A Simplified Method for Calculating Surface Area of Mammalian Erythrocytes

Abstract

Knowledge of the geometric quantities of the erythrocyte is useful in several physiological studies, both for zoologists and veterinarians. While the diameter and volume (MCV) are easily obtained from observations of blood smears and complete blood count, respectively, the thickness and surface area are instead much more difficult to measure. The precise description of the erythrocyte geometry is given by the equation of the oval of Cassini, but the formulas deriving from it are very complex, comprising elliptic integrals. In this article, three solids are proposed as models approximating the erythrocyte: sphere, cylinder and a spheroid with concave caps. The volumes and surface areas obtained with these models are compared to those effectively measured. The spheroid with concave caps gives the best approximation and can be used as a simple model to determine the erythrocyte surface area. With this model, a simple method that allows one to estimate the surface area by knowing only the diameter and MCV is proposed.

Keywords: MCV; RBC; area; mammals; red blood indices; volume.

Figure 1

Erythrocyte geometry: (A) Top view; (B) cross section.

Figure 2

Cross sections of different solids: (A) Erythrocyte; (B) sphere; (C) cylinder; (D) spheroid with concave caps; d = diameter; t = thickness; A = major axis of the large spheroid; B = minor axis of the large spheroid; a = major axis of the small spheroid (cap); b = minor axis of the small spheroid.

Figure 3

Comparison of different models to calculate RBC volume: (A) Correlations of measured and calculated volumes with diameter; (B) percentage errors of calculated volumes; MCV = Mean Corpuscular Volume (measured), V_s = Volume of the sphere, V_c = Volume of the cylinder, V_b = Volume of the biconcave spheroid.

Figure 4

Comparison of different models to calculate RBC surface area: (A) Correlations of measured and calculated surface areas with diameter; (B) percentage errors of calculated surface areas; SA_m = measured surface area, SA_s = Surface area of the sphere, SA_c = Surface area of the cylinder, SA_b = Surface area of the biconcave spheroid.

Figure 5

Cross sections of normal and abnormal RBCs: (A) Normal erythrocyte (discocyte); (B) leptocyte (increased diameter, but normal volume); (C) macrocyte (increased diameter and volume); (D) codocyte (bell-shaped); (E) spherocyte.