Analysis of Mechanical Behavior of Red Blood Cell Membrane with Malaria Infection

ABSTRACT

Human red blood cells (RBCs) are responsible to transport oxygen and carbon dioxide for human bodies. The physiological functions of RBCs are greatly influenced by their mechanical properties. When RBC is infected by Malaria parasite called Plasmodium falciparum, it shows progressive changes in mechanical properties and loses its deformability. The infected red blood cells (IRBCs) develop properties of cytoadherence (stickiness) and rosetting (the binding of non-infected RBCs to parasitized RBCs). In this paper to analyze the mechanical properties and deformability of the IRBC, we applied stress-stretch ratio relation of its biomembrane .To express this constitutive relation, we proposed a mathematical model (Neo-Hookean model) based on membrane theory. On this model, we present continuous stress-stretch ratio curves for the relation derived from the model for different intracellular developmental stages of the parasite, to determine the mechanical properties of IRBC. The analytical results obtained from the mathematical model are more closed with the experimental data [1] which demonstrates the validity of the model. By restricting our attention to spherically symmetric deformation in the final schizont stage of parasite development, the pressure-extension ratio relation curve also adapted from the proposed strain energy function. The change in osmotic pressure versus volumetric ratio has been also considered for IRBC before hemolysis.

Human red blood cells (RBCs) are responsible to transport oxygen and carbon dioxide for human bodies. The physiological functions of RBCs are greatly influenced by their mechanical properties. When RBC is infected by Malaria parasite called Plasmodium falciparum, it shows progressive changes in mechanical properties and loses its deformability. The infected red blood cells (IRBCs) develop properties of cytoadherence (stickiness) and rosetting (the binding of non-infected RBCs to parasitized RBCs). In this paper to analyze the mechanical properties and deformability of the IRBC, we applied stress-stretch ratio relation of its biomembrane .To express this constitutive relation, we proposed a mathematical model (Neo-Hookean model) based on membrane theory. On this model, we present continuous stress-stretch ratio curves for the relation derived from the model for different intracellular developmental stages of the parasite, to determine the mechanical properties of IRBC. The analytical results obtained from the mathematical model are more closed with the experimental data [1] which demonstrates the validity of the model. By restricting our attention to spherically symmetric deformation in the final schizont stage of parasite development, the pressure-extension ratio relation curve also adapted from the proposed strain energy function. The change in osmotic pressure versus volumetric ratio has been also considered for IRBC before hemolysis.

KEYWORDS

Cell Mechanics, Malaria Infected Red Blood Cell, Mathematical Model, RBC Membrane Elasticity

Cell Mechanics, Malaria Infected Red Blood Cell, Mathematical Model, RBC Membrane Elasticity

Cite this paper

nullV. Katiyar and D. Fisseha, "Analysis of Mechanical Behavior of Red Blood Cell Membrane with Malaria Infection,"*World Journal of Mechanics*, Vol. 1 No. 3, 2011, pp. 100-108. doi: 10.4236/wjm.2011.13014.

nullV. Katiyar and D. Fisseha, "Analysis of Mechanical Behavior of Red Blood Cell Membrane with Malaria Infection,"

References

[1] S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Biel and T. Seufferlein, “Connection between Single-Cell Biomechanics and Human Disease States: Gastrointestinal Cancer and Malaria,” Acta Biomaterialia, Vol. 1, No. 1, 2005, pp.15-30. doi:10.1016/j.actbio.2004.09.001

[2] M. Dao, C. T. Lim and S. Suresh, “Mechanics of the Human Red Blood Cell Deformed by Optical Tweezers,” Journal of the Mechanics and Physics Solids, Vol. 51, No. 11-12, 2003, pp. 2259-2280. doi:10.1016/j.jmps.2003.09.019

[3] E. A. Evans and R. Skalak, “Mechanics and Thermal Dynamics of Biomembranes,” CRC Press, Boca Raton, 1980.

[4] D. Boal, “Mechanics of the Cell,” Cambridge University Press, Cambridge, 2002.

[5] S. Suresh, “Mechanical Response of Human Red Blood Cells in Health and Disease: Some Structure-Property-Function Relationships,” Journal of Materials Research, Vol. 21, No. 8, 2006, pp. 1871-1877. doi:10.1557/jmr.2006.0260

[6] G. Y. H. Lee and C. T. Lim, “Biomechanics Approaches to Studying Human Diseases,” Trends in Biotechnology, Vol. 25, No. 3, pp. 112-118.

[7] World Health Organization, “World Malaria Report,” 2008. http://www.who.int/malaria/wmr2008

[8] Y. Imai, H. Kondo, T. Ishikawa, C. T. Lim and T. Yamaguchi, “Modeling of Hemodynamic Arising from Malaria Infection,” Journal of Biomechanics, Vol. 43, No. 7, pp. 1386-1393. doi:10.1016/j.jbiomech.2010.01.011

[9] H. Kondo, Y. Imai, T. Ishikawa, K. Tsubota and T. Yamaguchi, “Hemodynamic Analysis of Microcirculation in Malaria Infection,” Annals of Biomedical Engineering, Vol. 37, No. 4, 2009, pp. 702-709. doi:10.1007/s10439-009-9641-1

[10] F. K. Glenister, R. L. Goppel, A. F. Cowman, N. Mohan das and B. M. Cooke, “Contribution of Parasite Proteins to Altered Mechanical Prop Erties of Malaria-Infected Red Blood Cells,” Blood, Vol. 99, No. 3, 2002, pp. 1060-1063. doi:10.1182/blood.V99.3.1060

[11] N. B. Nash, E. O’. Brien, E. C. Gorden-Smith and J. A. Dormandy, “Abnormalities in the Mechanical Properties of Red Blood Cells Caused by Plasmodium Falciparum,” Blood, Vol. 74, No. 2, 1989, pp. 855-861.

[12] M. Paulitschke and G. B. Nash, “Membrane Rigidity of Red Blood Cells Parasitized by Different Strains of Plasmodium Falciparum,” Journal of Laboratory and Clinical Medicine, Vol. 122, No. 5, 1993, pp. 581-589.

[13] C. T. Lim, “Single Cell Mechanics Study of the Human Disease Malaria,” Journal of Biomechanical Science and Engineering, Vol. 1, No. 1, 2006, pp. 82-92. doi:10.1299/jbse.1.82

[14] J. M. A. Mauritz, T. Tiffert, R. Seear, F. Lautensclager, A. Esposito, V. L. Lew, J. Guck and C. F. Kaminki, “Detection of Plasmodium Falciparum-Infected Red Blood Cells by Optial Tretching,” Journal of Biomedical Optics, Vol. 15, No. 3, 2010. doi:10.1117/1.3458919

[15] G. Lenormand, S. Hkenon, A. Richert, S. SimKeon and F. Gallet, “Direct Measurement of the Area Expansion and Shear Moduli of the Human Red Blood Cell Mem Brane Skeleton,” Biophysical Journal, Vol. 81, No. 1, 2001, pp. 43-56. doi:10.1016/S0006-3495(01)75678-0

[16] K. B. Sahay, “On the Choice of the Strain Energy Function for Mechanical Characterization of Soft Biological Tissues,” Mineral Engineering Processes Ltd., Vol. 13, No. 1, 1984, pp. 11-14.

[17] J. P. Mills, L. Qie, M. Dao, C. T. Lim and S. Suresh, “Nonlinear Elastic and Viscoelastic Deformation of the Human Red Blood Cell with Optical Tweezers,” Mechanics and Chemistry of Biosystems, Vol. 1, No. 3, 2004, pp. 169-180.

[18] E. A. Evans, “New Membrane Concept Applied to the Analysis of Fluid Shear- and Micropipette-Deformed Red Blood Cells,” Biophysical Journal, Vol. 13, No. 9, 1973, pp. 941-954. doi:10.1016/S0006-3495(73)86036-9

[19] R. Skalak, “Strain Energy Function of Red Blood Cell Membrane,” Biophysical Journal, Vol.13, No. 3, 1973, pp. 245-264. doi:10.1016/S0006-3495(73)85983-1

[20] A. M. Dondorp, P. A. Kager, J. Vreeken and N. J. White, “Abnormal Blood Flow and Red Blood Cell Deformability in severe Malaria,” Parasitology Today, Vol. 16, No. 6, 2000, pp. 228-232. doi:10.1016/S0169-4758(00)01666-5

[21] C. T. Lim, E. H. Zhou and S. T. Quek, “Mechanical Model for Living Cells—A Review,” Journal of Biomechanics, Vol. 39, No. 2, 2006, pp. 195-216. doi:10.1016/j.jbiomech.2004.12.008

[22] Ali, M. Hosseini and B. B. Sahari, “A Review of Constitutive Models for Rubber-Like Materials,” American Journal of Engineering and Applied Sciences, Vol. 3, No. 1, 2010, pp. 232-239. doi:10.3844/ajeassp.2010.232.239

[23] H. A. Cranston, C. W. Boylan, G. L. Carroll, S. P. Sutera, J. R. Williamson, I. Y. Gluzman and D. J. Krogstad, “Plasmodium Falciparum Maturation Abolishes Physiologic Red Cell Deformability,” Science, Vol. 223, No. 4634, 1984, pp. 400-403. doi:10.1126/science.6362007

[24] R. Suwanarusk, B. M. Cooke, A. M. Dondorp, K. Si lamut, J. Sattabongkot, N. J. White and R. Udomsang Petch, “The Deformability of Red Blood Cells Parasitized by Plasma Dium Falciparum and P. Vivax,” Journal of Infectious Diseases, Vol. 189. No. 2004, pp. 190-194.

[25] Y. Tan, D. Sun and W. Huang, “Mechanical Modeling of Red Blood Cells during Optical Stret Ching,” Journal of Biomechanical Engineering, Vol. 132, No. 4, 2010, pp. 04450(1-5).

[26] V. Wiwanitkit, “Volume Added, Malarial Infection and Fragility of Red Blood Cell,” Iranian Journal of Medical Hypotheses and Ideas, Vol. 3, No. 4, 2009. http://journals.tums.ac.ir/abs/12485

[27] S. P. Sutera and D. S. Krogstad, “Reduction of the Surface-Volume Ratio: A Physical Mechanism Contributing to the Loss of Red Cell Deformability in Malaria,” Biorheology, Vol. 28, No. 3-4, 1991, pp. 221-229.

[28] D. C. Pamplona, P. B. Goncalves and S. X. R. Lopes, “Finite Deformations of Cylindrical Membrane under Internal Pressure,” International Journal of Mechanical Sciences, Vol. 48, No. 6, 2006, pp. 683-696. doi:10.1016/j.ijmecsci.2005.12.007

[29] P. B. Canham and D. R. Parkinson, “The Area and Volume of Single Human Erythrocytes during Gradual Osmotic Swelling to Hemolysis,” Canadian Journal of Physiology and Pharmacology, Vol. 48, No. 6, 1970, pp. 369-376. doi:10.1139/y70-059

[30] C. Magowan, J. T. Brown, J. Liang, J. Heck, R. L. Coppel, N. Mohandas, W. Meyer-Ilse, “Intracellular Structures of Normal and aberrant Plasmodium Falciparum Malaria Parasites Imaged by Soft X-Ray Microscopy,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 94, No. 12, 1997, pp. 6222-6227. doi:10.1073/pnas.94.12.6222

[31] A. W. L. Jay, “Viscoelastic Properties of the Human Red Blood Cell Membrane I, Defromation, Volume Loss, and Rapture of Red Blood Cells in Micropipettes,” Biophysical Journal, Vol. 13, No. 11, 1973, pp. 1166-1182. doi:10.1016/S0006-3495(73)86053-9

[1] S. Suresh, J. Spatz, J. P. Mills, A. Micoulet, M. Dao, C. T. Lim, M. Biel and T. Seufferlein, “Connection between Single-Cell Biomechanics and Human Disease States: Gastrointestinal Cancer and Malaria,” Acta Biomaterialia, Vol. 1, No. 1, 2005, pp.15-30. doi:10.1016/j.actbio.2004.09.001

[2] M. Dao, C. T. Lim and S. Suresh, “Mechanics of the Human Red Blood Cell Deformed by Optical Tweezers,” Journal of the Mechanics and Physics Solids, Vol. 51, No. 11-12, 2003, pp. 2259-2280. doi:10.1016/j.jmps.2003.09.019

[3] E. A. Evans and R. Skalak, “Mechanics and Thermal Dynamics of Biomembranes,” CRC Press, Boca Raton, 1980.

[4] D. Boal, “Mechanics of the Cell,” Cambridge University Press, Cambridge, 2002.

[5] S. Suresh, “Mechanical Response of Human Red Blood Cells in Health and Disease: Some Structure-Property-Function Relationships,” Journal of Materials Research, Vol. 21, No. 8, 2006, pp. 1871-1877. doi:10.1557/jmr.2006.0260

[6] G. Y. H. Lee and C. T. Lim, “Biomechanics Approaches to Studying Human Diseases,” Trends in Biotechnology, Vol. 25, No. 3, pp. 112-118.

[7] World Health Organization, “World Malaria Report,” 2008. http://www.who.int/malaria/wmr2008

[8] Y. Imai, H. Kondo, T. Ishikawa, C. T. Lim and T. Yamaguchi, “Modeling of Hemodynamic Arising from Malaria Infection,” Journal of Biomechanics, Vol. 43, No. 7, pp. 1386-1393. doi:10.1016/j.jbiomech.2010.01.011

[9] H. Kondo, Y. Imai, T. Ishikawa, K. Tsubota and T. Yamaguchi, “Hemodynamic Analysis of Microcirculation in Malaria Infection,” Annals of Biomedical Engineering, Vol. 37, No. 4, 2009, pp. 702-709. doi:10.1007/s10439-009-9641-1

[10] F. K. Glenister, R. L. Goppel, A. F. Cowman, N. Mohan das and B. M. Cooke, “Contribution of Parasite Proteins to Altered Mechanical Prop Erties of Malaria-Infected Red Blood Cells,” Blood, Vol. 99, No. 3, 2002, pp. 1060-1063. doi:10.1182/blood.V99.3.1060

[11] N. B. Nash, E. O’. Brien, E. C. Gorden-Smith and J. A. Dormandy, “Abnormalities in the Mechanical Properties of Red Blood Cells Caused by Plasmodium Falciparum,” Blood, Vol. 74, No. 2, 1989, pp. 855-861.

[12] M. Paulitschke and G. B. Nash, “Membrane Rigidity of Red Blood Cells Parasitized by Different Strains of Plasmodium Falciparum,” Journal of Laboratory and Clinical Medicine, Vol. 122, No. 5, 1993, pp. 581-589.

[13] C. T. Lim, “Single Cell Mechanics Study of the Human Disease Malaria,” Journal of Biomechanical Science and Engineering, Vol. 1, No. 1, 2006, pp. 82-92. doi:10.1299/jbse.1.82

[14] J. M. A. Mauritz, T. Tiffert, R. Seear, F. Lautensclager, A. Esposito, V. L. Lew, J. Guck and C. F. Kaminki, “Detection of Plasmodium Falciparum-Infected Red Blood Cells by Optial Tretching,” Journal of Biomedical Optics, Vol. 15, No. 3, 2010. doi:10.1117/1.3458919

[15] G. Lenormand, S. Hkenon, A. Richert, S. SimKeon and F. Gallet, “Direct Measurement of the Area Expansion and Shear Moduli of the Human Red Blood Cell Mem Brane Skeleton,” Biophysical Journal, Vol. 81, No. 1, 2001, pp. 43-56. doi:10.1016/S0006-3495(01)75678-0

[16] K. B. Sahay, “On the Choice of the Strain Energy Function for Mechanical Characterization of Soft Biological Tissues,” Mineral Engineering Processes Ltd., Vol. 13, No. 1, 1984, pp. 11-14.

[17] J. P. Mills, L. Qie, M. Dao, C. T. Lim and S. Suresh, “Nonlinear Elastic and Viscoelastic Deformation of the Human Red Blood Cell with Optical Tweezers,” Mechanics and Chemistry of Biosystems, Vol. 1, No. 3, 2004, pp. 169-180.

[18] E. A. Evans, “New Membrane Concept Applied to the Analysis of Fluid Shear- and Micropipette-Deformed Red Blood Cells,” Biophysical Journal, Vol. 13, No. 9, 1973, pp. 941-954. doi:10.1016/S0006-3495(73)86036-9

[19] R. Skalak, “Strain Energy Function of Red Blood Cell Membrane,” Biophysical Journal, Vol.13, No. 3, 1973, pp. 245-264. doi:10.1016/S0006-3495(73)85983-1

[20] A. M. Dondorp, P. A. Kager, J. Vreeken and N. J. White, “Abnormal Blood Flow and Red Blood Cell Deformability in severe Malaria,” Parasitology Today, Vol. 16, No. 6, 2000, pp. 228-232. doi:10.1016/S0169-4758(00)01666-5

[21] C. T. Lim, E. H. Zhou and S. T. Quek, “Mechanical Model for Living Cells—A Review,” Journal of Biomechanics, Vol. 39, No. 2, 2006, pp. 195-216. doi:10.1016/j.jbiomech.2004.12.008

[22] Ali, M. Hosseini and B. B. Sahari, “A Review of Constitutive Models for Rubber-Like Materials,” American Journal of Engineering and Applied Sciences, Vol. 3, No. 1, 2010, pp. 232-239. doi:10.3844/ajeassp.2010.232.239

[23] H. A. Cranston, C. W. Boylan, G. L. Carroll, S. P. Sutera, J. R. Williamson, I. Y. Gluzman and D. J. Krogstad, “Plasmodium Falciparum Maturation Abolishes Physiologic Red Cell Deformability,” Science, Vol. 223, No. 4634, 1984, pp. 400-403. doi:10.1126/science.6362007

[24] R. Suwanarusk, B. M. Cooke, A. M. Dondorp, K. Si lamut, J. Sattabongkot, N. J. White and R. Udomsang Petch, “The Deformability of Red Blood Cells Parasitized by Plasma Dium Falciparum and P. Vivax,” Journal of Infectious Diseases, Vol. 189. No. 2004, pp. 190-194.

[25] Y. Tan, D. Sun and W. Huang, “Mechanical Modeling of Red Blood Cells during Optical Stret Ching,” Journal of Biomechanical Engineering, Vol. 132, No. 4, 2010, pp. 04450(1-5).

[26] V. Wiwanitkit, “Volume Added, Malarial Infection and Fragility of Red Blood Cell,” Iranian Journal of Medical Hypotheses and Ideas, Vol. 3, No. 4, 2009. http://journals.tums.ac.ir/abs/12485

[27] S. P. Sutera and D. S. Krogstad, “Reduction of the Surface-Volume Ratio: A Physical Mechanism Contributing to the Loss of Red Cell Deformability in Malaria,” Biorheology, Vol. 28, No. 3-4, 1991, pp. 221-229.

[28] D. C. Pamplona, P. B. Goncalves and S. X. R. Lopes, “Finite Deformations of Cylindrical Membrane under Internal Pressure,” International Journal of Mechanical Sciences, Vol. 48, No. 6, 2006, pp. 683-696. doi:10.1016/j.ijmecsci.2005.12.007

[29] P. B. Canham and D. R. Parkinson, “The Area and Volume of Single Human Erythrocytes during Gradual Osmotic Swelling to Hemolysis,” Canadian Journal of Physiology and Pharmacology, Vol. 48, No. 6, 1970, pp. 369-376. doi:10.1139/y70-059

[30] C. Magowan, J. T. Brown, J. Liang, J. Heck, R. L. Coppel, N. Mohandas, W. Meyer-Ilse, “Intracellular Structures of Normal and aberrant Plasmodium Falciparum Malaria Parasites Imaged by Soft X-Ray Microscopy,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 94, No. 12, 1997, pp. 6222-6227. doi:10.1073/pnas.94.12.6222

[31] A. W. L. Jay, “Viscoelastic Properties of the Human Red Blood Cell Membrane I, Defromation, Volume Loss, and Rapture of Red Blood Cells in Micropipettes,” Biophysical Journal, Vol. 13, No. 11, 1973, pp. 1166-1182. doi:10.1016/S0006-3495(73)86053-9