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Volumn 227, Issue 11, 2008, Pages 5816-5835

Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics

Author keywords

Artificial viscosity; Biomembranes; Finite element; Lipid bilayer mechanics; r Adaptive remeshing

Indexed keywords

CONSTRAINED OPTIMIZATION; FINITE ELEMENT METHOD; LAGRANGE MULTIPLIERS; MESH GENERATION; PHASE SEPARATION; SHEAR STRESS;

EID: 42649117766     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.02.019     Document Type: Article
Times cited : (69)

References (59)
  • 2
    • 0030735760 scopus 로고    scopus 로고
    • Configurations of fluid membranes and vesicles
    • U. Seifert Configurations of fluid membranes and vesicles Adv. Phys. 46 1 1997 13 137
    • (1997) Adv. Phys. , vol.46 , Issue.1 , pp. 13-137
    • Seifert, U.1
  • 3
    • 0014709498 scopus 로고
    • The minimum energy of bending as a possible explanation of the biconcave shape of the red blood cell
    • P.B. Canham The minimum energy of bending as a possible explanation of the biconcave shape of the red blood cell J. Theor. Biol. 26 1970 61 81
    • (1970) J. Theor. Biol. , vol.26 , pp. 61-81
    • Canham, P.B.1
  • 4
    • 84943997802 scopus 로고
    • Elastic properties of lipid bilayers: theory and possible experiments
    • W. Helfrich Elastic properties of lipid bilayers: theory and possible experiments Z. Naturforsch. 28c 1973 693 703
    • (1973) Z. Naturforsch. , vol.28c , pp. 693-703
    • Helfrich, W.1
  • 5
    • 0016377872 scopus 로고
    • Bending resistance and chemically-induced moments in membrane bilayers
    • E.A. Evans Bending resistance and chemically-induced moments in membrane bilayers Biophys. J. 14 12 1974 923 931
    • (1974) Biophys. J. , vol.14 , Issue.12 , pp. 923-931
    • Evans, E.A.1
  • 6
    • 0020056968 scopus 로고
    • Membrane bending energy in relation to bilayer couples concept of red blood cell shape transformations
    • S. Svetina A. Ottova-Leitmanova R. Glaser Membrane bending energy in relation to bilayer couples concept of red blood cell shape transformations J. Theor. Biol. 94 1982 13 23
    • (1982) J. Theor. Biol. , vol.94 , pp. 13-23
    • Svetina, S.1    Ottova-Leitmanova, A.2    Glaser, R.3
  • 7
    • 0020918438 scopus 로고
    • Bilayer couple hypothesis of red cell shape transformations and osmotic hemolysis
    • S. Svetina B. Zeks Bilayer couple hypothesis of red cell shape transformations and osmotic hemolysis Biochem. Biophys. Acta 42 1983 86 90
    • (1983) Biochem. Biophys. Acta , vol.42 , pp. 86-90
    • Svetina, S.1    Zeks, B.2
  • 10
    • 0026519746 scopus 로고
    • Role of lamellar membrane structure in tether formation from bilayer vesicles
    • B. Bozic S. Svetina B. Zeks R.E. Waugh Role of lamellar membrane structure in tether formation from bilayer vesicles Biophys. J. 61 1992 963 973
    • (1992) Biophys. J. , vol.61 , pp. 963-973
    • Bozic, B.1    Svetina, S.2    Zeks, B.3    Waugh, R.E.4
  • 11
    • 0017644098 scopus 로고
    • Static equilibrium configurations of a model red blood cell
    • J.T. Jenkins Static equilibrium configurations of a model red blood cell J. Math. Biol. 4 1977 149 169
    • (1977) J. Math. Biol. , vol.4 , pp. 149-169
    • Jenkins, J.T.1
  • 12
    • 0037534552 scopus 로고
    • The equations of mechanical equilibrium of a model membrane
    • J.T. Jenkins The equations of mechanical equilibrium of a model membrane SIAM J. Appl. Math. 32 4 1977 755 764
    • (1977) SIAM J. Appl. Math. , vol.32 , Issue.4 , pp. 755-764
    • Jenkins, J.T.1
  • 13
    • 0346167600 scopus 로고
    • Minimizing the squared mean curvature integral for surfaces in space forms
    • L. Hsu R. Kusner J. Sullivan Minimizing the squared mean curvature integral for surfaces in space forms Exp. Math. 1 3 1992 191 207
    • (1992) Exp. Math. , vol.1 , Issue.3 , pp. 191-207
    • Hsu, L.1    Kusner, R.2    Sullivan, J.3
  • 14
    • 0000455489 scopus 로고
    • Vesicular instabilities: the prolate-to-oblate transition and other shape instabilities of fluid bilayer membranes
    • M. Jaric U. Seifert W. Wintz M. Wortis Vesicular instabilities: the prolate-to-oblate transition and other shape instabilities of fluid bilayer membranes Phys. Rev. Lett. 52 1995 6623
    • (1995) Phys. Rev. Lett. , vol.52 , pp. 6623
    • Jaric, M.1    Seifert, U.2    Wintz, W.3    Wortis, M.4
  • 15
    • 77951760655 scopus 로고
    • Gravity-induced shape transformations of vesicles
    • M. Kraus U. Seifert R. Lipowsky Gravity-induced shape transformations of vesicles Europhys. Lett. 32 5 1995 431 436
    • (1995) Europhys. Lett. , vol.32 , Issue.5 , pp. 431-436
    • Kraus, M.1    Seifert, U.2    Lipowsky, R.3
  • 17
    • 33750972883 scopus 로고    scopus 로고
    • Finite element modeling of lipid bilayer membranes
    • F. Feng W.S. Klug Finite element modeling of lipid bilayer membranes J. Comput. Phys. 220 2006 394 408
    • (2006) J. Comput. Phys. , vol.220 , pp. 394-408
    • Feng, F.1    Klug, W.S.2
  • 18
    • 0031249493 scopus 로고    scopus 로고
    • Network models of fluid, hexatic and polymerized membranes
    • G. Gompper D.M. Kroll Network models of fluid, hexatic and polymerized membranes J. Phys.: Condens. Matter 9 1997 8795 8834
    • (1997) J. Phys.: Condens. Matter , vol.9 , pp. 8795-8834
    • Gompper, G.1    Kroll, D.M.2
  • 20
    • 84956268024 scopus 로고
    • Simulations of fluid self-avoiding membranes
    • J.-S. Ho A. Baumgärtner Simulations of fluid self-avoiding membranes Europhys. Lett. 12 4 1990 295 300
    • (1990) Europhys. Lett. , vol.12 , Issue.4 , pp. 295-300
    • Ho, J.-S.1    Baumgärtner, A.2
  • 21
    • 27244436915 scopus 로고    scopus 로고
    • Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations
    • H. Noguchi G. Gompper Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations Phys. Rev. E 72 2005 0119011 0119014
    • (2005) Phys. Rev. E , vol.72 , pp. 0119011-0119014
    • Noguchi, H.1    Gompper, G.2
  • 22
    • 0000238191 scopus 로고
    • Nonaxisymmetric vesicle shapes in a generalized bilayer-couple model and the transition between oblate and prolate axisymmetric shapes
    • V. Heinrich S. Saša B. Žekš Nonaxisymmetric vesicle shapes in a generalized bilayer-couple model and the transition between oblate and prolate axisymmetric shapes Phys. Rev. E 48 4 1993 3112 3123
    • (1993) Phys. Rev. E , vol.48 , Issue.4 , pp. 3112-3123
    • Heinrich, V.1    Saša, S.2    Žekš, B.3
  • 23
    • 0344348825 scopus 로고    scopus 로고
    • Vesicle deformation by an axial load: from elongated shapes to tethered vesicles
    • V. Heinrich B. Božič S. Saša B. Žekš Vesicle deformation by an axial load: from elongated shapes to tethered vesicles Biophys. J. 76 1999 2056 2071
    • (1999) Biophys. J. , vol.76 , pp. 2056-2071
    • Heinrich, V.1    Božič, B.2    Saša, S.3    Žekš, B.4
  • 24
    • 3242875567 scopus 로고    scopus 로고
    • A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
    • Q. Du C. Liu X. Wang A phase field approach in the numerical study of the elastic bending energy for vesicle membranes J. Comput. Phys. 198 2004 450 468
    • (2004) J. Comput. Phys. , vol.198 , pp. 450-468
    • Du, Q.1    Liu, C.2    Wang, X.3
  • 25
    • 29144520935 scopus 로고    scopus 로고
    • Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
    • Q. Du C. Liu X. Wang Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions J. Comput. Phys. 212 2 2006 757 777
    • (2006) J. Comput. Phys. , vol.212 , Issue.2 , pp. 757-777
    • Du, Q.1    Liu, C.2    Wang, X.3
  • 26
    • 33344456459 scopus 로고    scopus 로고
    • Meshless membrane model based on the moving least-squares method
    • H. Noguchi G. Gompper Meshless membrane model based on the moving least-squares method Phys. Rev. E 73 2006 021903
    • (2006) Phys. Rev. E , vol.73 , pp. 021903
    • Noguchi, H.1    Gompper, G.2
  • 27
    • 0003584817 scopus 로고
    • Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua
    • I.S. Sokolnikoff Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua second ed. 1964 Wiley New York
    • (1964)
    • Sokolnikoff, I.S.1
  • 28
    • 0003533718 scopus 로고
    • Differential Geometry of Curves and Surfaces
    • M. Do Carmo Differential Geometry of Curves and Surfaces 1976 Prentice Hall
    • (1976)
    • Do Carmo, M.1
  • 29
    • 0003982971 scopus 로고    scopus 로고
    • Numerical Optimization
    • J. Nocedal S.J. Wright Numerical Optimization 1999 Springer-Verlag
    • (1999)
    • Nocedal, J.1    Wright, S.J.2
  • 30
    • 0034171519 scopus 로고    scopus 로고
    • Subdivision surfaces: a new paradigm for thin-shell finite-element analysis
    • F. Cirak M. Ortiz P. Schröder Subdivision surfaces: a new paradigm for thin-shell finite-element analysis Int. J. Numer. Method Eng. 47 2000 2039 2072
    • (2000) Int. J. Numer. Method Eng. , vol.47 , pp. 2039-2072
    • Cirak, F.1    Ortiz, M.2    Schröder, P.3
  • 32
    • 0033267258 scopus 로고    scopus 로고
    • Fluid films with curvature elasticity
    • D.J. Steigmann Fluid films with curvature elasticity Arch. Rational Mech. Anal. 150 1999 127 152
    • (1999) Arch. Rational Mech. Anal. , vol.150 , pp. 127-152
    • Steigmann, D.J.1
  • 33
    • 0003952047 scopus 로고
    • Mechanics and Thermodynamics of Biomembranes
    • E.A. Evans R. Skalak Mechanics and Thermodynamics of Biomembranes 1980 CRC Press Boca Raton, FL
    • (1980)
    • Evans, E.A.1    Skalak, R.2
  • 34
    • 0000732463 scopus 로고
    • A limited memory algorithm for bound constrained optimization
    • R.H. Byrd P. Lu J. Nocedal C. Zhu A limited memory algorithm for bound constrained optimization SIAM J. Sci. Comput. 16 5 1995 1190 1208
    • (1995) SIAM J. Sci. Comput. , vol.16 , Issue.5 , pp. 1190-1208
    • Byrd, R.H.1    Lu, P.2    Nocedal, J.3    Zhu, C.4
  • 35
    • 0031345518 scopus 로고    scopus 로고
    • Algorithm 778: L-bfgs-b: Fortran subroutines for large-scale bound-constrained optimization
    • C. Zhu R.H. Byrd P. Lu J. Nocedal Algorithm 778: L-bfgs-b: Fortran subroutines for large-scale bound-constrained optimization ACM Trans. Math. Softw. 23 4 1997
    • (1997) ACM Trans. Math. Softw. , vol.23 , Issue.4
    • Zhu, C.1    Byrd, R.H.2    Lu, P.3    Nocedal, J.4
  • 36
    • 85190081493 scopus 로고    scopus 로고
    • Free L-BFGS-B software. Available at .
  • 37
    • 0024324636 scopus 로고
    • Membrane bending energy and shape determination of phospholipid vesicles and red blood cells
    • S. Svetina B. Zeks Membrane bending energy and shape determination of phospholipid vesicles and red blood cells Eur. Biophys. J. 17 2 1989 101 111
    • (1989) Eur. Biophys. J. , vol.17 , Issue.2 , pp. 101-111
    • Svetina, S.1    Zeks, B.2
  • 38
    • 0000924897 scopus 로고
    • Shape transformations of vesicle-phase-diagram for spontaneous-curvature and bilayer-coupling models
    • U. Seifert K. Berndl R. Lipowsky Shape transformations of vesicle-phase-diagram for spontaneous-curvature and bilayer-coupling models Phys. Rev. A 44 1991 1182 1202
    • (1991) Phys. Rev. A , vol.44 , pp. 1182-1202
    • Seifert, U.1    Berndl, K.2    Lipowsky, R.3
  • 39
  • 40
    • 0000256477 scopus 로고    scopus 로고
    • Theoretical analysis of the formation of membrane microtubes on axially strained vesicles
    • B. Božič S. Svetina B. Žekš Theoretical analysis of the formation of membrane microtubes on axially strained vesicles Phys. Rev. E 55 5 1997 5834 5842
    • (1997) Phys. Rev. E , vol.55 , Issue.5 , pp. 5834-5842
    • Božič, B.1    Svetina, S.2    Žekš, B.3
  • 41
    • 19044375887 scopus 로고    scopus 로고
    • Formation and interaction of membrane tubes
    • I. Derényi F. Jülicher J. Prost Formation and interaction of membrane tubes Phys. Rev. Lett. 88 23 2002 238101 238104
    • (2002) Phys. Rev. Lett. , vol.88 , Issue.23 , pp. 238101-238104
    • Derényi, I.1    Jülicher, F.2    Prost, J.3
  • 42
    • 84876125465 scopus 로고    scopus 로고
    • Fluid-membrane tethers: minimal surfaces and elastic boundary layers
    • T.R. Powers G. Huber R.E. Goldstein Fluid-membrane tethers: minimal surfaces and elastic boundary layers Phys. Rev. E 65 4 2002 041901 041911
    • (2002) Phys. Rev. E , vol.65 , Issue.4 , pp. 041901-041911
    • Powers, T.R.1    Huber, G.2    Goldstein, R.E.3
  • 43
    • 85088491815 scopus 로고    scopus 로고
    • Pulling tethers from adhered vesicles
    • A.S. Smith E. Sackmann U. Seifert Pulling tethers from adhered vesicles Phys. Rev. Lett. 92 20 2004 208101 208104
    • (2004) Phys. Rev. Lett. , vol.92 , Issue.20 , pp. 208101-208104
    • Smith, A.S.1    Sackmann, E.2    Seifert, U.3
  • 44
    • 0242331729 scopus 로고    scopus 로고
    • Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension
    • T. Baumgart S.T. Hess W.W. Webb Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension Nature 425 2003 821 824
    • (2003) Nature , vol.425 , pp. 821-824
    • Baumgart, T.1    Hess, S.T.2    Webb, W.W.3
  • 45
    • 14744278787 scopus 로고    scopus 로고
    • Sterol structure determines the separation of phases and the curvature of the liquid-ordered phase in model membranes
    • K. Bacia P. Schwille T. Kurzchalia Sterol structure determines the separation of phases and the curvature of the liquid-ordered phase in model membranes Proc. Natl. Acad. Sci. USA 102 2005 3272 3277
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , pp. 3272-3277
    • Bacia, K.1    Schwille, P.2    Kurzchalia, T.3
  • 46
    • 23244446181 scopus 로고    scopus 로고
    • Membrane elasticity in giant vesicles with fluid phase coexistence
    • T. Baumgart S. Das W.W. Webb T. Jenkins Membrane elasticity in giant vesicles with fluid phase coexistence Biophys. J. 89 2005 1067 1080
    • (2005) Biophys. J. , vol.89 , pp. 1067-1080
    • Baumgart, T.1    Das, S.2    Webb, W.W.3    Jenkins, T.4
  • 47
    • 0001335174 scopus 로고
    • Budding of membranes induced by intramembrane domains
    • R. Lipowsky Budding of membranes induced by intramembrane domains J. Phys. II (France) 2 1992 1825 1840
    • (1992) J. Phys. II (France) , vol.2 , pp. 1825-1840
    • Lipowsky, R.1
  • 48
    • 0000692927 scopus 로고
    • Domain-induced budding of vesicles
    • F. Jülicher R. Lipowsky Domain-induced budding of vesicles Phys. Rev. Lett. 70 19 1993 2964 2967
    • (1993) Phys. Rev. Lett. , vol.70 , Issue.19 , pp. 2964-2967
    • Jülicher, F.1    Lipowsky, R.2
  • 49
    • 0001015928 scopus 로고    scopus 로고
    • Shape transitions of vesicles with intramembrane domains
    • F. Jülicher R. Lipowsky Shape transitions of vesicles with intramembrane domains Phys. Rev. E 53 1996 2670 2683
    • (1996) Phys. Rev. E , vol.53 , pp. 2670-2683
    • Jülicher, F.1    Lipowsky, R.2
  • 51
    • 0003549216 scopus 로고
    • The Landau Theory of Phase Transitions
    • J.C. Toledano P. Toledano The Landau Theory of Phase Transitions 1987 World Scientific Singapore
    • (1987)
    • Toledano, J.C.1    Toledano, P.2
  • 52
    • 0000693828 scopus 로고
    • Phase transitions and shapes of two component membranes and vesicles. I: Strong segregation limit
    • T. Kawakatsu D. Andelman K. Kawasaki T. Taniguchi Phase transitions and shapes of two component membranes and vesicles. I: Strong segregation limit J. Phys. II (France) 3 1993 971 997
    • (1993) J. Phys. II (France) , vol.3 , pp. 971-997
    • Kawakatsu, T.1    Andelman, D.2    Kawasaki, K.3    Taniguchi, T.4
  • 53
    • 0000174468 scopus 로고
    • Phase transitions and shapes of two component membranes and vesicles. II: Weak segregation limit
    • T. Taniguchi K. Kawasaki D. Andelman T. Kawakatsu Phase transitions and shapes of two component membranes and vesicles. II: Weak segregation limit J. Phys. II (France) 4 1994 1333 1362
    • (1994) J. Phys. II (France) , vol.4 , pp. 1333-1362
    • Taniguchi, T.1    Kawasaki, K.2    Andelman, D.3    Kawakatsu, T.4
  • 54
    • 7244255733 scopus 로고    scopus 로고
    • Shape deformation and phase separation dynamics of two-component vesicles
    • T. Taniguchi Shape deformation and phase separation dynamics of two-component vesicles Phys. Rev. Lett. 76 23 1996 4444 4447
    • (1996) Phys. Rev. Lett. , vol.76 , Issue.23 , pp. 4444-4447
    • Taniguchi, T.1
  • 55
    • 22244446431 scopus 로고    scopus 로고
    • Coupling field theory with continuum mechanics: a simulation of domain formation in giant unilamellar vesicles
    • G.S. Ayton J.L. McWhirter P. McMurtry G.A. Voth Coupling field theory with continuum mechanics: a simulation of domain formation in giant unilamellar vesicles Biophys. J. 88 6 2005 3855 3869
    • (2005) Biophys. J. , vol.88 , Issue.6 , pp. 3855-3869
    • Ayton, G.S.1    McWhirter, J.L.2    McMurtry, P.3    Voth, G.A.4
  • 56
    • 0002217438 scopus 로고    scopus 로고
    • Phase separation and shape deformation of two-phase membranes
    • Y. Jiang T. Lookman A. Saxena Phase separation and shape deformation of two-phase membranes Phys. Rev. E 61 1 2000 57 60
    • (2000) Phys. Rev. E , vol.61 , Issue.1 , pp. 57-60
    • Jiang, Y.1    Lookman, T.2    Saxena, A.3
  • 57
    • 36749080310 scopus 로고    scopus 로고
    • Modeling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches
    • X. Wang Q. Du Modeling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches J. Math. Biol. 56 2008 347 371
    • (2008) J. Math. Biol. , vol.56 , pp. 347-371
    • Wang, X.1    Du, Q.2
  • 58
    • 0034235229 scopus 로고    scopus 로고
    • The internal structure of mitochondria
    • T.G. Frey C.A. Mannella The internal structure of mitochondria Trends Biochem. Sci. 25 2000 319 324
    • (2000) Trends Biochem. Sci. , vol.25 , pp. 319-324
    • Frey, T.G.1    Mannella, C.A.2


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