The effect of small changes in hematocrit on nitric oxide transport in arterioles

Abstract

We report the development of a mathematical model that quantifies the effects of small changes in systemic hematocrit (Hct) on the transport of nitric oxide (NO) in the microcirculation. The model consists of coupled transport equations for NO and oxygen (O2) and accounts for both shear-induced NO production by the endothelium and the effect of changing systemic Hct on the rate of NO production and the rate of NO scavenging by red blood cells. To incorporate the dependence of the plasma layer width on changes in Hct, the model couples the hemodynamics of blood in arterioles with NO and O2 transport in the plasma layer. A sensitivity analysis was conducted to determine the effects of uncertain model parameters (the thicknesses of endothelial surface layers and diffusion coefficients of NO and O2 in muscle tissues and vascular walls) on the model's predictions. Our analysis reveals that small increases in Hct may raise NO availability in the vascular wall. This finding sheds new light on the experimental data that show that the blood circulation responds to systematic increases of Hct in a manner that is consistent with increasing NO production followed by a plateau.

FIG. 1

Cross section of an arteriole. A version of the Krogh tissue cylinder model used in our analysis consists of RBC-rich core, RBC-free plasma layer, glycocalyx, endothelium, vascular wall, and smooth muscle tissue. RBC, red blood cell.

FIG. 2.

Blood velocity profiles corresponding to the two-phase flow model and their parabolic and plug-flow counterparts used in the previous analyses (5, 9).

FIG. 3.

Relationship between shear stress and systemic Hct for a vessel diameter of 40 μm (calculated using equation [22]). Hct, hematocrit.

FIG. 4.

Dependence of (a) R_NO,_max on shear stress for different values of the exponent m, and (b) eNOS activation on shear stress, for different dosages of rampmycin in mice. C, control; LD, low dosage; HD, high dosage. Experimental data from ref. (6). AU signifies arbitrary units used by the authors of ref. (6) to quantify eNOS activation. NO, nitric oxide.

FIG. 5.

Profiles of (a) NO concentration and (b) O2 partial pressure for several systemic Hct with the diffusion coefficients of NO and O2 same in all layers. O2, oxygen.

FIG. 6.

Profiles of (a) NO concentration and (b) O2 partial pressure for several systemic Hct. The model with fixed R_NO,max and the variable diffusion coefficients (D_r = 0.5).

FIG. 7.

Profiles of (a) NO concentration and (b) O2 partial pressure for 45% systemic Hct, with the model that accounts for the spatial variability of the diffusion coefficients (D_r = 0.5, dotted lines) and with model that ignores their variability (solid lines).

FIG. 8.

Profiles of (a) NO concentration and (b) O2 partial pressure for several systemic Hct. The model with shear-dependent R_NO,_max (equation [24] with m = 5) and the variable diffusion coefficients (D_r = 0.5).

FIG. 9.

The dependence of peak NO concentration on systemic Hct predicted by the shear-dependent NO production model with the constitutive equation [24] and several values of the exponent m.

FIG. 10.

The dependence of peak NO concentration on systemic Hct for several values of glycocalyx thickness.

FIG. 11.

Plasma layer (cell-free layer or CFL) width as a function of systemic Hct in rat cremaster muscles arterioles of 20–30 μm diameter.