Contributions on the shapes of red blood corpuscles

Abstract

(1) The shapes of the erythrocytes of vertebrates are in general represented. by the Cassinian oval, the expression (x2+y2+a2)2−4a2x2=c4; in the case of biconcave discoidal erythrocytes, (x2+y2+z2+a2)2−4a2(x2+z2)=c4, where [Formula Omitted] in the case of elliptical erythrocytes under the microscope, the projective shape is represented by (x2+y2+a2)2−4a2x2=c4, where [Formula Omitted]. (2) The lemniscate is a very close approximation to the shape of a bicon cave discoidal erythrocyte. (3) The erythrocyte of a vertebrate changes its shape phylogenetically to the direction of increasing the ratio a/c in the Cassinian oval. (4) The relation between the years since vertebrates have been generated on the earth and the ratio a/c in the Cassinian oval is nearly linear. © 1955, PHYSIOLOGICAL SOCIETY OF JAPAN. All rights reserved.