Biomechanics and Modeling in Mechanobiology

, Volume 14, Issue 2, pp 217–229 | Cite as

A computational model that predicts reverse growth in response to mechanical unloading

  • L. C. Lee
  • M. Genet
  • G. Acevedo-Bolton
  • K. Ordovas
  • J. M. Guccione
  • E. Kuhl
Original Paper


Ventricular growth is widely considered to be an important feature in the adverse progression of heart diseases, whereas reverse ventricular growth (or reverse remodeling) is often considered to be a favorable response to clinical intervention. In recent years, a number of theoretical models have been proposed to model the process of ventricular growth while little has been done to model its reverse. Based on the framework of volumetric strain-driven finite growth with a homeostatic equilibrium range for the elastic myofiber stretch, we propose here a reversible growth model capable of describing both ventricular growth and its reversal. We used this model to construct a semi-analytical solution based on an idealized cylindrical tube model, as well as numerical solutions based on a truncated ellipsoidal model and a human left ventricular model that was reconstructed from magnetic resonance images. We show that our model is able to predict key features in the end-diastolic pressure–volume relationship that were observed experimentally and clinically during ventricular growth and reverse growth. We also show that the residual stress fields generated as a result of differential growth in the cylindrical tube model are similar to those in other nonidentical models utilizing the same geometry.


Remodeling Reverse remodeling Growth End-diastolic pressure–volume relationship Finite element method Magnetic resonance imaging 



This work was supported by NIH Grants R01-HL-077921 and R01-HL-118627 (J.M. Guccione); K25-NS058573-05 (G. Acevedo-Bolton); NSF Grants 0952021 and 1233054 (E. Kuhl); and Marie Curie international outgoing fellowship within the 7th European Community Framework Program (M. Genet). We thank the reviewers for their valuable comments, which have helped us improve the presentation.


  1. Ambardekar AV, Buttrick PM (2011) Reverse remodeling with left ventricular assist devices: a review of clinical, cellular, and molecular effects. Circ Hear Fail 4(2):33–224Google Scholar
  2. Ambrosi D, Ateshian GA, Arruda EM, Cowin SC, Dumais J, Goriely A, Holzapfel GA, Humphrey JD, Kemkemer R, Kuhl E, Olberding JE, Taber LA, Garikipati K (2011) Perspectives on biological growth and remodeling. J Mech Phys Solid 59(4):863–883CrossRefMATHMathSciNetGoogle Scholar
  3. Brinke EA, Klautz RJ, Tulner SA, Verwey HF, Bax JJ, Delgado V, Holman ER, Schalij MJ, van der Wall EE, Braun J, Versteegh MI, Dion RA, Steendijk P (2010) Clinical and functional effects of restrictive mitral annuloplasty at midterm follow-up in heart failure patients. Ann Thorac Surg 90(6):1913–1920CrossRefGoogle Scholar
  4. Burkhoff D, Klotz S, Mancini DM (2006) LVAD-induced reverse remodeling: basic and clinical implications for myocardial recovery. J Card Fail 12(3):227–239CrossRefGoogle Scholar
  5. Choi HF, D’hooge J, Rademakers FE, Claus P (2010) Influence of left-ventricular shape on passive filling properties and end-diastolic fiber stress and strain. J Biomech 43(9):1745–1753CrossRefGoogle Scholar
  6. Cohn JN, Ferrari R, Sharpe N (2000) Cardiac remodeling concepts and clinical implications: a consensus paper from an international forum on cardiac remodeling. J Am Coll Cardiol 35(3):569–582CrossRefGoogle Scholar
  7. Drakos SG, Terrovitis JV, Anastasiou-Nana MI, Nanas JN (2007) Reverse remodeling during long-term mechanical unloading of the left ventricle. J Mol Cell Cardiol 43(3):231–242CrossRefGoogle Scholar
  8. Frost HM (2003) Bone’s mechanostat: a 2003 update. Anat Rec A Discov Mol Cell Evol Biol 275(2):1081–1101CrossRefMathSciNetGoogle Scholar
  9. Fung Y, Liu S (1989) Change of residual strains in arteries due to hypertrophy caused by aortic constriction. Circ Res 65(5):1340–1349CrossRefGoogle Scholar
  10. Gaasch WH, Meyer TE (2008) Left ventricular response to mitral regurgitation: implications for management. Circulation 118(22):2298–303CrossRefGoogle Scholar
  11. Gerdes AM, Clark LC, Capasso JM (1995) Regression of cardiac hypertrophy after closing an aortocaval fistula in rats. Am J Physiol 268(6 Pt 2):51–H2345Google Scholar
  12. Gerdes AM, Kellerman SE, Moore JA, Muffly KE, Clark LC, Reaves PY, Malec KB, McKeown PP, Schocken DD (1992) Structural remodeling of cardiac myocytes in patients with ischemic cardiomyopathy. Circulation 86(2):426–430CrossRefGoogle Scholar
  13. Göktepe S, Abilez OJ, Kuhl E (2010a) A generic approach towards finite growth with examples of athlete’s heart, cardiac dilation, and cardiac wall thickening. J Mech Phys Solids 58(10):1661–1680CrossRefMATHMathSciNetGoogle Scholar
  14. Göktepe S, Abilez OJ, Parker KK, Kuhl E (2010b) A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis. J Theor Biol 265(3):42–433CrossRefGoogle Scholar
  15. Grossman W, Jones D, McLaurin LP (1975) Wall stress and patterns of hypertrophy in the human left ventricle. J Clin Invest 56(1):56–64CrossRefGoogle Scholar
  16. Guccione JM, McCulloch AD, Waldman LK (1991) Passive material properties of intact ventricular myocardium determined from a cylindrical model. J Biomech Eng 113(1):42–55CrossRefGoogle Scholar
  17. Kerckhoffs RCP (2012) Computational modeling of cardiac growth in the post-natal rat with a strain-based growth law. J Biomech 45(5):865–871CrossRefGoogle Scholar
  18. Kerckhoffs RCP, Omens J, McCulloch AD (2012) A single strain-based growth law predicts concentric and eccentric cardiac growth during pressure and volume overload. Mech Res Commun 42:40–50CrossRefGoogle Scholar
  19. Klepach D, Lee LC, Wenk JF, Ratcliffe MB, Zohdi TI, Navia Ja, Kassab GS, Kuhl E, Guccione JM (2012) Growth and remodeling of the left ventricle: a case study of myocardial infarction and surgical ventricular restoration. Mech Res Commun 42:134–141CrossRefGoogle Scholar
  20. Kroon W, Delhaas T, Arts T, Bovendeerd P (2009) Computational modeling of volumetric soft tissue growth: application to the cardiac left ventricle. Biomech Model Mechanobiol 8(4):301–309CrossRefGoogle Scholar
  21. Lee EH (1969) Elastic-plastic deformation at finite strains. J Appl Mech 36(1):1–6CrossRefMATHGoogle Scholar
  22. Lee LC, Wall ST, Klepach D, Ge L, Zhang Z, Lee RJ, Hinson A, Gorman JH, Gorman RC, Guccione JM (2013) Algisyl-LVR with coronary artery bypass grafting reduces left ventricular wall stress and improves function in the failing human heart. Int J Cardiol 168(3):2022–2028CrossRefGoogle Scholar
  23. Legrice IJ, Hunter PJ, Smaill BH (1997) Laminar structure of the heart: a mathematical model. Am J Physiol 272(5 Pt 2):76–H2466Google Scholar
  24. Levin H, Oz M, Chen J, Packer M, Rose E, Burkhoff D (1995) Reversal of chronic ventricular dilation in patients with end-stage cardiomyopathy by prolonged mechanical unloading. Circulation 91(11):2717–2720CrossRefGoogle Scholar
  25. Madigan JD, Barbone A, Choudhri AF, Morales DL, Cai B, Oz MC, Burkhoff D (2001) Time course of reverse remodeling of the left ventricle during support with a left ventricular assist device. J Thorac Cardiovasc Surg 121(5):902–908CrossRefGoogle Scholar
  26. Omens JH (1998) Stress and strain as regulators of myocardial growth. Prog Biophys Mol Biol 69(2–3):559–572CrossRefGoogle Scholar
  27. Omens JH, McCulloch AD, Criscione JC (2003) Complex distributions of residual stress and strain in the mouse left ventricle: experimental and theoretical models. Biomech Model Mechanobiol 1(4):267–277CrossRefGoogle Scholar
  28. Omens JH, Vaplon SM, Fazeli B, Mcculloch AD (1998) Left ventricular geometric remodeling and residual stress in the rat heart. J Biomech Eng 120:715–719CrossRefGoogle Scholar
  29. Opie LH, Commerford PJ, Gersh BJ, Pfeffer MA (2006) Controversies in cardiology. Lancet 367(9519):1315; author reply 1315–6Google Scholar
  30. Rausch MK, Dam A, Göktepe S, Abilez OJ, Kuhl E (2011) Computational modeling of growth: systemic and pulmonary hypertension in the heart. Biomech Model Mechanobiol 10(6):799–811CrossRefGoogle Scholar
  31. Rodriguez EK, Hoger A, Mcculloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27(4):455–467CrossRefGoogle Scholar
  32. Rutz AK, Ryf S, Plein S, Boesiger P, Kozerke S (2008) Accelerated whole-heart 3D CSPAMM for myocardial motion quantification. Magn Reson Med 59(4):755–763CrossRefGoogle Scholar
  33. Taber LA (1995) Biomechanics of growth, remodeling, and morphogenesis. Appl Mech Rev 48(8):487–545CrossRefGoogle Scholar
  34. Taber LA (2001) Biomechanics of cardiovascular development. Annu Rev Biomed Eng 3:1–25CrossRefGoogle Scholar
  35. Taber LA, Chabert S (2002) Theoretical and experimental study of growth and remodeling in the developing heart. Biomech Model Mechanobiol 1(1):29–43CrossRefGoogle Scholar
  36. Wall ST, Walker JC, Healy KE, Ratcliffe MB, Guccione JM (2006) Theoretical impact of the injection of material into the myocardium: a finite element model simulation. Circulation 114(24):2627–35CrossRefGoogle Scholar
  37. Weis SM, Emery JL, Becker KD, McBride DJ, Omens JH, McCulloch aD (2000) Myocardial mechanics and collagen structure in the osteogenesis imperfecta murine (oim). Circ Res 87(8):663–669CrossRefGoogle Scholar
  38. Wells SM, Walter EJ (2010) Changes in the mechanical properties and residual strain of elastic tissue in the developing fetal aorta. Ann Biomed Eng 38(2):345–356CrossRefGoogle Scholar
  39. Wenk JF, Eslami P, Zhang Z, Xu C, Kuhl E, Gorman JH, Robb JD, Ratcliffe MB, Gorman RC, Guccione JM (2011) A novel method for quantifying the in-vivo mechanical effect of material injected into a myocardial infarction. Ann Thorac Surg 92(3):935–941CrossRefGoogle Scholar
  40. Wenk JF, Klepach D, Lee LC, Zhang Z, Ge L, Tseng EE, Martin A, Kozerke S, Gorman JH, Gorman RC, Guccione JM (2012) First evidence of depressed contractility in the border zone of a human myocardial infarction. Ann Thorac Surg 93(4):1188–1193 Google Scholar
  41. Zhang X, Javan H, Ms LL, Ms AS, Bs RZ, Deng Y, Selzman CH (2013) A modified murine model for the study of reverse cardiac remodelling. Exp Clin Cardiol 18(2):115–117Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • L. C. Lee
    • 1
  • M. Genet
    • 1
  • G. Acevedo-Bolton
    • 2
  • K. Ordovas
    • 2
  • J. M. Guccione
    • 1
  • E. Kuhl
    • 3
  1. 1.Department of Surgery, School of MedicineUniversity of California at San FranciscoSan FranciscoUSA
  2. 2.Department of Radiology and Biomedical Imaging, School of MedicineUniversity of California at San FranciscoSan FranciscoUSA
  3. 3.Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic SurgeryStanford UniversityStanfordUSA

Personalised recommendations