A phase field method for simulating morphological evolution of vesicles in electric fields

Journal of Computational Physics

Volumn 228, Issue 11, 2009, Pages 4162-4181

  Gao, Ling Tian ^a   Feng, Xi Qiao ^a   Gao, Huajian ^b  

^a FML   (China)

^b Brown University   (United States)

Author keywords

Biological interfaces; Cell membrane; Electric effects; Flexoelectricity; Mechanical electrical coupling; Phase field method

Indexed keywords

CYTOLOGY; ELECTRIC POTENTIAL; OSMOSIS; PHASE TRANSITIONS;

BIOLOGICAL INTERFACE; DIELECTRICITY; ELECTRIC EFFECT; FLEXOELECTRICITY; MECHANICAL; MECHANICAL-ELECTRICAL COUPLING; MORPHOLOGICAL EVOLUTION; PHASE FIELD METHODS; PHASE FIELDS; PRESSURE SURFACE;

ELECTRIC FIELDS;

EID: 64049116424     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.02.034     Document Type: Article

References (60)

1. Lipowsky R., and Sackmann E. Structure and Dynamics of Membranes (1995), Elsevier, Amsterdam
2. Yawata Y. Cell Membrane: The Red Blood Cell as a Model (2003), Wiley-VCH, Weinheim
3. McCaig C.D., Rajnicek A.M., Song B., and Zhao M. Controlling cell behavior electrically: current views and future potential. Physiol. Rev. 85 3 (2005) 943-978
4. Voldman J. Electrical forces for microscale cell manipulation. Annu. Rev. Biomed. Eng. 8 1 (2006) 425-454
5. Neumann E. Electroporation and Electrofusion in Cell Biology (1989), Springer-Verlag, New York
6. Chassy B.M. Guide to Electroporation and Electrofusion (1991), Academic Press, New York
7. Weaver J.C. Electroporation: a general phenomenon for manipulating cells and tissue. J. Cell Biochem. 51 (1993) 426-435
8. Cevc G., and Richardsen H. Lipid vesicles and membrane fusion. Adv. Drug Deliver. Rev. 38 3 (1999) 207-232
9. Petrov A.G. The Lyotropic States of Matter: Molecular Physics and Living Matter Physics (1999), Gordon & Breach Publishers, New York
10. Mehrishi J.N., and Bauer J. Electrophoresis of cells and the biological relevance of surface charge. Electrophoresis 23 13 (2002) 1984-1994
11. Weaver J.C. Electroporation of biological membranes from multicellular to nano scales. IEEE Trans. Dielect. Elect. Insul. 10 5 (2003) 754-768
12. Chen C., Smye S.W., Robinson M.P., and Evans J.A. Membrane electroporation theories: a review. Med. Biol. Eng. Comput. 44 1-2 (2006) 5-14
13. Riske K.A., and Dimova R. Electro-deformation and poration of giant vesicles viewed with high temporal resolution. Biophys. J. 88 (2005) 1143-1155
14. Riske K.A., and Dimova R. Timescales involved in electro-deformation, poration and fusion of giant vesicles resolved with fast digital imaging. Biophys. J. 88 (2005) 241
15. Haluska C.K., Riske K.A., Marchi-Artzner V., Lehn J.M., Lipowsky R., and Dimova R. From the cover: time scales of membrane fusion revealed by direct imaging of vesicle fusion with high temporal resolution. PNAS 103 (2006) 15841-15846
16. Riske K.A., and Dimova R. Electric pulses induce cylindrical deformations on giant vesicles in salt solutions. Biophys. J. 91 5 (2006) 1778-1786
17. Dimova R., Aranda S., Bezlyepkina N., Nikolov V., Riske K.A., and Lipowsky R. A practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy. J. Phys.: Condens. Matter. 18 (2006) S1151-S1176
18. Dimova R., Riske K.A., Aranda S., Bezlyepkina N., Knorr R.L., and Lipowsky R. Review: giant vesicles in electric fields. Soft Matter 3 (2007) 817-927
19. Gao L.T., Feng X.Q., Yin Y.J., and Gao H.J. A liquid crystal model of vesicles under mechanical and electric fields. J. Mech. Phys. Solids 56 (2008) 2844-2862
20. Seifert U. Configurations of fluid membranes and vesicles. Adv. Phys. 46 1 (1997) 13-137
21. Ou-Yang Z.C., Liu J.X., and Xie Y.Z. Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases (1999), World Scientific, Singapore
22. Kraus M., Wintz W., Seifert U., and Lipowsky R. Fluid vesicles in shear flow. Phys. Rev. Lett. 77 (1996) 3685
23. Seifert U. Fluid membranes in hydrodynamic flow fields: formalism and an application to fluctuating quasispherical vesicles in shear flow. Eur. Phys. J. B 8 (1999) 405
24. Noguchi H., and Gompper G. Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations. Phys. Rev. E 72 (2005) 011901
25. Cantat I., and Misbah C. Dynamics and similarity laws for adhering vesicles in haptotaxis. Phys. Rev. Lett. 83 (1999) 235
26. Cantat I., and Misbah C. Lift force and dynamical unbinding of adhering vesicles under shear flow. Phys. Rev. Lett. 83 (1999) 880
27. Misbah C. Vacillating breathing and tumbling of vesicles under shear flow. Phys. Rev. Lett. 96 (2006) 028104
28. Noguchi H., and Gompper G. Swinging and tumbling of fluid vesicles in shear flow. Phys. Rev. Lett. 98 (2007) 128103
29. Brakke K. The surface evolver. Exp. Math. 1 2 (1992) 141-165
30. Feng F., and Klug W.S. Finite element modeling of lipid bilayer membranes. J. Comput. Phys. 220 (2006) 394-408
31. Ma L., and Klug W.S. Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics. J. Comput. Phys. 227 (2008) 5816-5835
32. Hyuga H., Kinosita Jr. K., and Wakabayashi N. Deformation of vesicles under the influence of strong electric fields. Jap. J. Appl. Phys. 30 5 (1991) 1141-1148
33. Hyuga H., Kinosita Jr. K., and Wakabayashi N. Deformation of vesicles under the influence of strong electric fields II. Jap. J. Appl. Phys. 30 6 (1991) 1333-1335
34. Fan T.H., and Fedorov A.G. Electrohydrodynamics and surface force analysis in AFM imaging of a deformable charged, biological membrane in a dilute electrolyte solution. Langmuir 19 26 (2003) 10930-10939
35. Biben T., Kassner K., and Misbah C. Phase-field approach to three-dimensional vesicle dynamics. Phys. Rev. E 72 (2005) 041921
36. Sethian J.A. Level Set Methods and Fast Marching Methods (1999), Cambridge University Press, Cambridge
37. Osher S., and Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces (2002), Springer-Verlag
38. Belytschko T., Liu W.K., and Moran B. Nonlinear Finite Elements for Continua and Structures (2000), John Wiley & Son, New York
39. Chen L.Q. Phase-field models for microstructure evolution. Annu. Rev. Mater. Res. 32 (2002) 113-140
40. Biben T., and Misbah C. Tumbling of vesicles under shear flow within an advected-field approach. Phys. Rev. E 67 (2003) 031908
41. Du Q., Liu C., and Wang X.Q. A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. J. Comput. Phys. 198 2 (2004) 450-468
42. Campelo F., and Hernandez-Machado A. Dynamic model and stationary shapes of fluid vesicles. Eur. Phys. J. E 20 1 (2006) 37-45
43. Du Q., and Zhu L.Y. Analysis of a mixed finite element method for a phase field bending elasticity model of vesicle membrane deformation. J. Comput. Math. 24 3 (2006) 265-280
44. Du Q., Li M., and Liu C. Analysis of a phase field Navier-Stokes vesicle-fluid interaction model. Disc. Cont. Dyn. Sys. B 8 3 (2007) 539-556
45. Du Q., and Zhang J. Adaptive finite element method for a phase field bending elasticity model of vesicle membrane deformations. SIAM J. Sci. Comput. 30 3 (2008) 1634-1657
46. Glenn H.B., and Wolken J.J. Liquid Crystals and Biological Structures (1979), Academic Press, New York
47. Seifert U. Configurations of fluid membranes and vesicles. Adv. Phys. 46 (1997) 13-137
48. Rosso R., Verani M., and Virga E.G. Second variation of the energy functional for adhering vesicles in two space dimensions. J. Phys. A: Math. Gen. 36 (2003) 12475-12493
49. Brinkmann M., Kierfeld J., and Lipowsky R. A general stability criterion for droplets on structured substrates. J. Phys. A: Math. Gen. 37 (2004) 11429-11547
50. Shi W.D., Feng X.Q., and Gao H.J. Two-dimensional model of vesicle adhesion on curved substrates. Acta Mech. Sinica 22 (2006) 529-535
51. Eringen A.C. Microcontinuum Field Theories II: Fluent Media (2001), Springer, New York
52. Helfrich W. Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28 11 (1973) 693-703
53. de Gennes P.G., and Prost J. The Physics of Liquid Crystals (International Series of Monographs on Physics) (1994), Oxford University Press, USA
54. X. Wang, Phase Field Models and Simulations of Vesicle Bio-Membranes, Ph.D. Thesis. PQDT, The Pennsylvania State University, USA, 2005.
55. Press W.H., Flannery B.P., Teukolsky S.A., and Vetterling W.T. Numerical Recipes in C/C++: The Art of Scientific Computing (2002), Cambridge University Press, Cambridge
56. Fletcher R. Practical Methods of Optimization (2000), John Wiley & Son Ltd., Chichester
57. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method. fifth ed. The Basis vol. 1 (2000), Butterworth-Heinemann, Oxford
58. Kotnik T., and Miklavcic D. Second-order model of membrane electric field induced by alternating external electric fields. IEEE Trans. Biomed. Eng. 47 8 (2000) 1074-1081
59. Gowrishankar T.R., Stewart D.A., and Weaver J.C. Model of a confined spherical cell in uniform and heterogeneous applied electric fields. Bioelectrochemistry 68 2 (2006) 181-190
60. Brown P.N., Hindmarsh A.C., and Petzold L.R. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15 (1994) 1467-1488