• Previous Article
    Weak solution to compressible hydrodynamic flow of liquid crystals in dimension one
  • DCDS-B Home
  • This Issue
  • Next Article
    An optimal-order error estimate for a family of characteristic-mixed methods to transient convection-diffusion problems
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 and 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), 265-273. doi: 10.2166/wst.2007.267.

[2]

D. C. Bottino, Modeling viscoelastic networks and cell deformation in the context of the immersed boundary method, J. Comp. Phys., 147 (1998), 86-113. doi: 10.1006/jcph.1998.6074.

[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), 564-586. doi: 10.1016/S0006-3495(72)86104-6.

[4]

Charles J. Brokaw, Simulating the effects of fluid viscosity on the behavior of sperm flagella, Math. Meth. Appl. Sci., 24 (2001), 1351-1365. doi: 10.1002/mma.184.

[5]

Paul Dierckx, "Curve and Surface Fitting with Splines," Monographs on Numerical Analysis, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993.

[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., (). 

[7]

R. Dillon, L. Fauci, C. Omoto and X. Yang, Fluid dynamic models of flagellar and ciliary beating, NYAS, 1101 (2007), 494-505.

[8]

R. Dillon, L. Fauci and X. Yang, Sperm motility and multiciliary beating: An integrative mechanical model, Computers and Mathematics with Applications, 52 (2006), 749-758. doi: 10.1016/j.camwa.2006.10.012.

[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), 415-430. doi: 10.1006/jtbi.2000.2182.

[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, discrete and impulsive systems: Series A, 10 (2003), 745-757.

[11]

Robert Dillon and Zhilin Li, "An Introduction to the Immersed Boundary and Immersed Interface Methods," Lecture Note Series, Institute for Mathematical Sciences, National University of Singapore: Interface Problems and Methods in Biological and Physical Flows (B. C. Khoo, Z. Li and P. Lin, eds.), World Scientific, 2009.

[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), 415-430. doi: 10.1006/jtbi.2000.2182.

[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), 745-757, Progress in partial differential equations (Pullman, WA, 2002).

[14]

L. Fauci and R. Dillon, Biofluidmechanics of reproduction, Annu. Rev. Fluid Mech., 38 (2006), 371-394. doi: 10.1146/annurev.fluid.37.061903.175725.

[15]

G. R. Fulford, D. F. Katz and R. L. Powell, Swimming of spermatozoa in a linear viscoelastic fluid, Biorheology, 35 (1998), 295-309. doi: 10.1016/S0006-355X(99)80012-2.

[16]

H. Ho and S. Suarez, Hyperactivation of mammalian spermatozoa: function and regulation, Reproduction, 122 (2001), 519-526. doi: 10.1530/rep.0.1220519.

[17]

Daniel D. Joseph, "Fluid Dynamics of Viscoelastic Liquids," Springer-Verlag, New York, 1990.

[18]

D. F. Katz, R. N. Mills and T. R. Pritchett, The movement of human spermatazoa in cervical mucus, J. Reprod. Fertil., 53 (1978), 259-265. doi: 10.1530/jrf.0.0530259.

[19]

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

[20]

Eric Lauga, Propulsion in a viscoelastic fluid, Phys. Fluids, 19 (2007), 083104. doi: 10.1063/1.2751388.

[21]

M. Murase, "The Dynamics of Cellular Motility," John Wiley, Chichester, 1992.

[22]

Charles S. Peskin, The immersed boundary method, Acta Numer., 11 (2002), 479-517. doi: 10.1017/CBO9780511550140.007.

[23]

J. Teran, L. Fauci and M. Shelley, Peristaltic pumping and irreversibility of a stokesian viscoelastic fluid, Phys. Fluids, 20 (2008), 073101. doi: 10.1063/1.2963530.

[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), 038101. doi: 10.1103/PhysRevLett.104.038101.

[25]

P. Verdugo, Polymer biophysics of mucus in cystic fibrosis, Proceedings of the International Congress on Cilia, Mucus, and Mucociliary Interactions (New York) (G. L. Baum, Z. Priel, Y. Roth, N. Liron and E. J. Ostfeld, eds.), Marcel Dekker, 1998, 167-189.

[26]

G. B. Witman, Introduction to cilia and flagella, Ciliary and Flagellar Membranes (New York) (R. A. Bloodgood, ed.), Plenum, 1990, 1-30.

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), 265-273. doi: 10.2166/wst.2007.267.

[2]

D. C. Bottino, Modeling viscoelastic networks and cell deformation in the context of the immersed boundary method, J. Comp. Phys., 147 (1998), 86-113. doi: 10.1006/jcph.1998.6074.

[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), 564-586. doi: 10.1016/S0006-3495(72)86104-6.

[4]

Charles J. Brokaw, Simulating the effects of fluid viscosity on the behavior of sperm flagella, Math. Meth. Appl. Sci., 24 (2001), 1351-1365. doi: 10.1002/mma.184.

[5]

Paul Dierckx, "Curve and Surface Fitting with Splines," Monographs on Numerical Analysis, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993.

[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., (). 

[7]

R. Dillon, L. Fauci, C. Omoto and X. Yang, Fluid dynamic models of flagellar and ciliary beating, NYAS, 1101 (2007), 494-505.

[8]

R. Dillon, L. Fauci and X. Yang, Sperm motility and multiciliary beating: An integrative mechanical model, Computers and Mathematics with Applications, 52 (2006), 749-758. doi: 10.1016/j.camwa.2006.10.012.

[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), 415-430. doi: 10.1006/jtbi.2000.2182.

[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, discrete and impulsive systems: Series A, 10 (2003), 745-757.

[11]

Robert Dillon and Zhilin Li, "An Introduction to the Immersed Boundary and Immersed Interface Methods," Lecture Note Series, Institute for Mathematical Sciences, National University of Singapore: Interface Problems and Methods in Biological and Physical Flows (B. C. Khoo, Z. Li and P. Lin, eds.), World Scientific, 2009.

[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), 415-430. doi: 10.1006/jtbi.2000.2182.

[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), 745-757, Progress in partial differential equations (Pullman, WA, 2002).

[14]

L. Fauci and R. Dillon, Biofluidmechanics of reproduction, Annu. Rev. Fluid Mech., 38 (2006), 371-394. doi: 10.1146/annurev.fluid.37.061903.175725.

[15]

G. R. Fulford, D. F. Katz and R. L. Powell, Swimming of spermatozoa in a linear viscoelastic fluid, Biorheology, 35 (1998), 295-309. doi: 10.1016/S0006-355X(99)80012-2.

[16]

H. Ho and S. Suarez, Hyperactivation of mammalian spermatozoa: function and regulation, Reproduction, 122 (2001), 519-526. doi: 10.1530/rep.0.1220519.

[17]

Daniel D. Joseph, "Fluid Dynamics of Viscoelastic Liquids," Springer-Verlag, New York, 1990.

[18]

D. F. Katz, R. N. Mills and T. R. Pritchett, The movement of human spermatazoa in cervical mucus, J. Reprod. Fertil., 53 (1978), 259-265. doi: 10.1530/jrf.0.0530259.

[19]

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

[20]

Eric Lauga, Propulsion in a viscoelastic fluid, Phys. Fluids, 19 (2007), 083104. doi: 10.1063/1.2751388.

[21]

M. Murase, "The Dynamics of Cellular Motility," John Wiley, Chichester, 1992.

[22]

Charles S. Peskin, The immersed boundary method, Acta Numer., 11 (2002), 479-517. doi: 10.1017/CBO9780511550140.007.

[23]

J. Teran, L. Fauci and M. Shelley, Peristaltic pumping and irreversibility of a stokesian viscoelastic fluid, Phys. Fluids, 20 (2008), 073101. doi: 10.1063/1.2963530.

[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), 038101. doi: 10.1103/PhysRevLett.104.038101.

[25]

P. Verdugo, Polymer biophysics of mucus in cystic fibrosis, Proceedings of the International Congress on Cilia, Mucus, and Mucociliary Interactions (New York) (G. L. Baum, Z. Priel, Y. Roth, N. Liron and E. J. Ostfeld, eds.), Marcel Dekker, 1998, 167-189.

[26]

G. B. Witman, Introduction to cilia and flagella, Ciliary and Flagellar Membranes (New York) (R. A. Bloodgood, ed.), Plenum, 1990, 1-30.

[1]

V. Afraimovich, J. Schmeling, Edgardo Ugalde, Jesús Urías. Spectra of dimensions for Poincaré recurrences. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 901-914. doi: 10.3934/dcds.2000.6.901

[2]

B. Fernandez, E. Ugalde, J. Urías. Spectrum of dimensions for Poincaré recurrences of Markov maps. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 835-849. doi: 10.3934/dcds.2002.8.835

[3]

Juan Wang, Xiaodan Zhang, Yun Zhao. Dimension estimates for arbitrary subsets of limit sets of a Markov construction and related multifractal analysis. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2315-2332. doi: 10.3934/dcds.2014.34.2315

[4]

Godofredo Iommi, Bartłomiej Skorulski. Multifractal analysis for the exponential family. Discrete and Continuous Dynamical Systems, 2006, 16 (4) : 857-869. doi: 10.3934/dcds.2006.16.857

[5]

V. Afraimovich, Jean-René Chazottes, Benoît Saussol. Pointwise dimensions for Poincaré recurrences associated with maps and special flows. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 263-280. doi: 10.3934/dcds.2003.9.263

[6]

Julien Barral, Yan-Hui Qu. On the higher-dimensional multifractal analysis. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 1977-1995. doi: 10.3934/dcds.2012.32.1977

[7]

Mario Roy, Mariusz Urbański. Multifractal analysis for conformal graph directed Markov systems. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 627-650. doi: 10.3934/dcds.2009.25.627

[8]

Zhihui Yuan. Multifractal analysis of random weak Gibbs measures. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5367-5405. doi: 10.3934/dcds.2017234

[9]

Luis Barreira. Dimension theory of flows: A survey. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3345-3362. doi: 10.3934/dcdsb.2015.20.3345

[10]

Luis Barreira, César Silva. Lyapunov exponents for continuous transformations and dimension theory. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 469-490. doi: 10.3934/dcds.2005.13.469

[11]

Valentin Afraimovich, Jean-Rene Chazottes and Benoit Saussol. Local dimensions for Poincare recurrences. Electronic Research Announcements, 2000, 6: 64-74.

[12]

Yunping Wang, Ercai Chen, Xiaoyao Zhou. Mean dimension theory in symbolic dynamics for finitely generated amenable groups. Discrete and Continuous Dynamical Systems, 2022  doi: 10.3934/dcds.2022050

[13]

Zied Douzi, Bilel Selmi. On the mutual singularity of multifractal measures. Electronic Research Archive, 2020, 28 (1) : 423-432. doi: 10.3934/era.2020024

[14]

Mirela Domijan, Markus Kirkilionis. Graph theory and qualitative analysis of reaction networks. Networks and Heterogeneous Media, 2008, 3 (2) : 295-322. doi: 10.3934/nhm.2008.3.295

[15]

Jean-Pierre Francoise, Claude Piquet. Global recurrences of multi-time scaled systems. Conference Publications, 2011, 2011 (Special) : 430-436. doi: 10.3934/proc.2011.2011.430

[16]

Balázs Bárány, Michaƚ Rams, Ruxi Shi. On the multifractal spectrum of weighted Birkhoff averages. Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2461-2497. doi: 10.3934/dcds.2021199

[17]

Jerrold E. Marsden, Alexey Tret'yakov. Factor analysis of nonlinear mappings: p-regularity theory. Communications on Pure and Applied Analysis, 2003, 2 (4) : 425-445. doi: 10.3934/cpaa.2003.2.425

[18]

Lars Olsen. First return times: multifractal spectra and divergence points. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 635-656. doi: 10.3934/dcds.2004.10.635

[19]

Imen Bhouri, Houssem Tlili. On the multifractal formalism for Bernoulli products of invertible matrices. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1129-1145. doi: 10.3934/dcds.2009.24.1129

[20]

Yangjian Sun, Changjian Liu. The Poincaré bifurcation of a SD oscillator. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1565-1577. doi: 10.3934/dcdsb.2020173

2020 Impact Factor: 1.327

Metrics

  • PDF downloads (153)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]