Skeletal muscle capillary density and fiber type are possible determinants of in vivo insulin resistance in man.

We have compared the capillary density and muscle fiber type of musculus vastus lateralis with in vivo insulin action determined by the euglycemic clamp (M value) in 23 Caucasians and 41 Pima Indian nondiabetic men. M value was significantly correlated with capillary density (r = 0.63; P less than or equal to 0.0001), percent type I fibers (r = 0.29; P less than 0.02), and percent type 2B fibers (r = -0.38; P less than 0.003). Fasting plasma glucose and insulin concentrations were significantly negatively correlated with capillary density (r = -0.46, P less than or equal to 0.0001; r = -0.47, P less than or equal to 0.0001, respectively). Waist circumference/thigh circumference ratio was correlated with percent type 1 fibers (r = -0.39; P less than 0.002). These results suggest that diffusion distance from capillary to muscle cells or some associated biochemical change, and fiber type, could play a role in determining in vivo insulin action. The association of muscle fiber type with body fat distribution may indicate that central obesity is only one aspect of a more generalized metabolic syndrome. The data may provide at least a partial explanation for the insulin resistance associated with obesity and for the altered kinetics of insulin action in the obese.

Determination of local oxygen consumption rates in tumors.

At any location in a respiring tissue, partial pressure of oxygen (PO2) is influenced by the local oxygen consumption rate. Consumption rates in vascular tumor tissues have previously been estimated for macroscopic regions. Using oxygen electrodes, we measured PO2 profiles across microregions (87 microns to 286 microns wide) of tumors (R3230AC mammary adenocarcinoma) in a rat dorsal skin flap preparation and mapped adjacent microvessels. By comparing measured PO2 values with theoretical simulations, we deduced local consumption rates. Results for six profiles ranged from 0.83 to 2.22 cm3 O2/100 g/min. The mean (+/- SD) was 1.52 +/- 0.51 cm3 O2/100 g/min. This technique permits investigation of variations in consumption at a microregional level.

Fluctuations in red cell flux in tumor microvessels can lead to transient hypoxia and reoxygenation in tumor parenchyma.

Hypoxia occurs in two forms in tumors. Chronic or diffusion-limited hypoxia is relatively well characterized. In contrast, intermittent or perfusion-limited hypoxia is not well characterized, and it is not known how common it is in tumors. The purpose of this study was to determine whether spontaneous fluctuations in tumor microvessel flow rate can modify vessel oxygen tension (pO2) sufficiently to cause intermittent hypoxia (IH; tissue pO2 < 3 mmHg) in the tumor parenchyma supplied by such vessels. Microvessel red cell flux (RCF) and perivascular pO2 were measured simultaneously and continuously in dorsal flap window chambers of Fischer-344 rats with implanted R3230Ac tumors. In all vessels, RCF was unstable, with apex/nadir ratios ranging from 1.5 to 10. RCF and pO2 were temporally coordinated, and there were linear relationships between the two parameters. Vascular pO2 was less sensitive to changes in RCF in well-vascularized tumor regions compared with poorly vascularized regions. Simulations of oxygen transport in a well-vascularized region of a tumor demonstrated that two-fold variations in RCF can produce IH in 30% of the tissue in that region. In poorly vascularized regions, such fluctuations would lead to an even greater percentage of tissue involved in transient hypoxia. These results suggest that IH is a relatively common phenomenon. It could affect binding of hypoxic cytotoxins to tumor cells, in addition to being an important source of treatment resistance. Intermittent hypoxia also could contribute to tumor progression by providing repeated exposure of tumor cells to hypoxia-reoxygenation injury.

Biophysical aspects of blood flow in the microvasculature.

The main function of the microvasculature is transport of materials. Water and solutes are carried by blood through the microvessels and exchanged, through vessel walls, with the surrounding tissues. This transport function is highly dependent on the architecture of the microvasculature and on the biophysical behavior of blood flowing through it. For example, the hydrodynamic resistance of a microvascular network, which determines the overall blood flow for a given perfusion pressure, depends on the number, size and arrangement of microvessels, the passive and active mechanisms governing their diameters, and on the apparent viscosity of blood flowing in them. Suspended elements in blood, especially red blood cells, strongly influence the apparent viscosity, which varies with several factors, including vessel diameter, hematocrit and blood flow velocity. The distribution of blood flows and red cell fluxes within a network, which influences the spatial pattern of mass transport, is determined by the mechanics of red cell motion in individual diverging bifurcations. Here, our current understanding of the biophysical processes governing blood flow in the microvasculature is reviewed, and some directions for future research are indicated.

Blood flow resistance during hemodilution: effect of plasma composition.

OBJECTIVES: To investigate the causes of wide variations in reported effects of hemodilution on flow resistance of vascular beds. METHODS: (a) In a meta-analysis of 28 prior studies, resistance values at hematocrits of zero (R0) and 0.45 (R0.45) were derived. Study design characteristics (presence of vasodilatory reserve or leukocytes, species, tissue, hemodiluent) were tested by ANOVA for their relation to the ratio R0/R0.45. (b) Experiments were performed to determine flow resistance during hemodilution in the rat mesentery with (n = 8) and without (n = 11) pretreatment with heparinase, which modifies the endothelial glycocalyx. (c) A mathematical flow simulation for mesenteric microvascular networks was used to predict resistance effects of hemodilution and of a hypothetical layer on the endothelial surface. RESULTS: (a) In prior studies using native plasma for hemodilution R0 averaged 50 +/- 8% of R0.45, while in studies using artificial solutions R0 averaged 32 +/- 12% of R0.45. The larger reduction of flow resistance upon dilution with artificial media is independent of viscosity and oncotic pressure. Other design characteristics did not show strong significant effects. (b) Present experiments showed large reductions of flow resistance with saline hemodilution which were nearly halved after heparinase pretreatment. (c) Resistance effects of hemodilution with plasma or after heparinase treatment agree with model predictions based on tube flow rheology of blood. The larger resistance effects of dilution with artificial media can be explained by the removal of an endothelial surface layer of approximately 1.5 microns thickness. CONCLUSIONS: The results imply that changes of plasma composition, due to use of artificial infusion media, influence peripheral resistance and tissue perfusion. They are consistent with the hypothesis that interactions between endothelial glycocalyx structures and plasma components lead to formation of a thick layer at the endothelial surface which increases flow resistance.

A mathematical model for comparison of bolus injection, continuous infusion, and liposomal delivery of doxorubicin to tumor cells.

Determining the optimal mode of delivery for doxorubicin is important given the wide use of the drug against many tumor types. The relative performances of bolus injection, continuous infusion, liposomal and thermoliposomal delivery are not yet definitely established from clinical trials. Here, a mathematical model is used to compare bolus injection, continuous infusion for various durations, liposomal and thermoliposomal delivery of doxorubicin. Effects of the relatively slow rate, and saturability, of doxorubicin uptake by cells are included. Peak concentrations attained in tumor cells are predicted and used as a measure of antitumor effectiveness. To measure toxicity, plasma area under the curve (AUC) and peak plasma concentrations of free doxorubicin are computed. For continuous infusion, the duration of infusion significantly affects predicted outcome. The optimal infusion duration increases with dose, and is in the range 1 to 3 hours at typical doses. The simulations suggest that continuous infusion for optimal durations is superior to the other protocols. Nonthermosensitive liposomes approach the efficacy of continuous infusion only if they release drug at optimal rates. Predictions for thermosensitive liposomes indicate a potential advantage at some doses, but only if hyperthermia is applied locally so that the blood is not significantly heated.

Causes and effects of heterogeneous perfusion in tumors.

A characteristic of solid tumors is their heterogeneous distribution of blood flow, with significant hypoxia and acidity in low-flow regions. We review effects of heterogeneous tumor perfusion are reviewed and propose a conceptual model for its cause. Hypoxic-acidic regions are resistant to chemo- and radiotherapy and may stimulate progression to a more metastatic phenotype. In normal tissues, hypoxia and acidity induce angiogenesis, which is expected to improve perfusion. However, aggressive tumors can have high local microvessel density simultaneously with significant regions of hypoxia and acidosis. A possible explanation for this apparent contradiction is that the mechanisms regulating growth and adaptation of vascular networks are impaired. According to a recent theory for structural adaptation of vascular networks, four interrelated adaptive responses can work as a self-regulating system to produce a mature and efficient blood distribution system in normal tissues. It is proposed that heterogeneous perfusion in tumors may result from perturbation of this system. Angiogenesis may increase perfusion heterogeneity in tumors by increasing the disparity between parallel low- and high-resistance flow pathways. This conceptual model provides a basis for future rational therapies. For example, it indicates that selective destruction of tumor vasculature may increase perfusion efficiency and improve therapeutic efficacy.

Structural autoregulation of terminal vascular beds: vascular adaptation and development of hypertension.

-It is widely accepted that the early phase of primary hypertension is characterized by elevated cardiac output, whereas in later stages the increased blood pressure is due to increased peripheral resistance. To study long-term effects of increased blood flow on peripheral resistance, structural adaptation of microvascular networks in response to changes in blood flow was simulated using a previously developed theoretical model. The diameter of each vessel segment was assumed to change in response to local levels of shear stress, transmural pressure, a metabolic stimulus dependent on blood flow rate, and a conducted stimulus. Network morphologies and topologies were derived from intravital microscopy of the rat mesentery. Adaptive responses to the 4 stimuli were quantitatively balanced to yield stable and realistic distributions of vascular diameters and blood flow rates when the total flow rate was set to observed levels. To simulate effects of increased cardiac output, network flow resistance after structural adaptation was determined for a range of flow rates. Resistance increased with increasing flow, and increases in pressure were up to 3-fold greater than proportional to the increases in flow. According to the model, flow-dependent changes of network resistance result mainly from the vascular response to transmural pressure, which also causes arteriovenous asymmetry of diameters and pressure drops. Therefore, in vascular beds that exhibit arteriovenous asymmetry, increased flow may trigger increased flow resistance by a mechanism involving the tendency of vascular segments to reduce their luminal diameters in response to increased transmural pressure.

Effect of increasing vascular hydraulic conductivity on delivery of macromolecular drugs to tumor cells.

PURPOSE: To examine the assumption that increasing the hydraulic conductivity Lp of microvessels (by such strategies as radiation, hyperthermia, or inducing inflammation) improves the transport of macromolecular drugs to tumors. METHODS AND MATERIALS: A theoretical model is used to investigate the effect of varying Lp on macromolecular transport in spherical tumor nodules. The model is generalized to nonspherical tumors. The equations governing fluid flow in the tumors are solved numerically to obtain the pressure in the interior, and macromolecule fluxes are deduced using Starling's equation. RESULTS: Because of the interaction of two opposing effects, the filtration rate at the tumor center is maximized at an "optimum" value of Lp, which depends strongly on tumor size. Only for tumor nodules smaller than about 0.2 cm across is this value lower than the actual estimated value. By considering spheroidal tumor nodules, it is found that dependence on shape is much weaker than dependence on size, except for extremely elongated or flattened shapes. CONCLUSIONS: While total fluid filtration for the entire tumor region always increases with increasing Lp, the local filtration rate at points inside the tumor decreases if the tumor is larger than about 0.2 cm, leading to a less uniform distribution of the drug, and therapeutic disadvantage. Increased vessel leakiness is an unlikely explanation for reported experimental findings that hyperthermia and inflammation result in more uniform distributions of monoclonal antibodies throughout tumors much larger than 0.2 cm.

Analysis of oxygen transport to tumor tissue by microvascular networks.

We present theoretical simulations of oxygen delivery to tumor tissues by networks of microvessels, based on in vivo observations of vascular geometry and blood flow in the tumor microcirculation. The aim of these studies is to investigate the impact of vascular geometry on the occurrence of tissue hypoxia. The observations were made in the tissue (thickness 200 microns) contained between two glass plates in a dorsal skin flap preparation in the rat. Mammary adenocarcinomas (R3230 AC) were introduced and allowed to grow, and networks of microvessels in the tumors were mapped, providing data on length, geometric orientation, diameter and blood velocity in each segment. Based on these data, simulations were made of a 1 mm x 1 mm region containing five unbranched vascular segments and a 0.25 mm x 0.35 mm region containing 22 segments. Generally, vessels were assumed to lie in the plane midway between the glass plates, at 100 microns depth. Flow rates in the vessels were based on measured velocities and diameters. The assumed rate of oxygen consumption in the tissue was varied over a range of values. Using a Green's function method, partial pressure of oxygen (PO2) was computed at each point in the tissue region. As oxygen consumption is increased, tissue PO2 falls, with hypoxia first appearing at points relatively distant from the nearest blood vessel. The width of the well-oxygenated region is comparable to that predicted by simpler analyses. Cumulative frequency distributions of tissue PO2 were compared with predictions of a Krogh-type model with the same vascular densities, and it was found that the latter approach, which assumes a uniform spacing of vessels, may underestimate the extent of the hypoxic tissue. Our estimates of the maximum consumption rate that can be sustained without tissue hypoxia were substantially lower than those obtained from the Krogh-type model. We conclude that the heterogeneous structure of tumor microcirculation can have a substantial effect on the occurrence of hypoxic micro-regions.

Morphologic and hemodynamic comparison of tumor and healing normal tissue microvasculature.

The purpose of this study was to compare microvascular morphometric and hemodynamic characteristics of a tumor and granulating normal tissue to develop quantitative data that could be used to predict microvascular characteristics which would be most likely associated with hypoxia. The dorsal flap window chamber of the Fisher 344 rat was used to visualize the microvasculature of 10 granulating and 12 tumor (R3230 AC adenocarcinoma) tissues at 2 weeks following surgical implantation of the chamber. Morphometric measurements were made from photomontages and video techniques were used to assess red cell velocities in individual vessels. The percent vascular volume of both tissues was close to 20%, but significant differences were noted in other morphometric and hemodynamic measurements. Individual vessel dimensions (length and diameter) in tumors averaged twice as large as those in granulating tissues. Furthermore, red cell velocities were twice as high in tumors as in granulating tissues. In addition to these large differences in average values, there was significant heterogeneity in tumor microvascular morphometry, indicating spatial nonuniformity compared with the granulating tissue. Approximations of vessel spacing, indicated an average of 257 and 118 microns in tumors and granulating tissues, respectively. Vessel densities were four times greater in granulating tissues than in tumor tissues. These results indicated that intervessel distances were more likely to result in hypoxia in tumors, especially considering the wide variability in that tissue. Analysis of flow branching patterns showed that vascular shunts occurred frequently in vessels ranging from 10 to 90 microns in diameter. The results of this study indicate, in this tumor model, that conditions such as low vascular density, vascular shunts, excessive vascular length and/or low red cell velocity exist to a greater extent than the granulating tissue control. These conditions are likely to be conductive to the development of hypoxia.

Simultaneous administration of glucose and hyperoxic gas achieves greater improvement in tumor oxygenation than hyperoxic gas alone.

PURPOSE: To test the feasibility of hyperglycemic reduction of oxygen consumption combined with oxygen breathing (O(2)), to improve tumor oxygenation. METHODS AND MATERIALS: Fischer-344 rats bearing 1 cm R3230Ac flank tumors were anesthetized with Nembutal. Mean arterial pressure, heart rate, tumor blood flow ([TBF], laser Doppler flowmetry), pH, and pO(2) were measured before, during, and after glucose (1 or 4 g/kg) and/or O(2). RESULTS: Mean arterial pressure and heart rate were unaffected by treatment. Glucose at 1 g/kg yielded maximum blood glucose of 400 mg/dL, no change in TBF, reduced tumor pH (0.17 unit), and 3 mm Hg pO(2) rise. Glucose at 4 g/kg yielded maximum blood glucose of 900 mg/dL, pH drop of 0.6 unit, no pO(2) change, and reduced TBF (31%). Oxygen tension increased by 5 mm Hg with O(2). Glucose (1 g/Kg) + O(2) yielded the largest change in pO(2) (27 mm Hg); this is highly significant relative to baseline or either treatment alone. The effect was positively correlated with baseline pO(2), but 6 of 7 experiments with baseline pO(2) < 10 mm Hg rose above 10 mm Hg after combined treatment. CONCLUSION: We demonstrated the feasibility of combining hyperglycemia with O(2) to improve tumor oxygenation. However, some cell lines are not susceptible to the Crabtree effect, and the magnitude is dependent on baseline pO(2). Additional or alternative manipulations may be necessary to achieve more uniform improvement in pO(2).

Effects of bradykinin on the hemodynamics of tumor and granulating normal tissue microvasculature.

Bradykinin (BK) is an important endogenous mediator of microvascular flow modulation. Since the structure of the microcirculation is very different in tumor tissues than in normal tissues, bradykinin may elicit different responses in tumors. This study was designed to test the hypothesis that local administration of bradykinin increases blood flow preferentially in normal tissue relative to adjacent tumor tissue, resulting in a "vascular steal" phenomenon. Microvessel diameters (D), velocities (Vc), length densities, shear rates, and intermittent flow frequencies were measured every 10 min before, during, and after 40 min exposure to BK in rats with dorsal flap window chambers 9 days after tumor implantation. Separate studies were made of normal vessels outside the tumor margin, the hypervascular tumor periphery, and the tumor center. Bradykinin was administered with a suffusion medium flowing over the tissue at 1-2 ml/min with a BK concentration of 1.6 x 10(7) M. Administration of BK created five distinct changes in normal and tumor vessel function that varied over time, but coincidentally reached a maximum effect after 20 min exposure to BK. In normal vessels, increased Vc and D led to increased flow, which reached a peak 20 min after onset of suffusion with BK. In contrast, in centrally located tumor vessels, decreased D and Vc were observed in most vessels during the initial 10-20 min of suffusion. In addition, there was a significant increase in intermittent flow frequency in tumor central vessels, which peaked after 20 min of suffusion with BK. These five separate observations that coincided at 20 min of suffusion are consistent with a "vascular steal" phenomenon. The increase in normal microvessel D and Vc at 20 min suggests that BK causes vasodilation in arterioles. The coincident decrease in tumor microvessel D and Vc suggests that tumor feeding vessels are less able to respond to BK by vasodilating. The concomitant increase in intermittent flow frequency in tumor vessels suggests that a reduction in pressure drop occurred after 20 min exposure to BK, which is also consistent with "vascular steal." Since BK is also known to increase vascular permeability, it is possible that increases in interstitial fluid pressure brought on by exposure to BK contributed to the observed reduction in tumor blood flow. In normal vessels, reduced D and Vc, relative to peak values, were noted after 40 min suffusion with BK. Adherence of leukocytes to the vessel walls was prominent and microthrombi were also observed during this period. No evidence of such adhesion was seen in tumor vessels, although microthrombi were observed.(ABSTRACT TRUNCATED AT 400 WORDS)

Perivascular oxygen tensions in a transplantable mammary tumor growing in a dorsal flap window chamber.

Fischer 344 rats with R3230 Ac mammary carcinomas implanted in dorsal flap window chambers served as a model to obtain measurements of perivascular and stromal oxygen tension in normal and tumor tissues using Whalen recessed-tip microelectrodes (3- to 6-microns tip). Perivascular measurements were made adjacent to vessels with continuous blood flow. Thus the measurements and models provided are reflective of conditions leading to chronic hypoxia. Perivascular oxygen tensions averaged 72 +/- 13 mmHg in normal tissue vessels adjacent to tumor, 26 +/- 5 mmHg in tumor periphery, and 12 +/- 3 mmHg in tumor central vessels. There was a significant trend toward lower perivascular oxygen tensions in the tumor center (Kruskal-Wallis test, P = 0.002). A similar tendency was seen with a limited number of stromal measurements. Krogh cylinder models, which incorporate these data for perivascular oxygen tension, along with morphometric data obtained from the same tumor model suggest that hypoxic regions will exist between tumor vessels in the tumor center unless O2 consumption rates are well below 0.6 ml/100 g/min. The low perivascular measurements observed near the tumor center combined with the theoretical considerations suggest, for this model at least, that tissue oxygenation may best be improved by increasing red cell velocity and input pO2 and reducing oxygen consumption. The low perivascular oxygen tensions observed near the center also suggest that conditions conducive to increased red cell rigidity exist, that drugs which can decrease red cell rigidity could improve tumor blood flow and oxygenation, and that the endothelium of those vessels may be susceptible to hypoxia-reoxygenation injury.

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.

Theoretical models for drug delivery to solid tumors.

The effectiveness of anti-cancer drug therapies is often limited by the difficulty of achieving drug delivery throughout solid tumors. Mathematical models permit an analysis of the factors leading to inadequate drug delivery to tumors and can suggest strategies for improving delivery. An overview is given of key factors that influence drug delivery and the extent to which they have been incorporated into existing theoretical models. These factors include spatial gradients of drug concentration and other variables within tumors and other parts of the body, and the relative magnitudes of the time scales involved in drug transport, tumor cell kinetics, and host toxicity. Models for both systemic and regional delivery methods are considered, including intravenous, intraarterial, intraperitoneal, intrathecal, and intratumoral delivery. Strategies for improving delivery are discussed, including use of two-step therapies, hyperthermia, liposome encapsulation, and magnetic targeting. Until now, modeling has mainly developed in separate subfields of tumor growth and cell kill kinetics, compartmental modeling of the body, spatially distributed models for single tissues, radiation dose calculations, tumor oxygenation, tumor blood flow, and cellular pharmacokinetics. In the future, models that integrate these subfields should be developed.

Theoretical predictions of maximal oxygen consumption in hypoxia: effects of transport limitations.

A Krogh-type model for oxygen transport is used to predict maximal oxygen consumption (V(.-) O(2max)) of human skeletal muscle under hypoxic conditions. Assumed values of capillary density, blood flow, and hemoglobin concentration are based on measurements under normoxic and hypoxic exercise conditions. Arterial partial pressure of oxygen is assumed to decrease with reductions in inspired partial pressure of oxygen (P(I)O(2)), as observed experimentally. As a result of limitations of convective and diffusive oxygen delivery, predicted V(.-) O(2max) values decline gradually as P(I)O(2) is reduced from 150 mmHg to about 80 mmHg, and more rapidly as P(I)O(2) is further reduced. At very low levels of P(I)O(2), V(.-) O(2max) is limited primarily by convective oxygen supply. Experimentally observed values of V(.-) O(2max) in hypoxia show significant dispersion, with some values close to predicted levels and others substantially lower. These results suggest that maximal oxygen consumption rates in hypoxia are not necessarily determined by oxygen transport limitations and may instead reflect reduced muscle oxygen demand.

The Prony spectral line estimation (PSLE) method for the analysis of vascular oscillations.

The Prony spectral line estimation (PSLE) technique is implemented and tested on data consisting of sinusoids mixed with Gaussian noise and on recordings of oscillatory diameter changes (vasomotion) of arterioles. It is concluded that the PSLE method is well suited for the spectrum analysis of short oscillatory diameter records.

Effect of shear stress on efferent lymph-derived lymphocytes in contact with activated endothelial monolayers.

L.ymphocyte interactions with endothelial cells in microcirculation are an important regulatory step in the delivery of lymphocytes to peripheral sites of inflammation. In normal circumstances, the predicted wall shear stress in small venules range from 10 to 100 dyn/cm2. Attempts to measure the adhesion of lymphocytes under physiologic conditions have produced variable results, suggesting the importance of studying biologically relevant migratory lymphocytes. To quantify the effect of shear stress on these migratory lymphocytes, we used lymphocytes obtained from sheep efferent lymph ducts, defined as migratory cells, to perfuse sheep endothelial monolayers under conditions of flow. Quantitative cytomorphometry was used to distinguish cells in contact with the endothelial monolayers from cells in the flow stream. As expected, migratory cells in contact with the normal endothelial monolayer demonstrated flow velocities less than the velocity of cells in the adjacent flow stream. The flow velocities of these efferent lymphocytes were independent of cell size. To model the inflammatory microcirculation, lymphocytes were perfused over sequential endothelial monolayers to directly compare the velocity of cells in contact with cytokine-activated and unactivated control monolayers. The tumor necrosis factor and interleukin-1-activated endothelial monolayers marginally decreased cell velocities at 1.2 dyn/cm2 (3.6%), but significantly reduced cell velocities 0.3 dyn/cm2 (27.4%; P < 0.05). Similarly, the fraction of statically adherent lymphocytes decreased as shear stress increased to 1.2 dyn/cm2. These results suggest that typical wall shear stress in small venules. of the order of 20 dyn/cm2, are too high to permit adhesion and transmigration of migratory lymphocytes. Additional mechanisnis must be present in vivo to facilitate lymphocyte transmigration in the inflammatory microcircu-

A Green's function method for analysis of oxygen delivery to tissue by microvascular networks.

A theoretical model is formulated for analyzing oxygen delivery from an arbitrary network configuration of cylindrical microvessels to a finite region of tissue. In contrast to models based on the classical Krogh cylinder approach, this model requires no a priori assumptions concerning the extent of the tissue region supplied with oxygen by each vessel segment. Steady-state conditions are assumed, and oxygen consumption in the tissue is assumed to be uniform. The nonlinear dissociation characteristics of oxyhemoglobin are taken into account. A computationally efficient Green's function approach is used, in which the tissue oxygen field is expressed in terms of the distribution of source strengths along each segment. The utility of the model is illustrated by analyses of oxygen delivery to a cuboidal tissue region by a single segment and by a six-segment network. It is found that the fractional contribution of the proximal segments to total oxygen delivery increases with decreasing flow rate and metabolic rate.