Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 4, pp 1233–1245 | Cite as

A microscopically motivated model for the remodeling of cardiomyocytes

  • Noy CohenEmail author
  • Vikram S. Deshpande
  • Jeffrey W. Holmes
  • Robert M. McMeeking
Original Paper


We present a thermodynamically based model that captures the remodeling effects in cardiac muscle cells. This work begins with the formulation of the kinematics of a cardiomyocyte resulting from a prescribed macroscopic deformation and the reorganization of the internal structure. Specifically, relations between the macroscopic deformation and the number of sarcomeres, the sarcomere stretch, and the number of myofibrils in the cell are determined. The remodeling process is split into two separate phases—(1) elongation/shortening of the existing myofibrils by addition/detachment of sarcomeres and (2) formation of new myofibrils. The remodeling associated with each phase is modeled through a dissipation postulate. We show that remodeling is based on a competition between the internal energy, the entropy, the energy supplied to the system by ATP and other sources to drive the remodeling process, and dissipation mechanisms. While the variations in entropy associated with phase (1) are neglected, the substantial entropy loss associated with the formation of new myofibrils is determined. To illustrate the merit of the proposed framework, we compute the response of cardiomyocytes subjected to isometric axial stretch that are either free to deform or fixed in the transverse direction. We also examine the predictions of this model for cardiomyocytes subjected to various cyclic loadings. The proposed framework is capable of capturing a wide range of remodeling effects and agrees with experimental observations.


Remodeling in cardiomyocytes Cardiomyocytes Multi-scale modeling Statistical mechanics Actin/myosin interaction 



This research was supported, in part, through an Otis Williams Postdoctoral Fellowship granted by the Santa Barbara Foundation.


  1. Cherubini C, Filippi S, Nardinocchi P, Teresi L (2008) An electromechanical model of cardiac tissue: constitutive issues and electrophysiological effects. Prog Biophys Mol Biol 97(2):562–573CrossRefGoogle Scholar
  2. Dabiri GA, Turnacioglu KK, Sanger J, Sanger JW (1997) Myofibrillogenesis visualized in living embryonic cardiomyocytes. Proc Natl Acad Sci 94(17):9493–9498CrossRefGoogle Scholar
  3. de Tombe PP, Mateja RD, Tachampa K, Mou YA, Farman GP, Irving TC (2010) Myofilament length dependent activation. J Mol Cell Cardiol 48(5):851–858CrossRefGoogle Scholar
  4. Decker ML, Janes DM, Barclay MM, Harger L, Decker RS (1997) Regulation of adult cardiocyte growth: effects of active and passive mechanical loading. Am J Physiol Heart Circ Physiol 272(6):H2902–H2918CrossRefGoogle Scholar
  5. Gaasch WH (1979) Left ventricular radius to wall thickness ratio. Am J Cardiol 43(6):1189–1194CrossRefGoogle Scholar
  6. Goktepe S, Menzel A, Kuhl E (2014) The generalized hill model: a kinematic approach towards active muscle contraction. J Mech Phys Solids 72:20–39MathSciNetCrossRefzbMATHGoogle Scholar
  7. Grossman W, Jones D, McLaurin LP (1975) Wall stress and patterns of hypertrophy in the human left ventricle. J Clin Investig 56(1):56–64CrossRefGoogle Scholar
  8. Guterl KA, Haggart CR, Janssen PM, Holmes JW (2007) Isometric contraction induces rapid myocyte remodeling in cultured rat right ventricular papillary muscles. Am J Physiol Heart Circ Physiol 293(6):H3707–H3712CrossRefGoogle Scholar
  9. Hill A (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci 126(843):136–195CrossRefGoogle Scholar
  10. Holmes JW (2004) Candidate mechanical stimuli for hypertrophy during volume overload. J Appl Physiol 97(4):1453–1460CrossRefGoogle Scholar
  11. Kehat I, Molkentin JD (2010) Molecular pathways underlying cardiac remodeling during pathophysiological stimulation. Circulation 122(25):2727–2735CrossRefGoogle Scholar
  12. Liu Z, Hilbelink DR, Crockett WB, Gerdes AM (1991a) Regional changes in hemodynamics and cardiac myocyte size in rats with aortocaval fistulas. 1. Developing and established hypertrophy. Circ Res 69(1):52–58CrossRefGoogle Scholar
  13. Liu Z, Hilbelink DR, Gerdes AM (1991b) Regional changes in hemodynamics and cardiac myocyte size in rats with aortocaval fistulas. 2. Long-term effects. Circ Res 69(1):59–65CrossRefGoogle Scholar
  14. Mansour H, de Tombe PP, Samarel AM, Russell B (2004) Restoration of resting sarcomere length after uniaxial static strain is regulated by protein kinase Cepsilon and focal adhesion kinase. Circ Res 94(5):642–649CrossRefGoogle Scholar
  15. Mihl C, Dassen W, Kuipers H (2008) Cardiac remodelling: concentric versus eccentric hypertrophy in strength and endurance athletes. Neth Heart J 16(4):129–133CrossRefGoogle Scholar
  16. Murtada S-I, Holzapfel GA (2014) Investigating the role of smooth muscle cells in large elastic arteries: a finite element analysis. J Theor Biol 358:1–10MathSciNetCrossRefzbMATHGoogle Scholar
  17. Pangonytė D, Stalioraitytė E, Žiuraitienė R, Kazlauskaitė D, Palubinskienė J, Balnytė I (2008) Cardiomyocyte remodeling in ischemic heart disease. Medicina 44(11):848–854CrossRefGoogle Scholar
  18. Parikh SS, Zou SZ, Tung L (1993) Contraction and relaxation of isolated cardiac myocytes of the frog under varying mechanical loads. Circ Res 72(2):297–311CrossRefGoogle Scholar
  19. Pathak A, McMeeking RM, Evans AG, Deshpande VS (2011) An analysis of the cooperative mechano-sensitive feedback between intracellular signaling, focal adhesion development, and stress fiber contractility. J Appl Mech 78(4):041001CrossRefGoogle Scholar
  20. Ribeiro AJS, Ang Y-S, Fu J-D, Rivas RN, Mohamed TMA, Higgs GC, Srivastava D, Pruitt BL (2015) Contractility of single cardiomyocytes differentiated from pluripotent stem cells depends on physiological shape and substrate stiffness. Proc Natl Acad Sci 112(41):12705–12710CrossRefGoogle Scholar
  21. Sadoshima J, Izumo S (1997) The cellular and molecular response of cardiac myocytes to mechanical stress. Annu Rev Physiol 59(1):551–571CrossRefGoogle Scholar
  22. Stalhand J, McMeeking RM, Holzapfel GA (2016) On the thermodynamics of smooth muscle contraction. J Mech Phys Solids 94:490–503MathSciNetCrossRefGoogle Scholar
  23. Szibor M, Pöling J, Warnecke H, Kubin T, Braun T (2014) Remodeling and dedifferentiation of adult cardiomyocytes during disease and regeneration. Cell Mol Life Sci 71(10):1907–1916CrossRefGoogle Scholar
  24. Tan T, Vita RD (2015) A structural constitutive model for smooth muscle contraction in biological tissues. Int J Non-Linear Mech 75:46–53CrossRefGoogle Scholar
  25. ter Keurs H, Rijnsburger WH, van Heuningen R, Nagelsmit MJ (1980) Tension development and sarcomere length in rat cardiac trabeculae. Evidence of length-dependent activation. Circ Res 46(5):703–714CrossRefGoogle Scholar
  26. Vigliotti A, Ronan W, Baaijens FPT, Deshpande VS (2016) A thermodynamically motivated model for stress-fiber reorganization. Biomech Model Mechanobiol 15(4):761–789CrossRefGoogle Scholar
  27. Vita RD, Grange R, Nardinocchi P, Teresi L (2017) Mathematical model for isometric and isotonic muscle contractions. J Theor Biol 425:1–10MathSciNetCrossRefzbMATHGoogle Scholar
  28. Yang H, Schmidt LP, Wang Z, Yang X, Shao Y, Borg TK, Markwald R, Runyan R, Gao BZ (2016) Dynamic myofibrillar remodeling in live cardiomyocytes under static stretch. Sci Rep 6:20674CrossRefGoogle Scholar
  29. Yu J, Russell B (2005) Cardiomyocyte remodeling and sarcomere addition after uniaxial static strain in vitro. J Histochem Cytochem 53(7):839–844CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of MaterialsUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of Mechanical EngineeringUniversity of CaliforniaSanta BarbaraUSA
  3. 3.Department of EngineeringUniversity of CambridgeCambridgeUK
  4. 4.Department of Biomedical EngineeringUniversity of VirginiaCharlottesvilleUSA
  5. 5.Department of MedicineUniversity of VirginiaCharlottesvilleUSA
  6. 6.School of Engineering, King’s CollegeUniversity of AberdeenAberdeenUK
  7. 7.Department of Materials Science and EngineeringTechnion – Israel Institute of TechnologyHaifaIsrael

Personalised recommendations