Abstract
In this work, experimental determinations are carried out using a home-made device called an erythrodeformeter, which has been developed and constructed for rheological measurements on red blood cells subjected to definite fluid shear stress. A numerical method formulated on the basis of the fractal approximation for ordinary and fractionary Brownian motion1 is proposed to evaluate the viscoelastic behavior of mammalian erythrocyte membranes. The diffraction pattern, which is circular when the mammalian erythrocyte membranes are at rest, becomes elliptical when the cells undergo shear stress. Photometric readings of light intensity variation along the major axis of the elliptical diffraction pattern are recorded during the creep and recovery process. These data series are used to calculate, fractal rheological parameters of self-affine Brownian motion on the erythrocytes, averaged over several millions of cells. Three different parameters over the time dependent process could be obtained, which are: correlation coefficient <C(t)>, correlation integral, andK 2-entropy, and very different results were obtained.
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References
Korol, A. andRasia, R., “Correlated Random Walk: A Fractal Approach to Erythrocyte Viscoelastic Properties,”Clinical Hemorheology and Microcirculation,20,97–103 (1999).
Farmer, J. andSidorowich J., “Predicting Chaotic Time Series,”Phys. Rev. Lett.,59,845 (1987).
Rasia, R.J., “Quantitative Evaluation of Erythrocyte Viscoelastic Properties from Diffractometyric Data: Applications to Hereditary Spherocytosis and Hemoglobinopathies,”Clinical Hemorheology,15,177–189 (1995).
Takens, F., Lecture Notes in Mathematics, Vol. 898, ed. D.A. Rand andL.S. Young, Springer, Berlin (1981).
Tabor, M., Chaos and Integrability in Nonlinear Dynamics, J. Wiley and Sons, New York (1989).
Grassberger, P. andProcaccia, I., Phys. Rev. A,28,2591 (1983).
International Committee for Standarization in Hematology (ICSH9 Expert Panel on Blood Rheology), “Guidelines for Measurement of Blood Viscosity and Erythrocyte Deformability,”Clin. Hemorheol.,6,439–453 (1986).
Casdagli, M. and Weigend, A., Time Series: Forecasting the Future and Understanding the Past, Institute Studies in Sciences of Complexity Proc. Vol XV (1993).
Devany, R., Chaos, Fractals and Dynamics, Computer Experiments in Mathematics, Addison-Wesley, New York (19990).
Nakamura, S., Métodos Númericos Aplicados con Software, Prentice-Hall Hispanoamerica, México (1992).
Havstad, J. andEhlers, C., “Attractor Dimension of Nonstationary Dynamical Systems from Small Data Sets,”Phys. Rev. A,39,845–853 (1989).
Gershenfeld, N., “Dimension Measurements on High Dimensional Systems,”Physica D,55,135–154 (1992).
Luenberger, D., Linear and Nonlinear Programming, Addison-Wesley, Reading, MA (1984).
Grassberger, P. andProcaccia, I., “Measuring the Strangeness of a Strange Attractor,”Physica D,9,189 (1983).
Collins, J.J. andDe Luca, J., “A Statistical-biomechanics Approach to the Human Postural Control System,”Chaos,5,57–63 (1995).
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Korol, A.M., Valverde, J.R. & Rasia, R.J. Viscoelasticity: Fractal parameters studied on mammalian erythrocytes under shear stress. Experimental Mechanics 42, 172–177 (2002). https://doi.org/10.1007/BF02410879
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DOI: https://doi.org/10.1007/BF02410879