An Adaptive, Cartesian, Front-Tracking Method for the Motion, Deformation and Adhesion of Circulating Cells

Journal of Computational Physics

Volumn 143, Issue 2, 1998, Pages 346-380

  Agresar, G ^a   Linderman, J J ^b   Tryggvason, G ^a   Powell, K G ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b University of Michigan   (United States)

Author keywords

Adaptive refinement; Cell detachment; Cell mechanics; Drops; Immersed boundary method; Incompressible Navier Stokes; Micropipet; Micropipette

Indexed keywords

CARDIOVASCULAR SYSTEM; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; SHEAR FLOW; SOFTWARE TESTING; SOLS; TURBULENT FLOW;

ADAPTIVE REFINEMENT; CELL DETACHMENT; CELL MECHANICS; CELLS ADHESION; FRONT TRACKING METHOD; IMMERSED BOUNDARY METHODS; INCOMPRESSIBLE NAVIER-STOKES; LENGTH SCALE; MICRO-PIPETTE; MICROPIPET;

CELLS;

EID: 0000891254     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.5967     Document Type: Article

References (46)

1. Glaser V. Work on cell-adhesion-based interactions beginning to bear fruit. Genetic Engineering News. Nov. 15, 1995.
2. Richardson P. D. Physical and molecular biochemical aspects of cell adhesion: Viewpoints approaching a mutual understanding. Principles of Cell Adhesion. 1995.
3. Bell G., Dembo M., Bongrand P. Cell adhesion: Competition between nonspecific repulsion and specific bonding. Biophys. J. 45:1984;1051.
4. Evans E. Detailed mechanics of membrane-membrane adhesion and separation. I. Continuum of molecular cross-bridges. Biophys. J. 48:1985;185.
5. Evans E. Detailed mechanics of membrane-membrane adhesion and separation. II. Discrete kinetically trapped molecular cross-bridges. Biophys. J. 48:1985;175.
6. Dembo M., Torney D. C., Saxman K., Hammer D. The reaction-limited kinetics of membrane-to-surface adhesion and detachment. Proc. R. Soc. London B. 234:1988;55.
7. Tozeren A. Cell-cell, cell substrate adhesion: Theoretical and experimental considerations. J. Biomech. Eng. 112:1990;311.
8. Zhu C. A thermodynamic and biomechanical theory of cell adhesion. Part I: General formulism. J. Theor. Biol. 150:1991;27.
9. Hammer D. A., Lauffenburger D. A. A dynamical model for receptor-mediated cell adhesion to surfaces. Biophys. J. 52:1987;475.
10. Hammer D. A., Apte S. A. Simulation of cell rolling and adhesion on surfaces in shear flow: General results and analysis of selectin-mediated neutrophil adhesion. Biophys. J. 63:1992;35.
11. Evans E. A., Skalak R. Mechanics and Thermodynamics of Biomembranes. 1980.
12. Mow V. C., Guilak F., Tran-Son-Tay R., Hochmuth R. M. Cell Mechanics and Cellular Engineering. 1994.
13. Zhou H., Pozrikidis C. Deformation of liquid capsules with incompressible interfaces in simple shear flow. J. Fluid Mech. 283:1995;175.
14. Fogelson A. L. Continuum models of platelet aggregation: Formulation and mechanical properties. SIAM J. Appl. Math. 52:1992;1089.
15. Unverdi S. O., Tryggvason G. A front-tracking method for viscous, incompressible flows. J. Comput. Phys. 100:1992;25.
16. Bayyuk S. A., Powell K. G., van Leer B. A simulation technique for 2-D unsteady inviscid flows around arbitrarily moving and deforming bodies of arbitrary geometries. AIAA 11th CFD Conference. 1993.
17. Shyy W., Udaykumar H. S., Rao M. M., Smith R. W. Computational Fluid Dynamics with Moving Boundaries. 1996.
18. Sussman M., Smereka P., Osher S. A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114:1994;146.
19. H. Haj-Hariri, Q. Shi, A. Borhan, Boundary Elements XVII, C. A. BrebbiaS. KimT. A. OsswaldH. Power, Computational Mechanics Publications, Billerica, MA, 637.
20. Haj-Hariri H., Shi Q., Shi Q. Thermocapillary motion of deformable drops at finite Reynolds and Marangoni numbers. Phys. Fluids. 9:1997;845.
21. Sussman M., Almgren A. S., Bell J. B., Colella P., Howell L. H., Welcome M. An adaptive level set approach for incompressible two-phase flows. Proceedings of the ASME Fluids Engineering Summer Meeting: Forum on Advances in Numerical Modeling of Free Surface and Interface Dynamics. 3:1996;355.
22. De Zeeuw D. A Quadtree-Based Adaptively-Refined Cartesian-Grid Algorithm for Solution of the Euler Equations. 1993.
23. Bayyuk S. A. Flows about Moving Boundaries and Arbitrary Geometries. 1997.
24. De Zeeuw D., Powell K. G. An adaptively-refined cartesian mesh solver for the Euler equations. J. Comput. Phys. 104:1992;55.
25. Peskin C. S., McQueen D. M. Modeling prosthetic heart valves for numerical analysis of blood flow in the heart. J. Comput. Phys. 37:1980;113.
26. Jan Y. L. Computational Studies of Bubble Dynamics. 1994.
27. Issa R. I. Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62:1985;40.
28. Bell J. B., Colella P., Glaz H. M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85:1989;257.
29. Saad Y. SPARSKIT: A basic tool kit for sparse matrix computations. 1990.
30. Agresar G. A Computational Environment for the Study of Circulating Cell Mechanics and Adhesion. 1996.
31. Peyret R., Taylor T. D. Computational Methods for Fluid Flow. 1983.
32. Nobari M. R., Jan Y.-J, Tryggvason G. Head-on collision of drops - A numerical investigation. Phys. Fluids. 8:1996;1.
33. Esmaeeli A., Tryggvason G. An inverse energy cascade in two-dimensional, low Reynolds number bubbly flows. J. Fluid Mech. 314:1996;315.
34. Coirier W., Powell K. G. Solution-adaptive Cartesian cell approach for viscous and inviscid flows. AIAA J. 34:1996;938.
35. Lamb H. Hydrodynamics. 1932;471.
36. Bagge U., Bränemark P-I. White blood cell rheology. Adv. Microcirc. 7:1977;1.
37. Schmid-Schönbein G. W., Sung K. P., Tözeren H., Skalak R., Chien S. Passive mechanical properties of human leukocytes. Biophys. J. 36:1981;243.
38. Dong C., Skalak R. Leukocyte deformability: Finite element modeling of large viscoelastic deformation. J. Theor. Biol. 158:1992;173.
39. Needham D. N., Hochmuth R. M. A sensitive measure of surface stress in the resting neutrophil. Biophys. J. 61:1992;1664.
40. Evans E., Yeung A. Apparent viscosity and cortical tension of blood granulocytes determined by micropipet aspiration. Biophys. J. 56:1989;151.
41. R. Tran-Son-Tay, H. P. Ting-Beall, D. V. Zhelev, R. M. Hochmuth, Viscous behavior of leukocytes, Cell Mechanics and Cellular Engineering, V. C. MowF. GuilakR. Tran-Son-TayR. M. Hochmuth, Springer-Verlag, New York, 1994, 22.
42. Bray D., Heath J., Moss D. The membrane-associated 'cortex' of animal cells: Its structure and mechanical properties. J. Cell Sci. Suppl. 4:1986;71.
43. Needman D., Hochmuth R. M. Rapid flow of passive neutrophils into a 4 μm pipet and measurement of cytoplasmic viscosity. J. Biomech. Eng. 112:1990;269.
44. Chien S., Sung K.-L. P., Skalak R., Usami S., Tözeren A. Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane. Biophys. J. 24:1978;463.
45. Ingber D. E. Cellular tensegrity: Defining new rules of biological design that govern the cytoskeleton. J. Cell Science. 104:1993;613.
46. T. J. Mueller, Application of numerical methods to physiological flows, Numerical Methods in Fluid Dynamics, H. J. WirzJ. J. Smolderen, Hemisphere, Washington, DC, 1978.