On the Unique Functional Elasticity and Collagen Fiber Kinematics of Heart Valve Leaflets

  • Jun LiaoEmail author
  • Michael S. Sacks


With the growing prevalence of heart valve diseases, it is important to better understand the biomechanical behavior of normal and pathological heart valve tissues. Recent studies showed that heart valve leaflets exhibited a unique functionally elastic behavior, in which valvular tissues exhibited minimal hysteretic and creep behaviors under biaxial loading, yet allowed stress relaxation similar to other types of collagenous tissues. This unique behavior is in favor of heart valve function, enabling leaflets to bear peak physiological loading without time-dependent deformation. To explore the underlying micromechanical mechanisms, we used small angle X-ray scattering (SAXS) under biaxial stretch to explore the collagen fibril kinematics in stress relaxation and creep. We found that collagen fibril reorientation/realignment did not contribute to stress relaxation and creep. In stress relaxation, collagen fibril strain released largely during the first 20 min and the remaining collagen fibril strain stayed relatively constant in the remaining relaxation time. The overall reduction rate of the collagen fibril strain was much larger than the stress decay rate at the tissue level. When the leaflet tissue experienced negligible time-dependent deformation under constant load (negligible creep), the collagen fibril strain was maintained at a constant level during the time course. This difference in collagen fibril kinematics implies the mechanisms responsible for creep and stress relaxation in the leaflet tissue are functionally independent. We thus speculate some type of fibril-level “locking” mechanism exists in leaflet tissue that allows for stress release under constant strain condition, yet does not allow for continued straining under a constant stress. We speculate that the degenerated ECM components in diseased valvular tissues might cause changes in these quasi-elastic behaviors and thus contribute to malfunction of heart valves.


Heart valves Valve leaflets Viscoelasticity Stress relaxation Creep Negligible creep Collagen fibril D-period Collagen fibril kinematics Small angle X-ray scattering Biaxial stretching system Quasilinear viscoelastic model Quasi-elastic behavior 



The authors would like to thank the support from AHA BGIA-0565346, GRNT17150041, NIH 1R01EB022018-01, and UT STARS.


  1. 1.
    Schoen F, Edwards W. Valvular heart disease: general principles and stenosis. Cardiovasc Pathol. 2001;3:403–42.Google Scholar
  2. 2.
    Sacks MS, David Merryman W, Schmidt DE. On the biomechanics of heart valve function. J Biomech. 2009;42(12):1804–24.PubMedPubMedCentralCrossRefGoogle Scholar
  3. 3.
    Sacks MS, Yoganathan AP. Heart valve function: a biomechanical perspective. Philos Trans R Soc B Biol Sci. 2007;362(1484):1369–91.CrossRefGoogle Scholar
  4. 4.
    Mendelson K, Schoen FJ. Heart valve tissue engineering: concepts, approaches, progress, and challenges. Ann Biomed Eng. 2006;34(12):1799–819.PubMedPubMedCentralCrossRefGoogle Scholar
  5. 5.
    Merryman WD, Engelmayr GC Jr, Liao J, Sacks MS. Defining biomechanical endpoints for tissue engineered heart valve leaflets from native leaflet properties. Prog Pediatr Cardiol. 2006;21(2):153–60.CrossRefGoogle Scholar
  6. 6.
    Brazile B, Wang B, Wang G, Bertucci R, Prabhu R, Patnaik SS, Butler JR, Claude A, Brinkman-Ferguson E, Williams LN, Liao J. On the bending properties of porcine mitral, tricuspid, aortic, and pulmonary valve leaflets. J Long-Term Eff Med Implants. 2015;25(1–2):41–53.PubMedCrossRefPubMedCentralGoogle Scholar
  7. 7.
    Vesely I, Boughner D. Analysis of the bending behaviour of porcine xenograft leaflets and of natural aortic valve material: bending stiffness, neutral axis and shear measurements. J Biomech. 1989;22(6/7):655–71.PubMedCrossRefPubMedCentralGoogle Scholar
  8. 8.
    Mirnajafi A, Raymer J, Scott MJ, Sacks MS. The effects of collagen fiber orientation on the flexural properties of pericardial heterograft biomaterials. Biomaterials. 2005;26(7):795–804.PubMedCrossRefPubMedCentralGoogle Scholar
  9. 9.
    Christie GW, Barratt-Boyes BG. Mechanical properties of porcine pulmonary valve leaflets: how do they differ from aortic leaflets? Ann Thorac Surg. 1995;60:S195–S9.PubMedCrossRefPubMedCentralGoogle Scholar
  10. 10.
    Doehring TC, Kahelin M, Vesely I. Mesostructures of the aortic valve. J Heart Valve Dis. 2005;14(5):679–86.PubMedPubMedCentralGoogle Scholar
  11. 11.
    Vesely I. Reconstruction of loads in the fibrosa and ventricularis of porcine aortic valves. ASAIO J. 1996;42(5):M739–46.PubMedCrossRefPubMedCentralGoogle Scholar
  12. 12.
    Kunzelman KS, Cochran RP, Murphree SS, Ring WS, Verrier ED, Eberhart RC. Differential collagen distribution in the mitral valve and its influence on biomechanical behaviour. J Heart Valve Dis. 1993;2(2):236–44.PubMedPubMedCentralGoogle Scholar
  13. 13.
    Grande-Allen KJ, Liao J. The heterogeneous biomechanics and mechanobiology of the mitral valve: implications for tissue engineering. Curr Cardiol Rep. 2011;13(2):113–20.PubMedPubMedCentralCrossRefGoogle Scholar
  14. 14.
    Roberts WC. Morphologic features of the normal and abnormal mitral valve. Am J Cardiol. 1983;51(6):1005–28.PubMedCrossRefPubMedCentralGoogle Scholar
  15. 15.
    Anderson R, Becker A. Anatomy of the heart. Stuttgart, NY: Thieme; 1982.Google Scholar
  16. 16.
    Gross L, Kugel M. Topographic anatomy and histology of the valves in the human heart. Am J Pathol. 1931;7(5):445.PubMedPubMedCentralGoogle Scholar
  17. 17.
    Ho S. Anatomy of the mitral valve. Heart. 2002;88(Suppl 4):iv5–iv10.PubMedPubMedCentralGoogle Scholar
  18. 18.
    Bezerra A, DiDio L, Prates J. Dimensions of the left atrioventricular valve and its components in normal human hearts. Cardioscience. 1992;3(4):241–4.PubMedPubMedCentralGoogle Scholar
  19. 19.
    Misfeld M, Sievers H-H. Heart valve macro-and microstructure. Philos Trans R Soc B Biol Sci. 2007;362(1484):1421–36.CrossRefGoogle Scholar
  20. 20.
    Thubrikar M, Klemchuk PP. The aortic valve. Boca Raton, FL: CRC Press; 1990.Google Scholar
  21. 21.
    Joyce EM, Liao J, Schoen FJ, Mayer JE Jr, Sacks MS. Functional collagen fiber architecture of the pulmonary heart valve cusp. Ann Thorac Surg. 2009;87(4):1240–9.PubMedPubMedCentralCrossRefGoogle Scholar
  22. 22.
    Go AS, Mozaffarian D, Roger VL, Benjamin EJ, Berry JD, Borden WB, Bravata DM, Dai S, Ford ES, Fox CS. Heart disease and stroke statistics—2013 update a report from the American Heart Association. Circulation. 2013;127(1):e6–e245.PubMedPubMedCentralGoogle Scholar
  23. 23.
    Nkomo VT, Gardin JM, Skelton TN, Gottdiener JS, Scott CG, Enriquez-Sarano M. Burden of valvular heart diseases: a population-based study. Lancet. 2006;368(9540):1005–11.PubMedPubMedCentralCrossRefGoogle Scholar
  24. 24.
    Roger VL, Go AS, Lloyd-Jones DM, Benjamin EJ, Berry JD, Borden WB, Bravata DM, Dai S, Ford ES, Fox CS. Heart disease and stroke statistics—2012 update a report from the American Heart Association. Circulation. 2012;125(1):e2–e220.PubMedCrossRefPubMedCentralGoogle Scholar
  25. 25.
    Nishimura RA. Aortic valve disease. Circulation. 2002;106(7):770–2.PubMedCrossRefPubMedCentralGoogle Scholar
  26. 26.
    Lilly LS. Pathophysiology of heart disease: a collaborative project of medical students and faculty. Philadelphia: Wolters Kluwer Health; 2012.Google Scholar
  27. 27.
    Takkenberg JJ, Rajamannan NM, Rosenhek R, Kumar AS, Carapetis JR, Yacoub MH. The need for a global perspective on heart valve disease epidemiology the SHVD working group on epidemiology of heart valve disease founding statement. J Heart Valve Dis. 2008;17(1):135.PubMedPubMedCentralGoogle Scholar
  28. 28.
    Peeters F, Meex SJR, Dweck MR, Aikawa E, Crijns H, Schurgers LJ, Kietselaer B. Calcific aortic valve stenosis: hard disease in the heart: a biomolecular approach towards diagnosis and treatment. Eur Heart J. 2018;39(28):2618–24.PubMedCrossRefPubMedCentralGoogle Scholar
  29. 29.
    Katsi V, Georgiopoulos G, Oikonomou D, Aggeli C, Grassos C, Papadopoulos DP, Thomopoulos C, Marketou M, Dimitriadis K, Toutouzas K, Nihoyannopoulos P, Tsioufis C, Tousoulis D. Aortic Stenosis, Aortic Regurgitation and Arterial Hypertension. Current Vascular Pharmacology 2018;16:1. Scholar
  30. 30.
    Grande-Allen KJ, Griffin BP, Calabro A, Ratliff NB, Cosgrove DM 3rd, Vesely I. Myxomatous mitral valve chordae. II: Selective elevation of glycosaminoglycan content. J Heart Valve Dis. 2001;10(3):325–32; discussion 32–3PubMedPubMedCentralGoogle Scholar
  31. 31.
    Stephens EH, Timek TA, Daughters GT, Kuo JJ, Patton AM, Baggett LS, Ingels NB, Miller DC, Grande-Allen KJ. Significant changes in mitral valve leaflet matrix composition and turnover with tachycardia-induced cardiomyopathy. Circulation. 2009;120(11 Suppl):S112–9.PubMedPubMedCentralCrossRefGoogle Scholar
  32. 32.
    Breuer CK, Mettler BA, Anthony T, Sales VL, Schoen FJ, Mayer JE. Application of tissue-engineering principles toward the development of a semilunar heart valve substitute. Tissue Eng. 2004;10(11–12):1725–36.PubMedCrossRefPubMedCentralGoogle Scholar
  33. 33.
    Schoen FJ. Evolving concepts of cardiac valve dynamics the continuum of development, functional structure, pathobiology, and tissue engineering. Circulation. 2008;118(18):1864–80.PubMedPubMedCentralCrossRefGoogle Scholar
  34. 34.
    Rabkin-Aikawa E, Mayer JE Jr, Schoen FJ. Heart valve regeneration. Regenerative Medicine II. Berlin: Springer; 2005. p. 141–79.CrossRefGoogle Scholar
  35. 35.
    Katz A. Physiology of the heart. Philadelphia, PA: Wolters Kluwer Health; 2011.Google Scholar
  36. 36.
    Fung YC. Biomechanics: mechanical properties of living tissues. 2nd ed. New York: Springer; 1993. 568 pCrossRefGoogle Scholar
  37. 37.
    Provenzano P, Lakes R, Keenan T, Vanderby R Jr. Nonlinear ligament viscoelasticity. Ann Biomed Eng. 2001;29(10):908–14.PubMedCrossRefGoogle Scholar
  38. 38.
    Thornton GM, Oliynyk A, Frank CB, Shrive NG. Ligament creep cannot be predicted from stress relaxation at low stress: a biomechanical study of the rabbit medial collateral ligament. J Orthop Res. 1997;15(5):652–6.PubMedCrossRefGoogle Scholar
  39. 39.
    Lakes RS, Vanderby R. Interrelation of creep and relaxation: a modeling approach for ligaments. J Biomech Eng. 1999;121(6):612–5.PubMedCrossRefPubMedCentralGoogle Scholar
  40. 40.
    Thornton GM, Frank CB, Shrive NG. Ligament creep behavior can be predicted from stress relaxation by incorporating fiber recruitment. J Rheol. 2001;45(2):493–507.CrossRefGoogle Scholar
  41. 41.
    May-Newman K, Yin FC. Biaxial mechanical behavior of excised porcine mitral valve leaflets. Am J Phys. 1995;269(4 Pt 2):H1319–27.Google Scholar
  42. 42.
    Grashow JS, Yoganathan AP, Sacks MS. Biaxial stress-stretch behavior of the mitral valve anterior leaflet at physiologic strain rates. Ann Biomed Eng. 2006;34(2):315–25.PubMedCrossRefPubMedCentralGoogle Scholar
  43. 43.
    Kunzelman KS, Cochran RP. Stress/strain characteristics of porcine mitral valve tissue: parallel versus perpendicular collagen orientation. J Card Surg. 1992;7(1):71–8.PubMedCrossRefPubMedCentralGoogle Scholar
  44. 44.
    Liao J, Yang L, Grashow J, Sacks MS. The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet. J Biomech Eng. 2007;129(1):78–87.PubMedCrossRefPubMedCentralGoogle Scholar
  45. 45.
    Grashow JS, Sacks MS, Liao J, Yoganathan AP. Planar biaxial creep and stress relaxation of the mitral valve anterior leaflet. Ann Biomed Eng. 2006;34(10):1509–18.PubMedCrossRefPubMedCentralGoogle Scholar
  46. 46.
    Sacks MS, He Z, Baijens L, Wanant S, Shah P, Sugimoto H, Yoganathan AP. Surface strains in the anterior leaflet of the functioning mitral valve. Ann Biomed Eng. 2002;30(10):1281–90.PubMedCrossRefPubMedCentralGoogle Scholar
  47. 47.
    Sacks MS, Enomoto Y, Graybill JR, Merryman WD, Zeeshan A, Yoganathan AP, Levy RJ, Gorman RC, Gorman JH III. In-vivo dynamic deformation of the mitral valve anterior leaflet. Ann Thorac Surg. 2006;82(4):1369–77.PubMedCrossRefPubMedCentralGoogle Scholar
  48. 48.
    Stella JA, Liao J, Sacks MS. Time-dependent biaxial mechanical behavior of the aortic heart valve leaflet. J Biomech. 2007;40(14):3169–77.PubMedPubMedCentralCrossRefGoogle Scholar
  49. 49.
    Pierlot CM, Moeller AD, Lee JM, Wells SM. Biaxial creep resistance and structural remodeling of the aortic and mitral valves in pregnancy. Ann Biomed Eng. 2015;43(8):1772–85.PubMedCrossRefPubMedCentralGoogle Scholar
  50. 50.
    Hodge AJ, Petruska JA. Recent studies with the electron microscope on ordered aggregates of the tropocollagen molecule. London: Academic Press; 1963.Google Scholar
  51. 51.
    Nimni ME. The molecular organization of collagen and its role in determining the biophysical properties of the connective tissues. Biorheology. 1980;17:51–82.PubMedCrossRefPubMedCentralGoogle Scholar
  52. 52.
    Silver FH, Freeman JW, Seehra GP. Collagen self-assembly and the development of tendon mechanical properties. J Biomech. 2003;36(10):1529–53.PubMedCrossRefPubMedCentralGoogle Scholar
  53. 53.
    Chapman JA, Hulmes DJS. Electron microscopy of the collagen fibril. In: Ruggeri A, Motto PM, editors. Ultrastructure of the connective tissue matrix. Boston: Martinus Nijhoff; 1984. p. 1–33.Google Scholar
  54. 54.
    Scott JE. Proteoglycan: collagen interactions in connective tissues. Ultrastructural, biochemical, functional and evolutionary aspects. Int J Biol Macromol. 1991;13(3):157–61.PubMedCrossRefPubMedCentralGoogle Scholar
  55. 55.
    Weber IT, Harrison RW, Iozzo RV. Model structure of decorin and implications for collagen fibrillogenesis. J Biol Chem. 1996;271(50):31767–70.PubMedCrossRefPubMedCentralGoogle Scholar
  56. 56.
    McBride DJ, Trelstad RL, Silver FH. Structural and mechanical assessment of developing chick tendon. Int J Biol Macromol. 1988;10:194–200.CrossRefGoogle Scholar
  57. 57.
    Kastelic J, Palley I, Baer E. A structural mechanical model for tendon crimping. J Biomech. 1980;13(10):887–93.PubMedCrossRefPubMedCentralGoogle Scholar
  58. 58.
    Silver FH, Kato YP, Ohno M, Wasserman AJ. Analysis of mammalian connective tissue: relationship between hierarchical structures and mechanical properties. J Long-Term Eff Med Implants. 1992;2(2–3):165–98.PubMedPubMedCentralGoogle Scholar
  59. 59.
    Fratzl P, Misof K, Zizak I, Rapp G, Amenitsch H, Bernstorff S. Fibrillar structure and mechanical properties of collagen. J Struct Biol. 1998;122(1–2):119–22.PubMedCrossRefPubMedCentralGoogle Scholar
  60. 60.
    Screen HR, Lee DA, Bader DL, Shelton JC. An investigation into the effects of the hierarchical structure of tendon fascicles on micromechanical properties. Proc Inst Mech Eng H. 2004;218(2):109–19.PubMedCrossRefPubMedCentralGoogle Scholar
  61. 61.
    Elliott DM, Robinson PS, Gimbel JA, Sarver JJ, Abboud JA, Iozzo RV, Soslowsky LJ. Effect of altered matrix proteins on quasilinear viscoelastic properties in transgenic mouse tail tendons. Ann Biomed Eng. 2003;31(5):599–605.PubMedCrossRefPubMedCentralGoogle Scholar
  62. 62.
    Scott JE. Supramolecular organization of extracellular matrix glycosaminoglycans, in vitro and in the tissues. FASEB J. 1992;6(9):2639–45.PubMedCrossRefPubMedCentralGoogle Scholar
  63. 63.
    Grande-Allen KJ, Griffin BP, Ratliff NB, Cosgrove DM, Vesely I. Glycosaminoglycan profiles of myxomatous mitral leaflets and chordae parallel the severity of mechanical alterations. J Am Coll Cardiol. 2003;42(2):271–7.PubMedCrossRefPubMedCentralGoogle Scholar
  64. 64.
    Barber JE, Kasper FK, Ratliff NB, Cosgrove DM, Griffin BP, Vesely I. Mechanical properties of myxomatous mitral valves. J Thorac Cardiovasc Surg. 2001;122(5):955–62.PubMedCrossRefPubMedCentralGoogle Scholar
  65. 65.
    Dahners LE, Lester GE, Caprise P. The pentapeptide NKISK affects collagen fibril interactions in a vertebrate tissue. J Orthop Res. 2000;18(4):532–6.PubMedCrossRefPubMedCentralGoogle Scholar
  66. 66.
    Nishimura M, Yan W, Mukudai Y, Nakamura S, Nakamasu K, Kawata M, Kawamoto T, Noshiro M, Hamada T, Kato Y. Role of chondroitin sulfate-hyaluronan interactions in the viscoelastic properties of extracellular matrices and fluids. Biochim Biophys Acta. 1998;1380(1):1–9.PubMedCrossRefPubMedCentralGoogle Scholar
  67. 67.
    Liao J, Vesely I. A structural basis for the size-related mechanical properties of mitral valve chordae tendineae. J Biomech. 2003;36(8):1125–33.PubMedCrossRefPubMedCentralGoogle Scholar
  68. 68.
    Liao J, Vesely I. Skewness angle of interfibrillar proteoglycans increases with applied load on mitral valve chordae tendineae. J Biomech. 2007;40(2):390–8.PubMedCrossRefPubMedCentralGoogle Scholar
  69. 69.
    Liao J, Vesely I. Relationship between collagen fibrils, glycosaminoglycans, and stress relaxation in mitral valve chordae tendineae. Ann Biomed Eng. 2004;32(7):977–83.PubMedCrossRefPubMedCentralGoogle Scholar
  70. 70.
    Jeronimidis G, JFV V. Composite materials. In: Hukins DWL, editor. Connective. Tissue matrix. Weinheim: Verlag Chemie; 1984. p. 187–210.Google Scholar
  71. 71.
    Redaelli A, Vesentini S, Soncini M, Vena P, Mantero S, Montevecchi FM. Possible role of decorin glycosaminoglycans in fibril to fibril force transfer in relative mature tendons--a computational study from molecular to microstructural level. J Biomech. 2003;36(10):1555–69.PubMedCrossRefPubMedCentralGoogle Scholar
  72. 72.
    Vesentini S, Redaelli A, Montevecchi FM. Estimation of the binding force of the collagen molecule-decorin core protein complex in collagen fibril. J Biomech. 2005;38(3):433–43.PubMedCrossRefPubMedCentralGoogle Scholar
  73. 73.
    Cox HL. The elasticity and strength of paper and other fibrous materials. Br J Appl Phys. 1952;3:72–9.CrossRefGoogle Scholar
  74. 74.
    Fessel G, Snedeker JG. Equivalent stiffness after glycosaminoglycan depletion in tendon—an ultra-structural finite element model and corresponding experiments. J Theor Biol. 2011;268(1):77–83.PubMedCrossRefPubMedCentralGoogle Scholar
  75. 75.
    Rigozzi S, Muller R, Snedeker JG. Collagen fibril morphology and mechanical properties of the Achilles tendon in two inbred mouse strains. J Anat. 2010;216(6):724–31.PubMedPubMedCentralCrossRefGoogle Scholar
  76. 76.
    Biological Materials SFH. Structure, mechanical properties, and modeling of soft tissues. New York and London: New York University Press; 1987.Google Scholar
  77. 77.
    Billiar KL, Sacks MS. A method to quantify the fiber kinematics of planar tissues under biaxial stretch. J Biomech. 1997;30(7):753–6.PubMedCrossRefPubMedCentralGoogle Scholar
  78. 78.
    Gilbert TW, Sacks MS, Grashow JS, Woo SLY, Chancellor MB, Badylak SF. Fiber kinematics of small intestinal submucosa under uniaxial and biaxial stretch. J Biomech Eng. 2006;128(6):890–8.PubMedCrossRefPubMedCentralGoogle Scholar
  79. 79.
    Hilbert SL, Sword LC, Batchelder KF, Barrick MK, Ferrans VJ. Simultaneous assessment of bioprosthetic heart valve biomechanical properties and collagen crimp length. J Biomed Mater Res. 1996;31(4):503–9.PubMedCrossRefGoogle Scholar
  80. 80.
    Hansen KA, Weiss JA, Barton JK. Recruitment of tendon crimp with applied tensile strain. J Biomech Eng. 2002;124(1):72–7.PubMedCrossRefPubMedCentralGoogle Scholar
  81. 81.
    Kronick PL, Buechler PR. Fiber orientation in calfskin by laser light scattering or X-ray diffraction and quantitative relation to mechanical properties. J Am Leather Chem Assoc. 1986;81:221–9.Google Scholar
  82. 82.
    Sacks MS, Smith DB, Hiester ED. A small angle light scattering device for planar connective tissue microstructural analysis. Ann Biomed Eng. 1997;25(4):678–89.PubMedCrossRefPubMedCentralGoogle Scholar
  83. 83.
    Farkasjahnke M, Synecek V. Small-angle X-ray diffraction studies on rat-tail tendon. Acta Physiol Acad Sci. 1965;28(1):1–17.Google Scholar
  84. 84.
    Bigi A, Incerti A, Leonardi L, Miccoli G, Re G, Roveri N. Role of the orientation of the collagen fibers on the mechanical properties of the carotid wall. Boll Soc Ital Biol Sper. 1980;56(4):380–4.PubMedPubMedCentralGoogle Scholar
  85. 85.
    Aspden RM, Bornstein NH, Hukins DW. Collagen organisation in the interspinous ligament and its relationship to tissue function. J Anat. 1987;155:141–51.PubMedPubMedCentralGoogle Scholar
  86. 86.
    Sasaki N, Odajima S. Stress-strain curve and Young’s modulus of a collagen molecule as determined by the X-ray diffraction technique. J Biomech. 1996;29:655–8.PubMedCrossRefPubMedCentralGoogle Scholar
  87. 87.
    Folkhard W, Geercken W, Knorzer E, Mosler E, Nemetschek-Gansler H, Nemetschek T, Koch MH. Structural dynamic of native tendon collagen. J Mol Biol. 1987;193(2):405–7.CrossRefGoogle Scholar
  88. 88.
    Sasaki N, Odajima S. Elongation mechanism of collagen fibrils and force-strain relations of tendon at each level of structural hierarchy. J Biomech. 1996;29(9):1131–6.PubMedCrossRefPubMedCentralGoogle Scholar
  89. 89.
    Sasaki N, Shukunami N, Matsushima N, Izumi Y. Time resolved X-ray diffraction from tendon collagen during creep using synchrotron radiation. J Biomech. 1999;32:285–92.PubMedCrossRefPubMedCentralGoogle Scholar
  90. 90.
    Purslow PP, Wess TJ, Hukins DW. Collagen orientation and molecular spacing during creep and stress-relaxation in soft connective tissues. J Exp Biol. 1998;201 .(Pt 1:135–42.PubMedPubMedCentralGoogle Scholar
  91. 91.
    Liao J, Yang L, Grashow J, Sacks MS. Molecular orientation of collagen in intact planar connective tissues under biaxial stretch. Acta Biomater. 2005;1(1):45–54.PubMedCrossRefPubMedCentralGoogle Scholar

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Authors and Affiliations

  1. 1.Tissue Biomechanics and Bioengineering Laboratory, The Department of BioengineeringThe University of Texas at ArlingtonArlingtonUSA
  2. 2.The Oden Institute and the Department of Biomedical EngineeringThe University of Texas at AustinAustinUSA

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