[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

Multiphysics and multiscale modeling of uterine contractions: integrating electrical dynamics and soft tissue deformation with fiber orientation

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

The development of a comprehensive uterine model that seamlessly integrates the intricate interactions between the electrical and mechanical aspects of uterine activity could potentially facilitate the prediction and management of labor complications. Such a model has the potential to enhance our understanding of the initiation and synchronization mechanisms involved in uterine contractions, providing a more profound comprehension of the factors associated with labor complications, including preterm labor. Consequently, it has the capacity to assist in more effective preparation and intervention strategies for managing such complications. In this study, we present a computational model that effectively integrates the electrical and mechanical components of uterine contractions. By combining a state-of-the-art electrical model with the Hyperelastic Mass-Spring Model (HyperMSM), we adopt a multiphysics and multiscale approach to capture the electrical and mechanical activities within the uterus. The electrical model incorporates the generation and propagation of action potentials, while the HyperMSM simulates the mechanical behavior and deformations of the uterine tissue. Notably, our model takes into account the orientation of muscle fibers, ensuring that the simulated contractions align with their inherent directional characteristics. One noteworthy aspect of our contraction model is its novel approach to scaling the rest state of the mesh elements, as opposed to the conventional method of applying mechanical loads. By doing so, we eliminate artificial strain energy resulting from the resistance of soft tissues’ elastic properties during contractions. We validated our proposed model through test simulations, demonstrating its feasibility and its ability to reproduce expected contraction patterns across different mesh resolutions and configurations. Moving forward, future research efforts should prioritize the validation of our model using robust clinical data. Additionally, it is crucial to refine the model by incorporating a more realistic uterus model derived from medical imaging. Furthermore, applying the model to simulate the entire childbirth process holds immense potential for gaining deeper insights into the intricate dynamics of labor.

Graphical Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Wray S, Jones K, Kupittayanant S, Li Y, Matthew A, Monir-Bishty E, Noble K, Pierce SJ, Quenby S, Shmygol AV (2003) Calcium signaling and uterine contractility. J Soc Gynecol Investig 10(5):252–264

    Article  CAS  PubMed  Google Scholar 

  3. Hai C-M, Murphy RA (1988) Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am J Physiol Cell Physiol 254(1):C99–C106

    Article  CAS  Google Scholar 

  4. Beck S, Wojdyla D, Say L, Betran AP, Merialdi M, Requejo JH, Rubens C, Menon R, Van Look PF (2010) The worldwide incidence of preterm birth: a systematic review of maternal mortality and morbidity. Bull World Health Organ 88(1):31–38

    Article  PubMed  Google Scholar 

  5. Huddy C, Johnson A, Hope P (2001) Educational and behavioural problems in babies of 32–35 weeks gestation. Arch Dis Child-Fetal Neonatal Ed 85(1):F23–F28

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Leman H, Marque C, Gondry J (1999) Use of contractions during pregnancy. IEEE Trans Biomed Eng 46(10):1222–1229

    Article  CAS  PubMed  Google Scholar 

  7. Devedeux D, Marque C, Mansour S, Germain G, Duchêne J (1993) Uterine electromyography: a critical review. Am J Obstet Gynecol 169(6):1636–1653

    Article  CAS  PubMed  Google Scholar 

  8. Buhimschi C, Boyle MB, Saade GR, Garfield RE (1998) Uterine activity during pregnancy and labor assessed by simultaneous recordings from the myometrium and abdominal surface in the rat. Am J Obstet Gynecol 178(4):811–822

    Article  CAS  PubMed  Google Scholar 

  9. Chen S, Grimm MJ (2021) Childbirth computational models: characteristics and applications. Journal of Biomechanical Engineering. 143(5). https://doi.org/10.1115/1.4049226

  10. San-Vicente G, Aguinaga I, Celigueta JT (2012) Cubical mass-spring model design based on a tensile deformation test and nonlinear material model. IEEE Trans Vis Comput Graph 18:228–241. https://doi.org/10.1109/TVCG.2011.32

    Article  PubMed  Google Scholar 

  11. Golec K, Palierne JF, Zara F, Nicolle S, Damiand G (2020) Hybrid 3D mass-spring system for simulation of isotropic materials with any Poisson’s ratio. Vis Comput 36:809–825. https://doi.org/10.1007/s00371-019-01663-0

    Article  Google Scholar 

  12. Ballit A, Mougharbel I, Ghaziri H, Dao TT (2020) Fast soft tissue deformation and stump-socket interaction toward a computer-aided design system for lower limb prostheses. IRBM 41:276–285. https://doi.org/10.1016/j.irbm.2020.02.003.]

    Article  Google Scholar 

  13. Ballit A, Dao TT (2022) HyperMSM: a new MSM variant for efficient simulation of dynamic soft-tissue deformations. Comput Methods Programs Biomed 216:106659

    Article  PubMed  Google Scholar 

  14. 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(2):389–401

    Article  PubMed  Google Scholar 

  15. Andersen HF, Barclay ML (1995) A computer model of uterine contractions based on discrete contractile elements. Obstet Gynecol 86(1):108–111. https://doi.org/10.1016/0029-7844(95)00111-4

    Article  CAS  PubMed  Google Scholar 

  16. Young RC (1997) A computer model of uterine contractions based on action potential propagation and intercellular calcium waves. Obstet Gynecol 89(4):604–608. https://doi.org/10.1016/S0029-7844(96)00502-9

    Article  CAS  PubMed  Google Scholar 

  17. Moore JW, Ramon F (1974) On numerical integration of the Hodgkin and Huxley equations for a membrane action potential. J Theor Biol 45(1):249–273. https://doi.org/10.1016/0022-5193(74)90054-X

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Rihana S, Terrien J, Germain G, Marque C (2009) Mathematical modeling of electrical activity of uterine muscle cells. Med Biol Eng Compu 47:665–675

    Article  Google Scholar 

  19. Yochum M, Laforêt J, Marque C (2016) An electro-mechanical multiscale model of uterine pregnancy contraction. Comput Biol Med 1(77):182–194

    Article  Google Scholar 

  20. Yochum M, Laforêt J, Marque C (2018) Multi-scale and multi-physics model of the uterine smooth muscle with mechanotransduction. Comput Biol Med 1(93):17–30

    Article  Google Scholar 

  21. Kenedi RM, Gibson T, Evans JH, Barbenel JC (1975) Tissue mechanics. Phys Med Biol 20:001. https://doi.org/10.1088/0031-9155/20/5/001

    Article  Google Scholar 

  22. Bouaziz S, Martin S, Liu T, Kavan L, Pauly M (2014) Projective dynamics. ACM Trans Graph 33:1–11. https://doi.org/10.1145/2601097.2601116

    Article  Google Scholar 

  23. Ballit A, Hivert M, Rubod C, Dao TT (2023) Fast soft-tissue deformations coupled with mixed reality toward the next-generation childbirth training simulator. Med Biol Eng Compu 61:2207–2226. https://doi.org/10.1007/s11517-023-02864-5

    Article  Google Scholar 

  24. Lepage J, Jayyosi C, Lecomte-Grosbras P, Brieu M, Duriez C, Cosson M, Rubod C (2015) Biomechanical pregnant pelvic system model and numerical simulation of childbirth: impact of delivery on the uterosacral ligaments, preliminary results. Int Urogynecol J 26(4):497–504

    Article  CAS  PubMed  Google Scholar 

  25. Fung YC (1993) Biomechanics: Mechanical Properties of Living Tissues, Springer New York, pp 568. https://doi.org/10.1007/978-1-4757-2257-4

  26. Chen EJ, Novakofski J, Jenkins WK, O’Brien WD (1996) Young’s modulus measurements of soft tissues with application to elasticity imaging. IEEE Trans Ultrason Ferroelectr Freq Control. https://doi.org/10.1109/58.484478

    Article  Google Scholar 

  27. Li J, Liu T, Kavan L (2018) Laplacian damping for projective dynamics. In Proceedings of the 14th Workshop on Virtual Reality Interactions and Physical Simulations (VRIPHYS '18). Eurographics Association, Goslar, DEU, 29–36. https://doi.org/10.2312/vriphys.20181065

  28. Rihana S, and Marque C (2008) Preterm labor - modeling the uterine electrical activity from cellular level to surface recording, 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vancouver, BC, Canada, pp. 3726-3729.https://doi.org/10.1109/IEMBS.2008.4650018

  29. Young RC, Hession RO (1999) Three-dimensional structure of the smooth muscle in the term-pregnant human uterus. Obstet Gynecol 93(1):94–99

    CAS  PubMed  Google Scholar 

  30. Abe Y (1971) Effects of changing the ionic environment on passive and active membrane properties of pregnant rat uterus. J Physiol 214(1):173

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Kuriyama H, Suzuki H (1976) Changes in electrical properties of rat myometrium during gestation and following hormonal treatments. J Physiol 260(2):315–333

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Sims S, Daniel EE, Garfield R (1982) Improved electrical coupling in uterine smooth muscle is associated with increased numbers of gap junctions at parturition. J Gen Physiol 80(3):353–375

    Article  CAS  PubMed  Google Scholar 

  33. Koenigsberger M, Sauser R, Lamboley M, Bény J-L, Meister J-J (2004) Ca2þ dynamics in a population of smooth muscle cells: modeling the recruitment and synchronization. Biophys J 87(1):92–104

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Miller SM, Garfield RE, Daniel EE (1989) Improved propagation in myometrium associated with gap junctions during parturition. Am J Physiol Cell Physiol 256(1):C130–C141

    Article  CAS  Google Scholar 

  35. Kanda S, Kuriyama H (1980) Specific features of smooth muscle cells recorded from the placental region of the myometrium of pregnant rats. J Physiol 299(1):127–144

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Young RC, Goloman G (2011) Mechanotransduction in rat myometrium coordination of contractions of electrically and chemically isolated tissues. Reprod Sci 18(1):64–69

    Article  PubMed  Google Scholar 

  37. Zou H, Lifshitz LM, Tuft RA, Fogarty KE, Singer JJ (1999) Imaging ca2+ entering the cytoplasm through a single opening of a plasma membrane cation channel. J General Physiol 114(4):575–588

    Article  CAS  Google Scholar 

  38. Zou H, Lifshitz LM, Tuft RA, Fogarty KE, Singer JJ (2002) Visualization of ca2þ entry through single stretch-activated cation channels. Proc Natl Acad Sci 99(9):6404–6409

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  39. Zou H, Lifshitz LM, Tuft RA, Fogarty KE, Singer JJ (2004) Imaging calcium entering the cytosol through a single opening of plasma membrane ion channels: SCCaFTS fundamental calcium events. Cell Calcium 35(6):523–533

    Article  CAS  PubMed  Google Scholar 

  40. Takeda H (1965) Generation and propagation of uterine activity in situ. Fertil Steril 16:113

    Article  CAS  PubMed  Google Scholar 

  41. van Gelder A (1998) Approximate simulation of elastic membranes by triangulated spring meshes. J Graph Tools 3:21–41. https://doi.org/10.1080/10867651.1998.10487490

    Article  Google Scholar 

  42. Liu TIANTIAN, Bargteil AW, O’Brien JF et al (2013) Fast simulation of mass-spring systems. ACM Trans Graph (TOG) 32(6):1–7

    Google Scholar 

  43. 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(5):C1816–C1829

    Article  CAS  PubMed  Google Scholar 

  44. Maggio CD, Jennings SR, Robichaux JL, Stapor PC, Hyman JM (2012) A modified Hai murphy model of uterine smooth muscle contraction. Bull Math Biol 74(1):143–158

    Article  MathSciNet  PubMed  Google Scholar 

  45. Lutton EJ, Lammers WJEP, James S, van den Berg HA, Blanks AM (2018) Identification of uterine pacemaker regions at the myometrial-placental interface in the rat. J Physiol 596(14):2841–2852. https://doi.org/10.1113/JP275688. (Epub 2018 May 30. PMID: 29704394; PMCID: PMC6046083)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. Cignoni P, Corsini M, Ranzuglia G (2008) Meshlab: an open-source mesh processing tool. Eurographics Italian Chapter Conference 2008:129–136. https://doi.org/10.2312/LocalChapterEvents/ItalChap/ItalianChapConf2008/129-136

    Article  Google Scholar 

  47. Cochran AL, Gao Y (2013) A model and simulation of uterine contractions. Math Mech Solids 20(5):540–564

    Article  Google Scholar 

  48. Sharifimajd B, Thore C-J, StÅlhand J (2016) Simulating uterine contraction by using an electro-chemo-mechanical model. Biomechanics and modeling in mechanobiology 15:497–510. https://doi.org/10.1007/s10237-015-0703-z

    Article  PubMed  Google Scholar 

  49. Magisano D, Leonetti L, Garcea G (2022) Unconditional stability in large deformation dynamic analysis of elastic structures with arbitrary nonlinear strain measure and multi-body coupling. Comput Methods Appl Mech Eng 393:114776

    Article  ADS  MathSciNet  Google Scholar 

  50. Young RC (2018) The uterine pacemaker of labor. Best Pract Res Clin Obstet Gynaecol 52:68–87

    Article  PubMed  Google Scholar 

  51. Lammers WJ (2013) The electrical activities of the uterus during pregnancy. Reprod Sci 20(2):182–189. https://doi.org/10.1177/1933719112446082. (Epub 2012 May 30 PMID: 22649122)

    Article  PubMed  Google Scholar 

  52. Lammers WJ, Stephen B, Al-Sultan MA, Subramanya SB, Blanks AM (2015) The location of pacemakers in the uteri of pregnant guinea pigs and rats. Ame J Physiol-Regul Integr Comp Physiol 309(11):R1439–R1446

    Article  CAS  Google Scholar 

  53. Matsumoto J (1980) Changes of the contraction of the circular and longitudinal muscles of pregnant rat myometrium during pregnancy (authors transl). Nihon Sanka Fujinka Gakkai Zasshi 32(11):1749–1757

    CAS  PubMed  Google Scholar 

  54. Fang S, McLean J, Shi L, Vink JS, Hendon CP, Myers KM (2021) Anisotropic mechanical properties of the human uterus measured by spherical indentation. Ann Biomed Eng 49:1923–1942

    Article  PubMed  PubMed Central  Google Scholar 

  55. Alexandersson A, Steingrimsdottir T, Terrien J, Marque C, Karlsson B (2015) The Icelandic 16-electrode electrohysterogram database. Sci Data 2(1):1–9

    Article  Google Scholar 

  56. Fele-Žorž G, Kavšek G, Novak-Antolič Ž, Jager F (2008) A comparison of various linear and non-linear signal processing techniques to separate uterine EMG records of term and pre-term delivery groups. Med Biol Eng Compu 46(9):911–922

    Article  Google Scholar 

  57. Yochum M, Riahi P, Laforêt J, Marque C (2016) Computing EHG signals from a realistic 3D uterus model: a method to adapt a planar volume conductor. Proceedings of the Integrated Uncertainty in Knowledge Modelling and Decision Making: 5th International Symposium, IUKM pp. 381–388. https://doi.org/10.1007/978-3-319-49046-5_32

  58. Carriou V, Boudaoud S, Laforet J, Ayachi FS (2016) Fast generation model of high density surface EMG signals in a cylindrical conductor volume. Comput Biol Med 74:54–68

    Article  PubMed  Google Scholar 

  59. Farina D, Cescon C (2001) Concentric-ring electrode systems for noninvasive detection of single motor unit activity. IEEE Trans Biomed Eng 48(11):1326–1334

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Métropole Européenne de Lille (MEL) and the I-SITE ULNE (Université Lille Nord Europe) (R-TALENT-20-009-DAO) for funding.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tien-Tuan Dao.

Ethics declarations

Ethical approval

This work does not concern any ethical issue.

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ballit, A., Dao, TT. Multiphysics and multiscale modeling of uterine contractions: integrating electrical dynamics and soft tissue deformation with fiber orientation. Med Biol Eng Comput 62, 791–816 (2024). https://doi.org/10.1007/s11517-023-02962-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-023-02962-4

Keywords

Navigation