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How should the optical tweezers experiment be used to characterize the red blood cell membrane mechanics?

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Abstract

Stretching red blood cells using optical tweezers is a way to characterize the mechanical properties of their membrane by measuring the size of the cell in the direction of the stretching (axial diameter) and perpendicularly (transverse diameter). Recently, such data have been used in numerous publications to validate solvers dedicated to the computation of red blood cell dynamics under flow. In the present study, different mechanical models are used to simulate the stretching of red blood cells by optical tweezers. Results first show that the mechanical moduli of the membranes have to be adjusted as a function of the model used. In addition, by assessing the area dilation of the cells, the axial and transverse diameters measured in optical tweezers experiments are found to be insufficient to discriminate between models relevant to red blood cells or not. At last, it is shown that other quantities such as the height or the profile of the cell should be preferred for validation purposes since they are more sensitive to the membrane model.

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References

  • Abkarian M, Viallat A (2016) Fluid–structure interactions in low-Reynolds-number flows. In: On the importance of the deformability of red blood cells in blood flow. Royal Society of Chemistry, London

  • Barthès-Biesel D, Diaz A, Dhenin E (2002) Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation. J Fluid Mech 460:211–222

    Article  MATH  Google Scholar 

  • Charrier JM, Shrivastava S, Wu R (1989) Free and constrained inflation of elastic membranes in relation to thermoforming non-axisymmetric problems. J Strain Anal Eng Des 24(2):55–74

    Article  Google Scholar 

  • Chen M, Boyle FJ (2014) Investigation of membrane mechanics using spring networks: application to red-blood-cell modelling. Mater Sci Eng C 43:506–516

    Article  Google Scholar 

  • Chnafa C, Mendez S, Nicoud F (2014) Image-based large-eddy simulation in a realistic left heart. Comput Fluids 94:173–187

    Article  MathSciNet  Google Scholar 

  • Chorin A (1968) Numerical solution of the Navier–Stokes equations. Math Comput 22:745–762

    Article  MathSciNet  MATH  Google Scholar 

  • Cordasco D, Yazdani Bagchi P (2014) Comparison of erythrocyte dynamics in shear flow under different stress-free configurations. Phys Fluids 26:041902

    Article  Google Scholar 

  • Dao M, Lim CT, Suresh S (2003) Mechanics of the human red blood cell deformed by optical tweezers. J Mech Phys Solids 51:2259–2280

    Article  Google Scholar 

  • Dao M, Li J, Suresh S (2006) Molecularly based analysis of deformation of spectrin network and human erythrocyte. Mater Sci Eng C 26:1232–1244

    Article  Google Scholar 

  • Dimitrakopoulos P (2012) Analysis of the variation in the determination of the shear modulus of the erythrocyte membrane: effects of the constitutive law and membrane modeling. Phys Rev E 85:041917

    Article  Google Scholar 

  • Discher DE, Mohandas N, Evans EA (1994) Molecular maps of red cell deformation: hidden elastic and in situ connectivity. Science 266:1032–1035

    Article  Google Scholar 

  • Doddi SK, Bagchi P (2008) Lateral migration of a capsule in a plane Poiseuille flow in a channel. Int J Multiph Flow 34:966–986

    Article  Google Scholar 

  • Dupire J, Abkarian M, Viallat A (2015) A simple model to understand the effect of membrane shear elasticity and stress-free shape on the motion of red blood cells in shear flow. Soft Matter 11:8372–8382

    Article  Google Scholar 

  • Eggleton CD, Popel AS (1998) Large deformation of red blood cell ghosts in a simple shear flow. Phys Fluids 10(8):1834–1845

    Article  Google Scholar 

  • Evans EA (1973) New membrane concept applied to the analysis of fluid shear- and micropipette-deformed red blood cells. Biophys J 13:941–954

    Article  Google Scholar 

  • Evans EA, Fung YC (1972) Improved measurements of the erythrocyte geometry. Microvasc Res 4:335–347

    Article  Google Scholar 

  • Farutin A, Biben T, Misbah C (2014) 3D numerical simulations of vesicle and inextensible capsule dynamics. J Comput Phys 275:539–568

    Article  MathSciNet  MATH  Google Scholar 

  • Fedosov DA, Caswell B, Karniadakis G (2010a) Systematic coarse-graining of spectrin-level red blood cell models. Comput Methods Appl Mech Eng 199:1937–1948

    Article  MathSciNet  MATH  Google Scholar 

  • Fedosov DA, Caswell B, Karniadakis GE (2010b) A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. Biophys J 98:2215–2225

    Article  Google Scholar 

  • Fedosov DA, Noguchi H, Gompper G (2014) Multiscale modeling of blood flow: from single cells to blood rheology. Biomech Model Mechanobiol 13:239–258

    Article  Google Scholar 

  • Helfrich W (1973) Elastic properties of lipid bilayers: theory and possible experiments. Z Naturforsch 28c:693–703

    Google Scholar 

  • Hénon S (1999) A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers. Biophys J 76:1145–1151

    Article  Google Scholar 

  • Khairy K, Howard J (2011) Minimum-energy vesicle and cell shapes calculated using spherical harmonics parameterization. Soft Matter 7:2138–2143

    Article  Google Scholar 

  • Klöppel T, Wall WA (2011) A novel two-layer, coupled finite element approach for modeling the nonlinear elastic and viscoelastic behavior of human erythrocytes. Biomech Model Mechanobiol 10:445–459

    Article  Google Scholar 

  • Le DV, White J, Peraire J, Lim KM, Khoo BC (2009) An implicit immersed boundary method for three-dimensional fluid–membrane interactions. J Comput Phys 228:8427–8445

    Article  MathSciNet  MATH  Google Scholar 

  • Li J, Dao M, Lim CT, Suresh S (2005) Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophys J 88:3707–3719

    Article  Google Scholar 

  • Lim GHW, Wortiz 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):16,766–16,769

    Article  Google Scholar 

  • Lim GHW, Wortiz M, Mukhopadhyay R (2008) Red blood cell shapes and shape transformations: Newtonian mechanics of a composite membrane, soft matter, vol lipid bilayers and red blood cells, chap 2. WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

    Google Scholar 

  • Malandain M, Maheu N, Moureau V (2013) Optimization of the deflated conjugate gradient algorithm for the solving of elliptic equations on massively parallel machines. J Comput Phys 238:32–47

    Article  MathSciNet  Google Scholar 

  • Martins Afonso M, Mendez S, Nicoud F (2014) On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid. J Fluid Mech 746:300–331

    Article  Google Scholar 

  • Mendez S, Gibaud E, Nicoud F (2014) An unstructured solver for simulations of deformable particles in flows at arbitrary Reynolds numbers. J Comput Phys 256(1):465–483

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Mohandas N, Gallagher PG (2008) Red cell membrane: past, present, and future. Blood 112(10):3939–3948

    Article  Google Scholar 

  • Moureau V, Domingo P, Vervisch L (2011) Design of a massively parallel CFD code for complex geometries. Comp Rend Méc 339(2–3):141–148

    MATH  Google Scholar 

  • Peng Z, Mashayekh A, Zhu Q (2014) Erythrocyte responses in low-shear-rate flows: effects of non-biconcave stress-free state in the cytoskeleton. J Fluid Mech 742:96–118

    Article  Google Scholar 

  • Peng Z, Salehyar S, Zhu Q (2015) Stability of the tank treading modes of erythrocytes and its dependence on cytoskeleton reference states. J Fluid Mech 771:449–467

    Article  MathSciNet  Google Scholar 

  • Peskin CS (2002) The immersed boundary method. Acta Number 11:479–517

    MathSciNet  MATH  Google Scholar 

  • Pinelli A, Naqavi IZ, Piomelli U, Favier J (2010) Immersed-boundary methods for general finite-difference and finite-volume Navier–Stokes solvers. J Comput Phys 229:9073–9091

    Article  MathSciNet  MATH  Google Scholar 

  • Pivkin IV, Karniadakis GE (2008) Accurate coarse-grained modeling of red blood cells. Phys Rev Lett 101:118105

    Article  Google Scholar 

  • Sigüenza J, Mendez S, Nicoud F (2014) Characterisation of a dedicated mechanical model for red blood cells: numerical simulations of optical tweezers experiment. Comput Methods Biomech Biomed Eng 17(supp. 1):28–29

    Article  Google Scholar 

  • Sigüenza J, Mendez S, Ambard D, Dubois F, Jourdan F, Mozul R, Nicoud F (2016) Validation of an immersed thick boundary method for simulating fluid–structure interactions of deformable membranes. J Comput Phys 322:723–746

    Article  MathSciNet  MATH  Google Scholar 

  • Sinha K, Graham MD (2015) Dynamics of a single red blood cell in simple shear flow. Phys Rev E 92:042710

    Article  Google Scholar 

  • Skalak R, Tozeren A, Zarda RP, Chien S (1973) Strain energy function of red blood cell membranes. Biophys J 13:245–264

    Article  Google Scholar 

  • Sui Y, Chew YT, Roy P, Cheng YP, Low HT (2008) Dynamic motion of red blood cells in simple shear flow. Phys Fluids 20:112106

  • 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 1:15–30

    Article  Google Scholar 

  • Yeoh OH (1993) Some forms of the strain energy function for rubber. Rubber Chem Technol 66(5):754–771

    Article  Google Scholar 

  • Zhong-can OY, Helfrich W (1989) Bending energy of vesicle membranes: general expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. Phys Rev A 39(10):5280–5288

    Article  Google Scholar 

  • Zmijanovic V, Mendez S, Moureau V, Nicoud F (2017) About the numerical robustness of biomedical benchmark cases: interlaboratory FDA’s idealized medical device. Int J Numer Methods Biomed Eng 33(1):1–17

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Acknowledgements

V. Moureau and G. Lartigue from the CORIA lab, and the SUCCESS scientific group are acknowledged for providing the YALES2 solver which constitutes the basis of the YALES2BIO tool.

Funding This study was performed with supports from ANR (FORCE project ANR-11-JS09-0011), from BPIfrance (DAT@DIAG Project No. I1112018W) and from the NUMEV Labex (ANR-10-LABX-20).

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Correspondence to Julien Sigüenza.

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Sigüenza, J., Mendez, S. & Nicoud, F. How should the optical tweezers experiment be used to characterize the red blood cell membrane mechanics?. Biomech Model Mechanobiol 16, 1645–1657 (2017). https://doi.org/10.1007/s10237-017-0910-x

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  • DOI: https://doi.org/10.1007/s10237-017-0910-x

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