Brownian Characterization of Nonlinear Behavior of Red Blood Cells from Leukemia and Anemia Patients Through the Determination of the May-Sugihara Coefficients and the Hurst Exponents

Abstract

Blood diseases affect one or several parts of it and prevent blood to accomplish its function. These diseases could be chronic or acute. For example, leukemia is a type of blood cancer that starts in the bone marrow where blood cells are formed. Also, leukemia can be classified as lymphocytic or myelogenous. In some types of leukemia, it could be affected by any of the different precursors of the cell lines of the bone marrow as for example myeloid, erythroid or megakaryocytic precursors. Besides, iron deficiency anemia is one of the most common anemia and is caused by a deficiency in iron present in the hemoglobin of red blood cells (RBCs). Ektacytometry techniques quantify RBCs deformability by measuring the elongation of suspended RBCs subjected to shear stress. A patented optical system denominated Erythrocyte Rheometer was used to evaluate the viscoelastic properties of RBCs from patients with leukemia and iron deficiency anemia by ektacytometry. RBCs from healthy donors were used as a control. From the diffraction patterns of several of millions of RBCs (subjected to shear stress), photometric series were obtained. On this temporal series, it was evaluated non-lineal quantifiers in order to study fluctuations in the elongations of the RBCs. The dynamics of the cells were analyzed with the coefficient of non-linear correlation proposed by May and Sugihara and with the Hurst Exponent. Patterns of different behavior were observed in the utilized quantifiers. The patterns observed for the leukemia patients showed a chaotic behavior while patterns from iron deficiency anemia showed a random behavior like the control RBCs. The proposed quantifiers proved to be useful in the discernment of different pathologies associated with RBCs. Besides, the results shed light on the utilization of non-linear quantifiers on photometrically recorded series from erythrocytes subjected to shear stress for a quantitative characterization of the behavior of the system under study.