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

Affiliation(s)

Department of Mathematics, Faculty of Chemistry & Biochemistry, National University of Rosario, Rosario, Argentina.

Rosario Physics Institute-CONICET, Rosario, Argentina;Department of Statistic, Faculty of Chemistry & Biochemistry, National University of Rosario, Rosario, Argentina.

Department of Physics and Analytical Chemistry, Faculty of Chemistry & Biochemistry, National University of Rosario, Rosario, Argentina.

Department of Mathematics, Faculty of Chemistry & Biochemistry, National University of Rosario, Rosario, Argentina.

Rosario Physics Institute-CONICET, Rosario, Argentina;Department of Statistic, Faculty of Chemistry & Biochemistry, National University of Rosario, Rosario, Argentina.

Department of Physics and Analytical Chemistry, Faculty of Chemistry & Biochemistry, National University of Rosario, Rosario, Argentina.

ABSTRACT

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.

Cite this paper

A. Korol, B. Riquelme and M. D’Arrigo, "Crossover from Weak to Strong Nonlinear Disorder in the Viscoelasticity of Glucose Incubated Erythrocytes,"*Open Journal of Biophysics*, Vol. 3 No. 3, 2013, pp. 191-197. doi: 10.4236/ojbiphy.2013.33022.

A. Korol, B. Riquelme and M. D’Arrigo, "Crossover from Weak to Strong Nonlinear Disorder in the Viscoelasticity of Glucose Incubated Erythrocytes,"

References

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[10] B. Riquelme, P. Foresto, M. D’Arrigo, J. Valverde, R. Rasia, “Rheologic Alteration in Erythrocyte Membrane Produced by in Vitro No-Enzymatic Glycosilation,” Journal des Maladies Vasculaires, Vol. 25, 2000, pp. 172-180.

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[16] R. Rasia, P. Porta and M. García Rosasco, “Shear Deformation Measurement of Suspended Particles: Applications to Erythrocytes,” Review of Scientific Instruments, Vol. 57, No. 1, 1986, pp. 33-35. doi:10.1063/1.1139113

[17] J. Theiler, S. Eubank, A. Longtin, B. Galdrikian and J. Farmer, “Testing for Nonlinearity in Time Series: The Method of Surrogate Data,” Physica D, Vol. 58, No. 1-4, 1992, pp. 77-94. doi:10.1016/0167-2789(92)90102-S

[18] H. D. I. Abarbanel, R. Brown, J. J. Sidorowich and L. S. Tsimring, “The Analysis of Observed Chaotic Data in Physical Systems,” Reviews of Modern Physics, 1993, Vol. 65, No. 4, pp. 1331-1392. doi:10.1103/RevModPhys.65.1331

[19] F. Takens, “Detecting Strange Attractors in Turbulence— Dynamical Systems and Turbulence (Lecture Notes in Mathematics),” Springer-Verlag, Heidelberg, 1981, pp. 366-381.

[20] P. Hanggi and F. Marchesoni, “Introduction: 100 Years of Brownian Motion,” CHAOS, Vol. 15, No. 2, 2005, pp. 1-5.

[21] A. M. Korol and R. J. Rasia, “Signatures of Deterministic Chaos in Dyslipidemic Erythrocytes under Shear Stress,” Chaos, Vol. 13, No. 1, 2003, pp. 87-93. doi:10.1063/1.1544522

[22] A. M. Korol, J. R. Valverde and R. J. Rasia, “Viscoelasticity: Fractal Parameters Studied on Mammalian Erythrocytes under Shear Stress,” Experimental Mechanics, Vol. 42, No. 2, 2002, pp. 172-177. doi:10.1007/BF02410879

[23] P. Bak, “How Nature Works,” Springer-Verlag, New York, 1996.

[1] G. Sugihara and R. May, “Nonlinear Forecasting as a Way of Distinguishing Chaos from Measurement Error in Time Series,” Nature, Vol. 344, No. 6268, 1990, pp. 734-741.

[2] C. M. Peterson, R. L. Jones, R. J. Koenig, E. T. Melvin and M. L. Lehrman, “Reversible Hematologic Sequallae of Diabetes Mellitus,” Annals of Internal Medicine, Vol. 86, No. 4, 1993, pp. 425-429. doi:10.7326/0003-4819-86-4-425

[3] C. Brown, H. S. Ghali, Z. Zhao, L. L. Thomas and E. A. Friedman, “Association of Reduced Red Blood Cell Deformability with Diabetic Nephropathy,” Kidney International, Vol. 67, No. 1, 2005, pp. 295-300. doi:10.1111/j.1523-1755.2005.00082.x

[4] D. E. McMillan, N. G. Utterback and J. La Puma, “Reduced Erythrocytes Deformability in Diabetes,” Diabetes Vol. 27, No. 9, 1978, pp. 895-901.

[5] D. E. McMillan, N. G. Utterback and T. P. Mitchell, “Doublet Formation of Diabetic Erythrocytes as a Model of Impaired Membrane Viscous Deformation,” Microvascular Research, Vol. 26, No. 2, 1983, pp. 205-220. doi:10.1016/0026-2862(83)90071-7

[6] M. Szelachowska, W. Schaefer, A. F. Gries and I. Kinalska, “Activity of Ca/Mg ATPase in Erythrocyte Membrane of Women with Diabetes Mellitus Type I, Endocrynol,” Pology, Vol. 43, 1992, pp. 23-29.

[7] A. Korol, O. Rosso, M. Martin, M. D’Arrigo and B. Riquelme, “Impairment of Erythrocytes Incubated in Glucose Medium: A Wavelet-Information Theory Analysis,” Cell Biochemistry Biophysics, Vol. 60, No. 3, 2011, pp. 329-334. doi:10.1007/s12013-011-9155-y

[8] E. Bourdon, N. Loreau and D. Blanche, “Glucose and Free Radicals Impair the Antioxidant Properties of Serum Albumin,” The FASEB Journal, Vol. 13, No. 2, 1999, pp. 233-244.

[9] A. Lapolla, C. Gerhardiger, M. Dal Frá, A. Franchin, D. Fedele and G. Crepaldi, “Glycated Erythrocyte Membrane Proteins and Hemorheological Parameters in Insulin Dependen Diabetic Subjects,” Clinical Hemorheology, Vol. 11, No. 5, 1991, pp. 405-415.

[10] B. Riquelme, P. Foresto, M. D’Arrigo, J. Valverde, R. Rasia, “Rheologic Alteration in Erythrocyte Membrane Produced by in Vitro No-Enzymatic Glycosilation,” Journal des Maladies Vasculaires, Vol. 25, 2000, pp. 172-180.

[11] N. Lerda, B. Riquelme and M. D’Arrigo, “Alterations the Erythrocyte Hemorheologic Parameters by the in Vitro Effect of the Glucose,” Vox Sanguinis, Vol. 101, No. 1 2011, p. 153.

[12] International Committee of Standarization Haemathology (Expert Panel on Blood Rheology), “Guidelines for Measurements of Blood Viscosity and Erythrocyte Deformability,” Clinical Hemorheology and Microcirculation, Vol. 6, 1996, pp. 439-453.

[13] B. Riquelme, F. Foresto, M. Dárrigo, J. Valverde, R. Rasia, “A Dynamic and Stationary Rheological Study of Erythrocytes Incubated in a Glucose Medium,” Journal of Biochemical and Biophysical Methods, Vol. 62, No. 2, 2005, pp. 131-141. doi:10.1016/j.jbbm.2004.10.004

[14] R. Rasia, “Quantitative Evaluation of Erythrocyte Viscoelastic Properties from Difractometric Data: Applications to Hereditary Spherocitosis and Hemoglobinopathies,” Clinical Hemorheology, Vol. 15, 1995, pp. 177-189.

[15] B. Riquelme and R. Rasia, “Complex Viscoelasticity of Normal and Lectin Treated Erythrocyte Using Laser Diffractometry,” Biorheology, Vol. 35, No. 4-5, 1998, pp. 325-334.

[16] R. Rasia, P. Porta and M. García Rosasco, “Shear Deformation Measurement of Suspended Particles: Applications to Erythrocytes,” Review of Scientific Instruments, Vol. 57, No. 1, 1986, pp. 33-35. doi:10.1063/1.1139113

[17] J. Theiler, S. Eubank, A. Longtin, B. Galdrikian and J. Farmer, “Testing for Nonlinearity in Time Series: The Method of Surrogate Data,” Physica D, Vol. 58, No. 1-4, 1992, pp. 77-94. doi:10.1016/0167-2789(92)90102-S

[18] H. D. I. Abarbanel, R. Brown, J. J. Sidorowich and L. S. Tsimring, “The Analysis of Observed Chaotic Data in Physical Systems,” Reviews of Modern Physics, 1993, Vol. 65, No. 4, pp. 1331-1392. doi:10.1103/RevModPhys.65.1331

[19] F. Takens, “Detecting Strange Attractors in Turbulence— Dynamical Systems and Turbulence (Lecture Notes in Mathematics),” Springer-Verlag, Heidelberg, 1981, pp. 366-381.

[20] P. Hanggi and F. Marchesoni, “Introduction: 100 Years of Brownian Motion,” CHAOS, Vol. 15, No. 2, 2005, pp. 1-5.

[21] A. M. Korol and R. J. Rasia, “Signatures of Deterministic Chaos in Dyslipidemic Erythrocytes under Shear Stress,” Chaos, Vol. 13, No. 1, 2003, pp. 87-93. doi:10.1063/1.1544522

[22] A. M. Korol, J. R. Valverde and R. J. Rasia, “Viscoelasticity: Fractal Parameters Studied on Mammalian Erythrocytes under Shear Stress,” Experimental Mechanics, Vol. 42, No. 2, 2002, pp. 172-177. doi:10.1007/BF02410879

[23] P. Bak, “How Nature Works,” Springer-Verlag, New York, 1996.