Abstract
The red blood cell (RBC) deformability is a critical aspect, and assessing the cell deformation characteristics is essential for better diagnostics of healthy and deteriorating RBCs. There is a need to explore the connection between the cell deformation characteristics, cell morphology, disease states, storage lesion and cell shape-transformation conditions for better diagnostics and treatments. A numerical approach inspired from the previous research for RBC morphology predictions and for analysis of RBC deformations is proposed for the first time, to investigate the deformation characteristics of different RBC morphologies. The present study investigates the deformability characteristics of stomatocyte, discocyte and echinocyte morphologies during optical tweezers stretching and provides the opportunity to study the combined contribution of cytoskeletal spectrin network and the lipid-bilayer during RBC deformation. The proposed numerical approach predicts agreeable deformation characteristics of the healthy discocyte with the analogous experimental observations and is extended to further investigate the deformation characteristics of stomatocyte and echinocyte morphologies. In particular, the computer simulations are performed to investigate the influence of direct stretching forces on different equilibrium cell morphologies on cell spectrin link extensions and cell elongation index, along with a parametric analysis on membrane shear modulus, spectrin link extensibility, bending modulus and RBC membrane–bead contact diameter. The results agree with the experimentally observed stiffer nature of stomatocyte and echinocyte with respect to a healthy discocyte at experimentally determined membrane characteristics and suggest the preservation of relevant morphological characteristics, changes in spectrin link densities and the primary contribution of cytoskeletal spectrin network on deformation behaviour of stomatocyte, discocyte and echinocyte morphologies during optical tweezers stretching deformation. The numerical approach presented here forms the foundation for investigations into deformation characteristics and recoverability of RBCs undergoing storage lesion.
Similar content being viewed by others
References
Balanant MA (2018) Experimental studies of red blood cells during storage (Doctor of Philosophy), Queensland University of Technology
Barns S, Balanant MA, Sauret E, Flower R, Saha S, Gu Y (2017) Investigation of red blood cell mechanical properties using AFM indentation and coarse-grained particle method. Biomed Eng 16(1):140
Bento D, Rodrigues R, Faustino V, Pinho D, Fernandes C, Pereira A, Garcia V, Miranda J, Lima R (2018) Deformation of red blood cells, air bubbles, and droplets in microfluidic devices: flow visualizations and measurements. Micromachines 9(4):3–18
Bessis M (1973) Red cell shapes. An illustrated classification and its rationale. Paper presented at the Red Cell Shape, Berlin, Heidelberg
Boey SK, Boal DH, Discher DE (1998) Simulations of the erythrocyte cytoskeleton at large deformation: I. Microscopic models. Biophys J 75(3):1573–1583
Branton D, Cohen CM, Tyler J (1981) Interaction of cytoskeletal proteins on the human erythrocyte membrane. Cell 24(1):24–32
Brecher G, Bessis M (1972) Present status of spiculed red cells and their relationship to the discocyte-echinocyte transformation: a critical review. Blood 40(3):333–344
Chang H-Y, Li X, Li H, Karniadakis GE (2016) Md/dpd multiscale framework for predicting morphology and stresses of red blood cells in health and disease. PLoS Comput Biol 12(10):e1005173
Chen M, Boyle FJ (2017) An enhanced spring-particle model for red blood cell structural mechanics: application to the stomatocyte–discocyte–echinocyte transformation. J Biomech Eng 139(12):121009
Chen XY, Huang YX, Liu W, Yuan ZJ (2007) Membrane surface charge and morphological and mechanical properties of young and old erythrocytes. Curr Appl Phys 7:94–96
Czerwinska J, Wolf SM, Mohammadi H, Jeney S (2015) Red blood cell aging during storage, studied using optical tweezers experiment. Cell Mol Bioeng 8(2):258–266
Dao M, Lim CT, Suresh S (2003) Mechanics of the human red blood cell deformed by optical tweezers. J Mech Phys Solids 51(11):2259–2280
Dao M, Li J, Suresh S (2006) Molecularly based analysis of deformation of spectrin network and human erythrocyte. Mater Sci Eng, C 26(8):1232–1244
Discher DE, Boal DH, Boey SK (1998) Simulations of the erythrocyte cytoskeleton at large deformation: I. Micropipette aspiration. Biophys J 75(3):1584–1597
Etcheverry S, Gallardo MJ, Solano P, Suwalsky M, Mesquita ON, Saavedra C (2012) Real-time study of shape and thermal fluctuations in the echinocyte transformation of human erythrocytes using defocusing microscopy. J Biomed Opt 17(10):106013
Fedosov DA, Caswell B, Karniadakis GE (2009) Coarse-grained red blood cell model with accurate mechanical properties, rheology and dynamics. In: Annual international conference of the ieee engineering in medicine and biology society, vol 1–20, pp 4266–4269
Fedosov DA, Caswell B, Karniadakis GE (2010a) A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. Biophys J 98(10):2215–2225
Fedosov DA, Caswell B, Karniadakis GE (2010b) Systematic coarse-graining of spectrin-level red blood cell models. Comput Methods Appl Mech Eng 199(29–32):1937–1948
Fedosov DA, Dao M, Karniadakis GE, Suresh S (2014a) Computational biorheology of human blood flow in health and disease. Ann Biomed Eng 42(2):368–387
Fedosov DA, Noguchi H, Gompper G (2014b) Multiscale modeling of blood flow: from single cells to blood rheology. Biomech Model Mechanobiol 13(2):239–258
Gedde MM, Yang E, Huestis WH (1999) Resolution of the paradox of red cell shape changes in low and high ph. Biochim Biophys Acta (BBA) Biomembr 1417(2):246–253
Geekiyanage NM, Balanant MA, Sauret E, Saha S, Flower R, Lim CT, Gu Y (2019) A coarse-grained red blood cell membrane model to study stomatocyte-discocyte-echinocyte morphologies. PLoS ONE. https://doi.org/10.1371/journal.pone.0215447
Heinrich V, Svetina S, Žekš B (1993) Nonaxisymmetric vesicle shapes in a generalized bilayer-couple model and the transition between oblate and prolate axisymmetric shapes. Phys Rev E 48(4):3112–3123
Helfrich W (1974) Blocked lipid exchange in bilayers and its possible influence on the shape of vesicles. Z Nat 29(C):510–515
Hénon S, Lenormand G, Richert A, Gallet F (1999) A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers. Biophys J 76(2):1145–1151
Iglič A, Kralj-Iglič V, Hägerstrand H (1998) Amphiphile induced echinocyte-spheroechinoeyte transformation of red blood cell shape. Eur Biophys J 27(4):335–339
Israelachvili JN (2011) Intermolecular and surface forces, 3rd edn. Elsevier, Amsterdam
Jiang LG, Wu HA, Zhou XZ, Wang XX (2010) Coarse-grained molecular dynamics simulation of a red blood cell. Chin Phys Lett 27(2):028704
Ju M, Ye SS, Namgung B, Cho S, Low HT, Leo HL, Kim S (2015) A review of numerical methods for red blood cell flow simulation. Comput Methods Biomech Biomed Eng 18(2):130–140
Khairy K, Howard J (2011) Minimum-energy vesicle and cell shapes calculated using spherical harmonics parameterization. Soft Matter 7(5):2138–2143
Khairy K, Foo J, Howard J (2008) Shapes of red blood cells: comparison of 3d confocal images with the bilayer-couple model. Cell Mol Bioeng 1(2):173–181
Kim Y, Kim K, Park YK (2012) Measurement techniques for red blood cell deformability: recent advances. InTech, London
Kozlova E, Chernysh A, Moroz V, Sergunova V, Gudkova O, Manchenko E (2017) Morphology, membrane nanostructure and stiffness for quality assessment of packed red blood cells. Sci Rep 7(1):1–11
Kuzman D, Svetina S, Waugh RE, Žekš B (2004) Elastic properties of the red blood cell membrane that determine echinocyte deformability. Eur Biophys J 33(1):1–15
Lai L, Xu X, Lim Chwee T, Cao J (2015) Stiffening of red blood cells induced by cytoskeleton disorders: a joint theory-experiment study. Biophys J 109(11):2287–2294
Lee JCM, Discher DE (2001) Deformation-enhanced fluctuations in the red cell skeleton with theoretical relations to elasticity, connectivity, and spectrin unfolding. Biophys J 81(6):3178–3192
Li H, Lykotrafitis G (2014) Erythrocyte membrane model with explicit description of the lipid bilayer and the spectrin network. Biophys J 107(3):642–653
Li J, Dao M, Lim CT, Suresh S (2005) Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophys J 88(5):3707–3719
Li J, Lykotrafitis G, Dao M, Suresh S (2007) Cytoskeletal dynamics of human erythrocyte. Proc Natl Acad Sci USA 104(12):4937–4942
Li Y, Wen C, Xie H, Ye A, Yin Y (2009) Mechanical property analysis of stored red blood cell using optical tweezers. Colloids Surf B Biointerfaces 70(2):169–173
Li X, Dao M, Lykotrafitis G, Karniadakis GE (2016) Biomechanics and biorheology of red blood cells in sickle cell anemia. J Biomech 50:34–41
Li X, Li H, Chang HY, Lykotrafitis G, Karniadakis GE (2017) Computational biomechanics of human red blood cells in hematological disorders. J Biomech Eng. https://doi.org/10.1115/1.4035120
Li H, Lu L, Li X, Buffet PA, Dao M, Karniadakis GE, Suresh S (2018) Mechanics of diseased red blood cells in human spleen and consequences for hereditary blood disorders. Proc Natl Acad Sci USA 115(38):9574–9579
Liang Y, Xiang Y, Lamstein J, Bezryadina A, Chen Z (2019) Cell deformation and assessment with tunable “tug-of-war” optical tweezers. Paper presented at the Conference on Lasers and Electro-Optics, San Jose, California
Lim GHW, Wortis M, Mukhopadhyay R (2002) Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: evidence for the bilayer—couple hypothesis from membrane mechanics. Proc Natl Acad Sci USA 99(26):16766–16769
Lim CT, Dao M, Suresh S, Sow CH, Chew KT (2004) Large deformation of living cells using laser traps. Acta Mater 52(7):1837–1845
Lim GHW, Wortis M, Mukhopadhyay R (2009) Red blood cell shapes and shape transformations: Newtonian mechanics of a composite membrane—sections 2.5–2.8. In: Soft matter, pp 83–250
Matthews K, Myrand-Lapierre M-E, Ang RR, Duffy SP, Scott MD, Ma H (2015) Microfluidic deformability analysis of the red cell storage lesion. J Biomech 48(15):4065–4072
Miao L, Seifert U, Wortis M, Döbereiner H-G (1994) Budding transitions of fluid-bilayer vesicles: the effect of area-difference elasticity. Phys Rev E 49(6):5389–5407
Mills JP, Qie L, Dao M, Lim CT, Suresh S (2004) Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Mech Chem Biosyst 1(3):169–180
Mohandas N, Gallagher PG (2008) Red cell membrane: past, present, and future. Blood 112(10):3939–3948
Monzel C, Sengupta K (2016) Measuring shape fluctuations in biological membranes. J Phys D Appl Phys 49(24):243002
Mukhopadhyay R, Lim G, Wortis M (2002) Echinocyte shapes: bending, stretching, and shear determine spicule shape and spacing. Biophys J 82(4):1756–1772
Muñoz S, Sebastián JL, Sancho M, Álvarez G (2014) Elastic energy of the discocyte–stomatocyte transformation. Biochim Biophys (BBA) Acta Biomembr 1838(3):950–956
Nakamura M, Bessho S, Wada S (2014) Analysis of red blood cell deformation under fast shear flow for better estimation of hemolysis. Int J Numer Methods Biomed Eng 30(1):42–54
Pages G, Yau TW, Kuchel PW (2010) Erythrocyte shape reversion from echinocytes to discocytes: kinetics via fast-measurement NMR diffusion-diffraction. Magn Resonan Med 64(3):645–652
Park Y, Best CA, Badizadegan K, Dasari RR, Feld MS, Kuriabova T, Henle ML, Levine AJ, Popescu G (2010) Measurement of red blood cell mechanics during morphological changes. Proc Natl Acad Sci USA 107(15):6731–6736
Peng Z, Asaro RJ, Zhu Q (2010) Multiscale simulation of erythrocyte membranes. Phys Rev E 81(3):031904
Peng Z, Asaro RJ, Zhu Q (2011) Multiscale modelling of erythrocytes in stokes flow. J Fluid Mech 686:299–337
Peng Z, Li X, Pivkin IV, Dao M, Karniadakis GE, Suresh S (2013) Lipid bilayer and cytoskeletal interactions in a red blood cell. Proc Natl Acad Sci USA 110(33):13356–13361
Polwaththe-Gallage HN, Saha SC, Gu Y (2014) Deformation of a three-dimensional red blood cell in a stenosed microcapillary. Paper presented at the 8th Australasian Congress on Applied Mechanics (ACAM-8), Melbourne, Australia
Polwaththe-Gallage HN, Saha SC, Sauret E, Flower R, Senadeera W, Gu Y (2016) Sph-dem approach to numerically simulate the deformation of three-dimensional RBCS in non-uniform capillaries. Biomed Eng Online 15:354–370
Roussel C, Dussiot M, Marin M, Morel A, Ndour PA, Duez J, Kim CLV, Hermine O, Colin Y, Buffet PA, Amireault P (2017) Spherocytic shift of red blood cells during storage provides a quantitative whole cell–based marker of the storage lesion. Transfusion 57(4):1007–1018
Rudenko SV (2010) Erythrocyte morphological states, phases, transitions and trajectories. Biochim Biophys Acta Biomembr 1798(9):1767–1778
Rudenko SV, Saeid MK (2010) Reconstruction of erythrocyte shape during modified morphological response. Biochemistry (Moscow) 75(8):1025–1031
Seifert U, Berndl K, Lipowsky R (1991) Shape transformations of vesicles: phase diagram for spontaneous- curvature and bilayer-coupling models. Phys Rev A 44(2):1182–1202
Sheetz MP, Singer SJ (1974) Biological membranes as bilayer couples: molecular mechanisms of drug-erythrocyte interactions. Proc Natl Acad Sci USA 71(11):4457–4461
Sigüenza J, Mendez S, Nicoud F (2017) How should the optical tweezers experiment be used to characterize the red blood cell membrane mechanics? Biomech Model Mechanobiol 16(5):1645–1657
Suresh S, Spatz J, Mills JP, Micoulet A, Dao M, Lim CT, Beil M, Seufferlein T (2005) Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria. Acta Biomater 1(1):15–30
Svetina S (2009) Vesicle budding and the origin of cellular life. ChemPhysChem 10(16):2769–2776
Svetina S, Žekš B (1989) Membrane bending energy and shape determination of phospholipid vesicles and red blood cells. Eur Biophys J 17(2):101–111
Svetina S, Kuzman D, Waugh RE, Ziherl P, Žekš B (2004) The cooperative role of membrane skeleton and bilayer in the mechanical behaviour of red blood cells. Bioelectrochemistry 62(2):107–113
Tachev KD, Danov KD, Kralchevsky PA (2004) On the mechanism of stomatocyte-echinocyte transformations of red blood cells: experiment and theoretical model. Colloids Surf B Biointerfaces 34(2):123–140
Tomaiuolo G (2014) Biomechanical properties of red blood cells in health and disease towards microfluidics. Biomicrofluidics 8(5):051501
Tong Z-X, Chen X, He Y-L, Liao X-B (2018) Coarse-grained area-difference-elasticity membrane model coupled with ib–lb method for simulation of red blood cell morphology. Phys A Stat Mech Appl 509:1183–1194
Wang Y, You G, Chen P, Li J, Chen G, Wang B, Li P, Han D, Zhou H, Zhao L (2016) The mechanical properties of stored red blood cells measured by a convenient microfluidic approach combining with mathematic model. Biomicrofluidics 10(2):024104
Wong P (1999) A basis of echinocytosis and stomatocytosis in the disc–sphere transformations of the erythrocyte. J Theor Biol 196(3):343–361
Xing F, Xun S, Zhu Y, Hu F, Drevenšek-Olenik I, Zhang X, Pan L, Xu J (2019) Microfluidic assemblies designed for assessment of drug effects on deformability of human erythrocytes. Biochem Biophys Res Commun 512(2):303–309
Xu Z, Pu H, Xie S, Wang C, Sun Y (2017) Microfluidic measurement of RBC bending stiffness changes in blood storage. Paper presented at the 19th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS)
Xu Z, Zheng Y, Wang X, Shehata N, Wang C, Sun Y (2018) Stiffness increase of red blood cells during storage. Microsyst Nanoeng 4:1–6
Yazdani A, Li X, Karniadakis GE (2016) Dynamic and rheological properties of soft biological cell suspensions. Rheol Acta 55(6):433–449
Závodszky G, van Rooij B, Azizi V, Hoekstra A (2017) Cellular level in silico modeling of blood rheology with an improved material model for red blood cells. Front Physiol 8:563
Zheng Y, Chen J, Cui T, Shehata N, Wang C, Sun Y (2014) Characterization of red blood cell deformability change during blood storage. Lab Chip 14(3):577–583
Acknowledgements
The authors would like to acknowledge the Australian Research Council for their financial support through Linkage Grant (LP150100737), and Queensland University of Technology (QUT) for the financial assistance through QUT Postgraduate Research Award (QUTPRA), Higher Degree Research (HDR) Tuition Fee Sponsorship and QUT Excellence Top-Up Scholarship. Support provided by Dr. HN Polwaththe-Gallage, Dr. S Barns, QUT’s High Performance Computer Resources (HPC) and the Australian Red Cross Lifeblood is gratefully acknowledged. The Australian Government fully fund the Australian Red Cross Lifeblood for the provision of blood, blood products and services to the Australian community.
Author information
Authors and Affiliations
Contributions
Geekiyanage developed the CG–RBC model and algorithm, performed modelling, data analysis and composed the manuscript. Sauret guided the model development, data analysis and revised the manuscript. Saha revised the manuscript. Flower revised the manuscript. Gu guided the model development and revised the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Geekiyanage, N.M., Sauret, E., Saha, S.C. et al. Deformation behaviour of stomatocyte, discocyte and echinocyte red blood cell morphologies during optical tweezers stretching. Biomech Model Mechanobiol 19, 1827–1843 (2020). https://doi.org/10.1007/s10237-020-01311-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-020-01311-w