Advertisement

Biomechanics and Modeling in Mechanobiology

, Volume 13, Issue 3, pp 627–641 | Cite as

Simulation of the contraction of the ventricles in a human heart model including atria and pericardium

Finite element analysis of a frictionless contact problem
  • Thomas FritzEmail author
  • Christian Wieners
  • Gunnar Seemann
  • Henning Steen
  • Olaf Dössel
Original Paper

Abstract

During the contraction of the ventricles, the ventricles interact with the atria as well as with the pericardium and the surrounding tissue in which the heart is embedded. The atria are stretched, and the atrioventricular plane moves toward the apex. The atrioventricular plane displacement (AVPD) is considered to be a major contributor to the ventricular function, and a reduced AVPD is strongly related to heart failure. At the same time, the epicardium slides almost frictionlessly on the pericardium with permanent contact. Although the interaction between the ventricles, the atria and the pericardium plays an important role for the deformation of the heart, this aspect is usually not considered in computational models. In this work, we present an electromechanical model of the heart, which takes into account the interaction between ventricles, pericardium and atria and allows to reproduce the AVPD. To solve the contact problem of epicardium and pericardium, a contact handling algorithm based on penalty formulation was developed, which ensures frictionless and permanent contact. Two simulations of the ventricular contraction were conducted, one with contact handling of pericardium and heart and one without. In the simulation with contact handling, the atria were stretched during the contraction of the ventricles, while, due to the permanent contact with the pericardium, their volume increased. In contrast to that, in the simulations without pericardium, the atria were also stretched, but the change in the atrial volume was much smaller. Furthermore, the pericardium reduced the radial contraction of the ventricles and at the same time increased the AVPD.

Keywords

Cardiac electromechanical modeling  Pericardium Atria Contact problem Finite element simulation 

Notes

Acknowledgments

We acknowledge the support of the KIT competence field Mathematical Models in form of a start-up grant.

Supplementary material

Supplementary material 1 (mpg 4788 KB)

References

  1. Balay S, Brown J, Buschelman K, Gropp WD, Kaushik D, Knepley MG, Curfman McInnes L, Smith BF, Zhang H (2012) PETSc Web page. http://www.mcs.anl.gov/petsc
  2. Bellini C, Di Martino ES, Federico S (2012) Mechanical behaviour of the human atria. Ann Biomed Eng 41(7):1478–1490Google Scholar
  3. Belytschko T, Liu WK, Moran B et al (2000) Nonlinear finite elements for continua and structures. Wiley, New YorkzbMATHGoogle Scholar
  4. Carlsson M, Ugander M, Mosén H, Buhre T, Arheden H (2007) Atrioventricular plane displacement is the major contributor to left ventricular pumping in healthy adults, athletes, and patients with dilated cardiomyopathy. Am J Physiol Heart Circ Physiol 292(3):1452–1459Google Scholar
  5. Di Martino ES, Bellini C, Schwartzman DS (2011) In vivo porcine left atrial wall stress: computational model. J Biomech 44(15):2589–2594CrossRefGoogle Scholar
  6. Emilsson K, Brudin L, Wandt B (2001) The mode of left ventricular pumping: is there an outer contour change in addition to the atrioventricular plane displacement? Clin Physiol 21(4):437–446CrossRefGoogle Scholar
  7. Freeman GL, Little WC (1986) Comparison of in situ and in vitro studies of pericardial pressure-volume relation in dogs. Am J Physiol Heart Circ Physiol 251(2):H421–H427Google Scholar
  8. Guccione J, Costa K, McCulloch A (1995) Finite element stress analysis of left ventricular mechanics in the beating dog heart. J Biomech 28(10):1167–1177CrossRefGoogle Scholar
  9. Gurev V, Lee T, Constantino J, Arevalo H, Trayanova NA (2011) Models of cardiac electromechanics based on individual hearts imaging data. Biomech Model Mechanobiol 10(3):295–306CrossRefGoogle Scholar
  10. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544Google Scholar
  11. Holt JP (1970) The normal pericardium. Am J Cardiol 26(5):455–465CrossRefGoogle Scholar
  12. Keller DUJ, Kalayciyan R, Dössel O, Seemann G (2010) Fast creation of endocardial stimulation profiles for the realistic simulation of body surface ECGs. In: IFMBE proceedings world congress on medical physics and biomedical engineering, 25(4). Springer, Berlin, pp 145–148Google Scholar
  13. Kerckhoffs RCP, McCulloch AD, Omens JH, Mulligan LJ (2007) Effect of pacing site and infarct location on regional mechanics and global hemodynamics in a model based study of heart failure. In: Sachse FB, Seemann G (eds) Functional imaging and modeling of the heart. Springer, Berlin, pp 350–360Google Scholar
  14. Krishnamurthy A, Villongco CT, Chuang J, Frank LR, Nigam V, Belezzuoli E, Stark P, Krummen DE, Narayan S, Omens JH, McCulloch AD, Kerckhoffs RCP (2012) Patient-specific models of cardiac biomechanics. J Comput Phys. doi: 10.1016/j.jcp.2012.09.015
  15. Krueger M, Schmidt V, Tobón C, Weber F, Lorenz C, Keller D, Barschdorf H, Burdumy M, Neher P, Plank G et al (2011) Modeling atrial fiber orientation in patient-specific geometries: a semi-automatic rule-based approach. Funct Imaging Model Heart 6666:223–232CrossRefGoogle Scholar
  16. Lee JM, Boughner DR (1985) Mechanical properties of human pericardium. Differences in viscoelastic response when compared with canine pericardium. Circ Res 57(3):475–481CrossRefGoogle Scholar
  17. LeGrice IJ, Takayama Y, Covell JW (1995) Transverse shear along myocardial cleavage planes provides a mechanism for normal systolic wall thickening. Circ Res 77(1):182–193CrossRefGoogle Scholar
  18. Mantovani F, Barbieri A, Modena MG (2011) Congenital complete absence of the pericardium: a multimodality imaging diagnostic approach. Echocardiogr J 28(1):E21–E22CrossRefGoogle Scholar
  19. Marchesseau S, Delingette H, Sermesant M, Ayache N (2013) Fast parameter calibration of a cardiac electromechanical model from medical images based on the unscented transform. Biomech Model Mechanobiol, 12(4):815–831Google Scholar
  20. Martini FH, Timmons MJ, Tallitsch RB (2011) Human anatomy. Pearson Education, publishing as Pearson Benjamin Cummings, Upper Saddle RiverGoogle Scholar
  21. Omens JH, MacKenna DA, McCulloch AD (1993) Measurement of strain and analysis of stress in resting rat left ventricular myocardium. J Biomech 26(6):665–676CrossRefGoogle Scholar
  22. Psychidis-Papakyritsis P, de Roos A, Kroft LJM (2007) Functional mri of congenital absence of the pericardium. Am J Roentgenol 189(6):W312–W314Google Scholar
  23. Sachse FB, Glänzel KG, Seemann G (2003) Modeling of protein interactions involved in cardiac tension development. IJBC 13(12):3561–3578zbMATHGoogle Scholar
  24. Sato T, Tsujino I, Oyama-Manabe N, Ohira H, Ito Y, Yamada A, Ikeda D, Watanabe T, Nishimura M (2012) Right atrial volume and phasic function in pulmonary hypertension. Int J Cardiol. doi: 10.1016/j.ijcard.2012.09.133
  25. Seemann G, Sachse F, Karl M, Weiss D, Heuveline V, Dössel O (2010) Framework for modular, flexible and efficient solving the cardiac bidomain equations using PETSc. Prog Ind Math ECMI 2008 15:363–369Google Scholar
  26. Sherwood L (2007) Human physiology: from cells to systems. Thomson-Brooks/Cole, BelmontGoogle Scholar
  27. Stergiopulos N, Westerhof BE, Westerhof N (1999) Total arterial inertance as the fourth element of the windkessel model. Am J Physiol Heart Circ Physiol 276(1):H81–H88Google Scholar
  28. Streeter D (1979) Gross morphology and fiber geometry of the heart. In: Bethesda B (ed) Handbook of Physiology: the Cardiovascular System, vol 1, American Physiology Society, p 61–112 Google Scholar
  29. ten Tusscher K, Noble D, Noble P, Panfilov A (2004) A model for human ventricular tissue. Am J Physiol Heart Circ Physiol 286(4):1573–1589Google Scholar
  30. Topilsky Y, Tabatabaei N, Freeman WK, Saleh H, Villarraga H, Mulvagh SL (2010) Pendulum heart in congenital absence of the pericardium. Circulation 121(10):1272–1274Google Scholar
  31. Tyberg JV, Taichman GC, Smith ER, Douglas NW, Smiseth OA, Keon WJ (1986) The relationship between pericardial pressure and right atrial pressure: an intraoperative study. Circulation 73(3):428–432Google Scholar
  32. Watkins MW, LeWinter MM (1993) Physiologic role of the normal pericardium. Annu Rev Med 44(1):171–180CrossRefGoogle Scholar
  33. Westerhof N, Elzinga GIJS, Sipkema P (1971) An artificial arterial system for pumping hearts. J Appl Physiol 31(5):776–781Google Scholar
  34. Willenheimer R, Cline C, Erhardt L, Israelsson B (1997) Left ventricular atrioventricular plane displacement: an echocardiographic technique for rapid assessment of prognosis in heart failure. Heart 78(3):230–236Google Scholar
  35. Wriggers P (2006) Computational contact mechanics. Springer, BerlinCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Thomas Fritz
    • 1
    Email author
  • Christian Wieners
    • 2
  • Gunnar Seemann
    • 1
  • Henning Steen
    • 3
  • Olaf Dössel
    • 1
  1. 1.Department of Electrical Engineering and Information Technology, Institute of Biomedical EngineeringKarlsruhe Institute of Technology (KIT)KarlsruheGermany
  2. 2.Department of Mathematics, Institute for Applied and Numerical Mathematics 3Karlsruhe Institute of Technology (KIT)KarlsruheGermany
  3. 3.Department of Internal Medicine IIIUniversity Hospital HeidelbergHeidelbergGermany

Personalised recommendations