Effect of red blood cell shape on oxygen transport in capillaries

A mathematical model of oxygen (O₂) transport within a capillary utilizes axisymmetric red blood cell (RBC) shapes that were predicted theoretically by Zarda et al. in 1977. Chemical kinetics and both free and facilitated diffusion of O₂ are accounted for in this time-dependent model. The finite-element method is used to solve the governing partial differential equations. It is found that the shape of RBCs, characterized by the shape parameter θ adapted from Zarda et al., affects such important O₂ transport characteristics as capillary wall O₂ flux and hemoglobin (Hb) saturation. At an RBC residence time (time for an RBC to travel from the capillary inlet to a given point) of 0.22 s, a change in the shape parameter θ from 0 (underformed cell) to 26 (parachute-shaped cell) decreases the spatially averaged O₂ flux by 26%. The dependence of O₂ flux on RBC shape diminishes as the RBC residence time increases. The difference in Hb saturation at the RBC residence time of 0.22 s can be as large as 10% for different values of Θ. The mass transfer Nusselt number, which is inversely proportional to transport resistance, decreases with increases in Θ. The fractional transport resistance in the plasma region accounts for approximately 65-80% of the total intracapillary resistance. Calculations show that local chemical equilibrium in the O₂-Hb chemical reaction is attained everywhere except within a thin boundary layer adjacent to the erythrocyte membrane, where significant deviation from chemical equilibrium occurs.