In this study techniques of fractal analysis as well as a home made device are proposed to characterize viscoelastic properties on mammalian erythrocyte membranes. A numerical method formulated on the basis of the fractal approximation for ordinary (OBM) and fractionary Brownian motion (FBM), is proposed to evaluate sensitive dependence on initial conditions. We hypothesize that this photometric temporal series, could be modeled as a system of bounded correlated random walk. Hence, three phase spaces n-dimensional (n=2 to 8) are generated, and used to distinguish chaotic from white noise behavior. The time series was obtained by ektacytometry over several millions of shear elongated cells. These experimental determinations were carried out in a home made device called erythrodeformeter, that has been built for rheological measurements on red blood cells subjected to definite fluid shear stress. A laser beam traverses the layer of shear deformed erythrocytes producing an elliptical pattern and diffracted intensity corresponding to each principal diameter of the diffraction pattern falls onto a photomultiplier tube (PMT), after passing through a thin straight slot in a mask placed exactly on the corresponding axis of the elliptical pattern. These photometric reading performed while erythrocytes became deformed and relaxed are used to calculate three different parameters over the time dependent process, and very different results were obtained.
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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