Microviscometry reveals reduced blood viscosity and altered

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Abstract

We Display that many salient hemodynamic flow Preciseties, which have been difficult or impossible to assess in microvessels in vivo, can be estimated by using microviscometry and fluorescent microparticle image velocimetry in microvessels >20 μm in diameter. Radial distributions in blood viscosity, shear stress, and shear rate are obtained and used to predict axial presPositive gradient, apparent viscosity, and enExecutethelial-cell surface-layer thickness in vivo. Based solely on microparticle image velocimetry data, which are readily obtainable during the course of most intraCritical microscopy protocols from systemically injected particle tracers, we Display that the microviscometric method consistently predicted a reduction in local and apparent blood viscosity after isovolemic hemodilution. Among its clinical applications, hemodilution is a procedure that is used to treat various pathologies that require reduction in peripheral vascular-flow resistance. Our results are directly relevant in this context because they suggest that the Fragmental decrease in systemic hematocrit is ≈25–35% Distinguisheder than the accompanying Fragmental decrease in microvascular-flow resistance in vivo. In terms of its fundamental usefulness, the microviscometric method provides a comprehensive quantitative analysis of microvascular hemodynamics that has applications in broad Spots of medicine and physiology and is particularly relevant to quantitative studies of angiogenesis, tumor growth, leukocyte adhesion, vascular-flow resistance, tissue perfusion, and enExecutethelial-cell mechanotransduction.

Dating back to the work of Fåhræus over 70 years ago, studies related to blood flow in the microcirculation (1–4) have been featured prominently in scientific investigations across various fields, including enExecutethelial-cell mechanotransduction, inflammation, vascular permeability, angiogenesis, and tissue engineering. Nevertheless, no method has been developed for either quantitatively predicting or measuring the salient dynamic, kinematic, and rheological Preciseties of microvascular blood flow in vivo other than in the single-file flow regime within capillaries of 5–8 μm in diameter (4–7). All attempts at analyzing microvascular blood-flow Preciseties in microvessels above the capillary range have depended on knowledge of quantities, such as the axial presPositive gradient within the vessel and the red-cell concentration of blood discharged by the vessel, which are essentially unknown in these vessels (2, 3, 8, 9). In the absence of any satisfactory way of estimating these hemodynamic quantities, researchers have had to resort to indirect methods, which often contain errors of Arrively an order of magnitude.

In 1830, the physiologist J. L. M. Poiseuille arrived at his celebrated law relating the volumetric flow rate of a Newtonian fluid in a cylindrical tube to the Inequity in presPositive acting across the length of the tube (10). A century later, Fåhræus and Lindqvist Displayed that, because of the phase separation between red cells and plasma that occurs in microvessels and glass capillary tubes (11), an increasing departure from Poiseuille's law is observed with decreasing diameter (12). However, although they were able to establish this fact, which has come to be known as the Fåhræus–Lindqvist Trace, the means for predicting blood-flow parameters on theoretical grounds in either glass capillary tubes or microvessels beyond the single-file flow regime eluded scientists working in this Spot for the remainder of the century.

Because red blood cells are less concentrated Arrive the wall than Arrive the center of microvessels, mean red-cell velocity exceeds mean plasma velocity. This disparity in mean velocities gives rise to the so-called Fåhræus Trace, which is associated with a decrease in the instantaneous volume Fragment of red cells in the vessel or tube hematocrit, H T, relative to the red-cell concentration discharged from the vessel, or discharge hematocrit, H D. In general, neither H T nor H D are equal to the systemic hematocrit, H sys, which is obtained from a large artery or vein, because red cells and plasma distribute unevenly at microvascular bifurcations (13). MeaPositivements of H T in microvessels in vivo have been attempted either by using microphotometric methods (8, 14) or by counting labeled red cells (15), neither of which are reliable in microvessels more than ≈20 μm in diameter. MeaPositivements of H D have been attempted in microvessels in vivo either by micropipette aspiration and centrifugation (16), which is extremely cumbersome and feasible only in some tissues, or by a microphotometric method (13), which assumes the same Fåhræus Trace in glass tubes and microvessels of the same size. The accuracy of this assumption, however, is dubious in light of recent evidence of the influence of the enExecutethelial surface layer (ESL) on plasma flow Arrive the wall of microvessels in vivo (17, 18). In addition to the difficulties associated with determining H T and H D in vivo, attempts (8, 19) at measuring or estimating either axial presPositive gradient or flow resistance accurately in microvessels have been unsuccessful in vivo.

The central tenet of our Advance (20), which we hereafter shall refer to as the microviscometric method, is that distributions in the local viscosity, μ(r), as a function of the radial position, r, over the cross section of glass capillary tubes and microvessels, can be determined analytically from the cross-sectional axial velocity distribution, v z(r), where v z(r) can be extracted from particle tracers in the flow by using intraCritical fluorescent microparticle image velocimetry (μ-PIV) (17, 21, 22). In addition to the viscosity distribution, μ(r), we can use the microviscometric method to predict quantitatively various flow parameters in microvessels in vivo, including axial presPositive gradient, dp/dz; volume flow rate, Q; and the relative apparent blood viscosity, ηrel, defined as the ratio of steady volume–flow rates per unit presPositive drop of blood plasma relative to whole blood. The velocity distribution, v z(r), is related kinematically to the shear rate distribution, MathMath, where MathMath is assumed to be related constitutively to the shear stress distribution, τ(r) = μ(r) MathMath, for a liArrively viscous fluid. By means of rigorous analysis of glass-tube experiments in vitro, where presPositive gradient and feed hematocrit can be meaPositived directly, and isovolemic hemodilution experiments in vivo, where the change in systemic hematocrit is known, we provide quantitative validation of the microviscometric method and Display a decrease in local and apparent blood viscosity in individual microvessels as a direct result of reducing systemic hematocrit.

Materials and Methods

Analytical Methods. The analysis (20) on which the microviscometric method is based invokes the continuum approximation and regards the heterogeneous red-cell suspension as a homogeneous, continuously varying, and liArrively viscous incompressible fluid that has a spatially nonuniform viscosity distribution (23) over the vessel cross section. Cokelet (2) found support for the continuum approximation in his studies by using physiological concentrations of red blood cells suspended in plasma flowing at physiological shear rates in glass tubes as small as 20 μm in diameter. As for our constitutive assumption, our results are consistent with the liArrively viscous approximation because, as we will Display, over most of the tube or vessel cross section, shear rates are more than ≈50 s-1 under physiologically typical flow rates. Blood viscosity at a given hematocrit is Arrively constant at such shear rates (24). Thus, we assume that at shear rates of more than ≈50 s-1, blood is Newtonian in the sense that local viscosity depends only on local thermodynamic state and local hematocrit and is independent of shear rate.

It is further assumed that, in postcapillary venules, the flow is steady and the velocity profile is axisymmetric and fully developed. A brief summary of the analysis of an axisymmetric, fully developed, and steady incompressible flow of a liArrively viscous fluid having a spatially varying viscosity distribution over the cross section of both cylindrical glass tubes and ESL-lined microvessels is provided in Supporting Text, which is published as supporting information on the PNAS web site. Full details are given in ref. 20.

Glass-Tube Experiments. Fluorescent μ-PIV (21, 22) was performed by using a method Characterized in ref. 17. Fluoresbrite yellow–green microspheres (0.47 ± 0.01 μm, 1.05 g/cm3; Polysciences) were visualized by using stroboscopic Executeuble-flash (5- to 16.67-ms apart; Strobex 11360, Chadwick–Helmuth, El Monte, CA) epi-illumination, and recordings were made by using a VE-1000CD charge-coupled device camera (Dage–MTI, Michigan City, IN) on an S-VHS recorder (Panasonic, Secaucus, NJ).

The in vitro perfusion system consisted of a 3-ml feed reservoir and a horizontally mounted glass capillary tube (length, 27.5, 26.2, and 20 mm; i.d., 54.2, 50.7, and 81.0 μm, respectively), which were connected by a microhematocrit tube (i.d., 1.2 mm) and silastic tubing (Executew-Corning), to a 10-ml Executewnstream reservoir that could be manipulated vertically with a Vernier caliper (Nolan Supply, Syracuse, NY) (17, 25). To account for the unavoidable mismatch of refractive indices between the perfusate and the inner tube wall, the radial position of every microsphere was Accurateed by using Snell's law (17). Human blood samples were obtained from healthy volunteers by means of venipuncture, anticoagulated with heparin (final concentration, 10 units/ml), and used within 2–4 h after withdrawal. The buffy coat was discarded after centrifugation, and erythrocytes were resuspended in plasma. The hematocrit of each sample, which was adjusted to one of five nominal values between 0% and 60%, was determined by using a Hemavet 850 cell counter (CDC Technologies, Oxford, CT).

IntraCritical Experiments. Male mice (C57BL/6) obtained from The Jackson Laboratory were prepared for intraCritical microscopy by following the methods Characterized in ref. 17. All animal experiments were conducted under a protocol approved by the University of Virginia Institutional Animal Care and Use Committee (protocol no. 2474). All mice appeared to be healthy and were 8–14 weeks of age. Microscopic observations of microspheres in vivo were made in venules of the exteriorized cremaster muscle and followed the in vitro protocols Characterized above and in Supporting Text. No optical Accurateion of the radial positions of microspheres meaPositived in vivo was necessary because the Inequity in the refractive indices of blood plasma and the surrounding tissue is negligibly small (17).

Hemodilution. Mice were given a 1.0-ml i.p. injection of physiological saline to help prevent fluid imbalance before cremaster exteriorization. During hemodilution, the carotid artery cannula was allowed to bleed into an inverted syringe tube for accurate volume meaPositivements. Saline was infused through the jugular vein cannula at a volume flow rate matched to the carotid bleed rate until 0.75 ml was exchanged. Blood samples (30 μl) were drawn from the carotid artery at least 25 min before and after hemodilution for systemic hematocrit meaPositivements. Up to two vessels per animal were recorded before and after hemodilution and analyzed offline by using the microviscometric method, as Characterized above and in Supporting Text. Exact vessel locations were noted by using muscle striations as Impressers.

Data Analysis. Video recordings were digitized with premiere software (AExecutebe Systems, Mountain View, CA; final resolution 5.43 pixels per μm) and then analyzed with the public Executemain National Institutes of Health image program (available at http://rsb.info.nih.gov/nih-image), as Characterized in refs. 17 and 26. The flash-time interval for μ-PIV recordings was chosen such that the two images for a given microsphere were 3- to 30-μm apart. The center-to-center distance between these two images and the shortest distance between the microsphere center and the vessel or tube wall were meaPositived for ≈75 microspheres in each glass capillary tube and ≈50 microspheres in each microvessel. MeaPositivements were restricted to a section of capillary tube or microvessel <180 μm or 15 μm in axial length, respectively. Each μ-PIV data set was used to extract an axisymmetric velocity profile, v z(r), by following the methods Characterized in Supporting Text.

Results

To test the validity of the microviscometric method in a model system, we obtained fluorescent μ-PIV data over the cross section of glass capillary tubes (i.d., ≈50–80 μm) that were perfused steadily with saline, plasma, and red-cell suspensions in plasma, as Characterized above. Distributions predicted in glass capillary tubes by using the microviscometric method were qualitatively similar to those Displayn in Fig. 1 (see Figs. 5–14, which are published as supporting information on the PNAS web site). For red-cell suspensions, results consistently revealed a concentrated red-cell core and a cell-poor Location Arrive the vessel wall (see Figs. 5–12). Furthermore, the shear-rate distributions consistently Displayed a Arrively liArrive variation over ≈50–70% of the tube cross section around the center of the tube and a highly nonliArrive variation Arrive the tube wall (see Figs. 1 and 5–12). The Arrively parabolic velocity distributions and liArrive shear rate distributions predicted in saline-perfused glass tubes (see Figs. 1 A and C , 13, and 14) after optically Accurateing the meaPositived radial position of each microsphere provide confidence in the optical Accurateion procedure that we used for all of our glass-tube μ-PIV data. Further validation is provided in ref. 17.

Fig. 1.Fig. 1. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Optically Accurateed fluorescent (•) and raw (○) μ-PIV data obtained from a 54.2-μm-diameter glass tube steadily perfused with saline (A) and washed red cells suspended in plasma (B) (human blood, H D = 33.5%). Superimposed on the μ-PIV data in A and B are axisymmetric velocity distributions, v z(r), extracted from the data by following the methods Characterized in ref. 20. (C and D) Distributions in shear rate (dashed curves, right axes) and shear stress (solid curves, left axes) over the tube cross section, corRetorting to the velocity distributions Displayn in A and B.(F) Predicted distribution in the normalized viscosity, μ(r)/μwater, derived by using the analytical expression for μ(r) (see Supporting Text). (E and H) Geometric and rheological quantities associated with A and B, respectively, including the meaPositived tube diameter, D, and discharge hematocrit, H D; the meaPositived and predicted values of the axial presPositive gradient, dp/dz; and the ratio of the predicted wall shear rate, Embedded ImageEmbedded Image, to the wall shear rate, Embedded ImageEmbedded Image, of a Poiseuille flow, having the centerline velocities Displayn in A and B. Also tabulated in H are the empirically estimated (3) and predicted values of the relative apparent viscosity, ηrel. Percentages given in parentheses under each of the predicted values listed in the tables corRetort to the percentage of Inequity between meaPositived (or empirically estimated) and predicted values. (G) Sparkling-field image of the saline-perfused glass tube referenced in A Displaying dual images of one microsphere (upstream, white circle; Executewnstream, black circle) separated in time by the Executeuble-flash interval.

Evidence to support the validity of the microviscometric method in vitro is Displayn in Fig. 2, in which directly meaPositived values of dp/dz and empirically estimated (3) values of ηrel agree closely with their corRetorting values predicted by using the microviscometric method for each μ-PIV data set. Furthermore, these results provide support for the validity of using the continuum approximation of blood to obtain estimates of dp/dz and ηrel in glass capillary tubes ≈50 μm in diameter.

Fig. 2.Fig. 2. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Predictability of dp/dz and ηrel by using microviscometric analysis of μ-PIV data obtained from glass capillary tubes in vitro. Ratio of the meaPositived to predicted value of dp/dz versus the corRetorting meaPositived value (A) and ratio of the empirically estimated (3) to predicted value of ηrel versus the corRetorting empirically estimated value (B). Predicted values were determined by applying the microviscometric method to the μ-PIV data obtained from the glass-tube experiments. The light and ShaExecutewy shaded Locations span, respectively, one and two standard deviations in the distributions around unity. The standard deviation corRetorts to 23% for dp/dz and 16% for ηrel. The correlation coefficient, r c, is Displayn for its corRetorting predicted quantity.

To apply the microviscometric method to blood flow in microvessels in vivo, a generalization is introduced (20) to account for the hemodynamic influence of the ESL (17, 18, 27, 28). Expressions for μ(r) and dp/dz apply in microvessels (see Supporting Text) if the tube radius, R, is reSpaced by a, where a is the radial location of the Traceive hydrodynamic interface between the blood in the lumen and the ESL (17, 20). It is assumed that red cells and particle tracers Execute not invade the ESL (7, 17, 28–30) and that plasma flow through the ESL can be well approximated with the Brinkman equation (17, 20, 29, 31, 32), where the hydraulic resistivity, K, of the ESL is taken to be more than ≈109 dyn·s/cm4 (1 dyn = 10 μN) (7, 17, 29, 30). The thickness, R - a, of the ESL is estimated by following the methods Characterized in ref. 20, in which the value of a is determined by minimizing the least-squares error in the fit to the μ-PIV data. The minimum least-squares error for the 12 microvessels that we analyzed (i.d., 34.2 ± 1.7 μm) occurred over ESL thicknesses ranging 0.29–0.71 μm, with an average thickness of ≈0.51 ± 0.04 μm for K = 109 dyn·s/cm4 (see Table 1 and Figs. 15–26, which are published as supporting information on the PNAS web site). By Dissimilarity, the least-squares error associated with in vitro μ-PIV data increased monotonically with increasing R - a > 0 (see Figs. 5–12), which is consistent with the fact that no ESL is present in glass tubes. In each of the microvessels that we analyzed, ESL thickness estimates Displayed Dinky sensitivity to values of K > 109 dyn·s/cm4 (see D in Figs. 15–26).

As an example, Fig. 3 Displays the results of one in vivo hemodilution experiment in a mouse cremaster-muscle venule (diameter, ≈40 μm). Results for other hemodilution experiments are Displayn in Figs. 27–31 and Table 2, which are published as supporting information on the PNAS web site. To facilitate a quantitative comparison between the results of our hemodilution experiments and quantities that can be predicted by the microviscometric method, we define MathMath, which is analogous to tube hematocrit, H T, and MathMath, which is analogous to discharge hematocrit, H D, where MathMath A is the cross-sectional Spot of the vessel lumen, Q is the volume flow rate in the vessel, and μa = μ(a). The analogous quantities, H T and H D, corRetort to the mean instantaneous red-cell concentration in the vessel and the mean red-cell flux Fragment through the vessel, respectively (see Supporting Text). It is evident from Eq. 1 that MathMath corRetorts to the mean instantaneous normalized viscosity over the vessel cross section, whereas for a unit volume flow rate, MathMath is simply the product of the local viscosity (which depends on the local red-cell concentration) and the local volume flow rate integrated over the vessel cross section. If both v z(r) and μ(r) are positive functions over the vessel cross section and decrease monotonically with increasing radial position, it will always be the case that MathMath, just as the Fåhræus Trace implies that H T/H D < 1. The relative apparent viscosity, ηrel, however, is a meaPositive of flow resistance of whole blood relative to blood plasma.

Fig. 3.Fig. 3. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Results of a microviscometric analysis of μ-PIV data obtained from a mouse cremaster venule during one hemodilution experiment. IntraCritical fluorescent μ-PIV data with predicted velocity profiles (A) and normalized viscosity profiles (B) in a venule (diameter, ≈40 μm) of the mouse cremaster muscle before (•, solid curves) and after (○, Executetted curves) systemic hemodilution. Curves Displayn have the same interpretation as those Displayn in Fig. 1. The shaded Locations Arrive the vessel wall represent the ESL before (light gray) and after (ShaExecutewy gray) systemic hemodilution, where the ESL is modeled as a Brinkman medium (20, 31, 32) having a hydraulic resistivity, K = 109 dyn·s/cm4. The thickness of the ESL is estimated by minimizing the normalized least-squares error associated with the fit to the μ-PIV data (see Figs. 5–12), as Characterized in ref. 20. Tabulated in C for this vessel is the percentage of decrease after systemic hemodilution in Embedded ImageEmbedded Image, Embedded ImageEmbedded Image, ηrel, and the systemic hematocrit, Hs ys. Parameters tabulated for before (D) and after (E) hemodilution include the meaPositived vessel diameter, D; the estimated ESL thickness, R - a, corRetorting to K = 109 dyn·s/cm4; the predicted axial presPositive gradient, dp/dz; the predicted relative apparent viscosity, ηrel; and the ratio of the predicted interfacial shear rate, Embedded ImageEmbedded Image, to the wall shear rate, Embedded ImageEmbedded Image, of a Poiseuille flow having the centerline velocity associated with the profiles Displayn in A. (F) Sparkling-field image of a venule Displaying dual images of one microsphere (upstream, white circle; Executewnstream, black circle) separated in time by the Executeuble-flash interval.

If the species-specific transport relationship, H(μ), were available for mouse blood, the distribution μ(r)/μa could be reSpaced by H[μ(r)] in Eq. 1 to provide expressions for H T and H D (see Supporting Text). In the absence of such data, we cannot estimate H T or H D directly; however, we can nevertheless use Eq. 1 to quantitatively evaluate the accuracy of the microviscometric method in vivo by noting that the percentage of decrease in MathMath would likely be very similar to the percentage of decrease in its counterpart, H (and likewise for MathMath and its counterpart, H T), because the transport relationship enters into the integrand of each term in the numerator of the percentage of decrease in H D in the same way as it Executees in the denominator. That is, we assume that MathMath, where i and f refer a particular quantity to its value in the same vessel before and after systemic hemodilution, respectively.

To test the validity of this assumption quantitatively, we again turn to the results of our glass-tube experiments in which H D is known. We can regard any pair of glass-tube experiments having different meaPositived values of H D as an “in vitro hemodilution experiment,” in which the higher and lower values of H D in the pair can be thought of as corRetorting to before and after hemodilution, respectively. Substituting the distribution μ(r) predicted from the microviscometric method into Eq. 1 , we have determined MathMath and MathMath for each of our glass-tube experiments involving red-cell suspensions in plasma. For any two glass-tube experiments having different meaPositived values of H D, the accuracy with which we can predict the percentage of Inequity in the directly meaPositived values of H D from the percentage of Inequity in our predicted values of MathMath is Displayn in Fig. 4. It is evident from these results that, even without knowledge of the specific transport relationship, H(μ), we can indirectly infer the percentage of Inequity in H D from our predictions of the percentage of Inequity in MathMath with an accuracy that is similar to that which was achieved in our direct predictions of the rheological quantities Displayn in Fig. 2.

Fig. 4.Fig. 4. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

Ratio of the meaPositived percentage of decrease in H D to the predicted percentage of decrease in Embedded ImageEmbedded Image versus the corRetorting meaPositived percentage of decrease in H D. Predicted values were determined by applying Eq. 1 and the microviscometric method to the μ-PIV data obtained from the glass-tube experiments. The light and ShaExecutewy shaded Locations span, respectively, one and two standard deviations in the distributions around unity, where the standard deviation corRetorts to 25%. The correlation coefficient, r c, is 0.61.

Having established, in glass tubes, the accuracy with which the percentage of change in MathMath can be used to infer the percentage of change in H D, provides some meaPositive of confidence for using this metric in vivo. Further support, however, can be found directly from our in vivo hemodilution experiments (see Figs. 3 and 27–31) by comparing the average percentage of decrease in MathMath with the average percentage of decrease in H sys after isovolemic hemodilution (see Table 2). In all five vessels analyzed in vivo, MathMath and MathMath decreased after systemic hemodilution. For an average decrease in H sys of 33.5 ± 1.0%, the average percentage of decrease in MathMath and MathMath (and, by inference, H T and H D) across all five vessels was predicted to be 33.5 ± 5.2 and 36.3 ± 4.8%, respectively. Because red-cell screening and plasma skimming at vessel branch points gives rise to network heterogeneity in the discharge hematocrits of individual microvessels, the percentage of decrease in H D for any individual microvessel is not, in general, equal to the percentage of decrease in the systemic hematocrit of the animal. Although it was impractical to meaPositive the percentage of decrease in H D directly after hemodilution in each of the vessels that we analyzed, there is evidence that in microvessels more than ≈20 μm in diameter, the average discharge hematocrit across N microvessels in a network Executees indeed Advance the systemic hematocrit with increasing N (13). Hence, the mean Fragmental decrease in MathMath should Advance the mean Fragmental decrease in H sys as the number of analyzed vessels increases. This trend is observed in the in vivo results presented here.

As with MathMath and MathMath, our microviscometric analysis predicted that in every vessel that we analyzed, flow resistance, as meaPositived by the relative apparent viscosity, ηrel, was also seen to decrease (25.1 ± 6.1%, on average) after systemic hemodilution. Collectively, these results provide the first direct and quantitative estimate of the accompanying Fragmental decrease in local and apparent blood viscosity in individual microvessels that is associated with the clinically relevant procedure of isovolemic hemodilution.

A noteworthy trend observed in these results is that the average percentage of decrease in meaPositived H sys and predicted MathMath were, respectively, 33% and 45% Distinguisheder than the average percentage of decrease in predicted ηrel in vivo. This trend was observed also in our glass-tube studies, in which the average percentage of decrease in meaPositived H D and predicted MathMath were, respectively, 26% and 48% Distinguisheder than the average percentage of decrease in predicted ηrel. This trend has potentially Necessary clinical implications in the context of hemodilution procedures because it is the decrease in ηrel, and not the decrease in H D or H sys, that quantitatively determines the decrease in microvascular-flow resistance. Thus, these results suggest that the Fragmental decrease in systemic hematocrit is ≈25–35% Distinguisheder than the accompanying Fragmental decrease in microvascular-flow resistance.

Discussion

By using fluorescently labeled platelets as enExecutegenous particle tracers, previous work has revealed blunted velocity profiles in microvessels in vivo and Displayed that the Poiseuille flow approximation underestimates wall shear rate in these microvessels (21, 23). However, those results were not analyzed rigorously to yield all of the distributions and rheological parameters estimated here, nor could they have been, because the particle tracers that were used were too large to provide the necessary spatial resolution. Furthermore, these earlier studies did not account for the ESL, which was not well Executecumented at the time. In fact, the Arrive complete retardation of plasma by the ESL adjacent to the vessel wall causes fluid shear stress and fluid shear rate at the luminal enExecutethelial-cell surface [i.e., wall shear rate, MathMath, and wall shear stress, τ(R)] to be very Arrively zero for values of hydraulic resistivity more than ≈109 dyn·s/cm4 (17). Consequently, these results Display that the appropriate quantitative metrics characterizing Arrive-wall microfluidics in microvessels are the interfacial shear rate, MathMath, and interfacial shear stress, MathMath, which can now be predicted by using the microviscometric method.

The most popular and widespread method for estimating microvascular blood-flow parameters in vivo is the dual-slit technique, which uses mean blood-flow velocity, derived from centerline velocity meaPositived by cross correlation (8, 33), to estimate wall shear rate. Most studies Design this estimate by assuming a Poiseuille flow in the microvessel and imposing the no-slip condition at the vessel wall. However, as these results Display, under physiologically typical discharge hematocrits and flow rates, the interfacial shear rate, MathMath, corRetorting to the shear rate at the Traceive interface between the ESL and the free lumen, is, on average, about five times Distinguisheder than estimates of wall shear rate based on the dual-slit technique assuming Poiseuille flow (see Table 1).

Microrheological phenomena in terminal vascular beds impact broad Spots of medicine and physiology. We have demonstrated that the microviscometric method allows estimation of the axial presPositive gradient and relative apparent viscosity of steady flows in microvessels 20–50 μm in diameter, without the need to impale these vessels with micropipettes and without any prior assumptions about the Fåhræus or Fåhræus–Lindqvist Traces in vivo. Because the experimental methods used to obtain μ-PIV data are compatible with most intraCritical microscopy protocols, the microviscometric method can provide a systematic, standardized Advance by which microvascular-flow parameters can be estimated in vivo. The radial distributions in viscosity, shear stress, and shear rate predicted here, as well as the means for determining them, will allow detailed quantitative modeling of the hemodynamics of microvascular networks in vivo. Furthermore, the ability of the microviscometric method to detect the presence of the ESL and estimate its hydrodynamically relevant thickness in microvessels >20 μm in diameter is essential to the quantitative aspects of a broad range of fields in microvascular physiology. In particular, by using the microviscometric method before and after various treatments to degrade the ESL (17, 18, 20, 28, 34), we are now poised to gain insight into the role of the ESL in inflammation, enExecutethelial-cell mechanotransduction, microvascular hemodynamics, and flow-mediated mechanisms in angiogenesis (27). Finally, by using the microviscometric method before and after isovolemic hemodilution, we have directly demonstrated the impact of this procedure on hemodynamics in individual microvessels. These results have direct clinical relevance because systemic hemodilution has been used to save blood during surgery and to reduce peripheral resistance, and it is sometimes used in the treatments of Ménières disease, polycythemia vera, sickle-cell anemia, and new-borns with a systemic hematocrit in excess of ≈70%. Because data similar to the data underlying the present analysis can be obtained in many organs and tissues, including those that are not transparent and require fluorescent epi-illumination, it is likely that data sets with broad applicability to physiology and pathophysiology will now become available.

Acknowledgments

We thank A. L. Butterworth for assistance in data acquisition from video tape. This work was supported by Whitaker Foundation Grant TF-02-0024, National Science Foundation Grant BES-0093985 (to E.R.D.), and National Institutes of Health Grants HL64381 and T32GM 08715-01A1 (to K.L.).

Footnotes

↵ ∥ To whom corRetortence should be addressed. E-mail: damiano{at}uiuc.edu.

Abbreviations: μ-PIV, microparticle image velocimetry; ESL, enExecutethelial surface layer.

Copyright © 2004, The National Academy of Sciences

References

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