Question 7.7: The biconcave shape of the RBC increases its surface area-to...

Given the stated volume V and the surface area A of 98 \mu m^{3} and 130 \mu m^{2}, respectively, we have a ratio of 1.33 \mu m^{-1} for the biconcave shape. If the RBC were a sphere of volume 98 \mu m^{3}, then its radius would be

The associated surface area would thus be A=4\pi r^{2}=1.3\mu m^{2}; thus, for a sphere, the ratio of surface area to volume would be 103/98=1.05 \mu m^{-1}. This value is significantly less than that for the biconcave disk. Of course, in the capillary, the RBC deforms significantly from its baseline shape, which could further increase the ratio of surface area to volume, although some have suggested that the surface area tends to remain constant. A constant surface area can be accounted for constitutively for the membrane as a kinematic constraint (Humphrey 2002). The next most abundant cell type in blood is the platelets, which constitute about 4.9 % of the cell volume. There are  (2.5–3.0)\times10^{5}  platelets per cubic millimeter of blood, with cell diameters \sim 2.5 \mu m and thicknesses \sim 0.5 \mu m μm. As the name implies, they have a platelike disk shape. The platelets are major players in the coagulation of blood and thus the prevention of blood loss. The remaining 0.1 % of the cellular component of blood consists of leukocytes, or white blood cells (WBC_{s}), which form the cellular component of the immune system. There are (5–8)\times10^{3} WBC_{s} per cubic millimeter of blood in health. The three primary classes of WBCs are the monocytes (16–22 \mu m in diameter), granulocytes (10–12 \mu m in diameter), and lymphocytes (7 \mu m in diameter). Although much fewer in number than the RBC_{s}, there are \sim 37\times 10^{9} (37 billion) WBC_{s} circulating in the blood of a healthy adult. Because the white blood cells and platelets only constitute 5 % of the cellular component of blood, their effect on the macroscopic flow characteristics of blood is typically assumed to be negligible; that is, the non-Newtonian character of blood is controlled primarily by the hematocrit and, to a lesser degree, the fibrinogen.