Article Contents
Article Contents

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

• 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.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

 Citation:

•  [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.