Lingering Dynamics in Microvascular Blood Flow

The microvascular networks in the body of vertebrates consist of the smallest vessels such as arterioles, capillaries, and venules. The flow of red blood cells (RBCs) through these networks ensures the gas exchange in as well as the transport of nutrients to the tissues. Any alterations in this blood flow may have severe implications on the health state. Because the vessels in these networks obey dimensions similar to the diameter of RBCs, dynamic effects on the cellular scale play a key role. The steady progression in the numerical modeling of RBCs, even in complex networks, has led to novel findings in the field of hemodynamics, especially concerning the impact and the dynamics of lingering events when a cell meets a branch of the network. However, these results are yet to be matched by a detailed analysis of the lingering experiments in vivo. To quantify this lingering effect in in vivo experiments, this study analyzes branching vessels in the microvasculature of Syrian golden hamsters via intravital microscopy and the use of an implanted dorsal skinfold chamber. It also presents a detailed analysis of these lingering effects of cells at the apex of bifurcating vessels, affecting the temporal distribution of plasmatic zones of blood flow in the branches and even causing a partial blockage in severe cases.     

Red blood cell mechanics and capillary blood rheology.

Blood contains a high vol fraction of erythrocytes (red blood cells), which strongly influence its flow properties. Much is known about the mechanical properties of red cells, providing a basis for understanding and predicting the rheological behavior of blood in terms of the behavior of individual red cells. This review describes quantitative theoretical models that relate red cell mechanics to flow properties of blood in capillaries. Red cells often flow in single file in capillaries, and rheological parameters can then be estimated by analyzing the motion and deformation of an individual red cell and the surrounding plasma in a capillary. The analysis may be simplified by using lubrication theory to approximate the plasma flow in the narrow gaps between the cells and the vessels walls. If red cell shapes are assumed to be axisymmetric, apparent viscosities are predicted that agree with determinations in glass capillaries. Red cells flowing in microvessels typically assume nonaxisymmetric shapes, with cyclic "tank-treading" motion of the membrane around the interior. Several analyses have been carried out that take these effects into account. These analyses indicate that nonaxisymmetry and tank-treading do not significantly influence the flow resistance in single-file or two-file flow.     

Red blood cell orientation in pulmonary capillaries and its effect on gas diffusion.

When alveoli are inflated, the stretched alveolar walls draw their capillaries into oval cross sections. This causes the disk-shaped red blood cells to be oriented near alveolar gas, thereby minimizing diffusion distance. We tested these ideas by measuring red blood cell orientation in histological slides from rapidly frozen rat lungs. High lung inflation did cause the capillaries to have oval cross sections, which constrained the red blood cells within them to flow with their broad sides facing alveolar gas. Low lung inflation stretched alveolar walls less and allowed the capillaries to assume a circular cross section. The circular luminal profile permitted the red blood cells to have their edges facing alveolar gas, which increased the diffusion distance. Using a finite-element method to calculate the diffusing capacity of red blood cells in the broad-side and edge-on orientations, we found that edge-on red blood cells had a 40% lower diffusing capacity. This suggests that, when capillary cross sections become circular, whether through low-alveolar volume or through increased microvascular pressure, the red blood cells are likely to be less favorably oriented for gas exchange.     

Red blood cell mechanics and capillary blood rheology

Blood contains a high vol fraction of erythrocytes (red blood cells), which strongly influence its flow properties. Much is known about the mechanical properties of red cells, providing a basis for understanding and predicting the rheological behavior of blood in terms of the behavior of individual red cells. This review describes quantitative theoretical models that relate red cell mechanics to flow properties of blood in capillaries. Red cells often flow in single file in capillaries, and rheological parameters can then be estimated by analyzing the motion and deformation of an individual red cell and the surrounding plasma in a capillary. The analysis may be simplified by using lubrication theory to approximate the plasma flow in the narrow gaps between the cells and the vessel walls. If red cell shapes are assumed to be axisymmetric, apparent viscosities are predicted that agree with determinations in glass capillaries. Red cells flowing in microvessels typically assume nonaxisymmetric shapes, with cyclic “tank-treading” motion of the membrane around the interior. Several analyses have been carried out that take these effects into account. These analyses indicate that nonaxisymmetry and tank-treading do not significantly influence the flow resistance in single-file or two-file flow.     

Determination of microvascular flow pattern formation in vivo

Blood flow in microvessels differs significantly from that of red blood cells (RBC) flowing through long, straight glass tubes in vitro. The in vivo situation is characterized by the presence of plasma favoring aggregation, by the irregular geometry of vessel segments, and by frequent branching points. Here, a method is presented to characterize flow patterns in microvascular blood flow during intravital microscopy based on Fourier analysis of recorded light intensity patterns. The interpretation of the resulting power spectra in terms of pattern size distribution was validated by model experiments employing artificial textures and by reverse transformation of idealized spectra. The determined size of RBC flow patterns in microvessels ranged from approximately 8 microm in capillaries to approximately 14 microm in vessels of >30 microm. With increasing shear rate above approximately 100 s(-1) pattern size increased, possibly reflecting formation of short-lived flow clusters. Below approximately 100 s(-1) an increase of pattern size with decreasing shear rate was found in experiments using local occlusion and treatment with high-molecular-weight dextran, suggesting the formation of aggregates. The dynamic process of generation and destruction of RBC flow patterns could well contribute to flow resistance in vivo in peripheral vascular beds.     

Microvascular and capillary perfusion following glycocalyx degradation.

Systemic parameters and microvascular and capillary hemodynamics were studied in the hamster window chamber model before and after hyaluronan degradation by intravenous injection of Streptomyces hyaluronidase (100 units, 40-50 U/ml plasma). Glycocalyx permeation was estimated using fluorescent markers of different molecular size (40, 70, and 2,000 kDa), and electrical charge. Systemic parameters (blood pressure, heart rate, blood gases) and microhemodynamics (vascular tone, velocity, and blood flow) remained statistically unchanged after injection of hyaluronidase, compared with inactivated hyaluronidase. Conversely, capillary hemodynamics were drastically affected. Functional capillary density, the capillaries perfused with red blood cells (RBCs), decreased by 35%, capillary Hct of the remaining functional capillaries increased from 16 to 27%, and penetration of 70-kDa fluorescent marker increased. Furthermore, plasma-only perfused capillaries statistically increased 30 min after hyaluronidase. The decrease in functional capillary density accounted for an increased RBC flux in the remainder of the capillaries, since the same number of RBCs had to traverse a reduced number of capillaries. Flux balances showed a reduction from baseline of 11% for the RBC flux and 20% for the plasma flux after treatment. These discrepancies are within the margin of error of the techniques used and could be explained by accounting for RBC over-velocity compared with plasma. These findings suggest that the decrease in the glycocalyx leads to capillary perfusion impairments.     

Effect of sepsis on skeletal muscle oxygen consumption and tissue oxygenation: interpreting capillary oxygen transport data using a mathematical model

Inherent in the inflammatory response to sepsis is abnormal microvascular perfusion. Maldistribution of capillary red blood cell (RBC) flow in rat skeletal muscle has been characterized by increased 1) stopped-flow capillaries, 2) capillary oxygen extraction, and 3) ratio of fast-flow to normal-flow capillaries. On the basis of experimental data for functional capillary density (FCD), RBC velocity, and hemoglobin O2 saturation during sepsis, a mathematical model was used to calculate tissue O2 consumption (Vo2), tissue Po2 (Pt) profiles, and O2 delivery by fast-flow capillaries, which could not be measured experimentally. The model describes coupled capillary and tissue O2 transport using realistic blood and tissue biophysics and three-dimensional arrays of heterogeneously spaced capillaries and was solved numerically using a previously validated scheme. While total blood flow was maintained, capillary flow distribution was varied from 60/30/10% (normal/fast/stopped) in control to 33/33/33% (normal/fast/stopped) in average sepsis (AS) and 25/25/50% (normal/fast/stopped) in extreme sepsis (ES). Simulations found approximately two- and fourfold increases in tissue Vo2 in AS and ES, respectively. Average (minimum) Pt decreased from 43 (40) mmHg in control to 34 (27) and 26 (15) mmHg in AS and ES, respectively, and clustering fast-flow capillaries (increased flow heterogeneity) reduced minimum Pt to 14.5 mmHg. Thus, although fast capillaries prevented tissue dysoxia, they did not prevent increased hypoxia as the degree of microvascular injury increased. The model predicts that decreased FCD, increased fast flow, and increased Vo2 in sepsis expose skeletal muscle to significant regions of hypoxia, which could affect local cellular and organ function.     

Parameters of red blood cell aggregation as correlates of the inflammatory state

To identify clinically relevant parameters of red blood cell (RBC) aggregation, we examined correlations of aggregation parameters with C-reactive protein and fibrinogen in unstable angina (UA), acute myocardial infarction (AMI), and bacterial infection (BI). Aggregation parameters were derived from the distribution of RBC population into aggregate sizes (cells per aggregate) and changing of the distribution by flow-derived shear stress. Increased aggregation was observed in the following order: UA, AMI, and BI. The best correlation was obtained by integration of large aggregate fraction as a function of shear stress. To differentiate plasmatic from cellular factors in RBC aggregation, we determined the aggregation in the presence and absence of plasma and formulated a "plasma factor" (PF) ranging from 0 to 1. In AMI the enhanced aggregation was entirely due to PF (PF = 1), whereas in UA and BI it was due to both plasmatic and cellular factors (0 < or = PF < or = 1). It is proposed that clinically relevant parameters of RBC aggregation should express both RBC aggregate size distribution and aggregate resistance to disaggregation and distinguish between plasmatic and cellular factors.     

Leukocyte kinetics in the microcirculation

The transport of leukocytes in the microcirculation is specific for the type, size, and the rheological and adhesive properties, the microanatomy of the host organ, and the hemodynamics. The adhesion to the endothelium is determined largely by the degree of activation via chemotactic factors. Leukocyte motion differs from that of red cells or platelets in several respects. When granulocytes enter into capillaries, they are deformed just like red cells. Under normal flow conditions, the time to deform at the entry to capillaries is typically 1,000 times larger than for the red cell, leading to temporary obstruction of the capillaries. After entry, granulocytes move with lower velocity than red cells which causes a cell train formation inside the capillary. At the venular side, the granulocyte is displaced from the center stream toward the endothelium by faster moving red cells. This process leads to systematic attachment of the granulocytes to the endothelium. At a reduced perfusion pressure or in the presence of locally elevated levels of chemotactic factors, the granulocytes may not be able to pass through the capillary network, which leads to microvascular obstruction. Organs with a narrow capillary network may thereby become filters for circulating granulocytes. This event is accompanied in many situations with damage to the host organ.     

Numerical study on flows of red blood cells with liposome-encapsulated hemoglobin at microvascular bifurcation

Flow analysis at microvascular bifurcation after partial replacement of red blood cell (RBC) with liposome-encapsulated hemoglobin (LEH) was performed using the lattice Boltzmann method. A two-dimensional symmetric Y bifurcation model with a parent vessel diameter of 20 mum and daughter branch diameters of 20 microm was considered, and the distributions of the RBC, LEH, and oxygen fluxes were calculated. When only RBCs flow into the daughter branches with unevenly distributed flows, plasma separation occurred and the RBC flow to the lower-flow branch was disproportionately decreased. On the other hand, when half of RBC are replaced by LEH, the biasing of RBC flow was enhanced whereas LEH flowed favorably into the lower-flow branch, because many LEH within the parent vessel are suspended in the plasma layer, where no RBCs exist. Consequently, the branched oxygen fluxes became nearly proportional to flows. These results indicate that LEH facilitates oxygen supply to branches that are inaccessible to RBCs.     

Red cell distribution and the recruitment of pulmonary diffusing capacity.

The distribution of red blood cells in alveolar capillaries is typically nonuniform, as shown by intravital microscopy and in alveolar tissue fixed in situ. To determine the effects of red cell distribution on pulmonary diffusive gas transport, we computed the uptake of CO across a two-dimensional geometric capillary model containing a variable number of red blood cells. Red blood cells are spaced uniformly, randomly, or clustered without overlap within the capillary. Total CO diffusing capacity (DLCO) and membrane diffusing capacity (DmCO) are calculated by a finite-element method. Results show that distribution of red blood cells at a fixed hematocrit greatly affects capillary CO uptake. At any given average capillary red cell density, the uniform distribution of red blood cells yields the highest DmCO and DLCO, whereas the clustered distribution yields the lowest values. Random nonuniform distribution of red blood cells within a single capillary segment reduces diffusive CO uptake by up to 30%. Nonuniform distribution of red blood cells among separate capillary segments can reduce diffusive CO uptake by >50%. This analysis demonstrates that pulmonary microvascular recruitment for gas exchange does not depend solely on the number of patent capillaries or the hematocrit; simple redistribution of red blood cells within capillaries can potentially account for 50% of the observed physiological recruitment of DLCO from rest to exercise.     

Targeted O2 delivery by low-P50 hemoglobin: a new basis for O2 therapeutics

To assess O2 delivery to tissue by a new surface-modified, polyethylene glycol-conjugated human hemoglobin [MP4; Po2 at 50% saturation of hemoglobin (P50); 5.4 mmHg], we studied microcirculatory hemodynamics and O2 release in golden Syrian hamsters hemodiluted with MP4 or polymerized bovine hemoglobin (PolyBvHb; P50 54.2 mmHg). Comparisons were made with the animals' hemodiluted blood with a non-O2 carrying plasma expander with similar solution properties (Dextran-70). Systemic hemodynamics (arterial blood pressure and heart rate) and acid-base parameters were not correlated with microhemodynamics (arteriolar and venular diameter, red blood cell velocity, and flow). Microscopic measurements of Po2 and the O2 equilibrium curves permitted analysis of O2 release in precapillary and capillary vessels by red blood cells and plasma hemoglobin separately. No significant differences between the groups of animals with respect to arteriolar diameter, flow, or flow velocity were observed, but the functional capillary density was significantly higher in the MP4-treated animals (67%) compared with PolyBvHb-treated animals (37%; P < 0.05) or dextran-treated animals (53%). In the PolyBvHb-treated animals, predominant O2 release (both red blood cells and plasma hemoglobin) occurred in precapillary vessels, whereas in MP4 animals most of the O2 was released from both red blood cells and plasma hemoglobin in capillaries. Base excess correlated directly with capillary O2 release but not systemic O2 content or total O2 release. Higher O2 extraction of both red blood cell and plasma hemoglobin in capillaries represents a new mechanism of action of cell-free hemoglobin. High O2 affinity appears to be an important property for cell-free hemoglobin solutions.     

Blood flow in the capillary bed

From arteries to veins, the blood has to go through the ‘capillary’ blood vessels. These blood vessels are so small that often their diameter is smaller than that of the red blood cells. Intimate interactions occur, therefore, between the blood cells and the blood vessels.

A general survey of recent works on capillary blood flow is given in this article. Some details are presented for two problems: the problem of deformation of the flexible red blood cells, their motion in the capillary blood vessels, and the pressure drop due to the red cell blood vessel interaction; and the problem of the flow of plasma ‘bolus’ between neighboring red cells.

The solution supplies many details about the microcirculation phenomenon. Taken together, a method is offered for the calculation of pressure drop in the capillary as a function of various physical parameters: the red cell volume per unit blood volume, (hematocrit), the ratio of the cell diameter to the blood vessel diameter, the ratio of the length of the blood vessel to its length, the volume of individual red cells, and a parameter relating the cell membrane elasticity, plasma viscosity and the cell velocity.     

Deduction of pulmonary microvascular hematocrit from indicator dilution curves

We have developed a new model describing the relationship between plasma and red cell tracers flowing through the lung. The model is the result of an analysis of the transport of radiolabeled plasma albumin between two flowing phases and shows that differences between red cell and plasma tracer curves are related to microvascular hematocrit. The model was tested in an isolated, blood-perfused dog lung preparation in which we injected⁵¹Cr-labeled red cells and¹²⁵I-labeled plasma albumin into the pulmonary artery. From the tracer concentration-time curves at the venous outflow, we calculatedh _r, the ratio of microvascular hematocrit to large-vessel hematocrit. In 18 baseline experiments,h _r=0.92±0.01 (mn±sem) at a blood flow rate of 10.7±0.3 ml s⁻¹. We determined the effects of (a) glass bead embolization, (b) alloxan, and (c) lobe ligation onh _r. Embolization attenuated the separation between plasma and red cells (increasedh _r), probably as a consequence of passive vasodilation. Alloxan enhanced separation of plasma and red cells (decreasedh _r), possibly as a result of arteriolar vasoconstriction. Ligation of a fraction of the perfused tissue at constant flow did not cause significant change inh _r in the remaining perfused tissue. The model assumes that large-vessel transit times are uniform and that all dispersion occurs in the microvasculature. A theoretical analysis apportioning dispersion between large and small vessels disclosed that the error associated with these assumptions is likely to be less than 15% of the measuredh _r. We conclude from this study that the microvascular hematocrit model describes experimental plasma and red cell curves. The results imply thath _r can be readily deduced from tagged red cells and plasma and can be accounted for in calculating permeability-surface area in diffusing tracer experiments.     

A probabilistic approach for evaluating a technique for an indirect monitoring of the capillary blood flow to the gastric parietal cells

The superficial capillary network of the gastric mucosa can be monitored for red blood cell velocity measurements by a microscopic technique. This network, however, reflects the blood flow in capillaries of more physiological interest, namely those passing by the acid-producing cells and emptying into the superficial network. It is, however, not possible to study these capillaries directly and therefore the problem is to determine in what way and to what degree blood flow measurements in the superficial network reflect the capillary flow of interest. A probabilistic approach where the movements of the red blood cells have been analysed, gives indications of determinable relations between observations on the superficial network flow and the flow passing the acid-producing cells.     

Time-dependent rheological behaviour of blood flow at low shear in narrow horizontal tubes

Magnitude and time-dependence of the effects of red cell aggregation and sedimentation on the rheology of human blood were studied during low shear (tau W 2.5 to 92 mPa) flow through horizontal tubes (ID 25 to 105 microns). Immediately following reduction of perfusion pressure to a low value the red cell concentration near the tube walls decreases as a result of red cell aggregation. This is associated with a transient increase of centerline velocity. Simultaneously, sedimentation begins to occur and eventually leads to the formation of a cell-free supernatant plasma layer. Time-course and extent of this sedimentation process are strongly affected by wall shear stress variation, particularly in the larger tubes. At the lower shear stresses, centerline velocity decreases (flow resistance increases) with time following the initial acceleration period, due to sedimentation of red cells. This is followed by a further increase of resistance caused by the elevation of hematocrit occurring because of the reduction of cell/plasma velocity ratio. The time dependence of blood rheological behaviour under these flow conditions is interpreted to reflect the net effect of the partially counteracting phenomena of sedimentation and red cell aggregation.     

Numerical Simulation of Blood Flow Through Microvascular Capillary Networks

A numerical method is implemented for computing blood flow through a branching microvascular capillary network. The simulations follow the motion of individual red blood cells as they enter the network from an arterial entrance point with a specified tube hematocrit, while simultaneously updating the nodal capillary pressures. Poiseuille’s law is used to describe flow in the capillary segments with an effective viscosity that depends on the number of cells residing inside each segment. The relative apparent viscosity is available from previous computational studies of individual red blood cell motion. Simulations are performed for a tree-like capillary network consisting of bifurcating segments. The results reveal that the probability of directional cell motion at a bifurcation (phase separation) may have an important effect on the statistical measures of the cell residence time and scattering of the tube hematocrit across the network. Blood cells act as regulators of the flow rate through the network branches by increasing the effective viscosity when the flow rate is high and decreasing the effective viscosity when the flow rate is low. Comparison with simulations based on conventional models of blood flow regarded as a continuum indicates that the latter underestimates the variance of the hematocrit across the vascular tree.     

Dynamical clustering of red blood cells in capillary vessels

We have modeled the dynamics of a 3-D system consisting of red blood cells (RBCs), plasma and capillary walls using a discrete-particle approach. The blood cells and capillary walls are composed of a mesh of particles interacting with harmonic forces between nearest neighbors. We employ classical mechanics to mimic the elastic properties of RBCs with a biconcave disk composed of a mesh of spring-like particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, translational and angular momenta. Realistic behavior of blood cells is modeled by considering RBCs and plasma flowing through capillaries of various shapes. Three types of vessels are employed: a pipe with a choking point, a curved vessel and bifurcating capillaries. There is a strong tendency to produce RBC clusters in capillaries. The choking points and other irregularities in geometry influence both the flow and RBC shapes, considerably increasing the clotting effect. We also discuss other clotting factors coming from the physical properties of blood, such as the viscosity of the plasma and the elasticity of the RBCs. Modeling has been carried out with adequate resolution by using 1 to 10 million particles. Discrete particle simulations open a new pathway for modeling the dynamics of complex, viscoelastic fluids at the microscale, where both liquid and solid phases are treated with discrete particles. Figure A snapshot from fluid particle simulation of RBCs flowing along a curved capillary. The red color corresponds to the highest velocity. We can observe aggregation of RBCs at places with the most stagnant plasma flow.     

Plasma ATP during exercise: possible role in regulation of coronary blood flow

It was previously shown that red blood cells release ATP when blood oxygen tension decreases. ATP acts on microvascular endothelial cells to produce a retrograde conducted vasodilation (presumably via gap junctions) to the upstream arteriole. These observations form the basis for an ATP hypothesis of local metabolic control of coronary blood flow due to vasodilation in microvascular units where myocardial oxygen extraction is high. Dogs (n = 10) were instrumented with catheters in the aorta and coronary sinus, and a flow transducer was placed around the circumflex coronary artery. Arterial and coronary venous plasma ATP concentrations were measured at rest and during three levels of treadmill exercise by using a luciferin-luciferase assay. During exercise, myocardial oxygen consumption increased approximately 3.2-fold, coronary blood flow increased approximately 2.7-fold, and coronary venous oxygen tension decreased from 19 to 12.9 mmHg. Coronary venous plasma ATP concentration increased significantly from 31.1 to 51.2 nM (P < 0.01) during exercise. Coronary blood flow increased linearly with coronary venous ATP concentration (P < 0.01). Coronary venous-arterial plasma ATP concentration difference increased significantly during exercise (P < 0.05). The data support the hypothesis that ATP is one of the factors controlling coronary blood flow during exercise.