Applications of temporal chaos: sensitive dependence on initial conditions and K2-entropy on erythrocytes viscoelastic properties

Ana Maria Korol; Juana R. Valverde; Rodolfo Jose Rasia

doi:10.1117/12.384164

28 April 2000 Applications of temporal chaos: sensitive dependence on initial conditions and K₂-entropy on erythrocytes viscoelastic properties

Ana Maria Korol, Juana R. Valverde, Rodolfo Jose Rasia

Author Affiliations +

Proceedings Volume 3915, Coherence Domain Optical Methods in Biomedical Science and Clinical Applications IV; (2000) https://doi.org/10.1117/12.384164
Event: BiOS 2000 The International Symposium on Biomedical Optics, 2000, San Jose, CA, United States

Abstract

The photometric readings are obtained by ektacytometry over several millions of shear elongated cells, using a home-made device called Erythrodeformeter. This time series is used to study the fractal behavior of erythrocyte viscoelastic properties. We have only a scalar signal and no governing equations. Therefore the complete behavior has to be reconstructed in an artificial phase space. We used the technique of time delay coordinates by Takens. A numerical method based on self-affine Brownian motion is proposed to analyze sensitive dependence on initial conditions. We hypothesize that this photometric temporal series, could be modeled as a system of bounded correlated random walk. Hence, two phase spaces n-dimensional are generated, and used to distinguish chaotic from white noise behavior. We have applied modified methods of Grassberger and Procaccia not only on our photometric readings but also on a pseudo- aleatory series in order to check their results. It was found that while the pseudo-aleatory series is high- dimensional, our series are low-dimensional. The role of random noise and the number of data points are discussed. Finally, our results, allow us to conclude that these methods could be used to evaluate the predictability and clinical aspects of erythrocyte rheological properties.

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Ana Maria Korol, Juana R. Valverde, and Rodolfo Jose Rasia "Applications of temporal chaos: sensitive dependence on initial conditions and K₂-entropy on erythrocytes viscoelastic properties", Proc. SPIE 3915, Coherence Domain Optical Methods in Biomedical Science and Clinical Applications IV, (28 April 2000); https://doi.org/10.1117/12.384164

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KEYWORDS

Chaos

Fractal analysis

Astatine

Biological research

Systems modeling

Biomedical optics

Stochastic processes

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