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