Assessment and impact of heterogeneities of convective oxygen transport parameters in capillaries of striated muscle: experimental and theoretical

Abstract

Convective oxygen transport parameters were determined in arteriolar (n = 5) and venular (n = 5) capillary networks in the hamster cheek pouch retractor muscle. Simultaneously determined values of red blood cell velocity, lineal density, red blood cell frequency, hemoglobin oxygen saturation (SO2), oxygen flow (QO2), longitudinal SO2 gradient, and diameter were obtained in a total of 73 capillaries, 39 at the arteriolar ends of the network (arteriolar capillaries) and 34 at the venular ends (venular capillaries). We found that the hemodynamic variables were not different at the two ends. However, not unexpectedly, SO2 and QO2 were significantly higher at the upstream end of arteriolar capillaries (60.8 +/- 9.8 (SD)% and 0.150 +/- 0.081 pl/sec, respectively) compared with the downstream end of venular capillaries (39.9 +/- 13.6% and 0.108 +/- 0.095 pl/sec, respectively). Heterogeneities in red blood cell velocity, lineal density, SO2, and QO2, assessed by their coefficients of variation, were significantly greater in venular capillaries. To evaluate the impact of these heterogeneities on oxygen exchange, we incorporated these unique experimental data into a mathematical model of oxygen transport which accounts for variability in red blood cell frequency, lineal density, inlet SO2, capillary diameter, and, to some degree, capillary flow path lengths. An unexpected result of the simulation is that only the incorporation of variability in capillary flow path lengths had any marked effect on the heterogeneity in end-capillary SO2 in resting muscle due to extensive diffusional shunting of oxygen among adjacent capillaries. We subsequently evaluated, through model simulations, the effect of these heterogeneities under conditions of increased flow and high oxygen consumption. Under these conditions, the model predicts that heterogeneities in the hemodynamic parameters will have a marked effect on oxygen transport in this muscle.

FIG. 1.

Example of an arteriolar capillary network showing all readily distinguishable portions of capillaries. An arteriolar capillary is defined as that portion of the total capillary pathway which is in the same projected microscopic field as the arteriole which feeds it. The dashed lines represent capillaries which were barely visible and thus were not sampled for technical reasons. Note the relatively straight capillaries that are typical of both arteriolar and venular capillaries in the hamster retractor muscle.

FIG. 2.

Histograms of red blood cell velocity (v), lineal density (N), red blood cell fequency (f), oxygen saturation (SO₂), oxygen flow (Q0₂), and the longitudinal oxygen saturation gradient (ΔS0₂/Δz) in arteriolar and venular capillaries.

FIG. 3.

Average coefficients of variation (CV) of oxygen transport parameters obtained for five arteriolar (open bars) and five venular (hatched bars) capillary networks. ** and * indicate significant difference between data obtained for arteriolar and venular capillary networks at P < 0.01 and P < 0.05, respectively.

FIG. 4.

Geometry of the theoretical models: (A) Constant capillary flow path length; (B) Distributed capillary flow path length (see text).

FIG. 5.

Model predictions of the standard deviation (SD) and coefficient of variation (CV) of fractional hemoglobin oxygen saturation (SO₂) along a tissue slab containing 16 parallel capillaries of uniform flow path length distributed randomly in resting muscle.

FIG. 6.

Model predictions of the distribution of fractional oxygen saturation (SO₂) in 6 of the 16 parallel capillaries of uniform flow path length (labeled 1—6 in Fig. 4A) in resting muscle.

FIG. 7.

Model predictions of the standard deviation (SD) and coefficient of variation (CV) of fractional hemoglobin oxygen saturation (S02) along a tissue slab for a group of 16 parallel capillaries of uniform flow path length distributed randomly in contracting muscle. Note that the vertical scales differ from those used in Fig. 5 for resting muscle.

FIG. 8.

Model predictions of the distribution of fractional oxygen saturation (SOJ in 6 of the 16 capillaries of uniform flow path length in contracting muscle. Capillary locations and designations are identical to those used in Fig. 6. Note that the vertical scale differs from that used in Fig. 6 for resting muscle.