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March  2011, 15(2): 343-355. doi: 10.3934/dcdsb.2011.15.343

Using the immersed boundary method to model complex fluids-structure interaction in sperm motility

1. 

Department of Mathematics, Washington State University, Pullman, WA 99164, United States, United States

Received  November 2009 Revised  January 2010 Published  December 2010

We describe work on the development of immersed boundary methods for sperm motility in complex fluids. This includes an Oldroyd-B formulation and a Lagrangian mesh method. We also describe the development of an immersed boundary rheometer for the studying the properties of viscoelastic fluids. We present preliminary simulation results for the Oldroyd-B and Lagrangian mesh rheometers and compare sperm motility in Newtonian, Oldroyd-B and Lagrangian mesh fluids using an existing immersed boundary model for sperm motility.
Citation: Robert H. Dillon, Jingxuan Zhuo. Using the immersed boundary method to model complex fluids-structure interaction in sperm motility. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 343-355. doi: 10.3934/dcdsb.2011.15.343
References:
[1]

E. Alpkvist and I. Klapper, Description of mechanical response including detachment using a novel particle method of biofilm/flow interaction,, Wat. Sci. Tech., 55 (2007), 265.  doi: 10.2166/wst.2007.267.  Google Scholar

[2]

D. C. Bottino, Modeling viscoelastic networks and cell deformation in the context of the immersed boundary method,, J. Comp. Phys., 147 (1998), 86.  doi: 10.1006/jcph.1998.6074.  Google Scholar

[3]

C. J. Brokaw, Computer simulation of flagellar movement. I. Demonstration of stable bend propagation and bend initiation by the sliding filament model,, Biophys. J., 12 (1972), 564.  doi: 10.1016/S0006-3495(72)86104-6.  Google Scholar

[4]

Charles J. Brokaw, Simulating the effects of fluid viscosity on the behavior of sperm flagella,, Math. Meth. Appl. Sci., 24 (2001), 1351.  doi: 10.1002/mma.184.  Google Scholar

[5]

Paul Dierckx, "Curve and Surface Fitting with Splines,", Monographs on Numerical Analysis, (1993).   Google Scholar

[6]

R. Dillon, L. Fauci and C. Omoto, Internally-driven elastic model of a motile sperm-effects of viscosity and dynein activation on emergent waveform,, in preparation., ().   Google Scholar

[7]

R. Dillon, L. Fauci, C. Omoto and X. Yang, Fluid dynamic models of flagellar and ciliary beating,, NYAS, 1101 (2007), 494.   Google Scholar

[8]

R. Dillon, L. Fauci and X. Yang, Sperm motility and multiciliary beating: An integrative mechanical model,, Computers and Mathematics with Applications, 52 (2006), 749.  doi: 10.1016/j.camwa.2006.10.012.  Google Scholar

[9]

R. Dillon and L. J. Fauci, An integrative model of internal axoneme mechanics and external fluid dynamics in ciliary beating,, J. theor. Biol., 207 (2000), 415.  doi: 10.1006/jtbi.2000.2182.  Google Scholar

[10]

R. Dillon, L. J. Fauci and Charlotte Omoto, Mathematical modeling of axoneme mechanics and fluid dynamics in ciliary and sperm motility,, Dynamics of continuous, 10 (2003), 745.   Google Scholar

[11]

Robert Dillon and Zhilin Li, "An Introduction to the Immersed Boundary and Immersed Interface Methods,", Lecture Note Series, (2009).   Google Scholar

[12]

Robert H. Dillon and Lisa J. Fauci, An integrative model of internal axoneme mechanics and external fluid dynamics in ciliary beating,, Journal of Theoretical Biology, 207 (2000), 415.  doi: 10.1006/jtbi.2000.2182.  Google Scholar

[13]

Robert H. Dillon, Lisa J. Fauci and Charlotte Omoto, Mathematical modeling of axoneme mechanics and fluid dynamics in ciliary and sperm motility,, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 10 (2003), 745.   Google Scholar

[14]

L. Fauci and R. Dillon, Biofluidmechanics of reproduction,, Annu. Rev. Fluid Mech., 38 (2006), 371.  doi: 10.1146/annurev.fluid.37.061903.175725.  Google Scholar

[15]

G. R. Fulford, D. F. Katz and R. L. Powell, Swimming of spermatozoa in a linear viscoelastic fluid,, Biorheology, 35 (1998), 295.  doi: 10.1016/S0006-355X(99)80012-2.  Google Scholar

[16]

H. Ho and S. Suarez, Hyperactivation of mammalian spermatozoa: function and regulation,, Reproduction, 122 (2001), 519.  doi: 10.1530/rep.0.1220519.  Google Scholar

[17]

Daniel D. Joseph, "Fluid Dynamics of Viscoelastic Liquids,", Springer-Verlag, (1990).   Google Scholar

[18]

D. F. Katz, R. N. Mills and T. R. Pritchett, The movement of human spermatazoa in cervical mucus,, J. Reprod. Fertil., 53 (1978), 259.  doi: 10.1530/jrf.0.0530259.  Google Scholar

[19]

I. Klapper and E. Alpkvist, A computational parallel plate rheometer for inhomogenous biofilms,, manuscript (2007)., (2007).   Google Scholar

[20]

Eric Lauga, Propulsion in a viscoelastic fluid,, Phys. Fluids, 19 (2007).  doi: 10.1063/1.2751388.  Google Scholar

[21]

M. Murase, "The Dynamics of Cellular Motility,", John Wiley, (1992).   Google Scholar

[22]

Charles S. Peskin, The immersed boundary method,, Acta Numer., 11 (2002), 479.  doi: 10.1017/CBO9780511550140.007.  Google Scholar

[23]

J. Teran, L. Fauci and M. Shelley, Peristaltic pumping and irreversibility of a stokesian viscoelastic fluid,, Phys. Fluids, 20 (2008).  doi: 10.1063/1.2963530.  Google Scholar

[24]

J. Teran, L. Fauci and M. Shelley, Viscoelastic fluid response can increase the speed and efficiency of a free swimmer,, Phys. Rev. Lett., 104 (2010).  doi: 10.1103/PhysRevLett.104.038101.  Google Scholar

[25]

P. Verdugo, Polymer biophysics of mucus in cystic fibrosis,, Proceedings of the International Congress on Cilia, (1998), 167.   Google Scholar

[26]

G. B. Witman, Introduction to cilia and flagella,, Ciliary and Flagellar Membranes (New York) (R. A. Bloodgood, (1990), 1.   Google Scholar

show all references

References:
[1]

E. Alpkvist and I. Klapper, Description of mechanical response including detachment using a novel particle method of biofilm/flow interaction,, Wat. Sci. Tech., 55 (2007), 265.  doi: 10.2166/wst.2007.267.  Google Scholar

[2]

D. C. Bottino, Modeling viscoelastic networks and cell deformation in the context of the immersed boundary method,, J. Comp. Phys., 147 (1998), 86.  doi: 10.1006/jcph.1998.6074.  Google Scholar

[3]

C. J. Brokaw, Computer simulation of flagellar movement. I. Demonstration of stable bend propagation and bend initiation by the sliding filament model,, Biophys. J., 12 (1972), 564.  doi: 10.1016/S0006-3495(72)86104-6.  Google Scholar

[4]

Charles J. Brokaw, Simulating the effects of fluid viscosity on the behavior of sperm flagella,, Math. Meth. Appl. Sci., 24 (2001), 1351.  doi: 10.1002/mma.184.  Google Scholar

[5]

Paul Dierckx, "Curve and Surface Fitting with Splines,", Monographs on Numerical Analysis, (1993).   Google Scholar

[6]

R. Dillon, L. Fauci and C. Omoto, Internally-driven elastic model of a motile sperm-effects of viscosity and dynein activation on emergent waveform,, in preparation., ().   Google Scholar

[7]

R. Dillon, L. Fauci, C. Omoto and X. Yang, Fluid dynamic models of flagellar and ciliary beating,, NYAS, 1101 (2007), 494.   Google Scholar

[8]

R. Dillon, L. Fauci and X. Yang, Sperm motility and multiciliary beating: An integrative mechanical model,, Computers and Mathematics with Applications, 52 (2006), 749.  doi: 10.1016/j.camwa.2006.10.012.  Google Scholar

[9]

R. Dillon and L. J. Fauci, An integrative model of internal axoneme mechanics and external fluid dynamics in ciliary beating,, J. theor. Biol., 207 (2000), 415.  doi: 10.1006/jtbi.2000.2182.  Google Scholar

[10]

R. Dillon, L. J. Fauci and Charlotte Omoto, Mathematical modeling of axoneme mechanics and fluid dynamics in ciliary and sperm motility,, Dynamics of continuous, 10 (2003), 745.   Google Scholar

[11]

Robert Dillon and Zhilin Li, "An Introduction to the Immersed Boundary and Immersed Interface Methods,", Lecture Note Series, (2009).   Google Scholar

[12]

Robert H. Dillon and Lisa J. Fauci, An integrative model of internal axoneme mechanics and external fluid dynamics in ciliary beating,, Journal of Theoretical Biology, 207 (2000), 415.  doi: 10.1006/jtbi.2000.2182.  Google Scholar

[13]

Robert H. Dillon, Lisa J. Fauci and Charlotte Omoto, Mathematical modeling of axoneme mechanics and fluid dynamics in ciliary and sperm motility,, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 10 (2003), 745.   Google Scholar

[14]

L. Fauci and R. Dillon, Biofluidmechanics of reproduction,, Annu. Rev. Fluid Mech., 38 (2006), 371.  doi: 10.1146/annurev.fluid.37.061903.175725.  Google Scholar

[15]

G. R. Fulford, D. F. Katz and R. L. Powell, Swimming of spermatozoa in a linear viscoelastic fluid,, Biorheology, 35 (1998), 295.  doi: 10.1016/S0006-355X(99)80012-2.  Google Scholar

[16]

H. Ho and S. Suarez, Hyperactivation of mammalian spermatozoa: function and regulation,, Reproduction, 122 (2001), 519.  doi: 10.1530/rep.0.1220519.  Google Scholar

[17]

Daniel D. Joseph, "Fluid Dynamics of Viscoelastic Liquids,", Springer-Verlag, (1990).   Google Scholar

[18]

D. F. Katz, R. N. Mills and T. R. Pritchett, The movement of human spermatazoa in cervical mucus,, J. Reprod. Fertil., 53 (1978), 259.  doi: 10.1530/jrf.0.0530259.  Google Scholar

[19]

I. Klapper and E. Alpkvist, A computational parallel plate rheometer for inhomogenous biofilms,, manuscript (2007)., (2007).   Google Scholar

[20]

Eric Lauga, Propulsion in a viscoelastic fluid,, Phys. Fluids, 19 (2007).  doi: 10.1063/1.2751388.  Google Scholar

[21]

M. Murase, "The Dynamics of Cellular Motility,", John Wiley, (1992).   Google Scholar

[22]

Charles S. Peskin, The immersed boundary method,, Acta Numer., 11 (2002), 479.  doi: 10.1017/CBO9780511550140.007.  Google Scholar

[23]

J. Teran, L. Fauci and M. Shelley, Peristaltic pumping and irreversibility of a stokesian viscoelastic fluid,, Phys. Fluids, 20 (2008).  doi: 10.1063/1.2963530.  Google Scholar

[24]

J. Teran, L. Fauci and M. Shelley, Viscoelastic fluid response can increase the speed and efficiency of a free swimmer,, Phys. Rev. Lett., 104 (2010).  doi: 10.1103/PhysRevLett.104.038101.  Google Scholar

[25]

P. Verdugo, Polymer biophysics of mucus in cystic fibrosis,, Proceedings of the International Congress on Cilia, (1998), 167.   Google Scholar

[26]

G. B. Witman, Introduction to cilia and flagella,, Ciliary and Flagellar Membranes (New York) (R. A. Bloodgood, (1990), 1.   Google Scholar

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