title: On the effect of prestrain and residual stress in thin biological membranes.
abstract: Understanding the difference between ex vivo and in vivo measurements is critical to interpret the load carrying mechanisms of living biological systems. For the past four decades, the ex vivo stiffness of thin biological membranes has been characterized using uniaxial and biaxial tests with remarkably consistent stiffness parameters, even across different species. Recently, the in vivo stiffness was characterized using combined imaging techniques and inverse finite element analyses. Surprisingly, ex vivo and in vivo stiffness values differed by up to three orders of magnitude. Here, for the first time, we explain this tremendous discrepancy using the concept of prestrain. We illustrate the mathematical modeling of prestrain in nonlinear continuum mechanics through the multiplicative decomposition of the total elastic deformation into prestrain-induced and load-induced parts. Using in vivo measured membrane kinematics and associated pressure recordings, we perform an inverse finite element analysis for different prestrain levels and show that the resulting membrane stiffness may indeed differ by four orders of magnitude depending on the prestrain level. Our study motivates the hypothesis that prestrain is important to position thin biological membranes in vivo into their optimal operating range, right at the transition point of the stiffening regime. Understanding the effect of prestrain has direct clinical implications in regenerative medicine, medical device design, and and tissue engineering of replacement constructs for thin biological membranes.
authors: Department of Mechanical Engineering, Stanford, California, USA.
authors: Manuel K
authors: MK
authors: Rausch
authors: Ellen
authors: E
authors: Kuhl
keywords: finite element method; mitral leaflet; parameter identification; prestrain; residual strain; residual stress
references: Philos Trans R Soc Lond B Biol Sci. 2007 Aug 29;362(1484):1369-91
references: 17588873
references: J Biomech Eng. 1992 Nov;114(4):461-6
references: 1487897
references: J Biomech Eng. 2004 Apr;126(2):276-83
references: 15179859
references: Circ Res. 1990 Jan;66(1):37-45
references: 2295143
references: Circ Res. 1989 Nov;65(5):1340-9
references: 2805247
references: Biomech Model Mechanobiol. 2009 Dec;8(6):431-46
references: 19123012
references: J Thorac Cardiovasc Surg. 2005 Sep;130(3):783-90
references: 16153929
references: Acta Biomater. 2006 Nov;2(6):609-18
references: 16945600
references: Circulation. 2010 Oct 26;122(17):1683-9
references: 20937973
references: J Mech Behav Biomed Mater. 2012 Nov;15:208-17
references: 23159489
references: J Thorac Cardiovasc Surg. 2007 Dec;134(6):1562-8
references: 18023684
references: J Biomech. 2009 Aug 25;42(12):1909-16
references: 19535081
references: J Mech Phys Solids. 2011 Oct 1;59(10):2177-2190
references: 22081726
references: Biomech Model Mechanobiol. 2011 Feb;10(1):11-26
references: 20419330
references: Med Biol Eng. 1973 Nov;11(6):691-702
references: 4787928
references: Biomech Model Mechanobiol. 2007 Sep;6(5):303-20
references: 17149642
references: Am J Physiol Heart Circ Physiol. 2008 Sep;295(3):H1141-H1149
references: 18621858
references: J Mech Phys Solids. 2011 Apr 1;59(4):863-883
references: 21532929
references: Am J Physiol Heart Circ Physiol. 2009 Jun;296(6):H1766-73
references: 19363135
references: J Thorac Cardiovasc Surg. 1973 Aug;66(2):202-8
references: 4720973
references: Biomech Model Mechanobiol. 2013 Oct;12(5):1053-71
references: 23263365
references: J Biomech Eng. 2005 Jun;127(3):504-11
references: 16060357
references: J Biomech. 2009 Dec 11;42(16):2697-701
references: 19766222
references: Am J Physiol. 1995 Oct;269(4 Pt 2):H1319-27
references: 7485564
references: Ann Thorac Surg. 2006 Oct;82(4):1369-77
references: 16996935
references: J Biomech. 2011 Apr 7;44(6):1149-57
references: 21306716
references: J Biomech Eng. 2001 Dec;123(6):528-35
references: 11783722
references: Biomech Model Mechanobiol. 2013 Jan;12(1):123-36
references: 22446834
references: Ann Biomed Eng. 1991;19(3):237-49
references: 1928868
references: J Card Surg. 1992 Mar;7(1):71-8
references: 1554980
references: J Biomech Eng. 1998 Feb;120(1):38-47
references: 9675679
references: Circulation. 2011 Sep 13;124(11 Suppl):S81-96
references: 21911823
references: ASAIO Trans. 1991 Jul-Sep;37(3):M447-8
references: 1751231
references: Ann Biomed Eng. 2011 Jun;39(6):1690-702
references: 21336803
references: Ann Biomed Eng. 2012 Mar;40(3):750-61
references: 22037916
references: Ann Biomed Eng. 2006 Feb;34(2):315-25
references: 16450193
references: Biomech Model Mechanobiol. 2009 Feb;8(1):43-55
references: 18193309
references: Ann Biomed Eng. 2005 Dec;33(12):1778-88
references: 16389526
references: Circulation. 2012 Sep 11;126(11 Suppl 1):S231-8
references: 22965988
references: Biomech Model Mechanobiol. 2010 Jun;9(3):281-93
references: 19890668
references: Ann Biomed Eng. 2012 Jul;40(7):1455-67
references: 22327292