Abstract
Even when a healthy individual is studied, his/her erythrocytes in capillaries continually change their shape in a synchronized erratic fashion. In this work, the problem of characterizing the cell behavior is studied from the perspective of bounded correlated random walk, based on the assumption that diffractometric data involves both deterministic and stochastic components. The photometric readings are obtained by ektacytometry over several millions of shear elongated cells, using a home-made device called Erythrodeformeter. We have only a scalar signal and no governing equations; therefore the complete behavior has to be reconstructed in an artificial phase space. To analyze dynamics we used the technique of time delay coordinates suggested by Takens, May algorithm, and Fourier transform. The results suggest that on random-walk approach the samples from healthy controls exhibit significant differences from those from diabetic patients and these could allow us to claim that we have linked mathematical nonlinear tools with clinical aspects of diabetic erythrocytes’ rheological properties.
Highlights
It is important to appreciate the role of mathematics in the analysis of physiological systems
The erythrocyte deformability depends on the surface-volume ratio, internal viscosity and dynamics properties of the erythrocyte membrane
The results of the present study suggest that on randomwalk approach the samples from healthy controls exhibit significant differences from those from diabetic patients and these could allow us to claim that we have linked mathematical nonlinear tools with clinical aspects of diabetic erythrocytes’ rheological properties
Summary
It is important to appreciate the role of mathematics in the analysis of physiological systems. When laser is applied during creep and recovery process, light intensity dynamically changes along the major axes of the elliptical diffraction pattern These experimental determinations are carried out with a home made device called Erythrodeformeter [2], which was developed and constructed for rheological measurements of red blood cells subjected to definite shear. The corresponding time series (diffracted intensity measured in the major axis of the elliptical pattern under creep or recovery process) can be used in order to obtain same insight of the corresponding associated dynamics under healthy or illness conditions. The results of the present study suggest that on randomwalk approach the samples from healthy controls exhibit significant differences (ordinary Brownian motion) from those from diabetic patients (fractional Brownian motion) and these could allow us to claim that we have linked mathematical nonlinear tools with clinical aspects of diabetic erythrocytes’ rheological properties
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