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Simulation of the uterine contractions and foetus expulsion using a chemo-mechanical constitutive model

  • M. C. P. Vila PoucaEmail author
  • J. P. S. Ferreira
  • D. A. Oliveira
  • M. P. L. Parente
  • M. T. Mascarenhas
  • R. M. Natal Jorge
Original Paper

Abstract

During vaginal delivery women sustain stretching of their pelvic floor, risking tissue injury and adverse outcomes. Since studies in pregnant women are limited with ethical constraints, computational models have become an interesting alternative to elucidate the pregnancy mechanisms. This research investigates the uterine contractions during foetus expulsion without an imposed trajectory. Such physical process is captured by means of a chemo-mechanical constitutive model, where the uterine contractions are triggered by chemical stimuli. The foetus descent, which includes both pushing and resting stages, has a descent rate within the physiological range. Moreover, the behaviour of the foetus and the uterus stretch agree well with clinical data presented in the literature. The follow-up of this study will be to obtain a complete childbirth simulation, considering also the pelvic floor muscles and its supporting structures. The simulation of a realistic rate of descent, including the pushing and resting stages, is of significant importance to study the pelvic floor muscles due to their viscoelastic nature.

Keywords

Childbirth Uterus contraction Chemo-mechanical model Finite element method Continuum mechanics 

Notes

Acknowledgements

The authors declare that they have no conflict of interest. Authors gratefully acknowledge the support from the Portuguese Foundation of Science under Grants IF/00159/2014 and SFRH/BD/107860/2015, and the funding of Project NORTE-01-0145-FEDER-030062 and NORTE-01-0145‐FEDER-000022 SciTech‐Science and Technology for Competitive and Sustainable Industries, cofinanced by Norte’s Regional Operational Programme (NORTE2020), through European Regional Development Fund (FEDER).

Supplementary material

10237_2019_1117_MOESM1_ESM.avi (435.7 mb)
The video submitted as supplementary material shows the evolution of the vertical displacement of the foetus head and the distributionof the maximum principal stresss (MPa) in the uterus throughout the simulation discussed in Sect. 4.1. (AVI 446167 kb)

References

  1. Abalos E, Oladapo OT, Chamillard M, Díaz V, Pasquale J, Bonet M, Souza JP, Gülmezoglu AM (2018) Duration of spontaneous labour in ‘low-risk’ women with ‘normal’ perinatal outcomes: a systematic review. Eur J Obstet Gynecol Reprod Biol 223:123–132.  https://doi.org/10.1016/j.ejogrb.2018.02.026 CrossRefGoogle Scholar
  2. Alvarez H, Caldeyro R (1950) Contractility of the human uterus recorded by new methods. Surg Gynecol Obstet 91(1):1–13Google Scholar
  3. Ashton-Miller JA, DeLancey JOL (2007) Functional anatomy of the female pelvic floor. Ann N Y Acad Sci 1101:266–296.  https://doi.org/10.1196/annals.1389.034 CrossRefGoogle Scholar
  4. Ashton-Miller JA, DeLancey JOL (2010) On the biomechanics of vaginal birth and common sequelae. Ann Rev Biomed Eng 11:163–176.  https://doi.org/10.1146/annurev-bioeng-061008-124823.On CrossRefGoogle Scholar
  5. Beckmann CRB, Ling FW, Herbert WNP, Laube DW, Smith RP, Casanova R, Chuang A, Goepfert AR, Hueppchen NA, Weiss PM (2014) Obstretrics and gynecology, 7th edn. Wolters Kluwer Health/Lippincott Williams & Wilkins, PhiladelphiaGoogle Scholar
  6. Buhimschi C, Boyle MB, Garfield RE (1997) Electrical activity of the human uterus during pregnancy as recorded from the abdominal surface. Obstet Gynecol 90:102–111CrossRefGoogle Scholar
  7. Bursztyn L, Eytan O, Jaffa AJ, Elad D (2007) Mathematical model of excitation-contraction in a uterine smooth muscle cell. Am J Physiol Cell Physiol 292:C1816–C1829.  https://doi.org/10.1152/ajpcell.00478.2006 CrossRefGoogle Scholar
  8. Buttin R, Zara F, Shariat B, Redarce T, Grangé G (2013) Biomechanical simulation of the fetal descent without imposed theoretical trajectory. Comput Methods Programs Biomed 111:389–401.  https://doi.org/10.1016/j.cmpb.2013.04.005 CrossRefGoogle Scholar
  9. Cochran AL, Gao Y (2015) A model and simulation of uterine contractions. Math Mech Solids 20:540–564.  https://doi.org/10.1177/1081286513507940 CrossRefzbMATHGoogle Scholar
  10. Conrad JT, Kuhn WK, Johnson WL (1966) Stress relaxation in human uterine muscle. Am J Obstet Gynecol 95:254–265.  https://doi.org/10.1016/0002-9378(66)90177-3 CrossRefGoogle Scholar
  11. Debold EP, Patlak JB, Warshaw DM (2005) Slip sliding away: load-dependence of velocity generated by skeletal muscle myosin molecules in the laser trap. Biophys J 89:L34–L36.  https://doi.org/10.1529/biophysj.105.072967 CrossRefGoogle Scholar
  12. Degani S, Leibovitz Z, Shapiro I, Gonen R, Ohel G (1998) Myometrial thickness in pregnancy: longitudinal sonographic study. J Ultrasound Med 17:661–665.  https://doi.org/10.7863/jum.1998.17.10.661 CrossRefGoogle Scholar
  13. Deyer TW, Ashton-Miller JA, Van Baren PM, Pearlman MD (2000) Myometrial contractile strain at uteroplacental separation during parturition. Am J Obstet Gynecol 183:156–159.  https://doi.org/10.1067/mob.2000.105819 Google Scholar
  14. Hai CM, Murphy RA (1988) Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am J Physiol Cell Physiol 254:C99–C106CrossRefGoogle Scholar
  15. Hills BA (1995) Remarkable lubricating capabilities of amniotic surfactant. Aust Nw Z J Obstet Gynaecol 35:186–189.  https://doi.org/10.1111/j.1479-828X.1995.tb01866.x CrossRefGoogle Scholar
  16. Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, EnglandzbMATHGoogle Scholar
  17. Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast Phys Sci Solids 61:1–48MathSciNetCrossRefzbMATHGoogle Scholar
  18. Hsiao AY, Okitsu T, Onoe H, Kiyosawa M, Teramae H, Iwanaga S, Kazama T, Matsumoto T, Takeuchi S (2015) Smooth muscle-like tissue constructs with circumferentially oriented cells formed by the cell fiber technology. PLoS ONE 10:1–16.  https://doi.org/10.1371/journal.pone.0119010 Google Scholar
  19. Jakeman AR (2016) Maternal positioning in the second stage of labor and incidence of spontaneous perineal trauma: a systematic review with meta-analysis of randomized controlled trials. Undergrad. Honor. Theses 1162Google Scholar
  20. Jing D, Ashton-Miller JA, DeLancey JOL (2012) A subject-specific anisotropic visco-hyperelastic finite element model of female pelvic floor stress and strain during the second stage of labor. J Biomech 45:455–460.  https://doi.org/10.1016/j.jbiomech.2011.12.002 CrossRefGoogle Scholar
  21. Kiserud T, Piaggio G, Carroli G, Widmer M, Carvalho J, Neerup Jensen L, Giordano D, Cecatti JG, Abdel Aleem H, Talegawkar SA, Benachi A, Diemert A, Tshefu Kitoto A, Thinkhamrop J, Lumbiganon P, Tabor A, Kriplani A, Gonzalez Perez R, Hecher K, Hanson MA, Gülmezoglu AM, Platt LD (2017) The world health organization fetal growth charts: a multinational longitudinal study of ultrasound biometric measurements and estimated fetal weight. PLoS Med.  https://doi.org/10.1371/journal.pmed.1002220
  22. Kroon M (2009) A constitutive model for smooth muscle including active tone and passive viscoelastic behaviour. Math Med Biol 27:129–155.  https://doi.org/10.1093/imammb/dqp017 MathSciNetCrossRefzbMATHGoogle Scholar
  23. Lien K-C, Mooney B, DeLancey JOL, Ashton-Miller J (2004) Levator ani muscle stretch induced by simulated vaginal birth. Obs Gynecol 103:31–40.  https://doi.org/10.1097/01.AOG.0000109207.22354.65 CrossRefGoogle Scholar
  24. Manoogian SJ, McNally C, Stitzel JD, Duma SM (2008) Dynamical biaxial tissue properties of pregnant porcine uterine tissue. Stapp Car Crash J 52:167–185Google Scholar
  25. Manoogian SJ, Bisplinghoff JA, Kemper AR, Duma SM (2012) Dynamic material properties of the pregnant human uterus. J Biomech 45:1724–1727.  https://doi.org/10.1016/j.jbiomech.2012.04.001 CrossRefGoogle Scholar
  26. Memon H, Handa VL (2012) Pelvic floor disorders following vaginal or cesarean delivery. Curr Opin Obstet Gynecol 24:349–354.  https://doi.org/10.1097/GCO.0b013e328357628b CrossRefGoogle Scholar
  27. Miftahof RN, Nam HG (2011) Biomechanics of the gravid human Uterus. Springer Science & Business Media, BerlinCrossRefGoogle Scholar
  28. Murtada S Il, Holzapfel GA (2014) Investigating the role of smooth muscle cells in large elastic arteries: a finite element analysis. J Theor Biol 358:1–10.  https://doi.org/10.1016/j.jtbi.2014.04.028 MathSciNetCrossRefGoogle Scholar
  29. Oliveira DA, Parente MPL, Calvo B, Mascarenhas T, Jorge RMN (2016a) A biomechanical analysis on the impact of episiotomy during childbirth. Biomech Model Mechanobiol 15:1–12.  https://doi.org/10.1007/s10237-016-0781-6 CrossRefGoogle Scholar
  30. Oliveira DA, Parente MPL, Calvo B, Mascarenhas T, Natal Jorge RM (2016b) Numerical simulation of the damage evolution in the pelvic floor muscles during childbirth. J Biomech 49:594–601.  https://doi.org/10.1016/j.jbiomech.2016.01.014 CrossRefGoogle Scholar
  31. Parente MPL, Jorge RMN, Mascarenhas T, Fernandes AA, Martins JAC (2008) Deformation of the pelvic floor muscles during a vaginal delivery. Int Urogynecol J Pelvic Floor Dysfunct 19:65–71.  https://doi.org/10.1007/s00192-007-0388-7 CrossRefGoogle Scholar
  32. Parente MPL, Natal Jorge RM, Mascarenhas T, Fernandes AA, Martins JAC (2009) The influence of the material properties on the biomechanical behavior of the pelvic floor muscles during vaginal delivery. J Biomech 42:1301–1306.  https://doi.org/10.1016/j.jbiomech.2009.03.011 CrossRefGoogle Scholar
  33. Parente M, Natal Jorge RM, Mascarenhas T, Fernandes AA, Silva-Filho AL (2010) Computational modeling approach to study the effects of fetal head flexion during vaginal delivery. Am J Obstet Gynecol 203:217.e1–217.e6.  https://doi.org/10.1016/j.ajog.2010.03.038 CrossRefGoogle Scholar
  34. Rivaux G, Rubod C, Dedet B, Brieu M, Gabriel B, Cosson M (2013) Comparative analysis of pelvic ligaments: a biomechanics study. Int Urogynecol J Pelvic Floor Dysfunct 24:135–139.  https://doi.org/10.1007/s00192-012-1861-5 CrossRefGoogle Scholar
  35. Sharifimajd B, Stålhand J (2013) A continuum model for excitation-contraction of smooth muscle under finite deformations. J Theor Biol 355:1–9.  https://doi.org/10.1016/j.jtbi.2014.03.016 MathSciNetCrossRefGoogle Scholar
  36. Sharifimajd B, Thore CJ, Stålhand J (2016) Simulating uterine contraction by using an electro-chemo-mechanical model. Biomech Model Mechanobiol 15:497–510.  https://doi.org/10.1007/s10237-015-0703-z CrossRefGoogle Scholar
  37. Stålhand J, Klarbring A, Holzapfel GA (2008) Smooth muscle contraction: mechanochemical formulation for homogeneous finite strains. Prog Biophys Mol Biol 96:465–481.  https://doi.org/10.1016/j.pbiomolbio.2007.07.025 CrossRefGoogle Scholar
  38. Vila Pouca MCP, Ferreira JPS, Oliveira DA, Parente MPL, Natal Jorge RM (2017) Viscous effects in pelvic floor muscles during childbirth: a numerical study. Int J Numer Method Biomed Eng 34(3):e2927.  https://doi.org/10.1002/cnm.2927 MathSciNetCrossRefGoogle Scholar
  39. Weiss S, Jaermann T, Schmid P, Staempfli P, Boesiger P, Niederer P, Caduff R, Bajka M (2006) Three-dimensional fiber architecture of the nonpregnant human uterus determined ex vivo using magnetic resonance diffusion tensor imaging. Anat Rec Part A Discov Mol Cell Evol Biol 288:84–90.  https://doi.org/10.1002/ar.a.20274 CrossRefGoogle Scholar
  40. Young R, Goloman G (2010) Mechanotransduction in rat myometrium: coordination of contractions of electrically and chemically isolated tissues. Reprod Sci 18:64–69CrossRefGoogle Scholar
  41. Young RC, Hession RO (1999) Three-dimensional structure of the smooth muscle in the term-pregnant human uterus. Obstet Gynecol 93:94–99.  https://doi.org/10.1016/S0029-7844(98)00345-7 Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of EngineeringUniversity of PortoOportoPortugal
  2. 2.INEGI – Institute of Science and Innovation in Mechanical and Industrial EngineeringOportoPortugal
  3. 3.Department of Obstetrics and Gynecology, São João Hospital Center –EPE, Faculty of MedicineUniversity of PortoOportoPortugal

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