in a control group. Exchange transfusion of a 12% polymeric hemoglobin solution resulted in pial arteriolar constriction and unchanged CBF and O2 transport. Coinfusion of PVP with albumin produced pial arteriolar dilation that was similar to that obtained with transfusion of albumin alone. In contrast, coinfusion of PVP with hemoglobin converted the constrictor response to a dilator response that prevented a decrease in CBF. Pial arteriolar dilation to hypercapnia was unimpaired in groups transfused with albumin or hemoglobin alone but was attenuated in the largest vessels in albumin and hemoglobin groups coinfused with PVP. Unexpectedly, hypocapnic vasoconstriction was blunted in all groups after transfusion of albumin or hemoglobin alone or with PVP. We conclude that 1) the increase in arteriolar diameter after albumin transfusion represents a compensatory response that prevents decreased O2 transport at reduced O2-carrying capacity, 2) the decrease in diameter associated with near-normal O2-carrying capacity after cell-free polymeric hemoglobin transfusion represents a compensatory mechanism that prevents increased O2 transport at reduced blood viscosity, 3) pial arterioles are capable of dilating to an increase in plasma viscosity when hemoglobin is present in the plasma, 4) decreasing hematocrit does not impair pial arteriolar dilation to hypercapnia unless plasma viscosity is increased, and 5) pial arteriolar constriction to hypocapnia is impaired at reduced hematocrit independently of O2-carrying capacity.     

Insensitivity of cerebral oxygen transport to oxygen affinity of hemoglobin-based oxygen carriers

The cerebrovascular effects of exchange transfusion of various cell-free hemoglobins that possess different oxygen affinities are reviewed. Reducing hematocrit by transfusion of a non-oxygen-carrying solution dilates pial arterioles on the brain surface and increases cerebral blood flow to maintain a constant bulk oxygen transport to the brain. In contrast, transfusion of hemoglobins with P50 of 4-34 Torr causes constriction of pial arterioles that offsets the decrease in blood viscosity to maintain cerebral blood flow and oxygen transport. The autoregulatory constriction is dependent on synthesis of 20-HETE from arachidonic acid. This oxygen-dependent reaction is apparently enhanced by facilitated oxygen diffusion from the red cell to the endothelium arising from increased plasma oxygen solubility in the presence of low or high-affinity hemoglobin. Exchange transfusion of recombinant hemoglobin polymers with P50 of 3 and 18 Torr reduces infarct volume from experimental stroke. Cell-free hemoglobins do not require a P50 as high as red blood cell hemoglobin to facilitate oxygen delivery.     

Calculations of intracapillary oxygen tension distributions in muscle

Characterizing the resistances to O(2) transport from the erythrocyte to the mitochondrion is important to understanding potential transport limitations. A mathematical model is developed to accurately determine the effects of erythrocyte spacing (hematocrit), velocity, and capillary radius on the mass transfer coefficient. Parameters of the hamster cheek pouch retractor muscle are used in the calculations, since significant amounts of experimental physiological data and mathematical modeling are available for this muscle. Capillary hematocrit was found to have a large effect on the PO(2) distribution and the intracapillary mass transfer coefficient per unit capillary area, k(cap), increased by a factor of 3.7 from the lowest (H=0.25) to the highest (H=0.55) capillary hematocrits considered. Erythrocyte velocity had a relatively minor effect, with only a 2.7% increase in the mass transfer coefficient as the velocity was increased from 5 to 25 times the observed velocity in resting muscle. The capillary radius is varied by up to two standard deviations of the experimental measurements, resulting in variations in k(cap) that are <15% at the reference case. The magnitude of these changes increases with hematocrit. An equation to approximate the dependence of the mass transfer coefficient on hematocrit is developed for use in simulations of O(2) transport from a capillary network.     

Regional cerebral blood flow in cats with cross-linked hemoglobin transfusion during focal cerebral ischemia

The beneficial effect of hemodilution on cerebral blood flow (CBF) during focal cerebral ischemia is mitigated by reduced arterial oxygen content (CaO2). In anesthetized cats subjected to permanent middle cerebral artery occlusion, the time course of regional CBF was evaluated after isovolemic exchange transfusion with either albumin or a tetrameric hemoglobin-based oxygen carrier. The transfusion started 30 min after arterial occlusion. We tested the hypothesis that bulk oxygen transport (CBF x CaO2) to ischemic tissue is increased by hemoglobin transfusion at a hematocrit of 18% compared with albumin-transfused cats at a hematocrit of 18% or control cats at a hematocrit of 30% and equivalent arterial pressure. In the nonischemic hemisphere, CBF increased selectively after albumin transfusion, and oxygen transport was similar among groups. In the ischemic cortex, albumin transfusion increased CBF, but oxygen transport was not increased above that of the control group. Hemoglobin transfusion increased both CBF and oxygen transport in the ischemic cortex above values in the control group, but the increase was delayed until 4 h of ischemia. Consequently, acute injury volume measured at 6 h of ischemia was not significantly attenuated. In contrast to the cortex, CBF in the ischemic caudate nucleus was not substantially increased by either albumin or hemoglobin transfusion. Therefore, in a large animal model of permanent focal ischemia in which transfusion starts 30 min after ischemia, tetrameric cross-linked hemoglobin transfusion can augment oxygen transport to the ischemic cortex, but the increase can be delayed and not necessarily provide protection. Moreover, an end-artery region such as the caudate nucleus is less likely to benefit from hemodilution.     

Cell-free oxygen carriers: scientific foundations, clinical development, and new directions

The most significant hurdle to the development of a safe and effective hemoglobin-based oxygen carrier ("blood substitute") is generally thought to be its propensity to cause vasoconstriction in the microcirculation and hypertension. Two theories for this effect are currently being studied: in one, scavenging NO by hemoglobin reduces vasorelaxation; in the other, cell-free hemoglobin oversupplies O2 (a known vasoconstrictor) to vascular walls by facilitated diffusion. While both mechanisms might lead to reduction of local NO concentration, the important distinction between the two is that if the NO scavenging theory is correct, it greatly diminishes the prospects to develop any solution based on free hemoglobin. However, if the O2-oversupply theory is correct, modifications to the hemoglobin molecule can be envisioned that can prevent oversupply and reduce toxicity. This review summarizes the development of Hemospan, a novel modification of human hemoglobin whose design is based on the O2-oversupply theory. Because of its low P50 and increased molecular size, the release of O2 in resistance vessels (arterioles) by Hemospan is restricted, and vasoconstriction is greatly reduced.     

PO2 profiles near arterioles and tissue oxygen consumption in rat mesentery

A scanning phosphorescence quenching microscopy technique, designed to prevent accumulated O(2) consumption by the method, was applied to Po(2) measurements in mesenteric tissue. In an attempt to further increase the accuracy of the measurements, albumin-bound probe was topically applied to the tissue and an objective-mounted pressurized bag was used to reduce the oxygen transport bypass through the thin layer of fluid over the mesentery. Po(2) was measured at multiple sites perpendicular to the blood/wall interface in the vicinity of 84 mesenteric arterioles (7-39 microm in diameter) at distances of 5, 15, 30, 60, 120, and 180 microm in seven anesthetized Sprague-Dawley rats, thereby creating Po(2) profiles. Interstitial Po(2) above and immediately beside arterioles was found to agree with known intravascular values. No significant difference in Po(2) profiles was found between small and large arterioles, indicating a small longitudinal Po(2) gradient in the precapillary mesenteric microvasculature. In addition, the Po(2) profiles were used to calculate oxygen consumption in the mesenteric tissue (56-65 nl O(2) x cm(-3) x s(-1)). Correction of these values for contamination with ambient oxygen yielded an oxygen consumption rate of 60-68 nl O(2) x cm(-3) x s(-1), the maximal limit for consumption in the mesentery. The results were compared with measurements made by other workers in regard to the employed techniques.     

The effects of chemical kinetics on oxygen delivery to tissue.

A mathematical model has been formulated to analyze the effect of nonequilibrium kinetics on oxygen delivery to tissue. The model takes into account molecular diffusion, facilitated diffusion in the capillary blood, convection, chemical kinetics of O2 with hemoglobin, and the rate of metabolic consumption. A line iterative technique is described to solve numerically the resulting coupled system of nonlinear partial differential equations with physiologically relevant boundary and entrance conditions. With nonequilibrium kinetics the end-capillary PO2 is found to be lower than that in the venous blood. The effect is more pronounced during hypoxia and anemia. It is found that the tissue PO2 at the lethal corner decreases with the decrease in blood velocity, arterial PO2, hemoglobin concentration, P50, and increase in COHb concentration or metabolic rate, while the difference between end-capillary PO2 and venous PO2 increases, which reflects the effect of nonequilibrium kinetics on the delivery of O2 to tissue. Thus, the consideration of venous PO2 as an indicator of tissue PO2 in clinical and experimental studies may be questionable.     

Role of 20-HETE in the pial arteriolar constrictor response to decreased hematocrit after exchange transfusion of cell-free polymeric hemoglobin.

The cerebrovascular response to decreases in hematocrit and viscosity depends on accompanying changes in arterial O2 content. This study examines whether 1) the arteriolar dilation seen after exchange transfusion with a 5% albumin solution can be reduced by the K(ATP) channel antagonist glibenclamide (known to inhibit hypoxic dilation), and 2) the arteriolar constriction seen after exchange transfusion with a cell-free hemoglobin polymer to improve O2-carrying capacity can be blocked by inhibitors of the synthesis or vasoconstrictor actions of 20-HETE. In anesthetized rats, decreasing hematocrit by one-third with albumin exchange transfusion dilated pial arterioles (14 +/- 2%; SD), whereas superfusion of the surface of the brain with 10 muM glibenclamide blocked this response (-10 +/- 7%). Exchange transfusion with polymeric hemoglobin decreased the diameter of pial arterioles by 20 +/- 3% without altering arterial pressure. This constrictor response was attenuated by superfusing the surface of the brain with a 20-HETE antagonist, WIT-002 (10 microM; -5 +/- 1%), and was blocked by two chemically dissimilar selective inhibitors of the synthesis of 20-HETE, DDMS (50 microM; 0 +/- 4%) and HET-0016 (1 microM; +6 +/- 4%). The constrictor response to hemoglobin transfusion was not blocked by an inhibitor of nitric oxide (NO) synthase, and the inhibition of the constrictor response by DDMS was not altered by coadministration of the NO synthase inhibitor. We conclude 1) that activation of K(ATP) channels contributes to pial arteriolar dilation during anemia, whereas 2) constriction to polymeric hemoglobin transfusion at reduced hematocrit represents a regulatory response that limits increased O2 transport and that is mediated by increased formation of 20-HETE, rather than by NO scavenging.     

Physiological factors affecting O2 transport by hemoglobin in an in vitro capillary system

O2 transport was examined by measuring the fractional saturation of concentrated hemoglobin solutions flowing through an artificial capillary that was approximately 27 micron in diameter and embedded in a silicone rubber film approximately 170 micron thick. The effects of pH, hemoglobin concentration, O2 tension, temperature, and organic phosphate were measured and analyzed quantitatively by a rigorous mathematical model that included the geometry of the capillary in the silicone film, parabolic flow velocity distributions inside the lumen, and cooperative O2 binding by hemoglobin. The rates of both oxygenation and deoxygenation were limited by diffusion and governed by the magnitude of the O2 gradient between the intracapillary fluid phase and the external gas space. In uptake experiments, O2 flux is determined primarily by the external O2 tension (16-160 mmHg in our experiments) because the internal O2 pressure is kept small due to chemical combination with hemoglobin. In release experiments, the external O2 tension is maintained at zero, and the transport rate is determined by the intracapillary partial pressure of O2 that is proportional to the O2 half-saturation pressure of hemoglobin value of the hemoglobin sample. As a result, factors that change the affinity of hemoglobin for O2, such as pH, temperature, and organic phosphate concentration, influence strongly the rate of O2 release but have little effect on the rate of O2 uptake. These properties are physiologically advantageous, since a decrease in pH or an increase in temperature during exercise increases both the rate and extent of deoxygenation while not altering the kinetics of oxygenation.     

Role of nitric oxide in capillary perfusion and oxygen delivery regulation during systemic hypoxia

The role of nitric oxide (NO) and reactive oxygen species (ROS) in regulating capillary perfusion was studied in the hamster cheek pouch model during normoxia and after 20 min of exposure to 10% O2-90% N2. We measured PO2 by using phosphorescence quenching microscopy and ROS production in systemic blood. Identical experiments were performed after treatment with the NO synthase inhibitor NG-monomethyl-L-arginine (L-NMMA) and after the reinfusion of the NO donor 2,2'-(hydroxynitrosohydrazono)bis-etanamine (DETA/NO) after treatment with L-NMMA. Hypoxia caused a significant decrease in the systemic PO2. During normoxia, arteriolar intravascular PO2 decreased progressively from 47.0 +/- 3.5 mmHg in the larger arterioles to 28.0 +/- 2.5 mmHg in the terminal arterioles; conversely, intravascular PO2 was 7-14 mmHg and approximately uniform in all arterioles. Tissue PO2 was 85% of baseline. Hypoxia significantly dilated arterioles, reduced blood flow, and increased capillary perfusion (15%) and ROS (72%) relative to baseline. Administration of L-NMMA during hypoxia further reduced capillary perfusion to 47% of baseline and increased ROS to 34% of baseline, both changes being significant. Tissue PO2 was reduced by 33% versus the hypoxic group. Administration of DETA/NO after L-NMMA caused vasodilation, normalized ROS, and increased capillary perfusion and tissue PO2. These results indicate that during normoxia, oxygen is supplied to the tissue mostly by the arterioles, whereas in hypoxia, oxygen is supplied to tissue by capillaries by a NO concentration-dependent mechanism that controls capillary perfusion and tissue PO2, involving capillary endothelial cell responses to the decrease in lipid peroxide formation controlled by NO availability during low PO2 conditions.     

Pericardial delivery of omega-3 fatty acid: a novel approach to reducing myocardial infarct sizes and arrhythmias

O2-carrying fluids based on hemoglobin (Hb) are in various stages of clinical trials to determine their suitability as O2-carrying plasma expanders. Polymerized Hb solutions are characterized by their vasoactivity, low O2 affinity, oncotic effect, prolonged shelf life, and stability. Physiological responses to facilitated O2 transport after exchange transfusion with polymerized bovine Hb (PBH) were studied in the hamster window chamber model during acute moderate anemia to determine how PBH affects microvascular perfusion and tissue oxygenation. The anemic state [29% hematocrit (Hct)] was induced by hemodilution with a plasma expander (70 kDa dextran). After hemodilution, animals were randomly assigned to different exchange transfusion groups. Study groups were based on the concentration of PBH used, namely: PBH at 13 g Hb/dl [PBH13], PBH diluted to 8 (PBH8) or 4 (PBH4) g Hb/dl in albumin solution at matching colloidal osmotic pressure (COP), and no PBH (only albumin solution) at matching COP (PBH0). Measurement of systemic parameters, microvascular hemodynamics, capillary perfusion, and intravascular and tissue O2 levels was performed at 18% Hct. Restitution of O2-carrying capacity with PBH13 increased arterial pressure and triggered vasoconstriction, low perfusion, and high peripheral resistance. PBH4 and PBH0 exhibited lower arterial pressures compared with PBH13. Exchange transfused animals with PBH8 and PBH4 better maintained perfusion and functional capillary density than PBH13. Blood gas parameters and acid-base balance were recovered proportional to microvascular perfusion. Arterial O2 tensions were improved with PBH4 and PBH8 by preventing O2 precapillary release and increasing O2 reserve. Further studies to establish PBH optimal dosage, efficacy, safety, and its effect on outcome are indicated before Hb-based O2-carrying blood substitutes are implemented in routine practice.     

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

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