Fractal geometry applied to compare the spaces occupied by normal erythrocytes and spherocytes

Objective: to develop a new methodology that evaluated the shape of the normal erythrocyte and the spherocyte from the spaces occupied by each one, as measured by the Box Counting method. Materials and methods: 20 images of peripheral blood smear were analyzed, in which a large number of normal erythrocytes and spherocytes were observed. Two Kp grids of 5 x 5 pixels and 10 x 10 pixels Kg were superimposed to calculate the space occupied by two regions of the normal erythrocyte which are, the disk and center of the latter, viewed frontally, as well as the occupied space by the spherocyte using the Box Counting method. Results: The spaces occupied by the exterior and interior of the normal erythrocyte with the Kp grid varied between 47 and 55, and between 8 and 16, respectively. In contrast, the spaces occupied by the spherocytes varied between 25 and 36. The proportions between the surface and the values of the K grid of the normal erythrocyte regions varied between 9.250 and 32.24, whereas the spherocytes varied between 34,63 and 71,39. Conclusions: alterations in the shape of the normal erythrocyte can be differentiated by the ranges found for the space occupied by the surface and the proportions S/Kp of each of the erythrocyte regions from the notions of fractal and Euclidean geometry.