Computer modelling of peristalsis-driven intrauterine fluid flow in the presence of electromagnetohydrodynamics

  • Jayavel Prakash
  • Ashu Yadav
  • Dharmendra TripathiEmail author
  • Abhishek Kumar Tiwari
Regular Article


The intrauterine fluid motion is responsible for embryo transport and its implantation at fundus. It is believed that myometrial contractions induced by peristaltic propulsion and pressure gradient typically regulate the intrauterine fluid movement. Several factors like changes in the mechanical behavior of uterus with age, hormonal variations, number of pregnancies, and mode of delivery (vaginal delivery versus cesarean), and any gestation may impair this mechanism. There are limited reports which indicate that the intrauterine fluid movement is possible to control with the help of external electric or magnetic fields. However, there are very few studies that investigate the intrauterine fluid motion in the presence of aforementioned external stimuli. This encouraged us to develop a computer model to study intrauterine fluid movement induced by peristalsis in the presence of electro-magnetohydrodynamics. Uterus geometry is idealized as a tapered micro-channel, whereas the Williamson fluid model is used to represent the intrauterine fluid. The Debye-Hückel linearization and perturbation method are employed to obtain the mathematical solution for fluid motion in the presence of any external field. The effect of the Debye-Hückel parameter, Helmholtz-Smoluchowski velocity, zeta potential and Hartmann number on pumping characteristics, flow characteristics, shear stress and trapping are studied to analyze the sensitivity of the fluid model. Overall, this study presents a model to understand the behavior of the intrauterine fluid motion in the presence of electric and magnetic fields. The model and associated results may be encouraged and may helpful for biomedical engineers in the design and development of such biomicrofluidic devices which can transport the embryo at a suitable location of the uterus for implantation.


  1. 1.
    G. Kunz, M. Noe, M. Herbertz, G. Leyendecker, Hum. Reprod. Update 4, 647 (1998)CrossRefGoogle Scholar
  2. 2.
    O. Eytan, A.J. Jaffa, J. Har-Toov, E. Dalach, D. Elad, Ann. Biomed. Eng. 27, 372 (1999)CrossRefGoogle Scholar
  3. 3.
    O. Eytan, D. Elad, Bull. Math. Biol. 61, 221 (1999)CrossRefGoogle Scholar
  4. 4.
    O. Eytan, A.J. Jaffa, D. Elad, Med. Eng. Phys. 23, 475 (2001)CrossRefGoogle Scholar
  5. 5.
    O. Eytan, I. Halevi, J. Har-Toov, I. Wolman, D. Elad, A.J. Jaffa, Fertil. Steril. 76, 337 (2001)CrossRefGoogle Scholar
  6. 6.
    S. Yaniv, A.J. Jaffa, O. Eytan, D. Elad, Eur. J. Obstet. Gynecol. Reprod. Biol. 144, S50 (2009)CrossRefGoogle Scholar
  7. 7.
    V. Aranda, R. Cortez, L. Fauci, J. Biomech. 48, 1631 (2015)CrossRefGoogle Scholar
  8. 8.
    M.S. Reddy, A.R. Rao, S. Sreenadh, Int. J. Non-Linear Mech. 42, 1153 (2007)CrossRefGoogle Scholar
  9. 9.
    N. Ali, T. Hayat, Appl. Math. Comput. 193, 535 (2007)MathSciNetGoogle Scholar
  10. 10.
    S. Nadeem, S. Akram, Commun. Nonlinear Sci. Numer. Simul. 15, 1705 (2010)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    S. Pandey, M. Chaube, J. Mech. Med. Biol. 11, 675 (2011)CrossRefGoogle Scholar
  12. 12.
    M. Kothandapani, J. Prakash, S. Srinivas, Int. J. Biomath. 8, 1550054 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    T. Hayat, R. Iqbal, A. Tanveer, A. Alsaedi, J. Magn. & Magn. Mater. 408, 168 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    T. Hayat, N. Aslam, M. Rafiq, F.E. Alsaadi, Results Phys. 7, 518 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    D. Tripathi, S. Bhushan, O.A. Bég, J. Mech. Med. Biol. 17, 1750052 (2017)CrossRefGoogle Scholar
  16. 16.
    S. Khaderi, J. den Toonder, P. Onck, J. Fluid Mech. 688, 44 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    S. Rydholm, T. Frisk, J.M. Kowalewski, H.A. Svahn, G. Stemme, H. Brismar, Biomed. Microdevices 10, 555 (2008)CrossRefGoogle Scholar
  18. 18.
    S. Chakraborty, J. Phys. Appl. Phys. 39, 5356 (2006)ADSCrossRefGoogle Scholar
  19. 19.
    A. Bandopadhyay, D. Tripathi, S. Chakraborty, Phys. Fluids 28, 052002 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    F.T. Hartley, Micromachined peristaltic pumps (Google Patents, 1999)Google Scholar
  21. 21.
    X. Zhang, Z. Chen, Y. Huang, Biomicrofluidics 9, 014118 (2015)CrossRefGoogle Scholar
  22. 22.
    B.D. Iverson, S.V. Garimella, Microfluid Nanofluidics 5, 145 (2008)CrossRefGoogle Scholar
  23. 23.
    P. Goswami, J. Chakraborty, A. Bandopadhyay, S. Chakraborty, Microvasc. Res. 103, 41 (2016)CrossRefGoogle Scholar
  24. 24.
    D. Tripathi, A. Yadav, O.A. Bég, Math. Biosci. 283, 155 (2017)MathSciNetCrossRefGoogle Scholar
  25. 25.
    G.C. Shit, N.K. Ranjit, A. Sinha, J. Bionic. Eng. 13, 436 (2016)CrossRefGoogle Scholar
  26. 26.
    D. Si, Y. Jian, J. Phys. Appl. Phys. 48, 085501 (2015)ADSCrossRefGoogle Scholar
  27. 27.
    M. Bhatti, A. Zeeshan, R. Ellahi, N. Ijaz, J. Mol. Liq. 230, 237 (2017)CrossRefGoogle Scholar
  28. 28.
    D. Tripathi, A. Sharma, O.A. Bég, Int. J. Heat Mass. Transfer 111, 138 (2017)CrossRefGoogle Scholar
  29. 29.
    N. Ranjit, G. Shit, Energy 128, 649 (2017)CrossRefGoogle Scholar
  30. 30.
    J. Prakash, A. Sharma, D. Tripathi, J. Mol. Liq. 249, 843 (2018)CrossRefGoogle Scholar
  31. 31.
    R. Krisher, M. Wheeler, Reprod. Fertil. Dev. 22, 32 (2009)CrossRefGoogle Scholar
  32. 32.
    S. Raty, E.M. Walters, J. Davis, H. Zeringue, D.J. Beebe, S.L. Rodriguez-Zas et al., Lab Chip 4, 186 (2004)CrossRefGoogle Scholar
  33. 33.
    D. Beebe, M. Wheeler, H. Zeringue, E. Walters, S. Raty, Theriogenology 57, 125 (2002)CrossRefGoogle Scholar
  34. 34.
    E.M. Walters, S.G. Clark, D.J. Beebe, M.B. Wheeler, Mammalian embryo culture in a microfluidic device, in Germ Cell Protocols (Springer, 2004) pp. 375--381Google Scholar
  35. 35.
    A.H. Shapiro, M.Y. Jaffrin, S.L. Weinberg, J. Fluid Mech. 37, 799 (1969)ADSCrossRefGoogle Scholar
  36. 36.
    H. Strohmer, A. Obruca, K.M. Radner, W. Feichtinger, Fertil. Steril. 61, 972 (1994)CrossRefGoogle Scholar
  37. 37.
    M. Ezzati, O. Djahanbakhch, S. Arian, B.R. Carr, J. Assist. Reprod. Genet. 31, 1337 (2014)CrossRefGoogle Scholar
  38. 38.
    B.J. Kirby, E.F. Hasselbrink, Electrophoresis 25, 203 (2004)CrossRefGoogle Scholar
  39. 39.
    K. Chalubinski, J. Deutinger, G. Bernaschek, Fertil. Steril. 59, 225 (1993)CrossRefGoogle Scholar
  40. 40.
    S. Yaniv, D. Elad, A.J. Jaffa, O. Eytan, Ann. Biomed. Eng. 31, 1255 (2003)CrossRefGoogle Scholar
  41. 41.
    S. Yaniv, A.J. Jaffa, D. Elad, J. Biomech. Eng. 134, 111003 (2012)CrossRefGoogle Scholar
  42. 42.
    F. Zara, O. Dupuis, Uterus -- Biomechanical modeling of uterus. Application to a childbirth simulation, in Biomechanics of Living Organs: Hyperelastic Constitutive Laws for Finite Element Modeling, edited by Yohan Payan, Jacques Ohayon (Elsevier, 2017)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Jayavel Prakash
    • 1
  • Ashu Yadav
    • 2
  • Dharmendra Tripathi
    • 3
    Email author
  • Abhishek Kumar Tiwari
    • 4
  1. 1.Department of MathematicsAvvaiyar Government College for WomenKaraikalIndia
  2. 2.Department of Mechanical EngineeringManipal UniversityJaipurIndia
  3. 3.Department of Science and HumanitiesNational Institute of TechnologyUttarakhandIndia
  4. 4.Department of Applied MechanicsMotilal Nehru National Institute of TechnologyAllahabad, PrayagrajIndia

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