Effect of the natural state of an elastic cellular membrane on tank-treading and tumbling motions of a single red blood cell.

A two-dimensional computer simulation model was proposed for tank-treading and tumbling motions of an elastic biconcave red blood cell (RBC) under steady shear flow. The RBC model consisted of an outer cellular membrane and an inner fluid; the membrane's elastic properties were modeled by springs for stretch/compression and bending to consider the membrane's natural state in a practical manner. Membrane deformation was coupled with incompressible viscous flow of the inner and outer fluids of the RBC using a particle method. The proposed simulation model was capable of reproducing tank-treading and tumbling motions of an RBC along with rotational oscillation, which is the transition between the two motions. In simulations using the same initial RBC shape with different natural states of the RBC membrane, only tank-treading motion was exhibited in the case of a uniform natural state of the membrane, and a nonuniform natural state was necessary to generate the rotational oscillation and tumbling motion. Simulation results corresponded to published data from experimental and computational studies. In the range of simulation parameters considered, the relative membrane elastic force versus fluid viscous force was approximately 1 at the transition when the natural state nonuniformity was taken into account in estimating the membrane elastic force. A combination of natural state nonuniformity and elastic spring constant determined that change in the RBC deformation at the transition is that from a large compressive deformation to no deformation, such as rigid body.

[1]  Sai K. Doddi,et al.  Three-dimensional computational modeling of multiple deformable cells flowing in microvessels. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Michael M. Dupin,et al.  Blood Cell Interactions and Segregation in Flow , 2008, Annals of Biomedical Engineering.

[3]  Thomas Podgorski,et al.  Micro-macro link in rheology of erythrocyte and vesicle suspensions. , 2008, Biophysical journal.

[4]  Thomas M Fischer,et al.  Tank-tread frequency of the red cell membrane: dependence on the viscosity of the suspending medium. , 2007, Biophysical journal.

[5]  Daniel A Beard,et al.  The Role of Theoretical Modeling in Microcirculation Research , 2008, Microcirculation.

[6]  C. Pozrikidis.  Resting shape and spontaneous membrane curvature of red blood cells. , 2005, Mathematical medicine and biology : a journal of the IMA.

[7]  Subra Suresh,et al.  The biomechanics toolbox: experimental approaches for living cells and biomolecules , 2003 .

[8]  Shigeo Wada,et al.  Particle method for computer simulation of red blood cell motion in blood flow , 2006, Comput. Methods Programs Biomed..

[9]  Takao Furukawa,et al.  Residual stress and strain in the lamellar unit of the porcine aorta: experiment and analysis. , 2004, Journal of biomechanics.

[10]  E. Evans,et al.  Mechanical properties of the red cell membrane in relation to molecular structure and genetic defects. , 1994, Annual review of biophysics and biomolecular structure.

[11]  Dominique Barthès-Biesel,et al.  Deformation of a capsule in simple shear flow: Effect of membrane prestress , 2005 .

[12]  Thomas M Fischer,et al.  Shape memory of human red blood cells. , 2004, Biophysical journal.

[13]  A. Pries,et al.  Two-Dimensional Simulation of Red Blood Cell Deformation and Lateral Migration in Microvessels , 2007, Annals of Biomedical Engineering.

[14]  Saroja Ramanujan,et al.  Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities , 1998, Journal of Fluid Mechanics.

[15]  T. Adachi,et al.  Uniform stress state in bone structure with residual stress. , 1998, Journal of biomechanical engineering.

[16]  Jack Lee,et al.  Theoretical Modeling in Hemodynamics of Microcirculation , 2008, Microcirculation.

[17]  Dominique Barthès-Biesel,et al.  Motion of a capsule in a cylindrical tube: effect of membrane pre-stress , 2007, Journal of Fluid Mechanics.

[18]  J. McWhirter,et al.  Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries , 2009, Proceedings of the National Academy of Sciences.

[19]  R. Kobayashi,et al.  Numerical Simulation of Various Shape Changes of a Swollen Red Blood Cell by Decrease of Its Volume. , 2003 .

[20]  Masako Sugihara-Seki,et al.  Blood flow and permeability in microvessels , 2005 .

[21]  R M Hochmuth,et al.  Erythrocyte membrane elasticity and viscosity. , 1987, Annual review of physiology.

[22]  Magalie Faivre,et al.  Swinging of red blood cells under shear flow. , 2007, Physical review letters.

[23]  Shigeo Wada,et al.  Simulation Study on Effects of Hematocrit on Blood Flow Properties Using Particle Method , 2006 .

[24]  H Schmid-Schönbein,et al.  The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. , 1978, Science.

[25]  A. Pries,et al.  Biophysical aspects of blood flow in the microvasculature. , 1996, Cardiovascular research.

[26]  T W Secomb,et al.  Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition. , 2007, Physical review letters.

[27]  C. Pozrikidis,et al.  Numerical Simulation of the Flow-Induced Deformation of Red Blood Cells , 2003, Annals of Biomedical Engineering.

[28]  Hiroshi Noguchi,et al.  Swinging and tumbling of fluid vesicles in shear flow. , 2007, Physical review letters.

[29]  M. Dupin,et al.  Modeling the flow of dense suspensions of deformable particles in three dimensions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Victor Steinberg,et al.  Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow. , 2006, Physical review letters.

[31]  R. Skalak,et al.  Motion of a tank-treading ellipsoidal particle in a shear flow , 1982, Journal of Fluid Mechanics.

[32]  F. C. Macintosh,et al.  Flow behaviour of erythrocytes - I. Rotation and deformation in dilute suspensions , 1972, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[33]  X. B. Chen,et al.  Transient deformation of elastic capsules in shear flow: effect of membrane bending stiffness. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  C. Pozrikidis,et al.  Buckling of a pre-compressed or pre-stretched membrane in shear flow , 2007 .

[35]  N. Gov,et al.  Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects. , 2005, Biophysical journal.

[36]  L. Munn,et al.  Particulate nature of blood determines macroscopic rheology: a 2-D lattice Boltzmann analysis. , 2005, Biophysical journal.

[37]  Dominique Barthès-Biesel,et al.  Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation , 2002, Journal of Fluid Mechanics.

[38]  P. Gaehtgens,et al.  Motion, deformation, and interaction of blood cells and plasma during flow through narrow capillary tubes. , 1980, Blood cells.

[39]  Subra Suresh,et al.  Cytoskeletal dynamics of human erythrocyte , 2007, Proceedings of the National Academy of Sciences.

[40]  S. Koshizuka,et al.  Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid , 1996 .

[41]  U. Seifert,et al.  Swinging and tumbling of elastic capsules in shear flow , 2007, Journal of Fluid Mechanics.

[42]  R. Skalak,et al.  Deformation of Red Blood Cells in Capillaries , 1969, Science.

[43]  H T Low,et al.  Tank-treading, swinging, and tumbling of liquid-filled elastic capsules in shear flow. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.