Skip to main content
SpringerLink
Log in

Unraveling Changes in Myocardial Contractility During Human Fetal Growth: A Finite Element Analysis Based on In Vivo Ultrasound Measurements

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Knowledge of normal fetal heart (FH) performance and development is crucial for evaluating and understanding how various congenital heart lesions may modify heart contractility during the gestational period. However, since biomechanical models of FH are still lacking, structural approaches proposed to describe the mechanical behavior of the adult human heart cannot be used to model the evolution of the FH. In this paper, a finite element model of the healthy FH wall is developed to quantify its mechanical properties during the gestational period. An idealized thick-walled ellipsoidal shape was used to model the left ventricle (LV). The diastolic LV geometry was reconstructed from in vivo ultrasound measurements performed on 24 normal FHs between 20 and 37 weeks of gestation. An anisotropic hyperelastic constitutive law describing the mechanical properties of the passive and active myocardium was used. The evolution of the mechanical properties of the normal LV myocardium during fetal growth was obtained by successfully fitting the ejection fraction predicted by the model to in vivo measurements. We found that only the active tension varies significantly during the gestational period, increasing linearly from 20 kPa (at 20 weeks) to 40 kPa (at 37 weeks of gestation). We propose a possible explanation of the increasing force-generating ability of the myocardial tissue during fetal heart development based on a combination of myocyte enlargement, differentiation, and proliferation kinetics.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

FIGURE 1
FIGURE 2
FIGURE 3
FIGURE 4
FIGURE 5
FIGURE 6
FIGURE 7
FIGURE 8
FIGURE 9
FIGURE 10
FIGURE 11

Similar content being viewed by others

References

  1. Bishop, S. P., and P. Hine. Cardiac muscle cytoplasmic and nuclear development during canine neonatal growth. Recent Adv. Stud. Card. Struct. Metab. 8:77–98, 1975.

    CAS  Google Scholar 

  2. Bourdarias, C., S. Gerbi, and J. Ohayon. A three dimensional finite element method for biological active soft tissue. Formulation in cylindrical polar coordinates. ESAIM: Math. Model Numer. Anal. 37:725–739, 2003.

    Article  Google Scholar 

  3. Chadwick, R. Mechanics of the left ventricle. Biophys. J. 39:279–288, 1982.

    Article  CAS  PubMed  Google Scholar 

  4. de Almeida, A., T. McQuinn, and D. Sedmera. Normal and hypoplastic fetal chick left ventricle increased ventricular preload is compensated by myocyte proliferation. Circ. Res. 100:1363–1370, 2007.

    Article  CAS  Google Scholar 

  5. Fiorina, P., D. Corradi, S. Pinelli, R. Maestri, C. Lagrasta, M. Buscaglia, A. Davalli, F. Folli, and E. Astorri. Apoptotic/mytogenic pathways during human heart development. Int. J. Cardiol. 96:409–417, 2004.

    Article  PubMed  Google Scholar 

  6. Friedman, W. The intrinsic physiologic properties of the developing heart. Prog. Cardiovasc. Dis. 15:87–111, 1972.

    Article  CAS  PubMed  Google Scholar 

  7. Fung, Y. C. Biomechanics. Mechanical Properties of Living Tissues. New York: Springer, 1993.

    Google Scholar 

  8. Garcia, R. H., M. P. Cabeza, A. Gallo, L. Palacios, and R. P. Laguens. DNA content and expression of cell cycle proteins in caterpillar nuclei from fetal human cardiac myocytes. Virchows. Arch. 440:45–49, 2002.

    Article  PubMed  Google Scholar 

  9. Garcia-Palomares, U. M., and J. F. Rodríguez. New sequential and parallel derivative-free algorithms for unconstrained minimization. SIAM J. Optim. 13:79, 2006.

    Article  Google Scholar 

  10. Garzón-Alvarado, D. A., J. M. García-Aznar, and M. Doblaré. A reaction–diffusion model for long bones growth. Biomechan. Model Mechanobiol. 8:381–395, 2009.

    Article  Google Scholar 

  11. Guccione, J., A. McCulloch, and L. Waldman. Passive material properties of intact ventricular myocardium determined from a cylindrical model. ASME J. Biomech. Eng. 113:42–55, 1991.

    Article  CAS  Google Scholar 

  12. Hibbit, Karlsson Sorensen, Inc. Abaqus User’s Guide, v.6.8. Pawtucket, RI, USA: HKS Inc., 2008.

    Google Scholar 

  13. Holzapfel, G. A. Nonlinear Solid Mechanics. New York: Wiley, 2000.

    Google Scholar 

  14. Hsieh, Y. Y., F. C. Chang, H. D. Tsai, and C. H. Tsai. Longitudinal survey of fetal ventricular ejection and shortening fraction throughout pregnancy. Ultrasound Obstet. Gynecol. 16:46–48, 2000.

    Article  CAS  PubMed  Google Scholar 

  15. Humphrey, J., and F. Yin. Constitutive relations and finite deformations of passive cardiac tissue. II: stress analysis in the left ventricle. Circ. Res. 65:805–817, 1989.

    CAS  PubMed  Google Scholar 

  16. Hunter, P., A. D. McCulloch, and H. ter Keurs. Modelling the mechanical properties of cardiac muscle. Prog. Biophys. Mol. Biol. 69:289–331, 1998.

    Article  CAS  PubMed  Google Scholar 

  17. Hunter, P., A. J. Pullan, and B. H. Smaill. Modeling total heart function. Annu. Rev. Biomed. Eng. 5:147–177, 2003.

    Article  CAS  PubMed  Google Scholar 

  18. Huttenbach, Y., M. L. Ostrowski, D. Thaller, and H. S. Kim. Cell proliferation in the growing human heart: MIB-1 immunostaining in preterm and term infants at autopsy. Cardiovasc. Pathol. 10:119–123, 2001.

    Article  CAS  PubMed  Google Scholar 

  19. Hoffman, J. I. E. Incidence, mortality, and natural history. In: Pediatric Cardiology, edited by R. A. Anderson et al. London: Churchill Livingstone. 2002, pp. 111–139

  20. Johnson, P., D. Maxwell, M. Tynan, and L. Allan. Intracardiac pressures in the human fetus. Heart 84:59–63, 2000.

    Article  CAS  PubMed  Google Scholar 

  21. Jonker, S., et al. Myocyte enlargement, differentiation, and proliferation kinetics in the fetal sheep heart. J. Appl. Physiol. 102:1130–1142, 2007.

    Article  PubMed  Google Scholar 

  22. Jouk, P., Y. Usson, G. Michalowicz, and L. Grossi. Three-dimensional cartography of the pattern of the myofibers in the second trimester fetal human heart. Anat. Embryol. 202:103–118, 2000.

    Article  CAS  PubMed  Google Scholar 

  23. Lin, D., and F. C. P. Yin. A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus. ASME J. Biomech. Eng. 120:504–517, 1998.

    Article  CAS  Google Scholar 

  24. McCartney, F. J., et al. (eds.). Pediatric Cardiology, 2nd ed. London: Churchill Livingstone, pp. 111–139, 2002.

  25. McLean, M., and J. Prothero. Myofiber orientation in the weanling mouse heart. Am. J. Anat. 192:425–441, 1991.

    Article  CAS  PubMed  Google Scholar 

  26. McLean, M., M. A. Ross, and J. Prothero. Three dimensional reconstruction of the myofiber pattern in the fetal and neonatal mouse heart. Anat. Rec. 224:392–406, 1989.

    Article  CAS  PubMed  Google Scholar 

  27. Meyer-Wittkopf, M., A. Cole, S. G. Cooper, S. Schmidt, and G. H. Sholler. Three-dimensional quantitative echocardiographic assessment of ventricular volume in healthy human fetuses and in fetuses with congenital heart disease. J. Ultrasound Med. 20:317–327, 2001.

    CAS  PubMed  Google Scholar 

  28. Molina, F. S., C. Faro, A. Sotiriadis, T. Dagklis, and H. Nicolaides. Heart stroke volume and cardiac output by four-dimensional ultrasound in normal fetuses. Ultrasound Obstet. Gynecol. 32:181–187, 2008.

    Article  CAS  PubMed  Google Scholar 

  29. Moulton, M. J., L. L. Creswell, S. W. Downing, R. L. Actis, B. A. Szabo, and M. K. Pasque. Myocardial material property determination in the in vivo heart using magnetic resonance imaging. Int. J. Card Imaging 12:153–167, 1996.

    Article  CAS  PubMed  Google Scholar 

  30. Ohayon, J., H. Cai, P. Jouk, Y. Usson, and A. Azancot. A model of structural and functional development of the normal human fetal left ventricle based on a global growth law. Comp. Meth. Biomech. Biomed. Eng. 2:113–126, 2002.

    Article  Google Scholar 

  31. Ohayon, J., and R. Chadwick. Effects of collagen microstructure on the mechanics of the left ventricle. Biophys. J. 54:1077–1088, 1988.

    Article  CAS  PubMed  Google Scholar 

  32. Ohayon, J., Y. Usson, P. Jouk, and H. Cai. Fibre orientation in human fetal heart and ventricular mechanics: A small perturbation analysis. Comp. Meth. Biomech. Biomed. Eng. 2:83–105, 1999.

    Article  Google Scholar 

  33. Okamoto, R. J., M. J. Moulton, S. J. Peterson, D. Li, and M. K. Pasque. Epicardial suction: a new approach to mechanical testing of the passive ventricular wall. ASME J. Biomech. Eng. 122:479–487, 2000.

    Article  CAS  Google Scholar 

  34. Omens, J. H., K. D. May, and A. D. Mcculloch. Transmural distribution of three-dimensional strain in the isolated arrested canine left ventricle. Am. J. Physiol. (Heart Circ. Physiol.) 30:H918–H928, 1991.

    Google Scholar 

  35. Peña, E., M. A. Martínez, B. Calvo, and M. Doblaré. On the numerical treatment of initial strains in soft biological tissues. Int. J. Numer. Meth. Eng. 68:836–860, 2006.

    Article  Google Scholar 

  36. Rychik, J. Fetal cardiovascular physiology. Pediatr. Cardiol. 25:201–209, 2004.

    Article  CAS  PubMed  Google Scholar 

  37. Siedner, S., M. Krüger, M. Schroeter, D. Metzler, W. Roell, B. K. Fleischmann, J. Hescheler, G. Pfitzer, and R. Stehle. Developmental changes in contractility and sarcomeric proteins from the early embryonic to the adult stage in the mouse heart. J. Physiol. 548:493–505, 2003.

    Article  CAS  PubMed  Google Scholar 

  38. Stalhand, J., A. Klarbring, and G. A. Holzapfel. Smooth muscle contraction: mechanochemical formulation for homogeneous finite strains. Progress Biophys. Mol. Biol. 96:465–481, 2008.

    Article  CAS  Google Scholar 

  39. Stevens, C., E. Remme, I. LeGrice, and P. Hunter. Ventricular mechanics in diastole: material parameter sensitivity. J. Biomech. 36:737–748, 2003.

    Article  PubMed  Google Scholar 

  40. Taber, L. A. On a nonlinear theory for muscle shells: Part II. Application to the beating left ventricle. ASME J. Biomech. Eng. 113:63–71, 1991.

    Article  CAS  Google Scholar 

  41. Taber, L. A., and S. Chabert. Theoretical and experimental study of growth and remodeling in the developing heart. Biomech. Model Mechanobiol. 1:29–43, 2002.

    Article  CAS  PubMed  Google Scholar 

  42. Tozeren, A. Static analysis of the left-ventricle. ASME J. Biomech. Eng. 105:39–46, 1983.

    Article  CAS  Google Scholar 

  43. van Campen, D., J. Huyghe, P. Bovendeerd, and T. Arts. Biomechanics of the heart muscle. Eur. J. Mech. A 13:19–41, 1994.

    Google Scholar 

  44. Walker, J. C., M. B. Ratcliffe, P. Zhang, A. W. Wallance, B. Fata, E. W. Hsu, D. Saloner, and J. M. Guccione. MRI-based finite element analysis of left ventricular aneurysm. Am. J. Physiol. Heart Circ. Physiol. 289:H692–H700, 2005.

    Article  CAS  PubMed  Google Scholar 

  45. Weiwad, W. K., W. A. Linke, and M. H. Wussling. Sarcomere length–tension relationship of rat cardiac myocytes at lengths greater than optimum. J. Mol. Cell Cardiol. 32:247–259, 2000.

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgments

The authors thank Dr. Pierre-Simon Jouk (Department of Paediatric and Fetal Cardiology, Grenoble Hospital, France) and Y. Usson (TIMC Laboratory, Grenoble, France) for their useful discussions. Grants: The authors gratefully acknowledge research support from the European Community through the Sixth Framework Program through the DISHEART project FP6-2002-SME-1-513226 and the Spanish Ministry of Science and Technology through research projects DPI2007-63254, DPI2007-65601-C03-00, and SINBAD PSE-010000-2008, and the Instituto de Salud Carlos III (ISCIII) through the CIBER initiative. We thank also the Europe Program of Grants developed by Caja de Ahorros de la Inmaculada (CAI) and Diputación General de Aragón for their financial support to E. Peña.

Author information

Authors and Affiliations

  1. Group of Structural Mechanics and Materials Modelling (GEMM), Aragón Institute of Engineering Research (I3A), Universidad de Zaragoza, Zaragoza, Spain

    E. Peña & M. Doblare

  2. Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Zaragoza, Spain

    E. Peña & M. Doblare

  3. Aragon Health Sciences Institute, María de Luna, 3, 50018, Zaragoza, Spain

    E. Peña & M. Doblare

  4. Laboratory TIMC-IMAG-DynaCell, CNRS UMR 5525, IN3S, Joseph Fourier University, BP 217, 38043, Grenoble Cedex 9, France

    P. Tracqui & J. Ohayon

  5. Perinatal Cardiology and Physiology, Robert Debré Hospital, 48 Blvd. Serurier, 75019, Paris, France

    A. Azancot

  6. Engineering School Polytech, University of Savoie, Chambéry, France

    J. Ohayon

Authors
  1. E. Peña
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Tracqui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Azancot
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Doblare
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. Ohayon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to E. Peña or J. Ohayon.

Additional information

Associate Editor Jane Grande-Allen oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peña, E., Tracqui, P., Azancot, A. et al. Unraveling Changes in Myocardial Contractility During Human Fetal Growth: A Finite Element Analysis Based on In Vivo Ultrasound Measurements. Ann Biomed Eng 38, 2702–2715 (2010). https://doi.org/10.1007/s10439-010-0010-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-010-0010-x

Keywords

Search

Navigation