A DLM/FD/IB method for simulating cell/cell and cell/particle interaction in microchannels

Tsorng-Whay Pan , Lingling Shi , Roland Glowinski

Chinese Annals of Mathematics, Series B ›› 2010, Vol. 31 ›› Issue (6) : 975 -990.

PDF
Chinese Annals of Mathematics, Series B ›› 2010, Vol. 31 ›› Issue (6) : 975 -990. DOI: 10.1007/s11401-010-0609-0
Article

A DLM/FD/IB method for simulating cell/cell and cell/particle interaction in microchannels

Author information +
History +
PDF

Abstract

A spring model is used to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the red blood cell (RBC) rheology in Poiseuille flow with an immersed boundary method. The lateral migration properties of many cells in Poiseuille flow have been investigated. The authors also combine the above methodology with a distributed Lagrange multiplier/fictitious domain method to simulate the interaction of cells and neutrally buoyant particles in a microchannel for studying the margination of particles.

Keywords

Red blood cells / Elastic spring model / Margination / Fictitious domain method / Immersed boundary method / Microchannel

Cite this article

Download citation ▾
Tsorng-Whay Pan, Lingling Shi, Roland Glowinski. A DLM/FD/IB method for simulating cell/cell and cell/particle interaction in microchannels. Chinese Annals of Mathematics, Series B, 2010, 31(6): 975-990 DOI:10.1007/s11401-010-0609-0

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Adams J., Swarztrauber P., Sweet R.. FISHPAK: A package of Fortran subprograms for the solution of separable elliptic partial differential equations, 1980, Boulder, Colorado: The National Center for Atmospheric Research

[2]

Alexeev A., Verberg R., Balazs A. C.. Modeling the interactions between deformable capsules rolling on a compliant surface. Soft Matter, 2006, 2: 499-509

[3]

Bagchi P.. Mesoscale simulation of blood flow in small vessels. Biophys. J., 2007, 92: 1858-1877

[4]

Bagchi P., Johnson P., Popel A.. Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow. J. Biomech. Eng., 2005, 127: 1070-1080

[5]

Beaucourt J., Rioual F., Séon T. Steady to unsteady dynamics of a vesicle in a flow. Phys. Rev. E, 2004, 9: 011906

[6]

Blackshear P. Jr Forstorm R., Dorman F., Voss G.. Effect of flow on cells near walls. Federal Proceedings, 1971, 30: 1600-1609

[7]

Chorin A. J., Hughes T. J. R., McCracken M. F., Marsden J. E.. Product formulas and numerical algorithms. Comm. Pure Appl. Math., 1978, 31: 205-256

[8]

Cristini V., Kassab G. S.. Computer modeling of red blood cell rheology in the microcirculation: a brief overview. Ann. Biomed. Eng., 2005, 33: 1724-1727

[9]

Crowl L. M., Fogelson A. L.. Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells. Int. J. Numer. Meth. Biomed. Engng., 2009, 26: 471-487

[10]

Dean E. J., Glowinski R.. A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow. C.R. Acad. Sc. Paris, Série 1, 1997, 325: 783-791

[11]

Dean E. J., Glowinski R., Pan T. W.. De Santo J. A.. A wave equation approach to the numerical simulation of incompressible viscous fluid flow modeled by the NavierStokes equations. Mathematical and Numerical Aspects of Wave Propagation, 1998, Philadelphia: SIAM 65-74

[12]

Dubus C., Fournier J. B.. A Gaussian model for the membrane of red blood cells with cytoskeletal defects. Europhys. Lett., 2006, 75: 181-187

[13]

Dupin M. M., Halliday I., Care C. M. Modeling the flow of dense suspensions of deformable particles in three dimensions. Phys. Rev. E, 2007, 75: 066707

[14]

Dzwinel W., Boryczko K., Yuen D.. A discrete-particle model of blood dynamics in capillary vessels. J. Colloid Interface Sci., 2003, 258: 163173

[15]

Eggleton C., Popel A.. Large deformation of red blood cell ghosts in a simple shear flow. Phys. Fluids, 1998, 10: 1834-1845

[16]

Fahraeus R., Lindqvist T.. The viscosity of blood in narrow capillary tubes. Am. J. of Physiol., 1931, 96: 562-568

[17]

Ferrari M.. Cancer nanotechnology: opportunities and challenges. Nat. Rev. Cancer, 2005, 5: 161-171

[18]

Fischer T. M.. Shape memory of human red blood cells. Biophys. J., 2004, 86: 3304-3313

[19]

Fischer T. M., Stöhr-Liesen M., Schmid-Schönbein H.. The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science, 1978, 202: 894-896

[20]

Glowinski R.. Ciarlet P. G., Lions J. L.. Finite element methods for incompressible viscous flow. Handbook of Numerical Analysis, Vol. IX, 2003, Amsterdam: North-Holland 7-1176

[21]

Glowinski R., Pan T.W., Hesla T. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comput. Phys., 2001, 169: 363-427

[22]

Hansen J. C., Skalak S., Hoger A.. An elastic network model based on the structure of the red blood cell membrane skeleton. Biophys. J., 1996, 70: 146-166

[23]

Hosseini S. M., Feng J. J.. A particle-based model for the transport of erythrocytes in capillaries. Chem. Engng. Sci., 2009, 64: 4488-4497

[24]

Keller S. R., Skalak R.. Motion of a tank-treading ellipsoidal particle in a shear flow. J. Fluid Mech., 1982, 120: 27-47

[25]

La Van A. D., Mcguire T. M., Langer R.. Small-scale systems for in vivo drug delivery. Nat. Biotech., 2003, 21: 1184-1191

[26]

Li H. B., Yi H. H., Shan X. W., Fang H. P.. Shape changes and motion of a vesicle in a fluid using a lattice Boltzmann model. Europhysics Letters, 2008, 81: 54002

[27]

Liu L., Liu W. K.. Rheology of red blood cell aggregation by computer simulation. J. Comput. Phys., 2006, 220: 139-154

[28]

Liu W. K., Liu Y., Farrell D. Immersed finite element method and its applications to biological systems. Comput. Methods Appl. Mech. Eng., 2006, 195: 1722-1749

[29]

Pan T. W., Glowinski R.. Direct simulation of the motion of neutrally buoyant circular cylinders in plane Poiseuille flow. J. Comput. Phys., 2002, 181: 260-279

[30]

Pan T. W., Joseph D. D., Bai R. Fluidization of 1204 spheres: simulation and experiments. J. Fluid Mech., 2002, 451: 169-191

[31]

Peskin C. S.. Numerical analysis of blood flow in the heart. J. Comput. Phys., 1977, 25: 220-252

[32]

Peskin C. S.. The immersed boundary method. Acta Numer., 2002, 11: 479-517

[33]

Peskin C. S., McQueen D. M.. Modeling prosthetic heart valves for numerical analysis of blood flow in the heart. J. Comput. Phys., 1980, 37: 11332

[34]

Pozrikidis C.. Modeling and Simulation of Capsules and Biological Cells, 2003, Boca Raton: Chapman & Hall/CRC

[35]

Secomb T. W., Styp-Rekowska B., Pries A. R.. Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels. Ann. Biomed. Eng., 2007, 35: 755-765

[36]

Tsubota K., Wada S., Yamaguchi T.. Simulation study on effects of hematocrit on blood flow properties using particle method. J. Biomech. Sci. Eng., 2006, 1: 159-170

[37]

Vera C., Skelton R., Bossens F., Sung L. A.. 3-D nanomechanics of an erythrocyte junctional complex in equibiaxial and anisotropic deformations. Ann. Biomed. Eng., 2005, 33: 1387-1404

[38]

Wang T., Pan T. W., Xing Z., Glowinski R.. Numerical simulation of rheology of red blood cell rouleaux in microchannels. Phys. Rev. E, 2009, 79: 041916

AI Summary AI Mindmap
PDF

99

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/