Microviscometry reveals reduced blood viscosity and altered shear rate and shear stress profiles in microvessels after hemodilution

Abstract

We show that many salient hemodynamic flow properties, 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 microm in diameter. Radial distributions in blood viscosity, shear stress, and shear rate are obtained and used to predict axial pressure gradient, apparent viscosity, and endothelial-cell surface-layer thickness in vivo. Based solely on microparticle image velocimetry data, which are readily obtainable during the course of most intravital microscopy protocols from systemically injected particle tracers, we show 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 fractional decrease in systemic hematocrit is approximately 25-35% greater than the accompanying fractional 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 areas of medicine and physiology and is particularly relevant to quantitative studies of angiogenesis, tumor growth, leukocyte adhesion, vascular-flow resistance, tissue perfusion, and endothelial-cell mechanotransduction.

Fig. 1.

Optically corrected 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 described in ref. . (C and D) Distributions in shear rate (dashed curves, right axes) and shear stress (solid curves, left axes) over the tube cross section, corresponding to the velocity distributions shown in A and B.(F) Predicted distribution in the normalized viscosity, μ(r)/μ_water, 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 measured tube diameter, D, and discharge hematocrit, H_D; the measured and predicted values of the axial pressure gradient, dp/dz; and the ratio of the predicted wall shear rate, , to the wall shear rate, , of a Poiseuille flow, having the centerline velocities shown in A and B. Also tabulated in H are the empirically estimated (3) and predicted values of the relative apparent viscosity, η_rel. Percentages given in parentheses under each of the predicted values listed in the tables correspond to the percentage of difference between measured (or empirically estimated) and predicted values. (G) Bright-field image of the saline-perfused glass tube referenced in A showing dual images of one microsphere (upstream, white circle; downstream, black circle) separated in time by the double-flash interval.

Fig. 2.

Predictability of dp/dz and η_rel by using microviscometric analysis of μ-PIV data obtained from glass capillary tubes in vitro. Ratio of the measured to predicted value of dp/dz versus the corresponding measured value (A) and ratio of the empirically estimated (3) to predicted value of η_rel versus the corresponding 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 dark shaded regions span, respectively, one and two standard deviations in the distributions around unity. The standard deviation corresponds to 23% for dp/dz and 16% for η_rel. The correlation coefficient, r_c, is shown for its corresponding predicted quantity.

Fig. 3.

Results of a microviscometric analysis of μ-PIV data obtained from a mouse cremaster venule during one hemodilution experiment. Intravital 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 (○, dotted curves) systemic hemodilution. Curves shown have the same interpretation as those shown in Fig. 1. The shaded regions near the vessel wall represent the ESL before (light gray) and after (dark 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 described in ref. . Tabulated in C for this vessel is the percentage of decrease after systemic hemodilution in , , η_rel, and the systemic hematocrit, H_sys. Parameters tabulated for before (D) and after (E) hemodilution include the measured vessel diameter, D; the estimated ESL thickness, R - a, corresponding to K = 10⁹ dyn·s/cm⁴; the predicted axial pressure gradient, dp/dz; the predicted relative apparent viscosity, η_rel; and the ratio of the predicted interfacial shear rate, , to the wall shear rate, , of a Poiseuille flow having the centerline velocity associated with the profiles shown in A. (F) Bright-field image of a venule showing dual images of one microsphere (upstream, white circle; downstream, black circle) separated in time by the double-flash interval.

Fig. 4.

Ratio of the measured percentage of decrease in H_D to the predicted percentage of decrease in versus the corresponding measured 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 dark shaded regions span, respectively, one and two standard deviations in the distributions around unity, where the standard deviation corresponds to 25%. The correlation coefficient, r_c, is 0.61.