Biomechanics of the swimming of self-propelling spermatozoa through slippery human cervical canal. (English) Zbl 1397.92074
Summary: The present theoretical investigation is concerned with the biomechanics of the swimming of self-propelling spermatozoa through the slippery human cervical canal. Partial differential equations arising from the mathematical modelling of the proposed model along with slip boundary conditions are solved analytically. Expressions for pressure gradient, propulsive velocity, mucus velocity and time mean flow rate are analysed for the pertinent parameters. Salient features of the pumping characteristics are explored. It is interesting to note that maximal slippage on the upper cervical wall and zero slippage on the lower cervical wall maximize the probability of the spermatozoa to fertilize an ovum. It is found that a pressure rise facilitates the motion of spermatozoa to fertilize an ovum in the female reproductive tract, whereas a pressure drop inverts the direction of spermatozoa to the vagina and controls the probability of pregnancy.
References:
| [1] | Taylor, GI, Analysis of the swimming of microscopic organisms, Proc. R. Soc., 209, 447-461, (1951) · Zbl 0043.40302 · doi:10.1098/rspa.1951.0218 |
| [2] | Reynolds, AJ, The swimming of minute organisms, J. Fluid Mech., 23, 241-260, (1965) · doi:10.1017/S0022112065001337 |
| [3] | Tuck, EO, A note on a swimming problem, J. Fluid Mech., 31, 305-308, (1968) · doi:10.1017/S0022112068000169 |
| [4] | Pak, OS; Lauga, E, The transient swimming of a waving sheet, Proc. R. Soc., 466, 107-126, (2010) · Zbl 1195.76451 · doi:10.1098/rspa.2009.0208 |
| [5] | Shack, WJ; Lardner, TJ, A long wavelength solution for a microorganism swimming in a channel, Bull. Math. Biol., 36, 435-444, (1974) · Zbl 0285.92012 · doi:10.1007/BF02464619 |
| [6] | Smelser, RE; Shack, WJ; Lardner, TJ, The swimming spermatozoa in an active channel, J. Biomech., 7, 349-355, (1974) · doi:10.1016/0021-9290(74)90030-X |
| [7] | Odeblad, E, Undulation of macromolecules in cervical mucus, Int. J. Fertil., 7, 313-319, (1962) |
| [8] | Shukla, JB; Rao, BRP; Parihar, RS, Swimming of spermatozoa in cervix: effect of dynamical interaction and peripheral layer viscosity, J. Biomech., 11, 15-19, (1978) · doi:10.1016/0021-9290(78)90039-8 |
| [9] | Sinha, P; Singh, C; Prasat, KR, A microcontinuum analysis of the self propulsion of the spermatozoa in the cervical canal, Int. J. Eng. Sci., 20, 1037-1048, (1982) · Zbl 0499.76119 · doi:10.1016/0020-7225(82)90037-4 |
| [10] | Shukla, JB; Chandra, P; Sharma, R; Radhakrishnamacharya, G, Effects of peristaltic and longitudinal wave motion of the channel wall on movement of micro-organisms: application to spermatozoa transport, J. Biomech., 21, 947-954, (1988) · doi:10.1016/0021-9290(88)90133-9 |
| [11] | Philip, D; Chandra, P, Self-propulsion of spermatozoa in microcontinua: effect of transverse wave motion of channel walls, Arch. Appl. Mech., 66, 90-99, (1995) · Zbl 0837.76100 · doi:10.1007/BF00786692 |
| [12] | Radhakrishnamacharya, G; Sharma, R, Motion of a self-propelling micro-organism in a channel under peristalsis: effects of viscosity variation, Nonlinear Anal. Model. Control, 12, 409-418, (2007) · Zbl 1134.92011 |
| [13] | Sathananthan, AH, Human centriole: origin, how it impacts fertilization, embryogenesis, infertility and cloning, Indian J. Med. Res., 129, 348-350, (2009) |
| [14] | Jones, R.E., Lopez, K.H.: Human Reproductive Biology, 3rd edn. Elsevier, Burlington (2006) |
| [15] | Neto, C; Evans, DR; Bonaccurso, E; Butt, HJ; Craig, VSJ, Boundary slip in Newtonian liquids: a review of experimental studies, Rep. Prog. Phys., 68, 2859-2897, (2005) · doi:10.1088/0034-4885/68/12/R05 |
| [16] | Lauga, E., Brenner, M.P., Stone, H.A.: Handbook of Experimental Fluid Dynamics. Edited by J. Foss, C. Tropea and A. Yarin. Springer, New York (2007) |
| [17] | Bocquet, L; Barrat, JL, Flow boundary conditions from nano- to micro-scales, Soft Matter, 3, 685-693, (2007) · doi:10.1039/b616490k |
| [18] | Holt, JK; Park, HG; Wang, Y; Stadermann, M; Artyukhin, AB; Grigoropoulos, CP; Noy, A; Bakajin, O, Fast mass transport through sub-2-nanometer carbon nanotubes, Science, 312, 1034-1037, (2006) · doi:10.1126/science.1126298 |
| [19] | Majumder, M; Chopra, N; Andrews, R; Hinds, BJ, Nanoscale hydrodynamics: enhanced flow in carbon nanotubes, Nature, 438, 44, (2005) · doi:10.1038/438044a |
| [20] | Ali, N; Hussain, Q; Hayat, T; Asghar, S, Slip effects on the peristaltic transport of MHD fluid with variable viscosity, Phys. Lett. A, 372, 1477-1489, (2008) · Zbl 1217.76100 · doi:10.1016/j.physleta.2007.09.061 |
| [21] | Srinivas, S; Gayathri, R; Kothandapani, M, The influence of slip conditions, wall properties and heat transfer on MHD peristaltic transport, Comput. Phys. Commun., 180, 2115-2122, (2009) · Zbl 1197.76157 · doi:10.1016/j.cpc.2009.06.015 |
| [22] | Yildirim, A; Sezer, SA, Effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel, Math. Comput. Model, 52, 618-625, (2010) · Zbl 1201.76318 · doi:10.1016/j.mcm.2010.04.007 |
| [23] | Hayat, T; Hussain, Q; Qureshi, MU; Ali, N; Hendi, AA, Influence of slip condition on the peristaltic transport in an asymmetric channel with heat transfer: an exact solution, Int. J. Numer. Methods Fluids, 67, 1944-1959, (2011) · Zbl 1440.76160 · doi:10.1002/fld.2473 |
| [24] | Tripathi, D; Gupta, PK; Das, S, Influence of slip condition on peristaltic transport of a viscoelastic fluid with fractional Burgers model, Therm. Sci., 15, 501-515, (2011) · doi:10.2298/TSCI100503061T |
| [25] | Akbar, NS; Hayat, T; Nadeem, S; Obaidat, S, Peristaltic flow of a williamson fluid in an inclined asymmetric channel with partial slip and heat transfer, Int. J. Heat Mass Trans., 55, 1855-1862, (2012) · doi:10.1016/j.ijheatmasstransfer.2011.11.038 |
| [26] | Afsar Khan, A; Ellahi, R; Usman, M, Effects of variable viscosity on the flow of non-Newtonian fluid through a porous medium in an inclined channel with slip conditions, J. Porous Media, 16, 59-67, (2013) · doi:10.1615/JPorMedia.v16.i1.60 |
| [27] | Hayat, T; Mehmood, OU, Slip effects on MHD flow of third order fluid in a planar channel, Commun. Nonlinear Sci. Numer. Simul., 16, 1363-1377, (2011) · Zbl 1221.76220 · doi:10.1016/j.cnsns.2010.06.034 |
| [28] | Ishijima, S; Oshio, S; Mohri, H, Flagellar movement of human spermatozoa, Mol. Reprod. Dev., 13, 185-197, (1986) |
| [29] | Martyn, F; McAuliffe, FM; Wingfield, M, The role of the cervix in fertility: is it time for a reappraisal?, Hum. Reprod., 29, 2092-2098, (2014) · doi:10.1093/humrep/deu195 |
| [30] | Munde, M.D.P.F.: Surgical Gynecology, A Manual Uterine Diagnosis and the Lesser Technicalities of Gynecological Practice for the Use of the Advance Students and General Practitioner. William Wood and Company, New York (1880) |
| [31] | Hatzikiriakos, SG; Mitsoulis, E, Slip effects in tapered dies, Polym. Eng. Sci., 49, 1960-1969, (2009) · doi:10.1002/pen.21430 |
| [32] | Papanastasiou, T., Georgiou, G., Alexandrou, A.N.: Viscous Fluid Flow. CRC Press, Boca Raton (1999) · Zbl 0946.76001 · doi:10.1201/9781420050288 |
| [33] | Gul, T; Shah, RA; Islam, S; Arif, M, MHD thin film flows of a third grade fluid on a vertical belt with slip boundary conditions, J. Appl. Math., 2013, 1-14, (2013) · Zbl 1397.76105 · doi:10.1155/2013/707286 |
| [34] | Farooq, M; Rahim, MT; Islam, S; Siddiqui, AM, Withdrawal and drainage of generalized second grade fluid on vertical cylinder with slip conditions, J. Prime Res. Math., 9, 51-64, (2013) · Zbl 1305.76011 |
| [35] | Zaman, H, Hall effects on the unsteady incompressible MHD fluid flow with slip conditions and porous walls, Appl. Math. Phys., 1, 31-38, (2013) |
| [36] | Ellahi, R; Hayat, T; Mahomed, FM, Generalized Couette flow of a third-grade fluid with slip: the exact solutions, Zeitschrift Fr Naturforschung A, 65, 1071-1076, (2010) |
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