Spontaneous oscillations in a model for active control of microvessel diameters.

A new theory is presented for the origin of spontaneous oscillations in blood vessel diameters that are observed experimentally in the microcirculation. These oscillations, known as vasomotion, involve timevarying contractions of the vascular smooth muscle in the walls of arterioles. It is shown that such oscillations can arise as a result of interactions between the mechanics of the vessel wall and the dynamics of the active contraction of smooth muscle cells in response to circumferential tension in the wall. A theoretical model is developed in which the diameter and the degree of activation in a vessel are dynamic variables. The model includes effects of wall shear stress and oxygen-dependent metabolic signals on smooth muscle activation and is applied to a single vessel and to simplified network structures. The model equations predict limit cycle oscillations for certain ranges of parameters such as wall shear stress, arterial pressure and oxygen consumption rate. Predicted characteristics of the oscillations, including their sensitivity to arterial pressure, are consistent with experimental observations.

The dicrotic pulse: a common, non-ominous finding after the Ross operation.

We noted a dicrotic pulse in several patients following a Ross operation. Although the etiology of this unique arterial waveform is not completely understood, it has been reported as a sign of low cardiac output and a poor prognosis. We reviewed preoperative echocardiograms and postoperative radial arterial pressure tracings in 33 patients who underwent a Ross procedure between 2000 and 2004. We found a dicrotic pulse to occur commonly (20/33; 61%) following a Ross operation. Moderate to severe preoperative aortic insufficiency was present in 19/20 patients (95%) in whom a dicrotic pulse was noted and in only 3/13 (23%) who did not exhibit a postoperative dicrotic pulse (p<0.001). A dicrotic pulse was not associated with an increased use of vasoactive infusions or longer hospitalization following the Ross operation. The dicrotic pulse should be recognized as a common postoperative finding in Ross patients that does not herald a delayed postoperative convalescence. The mechanism for a dicrotic pulse in these patients is speculative but may result from changes in vascular compliance secondary to chronic aortic insufficiency.

An imaging spectroscopy approach for measurement of oxygen saturation and hematocrit during intravital microscopy.

OBJECTIVE: Oxygen supply and partial pressure are key determinants of tissue metabolic status and are also regulators of vascular function including production of reactive oxygen species, vascular remodeling, and angiogenesis. The objective of this study was to develop an approach for the determination of oxygen saturation and hematocrit for individual microvessels in trans- and epi-illumination intravital microscopy. METHODS: A spectral approach was used, taking advantage of the availability of commercial imaging systems that allow digital recording of intravital images at a number of predetermined wavelengths within a relatively short time. The dependence of validity and precision of saturation measurements on critical experimental variables (reference spectra, number and selection of wavelengths, exposure time, analysis area, analysis model) was evaluated. In addition, a software approach for two-dimensional analysis of images was developed. RESULTS: Exposure times per wavelength of about 200 ms and use of up to 50 wavelengths evenly spaced from 500 to 598 nm allow automatic discrimination of microvessels from tissue background (segmentation) with reliable determination of oxygen saturation (in trans- and epi-illumination) and hematocrit (in transillumination). CONCLUSIONS: The present imaging spectroscopy approach allows detailed assessment of oxygen transport and other functional parameters at the microcirculatory level.

Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition.

We consider the motion of red blood cells and other nonspherical microcapsules dilutely suspended in a simple shear flow. Our analysis indicates that depending on the viscosity, membrane elasticity, geometry, and shear rate, the particle exhibits either tumbling, tank-treading of the membrane about the viscous interior with periodic oscillations of the orientation angle, or intermittent behavior in which the two modes occur alternately. For red blood cells, we compute the complete phase diagram and identify a novel tank-treading-to-tumbling transition as the shear rate decreases. Observations of such motions coupled with our theoretical framework may provide a sensitive means of assessing capsule properties.

Microvascular blood viscosity in vivo and the endothelial surface layer.

The apparent viscosity of blood in glass tubes declines with decreasing diameter (Fåhraeus-Lindqvist effect) and exhibits a distinctive minimum at 6-7 microm. However, flow resistance in vivo in small vessels is substantially higher than predicted by in vitro viscosity data. The presence of a thick endothelial surface layer (ESL) has been proposed as the primary cause for this discrepancy. Here, a physical model is proposed for microvascular flow resistance as a function of vessel diameter and hematocrit in vivo; it combines in vitro blood viscosity with effects of a diameter-dependent ESL. The model was developed on the basis of flow distributions observed in three microvascular networks in the rat mesentery with 392, 546, and 383 vessel segments, for which vessel diameters, network architecture, flow velocity, and hematocrit were determined by intravital microscopy. A previously described hemodynamic simulation was used to predict the distributions of flow and hematocrit from the assumed model for effective blood viscosity. The dependence of ESL thickness on vessel diameter was estimated by minimizing deviations of predicted values for velocities, flow directions, and hematocrits from measured data. Optimal results were obtained with a layer thickness of approximately 0.8-1 microm for 10- to 40-microm-diameter vessels and declined strongly for smaller diameters, with an additional hematocrit-dependent impact on flow resistance exhibiting a maximum for approximately 10-microm-diameter vessels. These results show that flow resistance in vivo can be explained by in vitro blood viscosity and the presence of an ESL and indicate the rheologically effective thickness of the ESL in microvessels.

Control of blood vessel structure: insights from theoretical models.

Blood vessels are capable of continuous structural adaptation in response to changing local conditions and functional requirements. Theoretical modeling approaches have stimulated the development of new concepts in this area and have allowed investigation of the complex relations between adaptive responses to multiple stimuli and resulting functional properties of vascular networks. Early analyses based on a minimum-work principle predicted uniform wall shear stress in all segments of vascular networks and led to the concept that vessel diameter is controlled by a feedback system based on responses to wall shear stress. Vascular reactions to changes in transmural pressure suggested feedback control of circumferential wall stress. However, theoretical simulations of network adaptation showed that these two mechanisms cannot, by themselves, lead to stable and realistic network structures. Models combining reactions to fluid shear stress, circumferential stress, and metabolic status of tissue, with propagation of stimuli upstream and downstream along vascular segments, are needed to explain stable and functionally adequate adaptation of vascular structure. Such models provide a basis for predicting the response of vascular segments exposed to altered conditions, as, for example, in vascular grafts.

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.

Estimation of capillary density in human skeletal muscle based on maximal oxygen consumption rates.

A previously developed Krogh-type theoretical model was used to estimate capillary density in human skeletal muscle based on published measurements of oxygen consumption, arterial partial pressure of oxygen, and blood flow during maximal exercise. The model assumes that oxygen consumption in maximal exercise is limited by the ability of capillaries to deliver oxygen to tissue and is therefore strongly dependent on capillary density, defined as the number of capillaries per unit cross-sectional area of muscle. Based on an analysis of oxygen transport processes occurring at the microvascular level, the model allows estimation of the minimum number of straight, evenly spaced capillaries required to achieve a given oxygen consumption rate. Estimated capillary density values were determined from measurements of maximal oxygen consumption during knee extensor exercise and during whole body cycling, and they range from 459 to 1,468 capillaries/mm2. Measured capillary densities, obtained with either histochemical staining techniques or electron microscopy on quadriceps muscle biopsies from healthy subjects, are generally lower, ranging from 123 to 515 capillaries/mm2. This discrepancy is partly accounted for by the fact that capillary density decreases with muscle contraction and muscle biopsy samples typically are strongly contracted. The results imply that estimates of maximal oxygen transport rates based on capillary density values obtained from biopsy samples do not fully reflect the oxygen transport capacity of the capillaries in skeletal muscle.

Structural response of microcirculatory networks to changes in demand: information transfer by shear stress.

Matching blood flow to metabolic demand in terminal vascular beds involves coordinated changes in diameters of vessels along flow pathways, requiring upstream and downstream transfer of information on local conditions. Here, the role of information transfer mechanisms in structural adaptation of microvascular networks after a small change in capillary oxygen demand was studied using a theoretical model. The model includes diameter adaptation and information transfer via vascular reactions to wall shear stress, transmural pressure, and oxygen levels. Information transfer is additionally effected by conduction along vessel walls and by convection of metabolites. The model permits selective blocking of information transfer mechanisms. Six networks, based on in vivo data, were considered. With information transfer, increases in network conductance and capillary oxygen supply were amplified by factors of 4.9 +/- 0.2 and 9.4 +/- 1.1 (means +/- SE), relative to increases when information transfer was blocked. Information transfer by flow coupling alone, in which increased shear stress triggers vascular enlargement, gave amplifications of 4.0 +/- 0.3 and 4.9 +/- 0.5. Other information transfer mechanisms acting alone gave amplifications below 1.6. Thus shear-stress-mediated flow coupling is the main mechanism for the structural adjustment of feeding and draining vessel diameters to small changes in capillary oxygen demand.

Rheology of the microcirculation.

The main function of the microvasculature is the controlled exchange of materials with surrounding tissues. This necessitates a large vessel surface established by a high number of vessels with small diameters and thus an inherently high individual resistance to flow. The hydrodynamic resistance of a microvascular network with given angioarchitecture depends on the apparent viscosity of blood flowing in the microvessels. Apparent viscosity declines with decreasing diameter (the Fahraeus-Lindqvist effect) and is minimal at diameters of about 5-7 micrometers due to the optimal alignment of red cells with the flow. In vivo, a number of additional phenomena influence blood rheology and network hemodynamics. The distribution of blood flow and red cell flux within networks is influenced by the mechanics of red cell motion at individual diverging bifurcations (phase-separation effect). Furthermore, recent studies have revealed the presence of a thick endothelial surface layer ( approximately 0.5 micrometers) on the luminal surface of microvessels which is attached to the endothelial glycocalyx. This layer modulates flow resistance and may be relevant for a number of other processes such as inflammatory responses and blood coagulation. Information on microvascular rheology can be used to develop mathematical models of network hemodynamics and vascular adaptation to the local environment (angioadaptation), to investigate the complex interrelated mechanisms which establish and maintain functionally adequate microvascular networks.

Blood flow and red blood cell deformation in nonuniform capillaries: effects of the endothelial surface layer.

OBJECTIVE: A theoretical model is used to examine the mechanics of red blood cell (RBC) motion in nonuniform capillaries. The model includes effects of the endothelial surface layer (ESL), which is a layer of macromolecules adjacent to the endothelium and which impedes plasma flow. METHODS: The motion of an RBC traversing a capillary with diameter varying sinusoidally between 5.4 microm and 7.4 microm is simulated numerically. The ESL is assumed to be 0.7-microm wide and deformable. Axisymmetric RBC shapes are assumed. Lubrication theory is used to analyze the motion of plasma around the RBC and through the ESL. RESULTS: In a nonuniform capillary with no ESL, moving RBCs undergo large transient deformations and predicted flow resistance is substantially higher than in a uniform capillary with the same mean diameter. The presence of a deformable ESL reduces the transient fluid shear stresses and deformations experienced by RBCs traversing a nonuniform capillary. With an ESL, the increase in flow resistance resulting from nonuniformity is less than twofold versus three- to fourfold with no ESL in vessel geometries with the same ESL-free luminal region. CONCLUSIONS: The presence of the ESL reduces the impact of capillary irregularity on flow resistance and may protect RBCs traversing irregular capillaries from damage due to large, rapidly fluctuating external stresses.

Structural adaptation of vascular networks: role of the pressure response.

Structural reductions in vessel luminal diameters in response to elevated pressure may play a role in the elevation of peripheral resistance generally observed in hypertension. In the present study, a theoretical model is used to simulate the effect of increased driving pressure on flow resistance in microvascular networks. The angioarchitecture (lengths and diameters of all segments, topology) of microvascular networks (n=6) in the rat mesentery was recorded by intravital microscopy. The model simulation of vascular adaptation in response to local wall shear stress, transmural pressure, and tissue PO(2) was used to predict changes in network pressure drop and flow resistance for a given change of driving pressure (DeltaP). For DeltaP increasing from 15% to 190% of the normotensive value, a 3.3-fold increase in flow resistance was observed (structural autoregulation). If vascular reactivity to pressure was suppressed, the resistance increase was abolished. Suppressing pressure sensitivity also led to a rise in mean capillary pressure at normal driving pressure from 23.8+/-7.3 mm Hg to 34+/-6.9 mm Hg. These results indicate that low capillary pressure levels as well as structural autoregulation depend on vascular responses to circumferential wall stress (corresponding to pressure). This tendency of peripheral vascular beds to increase flow resistance for a given increase of bulk flow or driving pressure may amplify and stabilize blood pressure elevation in the development of hypertension.

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 theoretical model for the elastic properties of very soft tissues.

A theoretical model is developed to predict the elastic properties of very soft tissues such as glands, tumors and brain. Tissues are represented as regular arrays of polyhedral (cubic or tetrakaidecahedral) cells, surrounded by extracellular spaces of uniform width. Cells are assumed to be incompressible, with very low resistance to shear deformation. Tissue shear rigidity is assumed to result mainly from the extracellular matrix, which is treated as a compressible elastic mesh of interconnected fibers. Small-strain elastic properties of tissue are predicted using a finite-element method and an analytical method. The model can be used to estimate the compressibility of a very soft tissue based on its Young's modulus and extracellular volume fraction.

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.

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).

Focal topographic changes in inflammatory microcirculation associated with lymphocyte slowing and transmigration.

Microcirculation is the primary mechanism for delivering lymphocytes to inflammatory tissues. Blood flow within microvessels ensures a supply of lymphocytes at the blood-endothelial interface. Whether the structure of the inflammatory microcirculation facilitates lymphocyte transmigration is less clear. To illuminate the microcirculatory changes associated with lymphocyte transmigration, we used intravital videomicroscopy to examine the dermal microcirculation after application of the epicutaneous antigen oxazolone. Intravascular injection of fluorescein-labeled dextran demonstrated focal topographic changes in the microcirculation. These focal changes had the appearance of loops or hairpin turns in the oxazolone-stimulated skin. Changes were maximal at 96 h and coincided with peak lymphocyte recruitment. To determine whether these changes were associated with lymphocyte transmigration, lymphocytes obtained from efferent lymph of draining lymph nodes at 96 h were fluorescently labeled and reinjected into inflammatory microcirculation. Epifuorescence intravital video microscopy demonstrated focal areas were associated with lymphocyte slowing and occasional transmigration. In contrast, focal loops and lymphocyte slowing were rarely observed in the contralateral control microcirculation. Results suggest that structural adaptations in inflammatory microcirculation represented by focal topographic changes may contribute to regulation of tissue entry by recirculating lymphocytes.

Structural adaptation of microvascular networks: functional roles of adaptive responses.

Terminal vascular beds continually adapt to changing demands. A theoretical model is used to simulate structural diameter changes in response to hemodynamic and metabolic stimuli in microvascular networks. Increased wall shear stress and decreased intravascular pressure are assumed to stimulate diameter increase. Intravascular partial pressure of oxygen (PO(2)) is estimated for each segment. Decreasing PO(2) is assumed to generate a metabolic stimulus for diameter increase, which acts locally, upstream via conduction along vessel walls, and downstream via metabolite convection. By adjusting the sensitivities to these stimuli, good agreement is achieved between predicted network characteristics and experimental data from microvascular networks in rat mesentery. Reduced pressure sensitivity leads to increased capillary pressure with reduced viscous energy dissipation and little change in tissue oxygenation. Dissipation decreases strongly with decreased metabolic response. Below a threshold level of metabolic response flow shifts to shorter pathways through the network, and oxygen supply efficiency decreases sharply. In summary, the distribution of vessel diameters generated by the simulated adaptive process allows the network to meet the functional demands of tissue while avoiding excessive viscous energy dissipation.

Motion of red blood cells in a capillary with an endothelial surface layer: effect of flow velocity.

Interior surfaces of capillaries are lined with macromolecules forming an endothelial surface layer (ESL). A theoretical model is used to investigate effects of flow velocity on motion and axisymmetric deformation of red blood cells in a capillary with an ESL. Cell deformation is analyzed, including effects of membrane shear and bending elasticity. Plasma flow around the cell and through the ESL is computed using lubrication theory. The ESL is represented as a porous layer that exerts compressive forces on red blood cells that penetrate it. According to the model, hydrodynamic pressures generated by plasma flow around the cell squeeze moving red blood cells into narrow elongated shapes. If the ESL is 0.7 microm wide, with hydraulic resistivity of 2 x 10(8) dyn x s x cm(-4), and exerts a force of 20 dyn/cm2, predicted variation with flow velocity of the gap width between red blood cell and capillary wall agrees well with observations. Predicted gap at a velocity of 0.1 mm/s is approximately 0.6 microm vs. approximately 0.2 microm with no ESL. Predicted flow resistance increases markedly at low velocities. The model shows that exclusion of red blood cells from the ESL in flowing capillaries can result from hydrodynamic forces generated by plasma flow through the ESL.

Effect of the endothelial surface layer on transmission of fluid shear stress to endothelial cells.

Responses of vascular endothelial cells to mechanical shear stresses resulting from blood flow are involved in regulation of blood flow, in structural adaptation of vessels, and in vascular disease. Interior surfaces of blood vessels are lined with a layer of bound or adsorbed macromolecules, known as the endothelial surface layer (ESL). In vivo investigations have shown that this layer has a width of order 1 microm, that it substantially impedes plasma flow, and that it excludes flowing red blood cells. Here, the effect of the ESL on transmission of shear stress to endothelial cells is examined using a theoretical model. The layer is assumed to consist of a matrix of molecular chains extending from the surface, held in tension by a slight increase in colloid osmotic pressure relative to that in free-flowing plasma. It is shown that, under physiological conditions, shear stress is transmitted to the endothelial surface almost entirely by the matrix, and fluid shear stresses on endothelial cell membranes are very small. Rapid fluctuations in shear stress are strongly attenuated by the layer. The ESL may therefore play an important role in sensing of shear stress by endothelial cells.