{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T23:39:13Z","timestamp":1776209953324,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T00:00:00Z","timestamp":1590969600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T00:00:00Z","timestamp":1590969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Theory Biosci."],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s12064-020-00315-5","type":"journal-article","created":{"date-parts":[[2020,6,2]],"date-time":"2020-06-02T17:05:01Z","timestamp":1591117501000},"page":"235-251","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Mathematical assessment of the spermatozoa transport through couple stress fluid in an asymmetric human cervical canal"],"prefix":"10.1007","volume":"139","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8924-3863","authenticated-orcid":false,"given":"Ahsan","family":"Walait","sequence":"first","affiliation":[]},{"given":"A. M.","family":"Siddiqui","sequence":"additional","affiliation":[]},{"given":"M. A.","family":"Rana","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,1]]},"reference":[{"key":"315_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.actaastro.2016.06.044","volume":"128","author":"NS Akbar","year":"2016","unstructured":"Akbar NS, Tripathi D, Beg OA, Khan ZH (2016) MHD dissipative flow and heat transfer of Casson fluids due to metachronal wave propulsion of beating cilia with thermal and velocity slip effects under an oblique magnetic field. Acta Astronaut 128:1\u201312","journal-title":"Acta Astronaut"},{"key":"315_CR2","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1016\/j.cjph.2017.03.005","volume":"55","author":"NS Akbar","year":"2017","unstructured":"Akbar NS, Tripathi D, Khan ZH, Beg OA (2017) Mathematical model for ciliary-induced transport in MHD flow of Cu-H2O nanofluids with magnetic induction. Chin J Phys 55:947\u2013962","journal-title":"Chin J Phys"},{"key":"315_CR3","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1007\/s12043-016-1354-z","volume":"88","author":"NS Akbar","year":"2017","unstructured":"Akbar NS, Butt AW, Tripathi D, Beg OA (2017) Physical hydrodynamic propulsion model study on creeping viscous flow through a ciliated porous tube. Pramana 88:52","journal-title":"Pramana"},{"key":"315_CR4","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.mbs.2018.04.001","volume":"301","author":"NS Akbar","year":"2018","unstructured":"Akbar NS, Tripathi D, Khan ZH, Beg OA (2018) Mathematical modelling of pressure-driven micropolar biological flow due to metachronal wave propulsion of beating cilia. Math Biosci 301:121\u2013128","journal-title":"Math Biosci"},{"key":"315_CR5","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1007\/s42241-018-0021-x","volume":"30","author":"NS Akbar","year":"2018","unstructured":"Akbar NS, Shoaib M, Tripathi D, Bhushan S, Beg OA (2018) Analytical approach to entropy generation and heat transfer in CNT-nanofluid dynamics through a ciliated porous medium. J Hydrodyn 30:296\u2013306","journal-title":"J Hydrodyn"},{"key":"315_CR6","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s11071-007-9245-y","volume":"51","author":"AR Ansari","year":"2008","unstructured":"Ansari AR, Siddiqui AM, Hayat T (2008) An analysis of the swimming problem of a singly flagellated micro-organism in an MHD fluid. Nonlinear Dyn 51:477\u2013481. https:\/\/doi.org\/10.1007\/s11071-007-9245-y","journal-title":"Nonlinear Dyn"},{"key":"315_CR7","doi-asserted-by":"crossref","first-page":"29","DOI":"10.15388\/NA.2010.15.1.14362","volume":"15","author":"M Devakar","year":"2010","unstructured":"Devakar M, Iyengar TKV (2010) Run up flow of a couple stress fluid between parallel plates. Nonlinear Anal Model Control 15:29\u201337","journal-title":"Nonlinear Anal Model Control"},{"key":"315_CR8","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1016\/j.aej.2014.06.005","volume":"53","author":"M Devakar","year":"2014","unstructured":"Devakar M, Sreenivasu D, Shankar B (2014) Analytical solutions of couple stress fluid flows with slip boundary conditions. Alex Eng J 53:723\u2013730","journal-title":"Alex Eng J"},{"key":"315_CR9","first-page":"225","volume":"347","author":"AA Farooq","year":"2019","unstructured":"Farooq AA, Tripathi D, Elnaqeeb T (2019) On the propulsion of micropolar fluid inside a channel due to ciliary induced metachronal wave. Appl Math Comput 347:225\u2013235","journal-title":"Appl Math Comput"},{"key":"315_CR10","doi-asserted-by":"publisher","first-page":"217","DOI":"10.5560\/ZNA.2012-0021","volume":"67","author":"T Hayat","year":"2012","unstructured":"Hayat T, Iqbal Z, Qasim M, Aldossary OM (2012) Heat transfer in a couple stress fluid over a continuous moving surface with internal heat generation and convective boundary. Conditions 67:217\u2013224. https:\/\/doi.org\/10.5560\/ZNA.2012-0021","journal-title":"Conditions"},{"key":"315_CR11","doi-asserted-by":"crossref","first-page":"47","DOI":"10.15388\/NA.17.1.14077","volume":"17","author":"T Hayat","year":"2012","unstructured":"Hayat T, Awais M, Safdar A, Hendi AA (2012b) Unsteady three dimensional flow of couple stress fluid over a stretching surface with chemical reaction. Nonlinear Anal Model Control 17:47\u201359","journal-title":"Nonlinear Anal Model Control"},{"key":"315_CR12","first-page":"348","volume":"129","author":"A Henry Sathananthan","year":"2009","unstructured":"Henry Sathananthan A (2009) Human centriole: origin, and how it impacts fertilization, embryogenesis, infertility and cloning. Indian J Med Res 129:348\u2013350","journal-title":"Indian J Med Res"},{"key":"315_CR13","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1002\/mrd.1120130302","volume":"13","author":"S Ishijima","year":"1986","unstructured":"Ishijima S, Oshio S, Mohri H (1986) Flagellar movement of human spermatozoa. Mol Reprod Dev 13:185\u2013197. https:\/\/doi.org\/10.1002\/mrd.1120130302","journal-title":"Mol Reprod Dev"},{"key":"315_CR14","unstructured":"Jones Richard E, Lopez Kristin H (2006) Human Reproductive biology 3, an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA"},{"key":"315_CR15","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1530\/jrf.0.0530259","volume":"53","author":"DF Katz","year":"1978","unstructured":"Katz DF, Mills RN, Pritchett TR (1978) The movement of human spermatozoa in cervical mucus. J Reprod Fertil 53:259\u2013265","journal-title":"J Reprod Fertil"},{"key":"315_CR16","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/S0015-0282(16)53772-8","volume":"54","author":"DF Katz","year":"1990","unstructured":"Katz DF, Morales P, Samuels SJ, Overstreet JW (1990) Mechanisms of filtration of morphologically abnormal human sperm by cervical mucus. Fertil Steril 54:513\u2013516","journal-title":"Fertil Steril"},{"key":"315_CR17","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1023\/A:1006543719401","volume":"13","author":"DF Katz","year":"1997","unstructured":"Katz DF, Slade DA, Nakajima ST (1997) Analysis of preovulatory changes in cervical mucus hydration and sperm penetrability. Adv Contracept 13:143\u2013151","journal-title":"Adv Contracept"},{"key":"315_CR18","first-page":"269","volume":"9","author":"SR Kumar","year":"2015","unstructured":"Kumar SR (2015) The effect of the couple stress fluid flow on MHD peristaltic motion with uniform porous medium in the presence of slip effect. Jordan J Mech Ind Eng 9:269\u2013278","journal-title":"Jordan J Mech Ind Eng"},{"key":"315_CR19","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1016\/j.fluiddyn.2007.04.001","volume":"39","author":"JR Lin","year":"2007","unstructured":"Lin JR, Hung CR (2007) Combined effects of non-Newtonian couple stresses and fluid inertia on the squeeze film characteristics between a long cylinder and an infinite plate. Fluid Dyn Res 39:616\u2013631","journal-title":"Fluid Dyn Res"},{"key":"315_CR20","doi-asserted-by":"publisher","first-page":"2092","DOI":"10.1093\/humrep\/deu195","volume":"29","author":"F Martyn","year":"2014","unstructured":"Martyn F, McAuliffe F, Wingfield M (2014) The role of the cervix in fertility: is it time for a reappraisal? Human Reprod 29:2092\u20132098. https:\/\/doi.org\/10.1093\/humrep\/deu195","journal-title":"Human Reprod"},{"key":"315_CR21","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1016\/S0301-679X(01)00064-0","volume":"34","author":"NB Naduvinamani","year":"2001","unstructured":"Naduvinamani NB, Hiremath PS, Gurubasavaraj G (2001) Squeeze film lubrication of a short porous journal bearing with couple stress fluids. Tribol Int 34:739\u2013747","journal-title":"Tribol Int"},{"key":"315_CR22","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/S0169-5983(02)00137-5","volume":"31","author":"NB Naduvinamani","year":"2002","unstructured":"Naduvinamani NB, Hiremath PS, Gurubasavaraj G (2002) Surface roughness effects in a short porous journal bearing with a couple stress fluid. Fluid Dyn Res 31:333\u2013354","journal-title":"Fluid Dyn Res"},{"key":"315_CR23","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1016\/S0301-679X(03)00092-6","volume":"36","author":"NB Naduvinamani","year":"2003","unstructured":"Naduvinamani NB, Fathima ST, Hiremath PS (2003) Hydrodynamic lubrication of rough slider bearings with couple stress fluids. Tribol Int 36:949\u2013959","journal-title":"Tribol Int"},{"issue":"5","key":"315_CR24","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/S0169-5983(03)00048-0","volume":"32","author":"NB Naduvinamani","year":"2003","unstructured":"Naduvinamani NB, Fathima Syeda Tasneem, Hiremath PS (2003) Effect of surface roughness on characteristics of couplestress squeeze film between anisotropic porous rectangular plates. Fluid Dyn Res 32(5):217\u2013231","journal-title":"Fluid Dyn Res"},{"key":"315_CR25","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.triboint.2004.09.001","volume":"38","author":"NB Naduvinamani","year":"2005","unstructured":"Naduvinamani NB, Hiremath PS, Gurubasavaraj G (2005) Effects of surface roughness on the couple stress squeeze film between a sphere and a flat Plate. Tribol Int 38:451\u2013458","journal-title":"Tribol Int"},{"key":"315_CR26","first-page":"313","volume":"7","author":"E Odeblad","year":"1962","unstructured":"Odeblad E (1962) Undulations of macromolecules in cervical mucus. Int J Fertil 7:313","journal-title":"Int J Fertil"},{"key":"315_CR27","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1098\/rspa.2009.0208","volume":"466","author":"OS Pak","year":"2010","unstructured":"Pak OS, Lauga E (2010) The transient swimming of a waving sheet. Proc R Soc A 466:107\u2013126. https:\/\/doi.org\/10.1098\/rspa.2009.0208","journal-title":"Proc R Soc A"},{"key":"315_CR28","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1007\/BF00786692","volume":"66","author":"D Philip","year":"1995","unstructured":"Philip D, Chandra P (1995) Self-propulsion of spermatozoa in microcontinua: effect of transverse wave motion of channel walls. Arch Appl Mech 66:90\u201399. https:\/\/doi.org\/10.1007\/BF00786692","journal-title":"Arch Appl Mech"},{"key":"315_CR29","doi-asserted-by":"crossref","first-page":"409","DOI":"10.15388\/NA.2007.12.3.14703","volume":"12","author":"G Radhakrishnamacharya","year":"2007","unstructured":"Radhakrishnamacharya G, Sharma R (2007) Motion of a self-propelling micro-organism in a channel under peristalsis: effects of viscosity variation. Nonlinear Anal 12:409\u2013418","journal-title":"Nonlinear Anal"},{"key":"315_CR30","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.jppr.2018.06.002","volume":"8","author":"K Ramesh","year":"2019","unstructured":"Ramesh K, Tripathi D, Beg OA (2019) Cilia-assisted hydromagnetic pumping of biorheological couple stress fluids. Propul Power Res 8:221\u2013233","journal-title":"Propul Power Res"},{"key":"315_CR31","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1017\/S0022112065001337","volume":"23","author":"AJ Reynolds","year":"1965","unstructured":"Reynolds AJ (1965) The swimming of minute organisms. J Fluid Mech 23:241\u2013260. https:\/\/doi.org\/10.1017\/S0022112065001337","journal-title":"J Fluid Mech"},{"key":"315_CR32","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/BF02464619","volume":"36","author":"WJ Shack","year":"1974","unstructured":"Shack WJ, Lardner TJ (1974) A long wavelength solution for a microorganism swimming in a channel. Bull Math Biol 36:435\u2013444. https:\/\/doi.org\/10.1007\/BF02464619","journal-title":"Bull Math Biol"},{"key":"315_CR33","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/0021-9290(78)90039-8","volume":"11","author":"JB Shukla","year":"1978","unstructured":"Shukla JB, Rao BRP, Parihar RS (1978) Swimming of spermatozoa in cervix: effects of dynamical interaction and peripheral layer viscosity. J Biomech 11:15\u201319. https:\/\/doi.org\/10.1016\/0021-9290(78)90039-8","journal-title":"J Biomech"},{"key":"315_CR34","doi-asserted-by":"publisher","first-page":"947","DOI":"10.1016\/0021-9290(88)90133-9","volume":"21","author":"JB Shukla","year":"1988","unstructured":"Shukla JB, Chandra P, Sharma R, Radhakrishnamacharya G (1988) Effects of peristaltic and longitudinal wave motion of the channel wall on movement of micro-organisms: application to spermatozoa transport. J Biomech 21:947\u2013954. https:\/\/doi.org\/10.1016\/0021-9290(88)90133-9","journal-title":"J Biomech"},{"key":"315_CR35","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1615\/JPorMedia.v8.i6.10","volume":"8","author":"AM Siddiqui","year":"2005","unstructured":"Siddiqui AM, Ansari AR (2005) A note on the the swimming problem of a singly flagellated micro-organism in a fluid flowing through a porous medium. J Porous Media 8:551\u2013556. https:\/\/doi.org\/10.1615\/JPorMedia.v8.i6.10","journal-title":"J Porous Media"},{"key":"315_CR36","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1016\/0020-7225(82)90037-4","volume":"20","author":"Prawal Sinha","year":"1982","unstructured":"Sinha Prawal, Singh Chandan, Prasad KRK (1982) A mecrocontinuum analysis of the self propulsion of the spermatozoa in the cervical canal. Int J Eng Sci 20:1037\u20131048","journal-title":"Int J Eng Sci"},{"key":"315_CR37","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/0021-9290(74)90030-X","volume":"7","author":"RE Smelser","year":"1974","unstructured":"Smelser RE, Shack WJ, Lardner TJ (1974) The swimming of spermatozoa in an active channel. J Biomech 7:349\u2013355. https:\/\/doi.org\/10.1016\/0021-9290(74)90030-X","journal-title":"J Biomech"},{"key":"315_CR38","first-page":"353","volume":"41","author":"D Srinivasacharya","year":"2011","unstructured":"Srinivasacharya D, Kaladhar K (2011) Soret and dufour effects in a mixed convection couple stress fluid with heat and mass fluxes. Latin Am Appl Res 41:353\u2013358","journal-title":"Latin Am Appl Res"},{"key":"315_CR39","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1063\/1.1761925","volume":"9","author":"VK Stokes","year":"1966","unstructured":"Stokes VK (1966) Couple stresses in fluids. Phys Fluids 9:1709\u20131715","journal-title":"Phys Fluids"},{"key":"315_CR40","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-82351-0","volume-title":"Theories of fluids with microstructure: an introduction","author":"VK Stokes","year":"1984","unstructured":"Stokes VK (1984) Theories of fluids with microstructure: an introduction. Springer, Berlin. https:\/\/doi.org\/10.1007\/978-3-642-82351-0"},{"key":"315_CR41","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1098\/rspa.1951.0218","volume":"209","author":"GI Taylor","year":"1951","unstructured":"Taylor GI (1951) Analysis of the swimming of microscopic organisms. Proc R Soc A 209:447\u2013461. https:\/\/doi.org\/10.1098\/rspa.1951.0218","journal-title":"Proc R Soc A"},{"key":"315_CR42","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1017\/S0022112068000169","volume":"31","author":"EO Tuck","year":"1968","unstructured":"Tuck EO (1968) A note on a swimming problem. J Fluid Mech 31:305\u2013308. https:\/\/doi.org\/10.1017\/S0022112068000169","journal-title":"J Fluid Mech"},{"issue":"3","key":"315_CR43","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s10867-018-9481-z","volume":"44","author":"A Walait","year":"2018","unstructured":"Walait A, Siddiqui AM, Rana MA (2018) Analysis of a self-propelling sheet with heat transfer through non-isothermal fluid in an inclined human cervical canal. J Biol Phys 44(3):273\u2013300","journal-title":"J Biol Phys"},{"issue":"7","key":"315_CR44","doi-asserted-by":"crossref","first-page":"2861","DOI":"10.1007\/s00707-018-2136-0","volume":"229","author":"A Walait","year":"2018","unstructured":"Walait A, Siddiqui AM, Rana MA (2018) Biomechanics of the swimming of self-propelling spermatozoa through slippery human cervical canal. Acta Mech 229(7):2861\u20132881","journal-title":"Acta Mech"},{"issue":"13","key":"315_CR45","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1615\/JPorMedia.2019028992","volume":"21","author":"A Walait","year":"2018","unstructured":"Walait A, Siddiqui AM, Rana MA (2018) Biomechanics of the self-propulsion of spermatozoa through porous medium in the human cervical canal. J Porous Media 21(13):1415\u20131437","journal-title":"J Porous Media"}],"container-title":["Theory in Biosciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12064-020-00315-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12064-020-00315-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12064-020-00315-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T05:55:06Z","timestamp":1622526906000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12064-020-00315-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,1]]},"references-count":45,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["315"],"URL":"https:\/\/doi.org\/10.1007\/s12064-020-00315-5","relation":{},"ISSN":["1431-7613","1611-7530"],"issn-type":[{"value":"1431-7613","type":"print"},{"value":"1611-7530","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,1]]},"assertion":[{"value":"19 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 April 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 June 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}