A structural mechanical model for tendon crimping

Kastelic, J.; Palley, I.; Baer, E.

Affiliations

¹Department of Macromolecular Science, Case Western Reserve University, Cleveland, Ohio 44106, U.S.A.

²Present address: Celanese Research Company, Box 1000, Summit, New Jersey 07901, U.S.A.

³Present address: The Allied Chemical Corporation Columbia Road and Park Avenue, Morristown, New Jersey 0760, U.S.A.

Abstract

For tendon collagen, an explanation is proposed for the “toe” region of the stress-strain curve. We ascribe the “toe” effect to the fascicle as a whole. Studies of tendon morphology have shown a distribution of crimp angles. In our model, restoring force arises from the elasticity of those fibrils which are already straightened. Resistance of a crimped fibril is assumed to be negligible. The model was found to fit experimental mechanical data for all ages and over the entire “toe” region.

Links

DOI: 10.1016/0021-9290(80)90177-3

PubMed: 7462263

WoS: A1980KS08300009

History

Received: 1979-07-09

Revised: 1979-11-14

Cited Works (6)

Year	Entry
1967	Abrahams M. Mechanical behaviour of tendon in vitro: a preliminary report. Med Biol Eng. September 1967;5(5):433-443.
1978	Kastelic J, Galeski A, Baer E. The multicomposite structure of tendon. Connect Tissue Res. 1978;6(1):11-23.
1965	Elliott DH. Structure and function of mammalian tendon. Biol Rev. August 1965;40(3):392-421.
1959	Rigby BJ, Hirai N, Spikes JD, Eyring H. The mechanical properties of rat tail tendon. J Gen Physiol. November 1959;43(2):265-283.
1972	Diamant J, Keller A, Baer E, Litt M, Arridge RG. Collagen: ultrastructure and its relation to mechanical properties as a function of ageing. Proc R Soc B. March 14, 1972;180(1060):293-315.
1976	Comninou M, Yannas IV. Dependence of stress-strain nonlinearity of connective tissues on the geometry of collagen fibres. J Biomech. 1976;9(7):427-433.

Cited By (40)

Year	Entry
2008	Lucas SR, Bass CR, Salzar RS, Oyen ML, Planchak C, Ziemba A, Shender BS, Paskoff G. Viscoelastic properties of the cervical spinal ligaments under fast strain-rate deformations. Acta Biomater. January 2008;4(1):117-125.
2003	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. May 2003;31(5):599-605.
2001	Weiss JA, Gardiner JC. Computational modeling of ligament mechanics. Crit Rev Biomed Eng. 2001;29(3):303-371.
1983	Lanir Y. Constitutive equations for fibrous connective tissues. J Biomech. 1983;16(1):1-12.
1999	Liao H, Belkof SM. A failure model for ligaments. J Biomech. 1999;32(2):183-188.
1985	Stouffer DC, Butler DL, Hosny D. The relationship between crimp pattern and mechanical response of human patellar tendon-bone units. J Biomech Eng. May 1985;107(2):158-165.
1992	Ault HK, Hoffman AH. A composite micromechanical model for connective tissues, I: theory. J Biomech Eng. February 1992;114(1):137-141.
1993	Woo SL-Y, Johnson GA, Smith BA. Mathematical modeling of ligaments and tendons. J Biomech Eng. November 1993;115(4B):468-473.
1997	Hurschler C, Loitz-Ramage B, Vanderby R Jr. A structurally based stress-stretch relationship for tendon and ligament. J Biomech Eng. November 1997;119(4):392-399.
1998	Wren TAL, Carter DR. A microstructural model for the tensile constitutive and failure behavior of soft skeletal connective tissues. J Biomech Eng. February 1998;120(1):55-61.
2002	Hansen KA, Weiss JA, Barton JK. Recruitment of tendon crimp with applied tensile strain. J Biomech Eng. February 2002;124(1):72-77.
2002	Arnoczky SP, Lavagnino M, Whallon JH, Hoonjan A. In situ cell nucleus deformation in tendons under tensile load: a morphological analysis using confocal laser microscopy. J Orthop Res. January 2002;20(1):29-35.
2005	Weiss JA, Gardiner JC, Ellis BJ, Lujan TJ, Phatak NS. Three-dimensional finite element modeling of ligaments: technical aspects. Med Eng Phys. December 2005;27(10):845-861.
2021	Golman M. Toughening Mechanisms for the Attachment of Architectured Materials: The Mechanics of the Tendon Enthesis [PhD thesis]. Columbia University; 2021.
2019	Groetsch A. Micro- and Nanomechanics of Mineralised Collagen Fibre Elasto-Plasticity [PhD thesis]. Ebinburgh, Scotland: Heriot-Watt University; November 2019.
2023	Pineda Guzman RA. Development of Novel Model Materials and Non-Invasive Microstructural Imaging Techniques of Connective Soft Tissues [PhD thesis]. University of Illinois at Urbana-Champaign; 2023.
2021	Notermans T. Computational Modeling of Mechanobiology in Intact and Healing Rat Achilles Tendon [PhD thesis]. Lund, Sweden: Lund University; June 18, 2021.
1990	Belkoff SM. A Microstructural Model of Skin: An Evaluation of Maturing Rat Dermis [PhD thesis]. East Lansing, MI: Michigan State University; April 1990.
1998	Atkinson TS. Experimental and Analytical Development of a Poroelastic Finite Element Model for Tendon [PhD thesis]. East Lansing, MI: Michigan State University; 1998.
2007	Lavagnino M. The Mechanotransduction Response of Tendon Cells to Tensile Loading [PhD thesis]. East Lansing, MI: Michigan State University; 2007.
2005	De Vita R. Structural Constitutive Models for Knee Ligaments [PhD thesis]. Pittsburgh, PA: University of Pittsburgh; 2005.
2011	Wagnac É. Expérimentation et modélisation détaillée de la colonne vertébrale pour étudier le rôle de facteurs anatomiques et biomécaniques sur les traumatismes rachidiens [PhD thesis]. École polytechnique de Montréal; November 2011.
2007	Hao H. Identification of the Effects of Axonal Coupling to the Glial Matrix on Axonal Kinematics [PhD thesis]. Rutgers University; October 2007.
1997	Wren TAL. Structure-Function Relationships for Soft Skeletal Connective Tissues [PhD thesis]. Stanford University; June 1997.
1999	Kukreti U. Structure-Function Relationship in Connective Tissues: A Study of Rabbit Medial Collateral Ligaments [PhD thesis]. Baltimore County, University of Maryland; 1999.
1986	Bylski DI. In Situ Measurement of Meniscal Mechanics in Human Knee Joints [PhD thesis]. University of Michigan; 1986.
1998	Derwin KA. A Quantitative Investigation of Structure-Function Relationships in a Tendon Fascicle Model [PhD thesis]. University of Michigan; 1998.
1998	Bain AC. In Vivo Mechanical Thresholds for Morphological and Functional Axonal Injury [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1998.
2004	Lin TW. Development and Utilization of a Transgenic Mouse Injury Model to Investigate the Role of Interleukin-4 and Interleukin-6 in Tendon Healing [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2004.
2005	Gimbel JA. The Role of Tension on Supraspinatus Tendon to Bone Healing in a Newly Developed Animal Model of Chronic Rotator Cuff Tears [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2005.
2005	Guerin HAL. A Nonlinear Anisotropic Continuum Model of Human Annulus Fibrosus Mechanical Behavior [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2005.
2006	Johannessen W. Nucleus Pulposus Degeneration and Its Role in Intervertebral Disc Mechanical Function [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2006.
2008	Lee KE. An Engineering Approach to Understanding Painful Facet -Mediated Injury: Insights on Biomechanics and Neuropeptide Responses in a Rat Model [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2008.
2009	Lake SP. Anisotropic, Inhomogeneous and Nonlinear Structure-Function of Human Supraspinatus Tendon [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2009.
1994	Weiss JA. A Constitutive Model and Finite Element Representation for Transversely Isotropic Soft Tissues [PhD thesis]. Salt Lake City, UT: University of Utah; December 1994.
2002	Gardiner JC. Computational Modeling of Ligament Mechanics [PhD thesis]. University of Utah; May 2002.
2008	Lucas SR. A Microstructural Viscoelastic Ligament Failure Model [PhD thesis]. Charlottesville, VA: University of Virginia; January 2008.
2016	Mane A. Representing Sub-Failure Quasi-Static Ligament Mechanics and Bone Kinematics in a Human Ankle Finite Element Model [Master's thesis]. Charlottesville, VA: University of Virginia; May 2016.
1997	Hurschler C. Collagen Matrix in Normal and Healing Ligaments: Microstructural Behavior, Biological Adaptation, and a Structural Mechanical Model [PhD thesis]. University of Wisconsin – Madison; 1997.
2017	Fang F. Composition-Dependent Mechanisms of Multiscale Tendon Mechanics [PhD thesis]. St. Louis, MO: Washington University in St. Louis; August 2017.