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Biomechanics is a wide interdisciplinary field, which includes all mechanical aspects from living organisms. As traditional erythrocytes viscoelastic analysis is mostly qualitative, the development of new quantitative methods capable of analyzing at the same time biological and mechanical aspects of the cells in flow, when changing from healthy controls to glucose incubated at different concentrations, is crucial for restricting the subjectivity in the study of the cell behaviour. On the other hand, it is important to appreciate the role of mathematics in the analysis of tissues and cells. Recent developed non linear mathematical methods are particularly fruitful when they are strongly correlated with cells sensitivity to initial conditions. An optic system called Erythrodeformeter has been developed and constructed in our laboratory, in order to evaluate the erythrocytes viscoelastic properties. To analyze the erythrocytes viscoelastic dynamics we used the technique of Time Delay Coordinates suggested by Takens, False Nearest Neighbours proposed by Abarbanel and co-workers, and the forecasting procedure proposed by Sugihara and May, the so called Correlation Coefficient. The results suggest that through this random walk analysis, apparent noise associated with deterministic chaos can be used not only to distinguish but also to characterize at the same time biological and mechanical aspects of the cells in flow, when changing from healthy controls to glucose incubated at different concentrations.

Crossover from Weak to Strong Nonlinear Disorder in the Viscoelasticity of Glucose Incubated Erythrocytes