Linear and quasi-linear viscoelastic characterization of ankle ligaments

Funk, J. R.; Hall, G. W.; Crandall, J. R.; Pilkey, W. D.

Affiliations

¹Automobile Safety Laboratory, Department of Mechanical, Nuclear, and Aerospace Engineering, University of Virginia, Charlottesville, VA 22903

Abstract

The objective of this study was to produce linear and nonlinear viscoelastic models of eight major ligaments in the human ankle/foot complex for use in computer models of the lower extremity. The ligaments included in this study were the anterior talofibular (ATaF), anterior tibiofibular (ATiF), anterior tibiotalar (ATT), calcaneofibular (CF), posterior talofibular (PTaF), posterior tibiofibular (PTiF), posterior tibiotalar (PTT), and tibiocalcaneal (TiC) ligaments. Step relaxation and ramp tests were performed. Back-extrapolation was used to correct for vibration effects and the error introduced by the finite rise time in step relaxation tests. Ligament behavior was found to be nonlinear viscoelastic, but could be adequately modeled up to 15 percent strain using Fung's quasilinear viscoelastic (QLV) model. Failure properties and the effects of preconditioning were also examined.

Links

DOI: 10.1115/1.429623

PubMed: 10790825

WoS: 000167110700003

History

Received: 1998-04-23

Revised: 1999-09-05

Cited Works (20)

Year	Entry
1993	Kwan MK, Lin TH-C, Woo SL-Y. On the viscoelastic properties of the anteromedial bundle of the anterior cruciate ligament. J Biomech. April–May 1993;26(4-5):447-452.
1998	Gerber JP, Williams GN, Scoville CR, Arciero RA, Taylor DC. Persistent disability associated with ankle sprains: a prospective examination of an athletic population. Foot Ankle Int. October 1998;19(10):653-660.
1980	Woo SL-Y, Simon BR, Kuei SC, Akeson WH. Quasi-linear viscoelastic properties of normal articular cartilage. J Biomech Eng. May 1980;102(2):85-90.
1981	Woo SL-Y, Gomez MA, Akeson WH. The time and history-dependent viscoelastic properties of the canine medical collateral ligament. J Biomech Eng. November 1981;103(4):293-298.
1998	Parenteau CS, Viano DC, Petit PY. Biomechanical properties of human cadaveric ankle-subtalar joints in quasi-static loading. J Biomech Eng. February 1998;120(1):105-111.
1997	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):652-656.
1996	Bedewi PG, Bedewi NE. Modelling of occupant biomechanics with emphasis on the analysis of lower extremity injuries. Int J Crashworthiness. 1996;1(1):50-72.
1996	Tannous RE, Bandak FA, Toridis TG, Eppinger RH. A three-dimensional finite element model of the human ankle: development and preliminary application to axial impulsive loading. In: Proceedings of the 40th Stapp Car Crash Conference. November 4-6, 1996; Albuquerque, NM. Warrendale, PA: Society of Automotive Engineers:219-238.219-238. SAE 962427.
1991	Myers BS, McElhaney JH, Doherty BJ. The viscoelastic responses of the human cervical spine in torsion: experimental limitations of quasi-linear theory, and a method for reducing these effects. J Biomech. 1991;24(9):811-817.
1985	Attarian DE, McCrackin HJ, DeVito DP, McElhaney JH, Garrett WE Jr. Biomechanical characteristics of human ankle ligaments. Foot Ankle. 1985;6(2):54-58.
1993	Scott SH, Winter DA. Biomechanical model of the human foot: kinematics and kinetics during the stance phase of walking. J Biomech. 1993;26(9):1091-1104.
1998	Quapp KM, Weiss JA. Material characterization of human medial collateral ligament. J Biomech Eng. December 1998;120(6):757-763.
1990	Monleón Pradas M, Diaz Calleja R. Nonlinear viscoelastic behaviour of the flexor tendon of the human hand. J Biomech. 1990;23(8):773-781.
1999	Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech. April 1999;32(4):437-441.
1987	Nigul I, Nigul U. On algorithms of evaluation of Fung's relaxation function parameters. J Biomech. 1987;20(4):343-352.
1997	Beaugonin M, Haug E, Cesari D. Improvement of numerical ankle/foot model: modeling of deformable bone. In: Proceedings of the 41st Stapp Car Crash Conference. November 13-14, 1997; Lake Buena Vista, FL. Warrendale, PA: Society of Automotive Engineers:225-237. SAE 973331.
1997	Klopp GS, Crandall JR, Hall GW, Pilkey WD, Hurwitz SR, Kuppa SM. Mechanisms of injury and injury criteria for the human foot and ankle in dynamic axial impacts to the foot. In: Proceedings of the 1997 International IRCOBI Conference on the Biomechanics of Impact. September 24-26, 1997; Hannover, Germany.73-86.
1988	Siegler S, Block J, Schenck CD. The mechanical characteristics of the collateral ligaments of the human ankle joint. Foot Ankle. April 1988;8(5):234-242.
1992	Chimich D, Shrive N, Frank C, Marchuk L, Bray R. Water content alters viscoelastic behaviour of the normal adolescent rabbit medial collateral ligament. J Biomech. August 1992;25(8):831-837.
1984	Dortmans LJMG, Sauren AAHJ, Rousseau EPM. Parameter estimation using the quasi-linear viscoelastic model proposed by Fung. J Biomech Eng. August 1984;106(3):198-203.

Cited By (58)

Year	Entry
2016	Dekker TJ, Lampley AJ, Godin JA, Easley ME. Acute ankle instability/ankle sprains in athletes. In: Valderrabano V, Easley M, eds. Foot and Ankle Sports Orthopaedics. Cham, Switzerland: Springer International Publishing; 2016:249-256.
2003	Kerrigan JR, Ivarsson BJ, Bose D, Madeley NJ, Millington SA, Bhalla KS, Crandall JR. Rate-sensitive constitutive and failure properties of human collateral knee ligaments. In: Proceedings of the 2003 International IRCOBI Conference on the Biomechanics of Impact. September 25, 2003; Lisbon, Portugal.177-190.
2012	Meyer EG, Wei F, Button K, Powell JW, Haut RC. Determination of ligament strain during high ankle sprains due to excessive external foot rotation in sports. In: Proceedings of the 2012 International IRCOBI Conference on the Biomechanics of Injury. September 12-14, 2012; Dublin, Ireland.277-287.
2014	Lopez‐Valdes FJ, Lau SH, Riley P, Kent RW. Characterization of the in‐vitro dynamic behavior of the human thoracic spine in flexion. In: Proceedings of the 2014 International IRCOBI Conference on the Biomechanics of Injury. September 10-12, 2014; Berlin, Germany.145-165.
2016	Nie B, Panzer MB, Forman JL, Mane A, Mait AR, Donlon J, Kent RW. A fiber‐based modelling approach of ankle ligaments in situ. In: Proceedings of the 2016 International IRCOBI Conference on the Biomechanics of Injury. September 14-16, 2016; Malaga, Spain.941-943.
2020	Roberts CW, Kerrigan JR, Forman JL, Pipkorn B. Sensitivity of local male and female ankle geometries on soft tissue injury prediction metrics in morphed finite element models. In: Proceedings of the 2020 International IRCOBI Conference on the Biomechanics of Injury. 2020; Munich, Germany.215-216.
2022	Mukherjee S, Zeng W, Roberts CW, Caudillo AF, Forman JL, Panzer MB. Validation of small female foot and ankle finite element model under shod automotive loading environment. In: Proceedings of the 2022 International IRCOBI Conference on the Biomechanics of Injury. September 14-16, 2022; Porto, Portugal.197-214.
2023	Ruparel T, Hasija V, Takhounts E. Simulation based ankle injury evaluation using GHBMC modular human body models. In: Proceedings of the 2023 International IRCOBI Conference on the Biomechanics of Injury. September 13-165, 2023; Cambridge, United Kingdom.614-625.
2005	van Dommelen JAW, Ivarsson BJ, Jolandan MM, Millington SA, Raut M, Kerrigan JR, Crandall JR, Diduch DR. Characterization of the rate-dependent mechanical properties and failure of human knee ligaments. In: Proceedings of the SAE World Congress & Exhibition. April 11-14, 2005; Detroit, MI. Warrendale, PA: Society of Automotive Engineers. SAE 2005-01-0293.
2002	Tamura A, Omori K, Miki K, Lee JB, Yang KH, King AI. Mechanical characterization of porcine abdominal organs. Stapp Car Crash J. 2002;46:55-69. SAE 2002-22-0003.
2008	Hubbard RD, Quinn KP, Martinez JJ, Winkelstein BA. The role of graded nerve root compression on axonal damage, neuropeptide changes, and pain-related behaviors. Stapp Car Crash J. 2008;52:33-58. SAE 2008-22-0002.
2009	Kent R, Salzar R, Kerrigan J, Parent D, Lessley D, Sochor M, Luck JF, Loyd A, Song Y, Nightingale R, Bass CRD, Maltese MR. Pediatric thoracoabdominal biomechanics. Stapp Car Crash J. 2009;53:373-401. SAE 2009-22-0013.
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.
2009	Duenwald SE, Vanderby R Jr, Lakes RS. Constitutive equations for ligament and other soft tissue: evaluation by experiment. Acta Mech. 2009;205(1-4):23-33.
2019	Mack CD, Hershman EB, Anderson RB, Coughlin MJ, McNitt AS, Sendor RR, Kent RW. Higher rates of lower extremity injury on synthetic turf compared with natural turf among National Football League athletes: epidemiologic confirmation of a biomechanical hypothesis. Am J Sports Med. January 2019;47(1):189-196.
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.
2011	Wei F, Hunley SC, Powell JW, Haut RC. Development and validation of a computational model to study the effect of foot constraint on ankle injury due to external rotation. Ann Biomed Eng. February 2011;39(2):756-765.
2012	Shin J, Yue N, Untaroiu CD. A finite element model of the foot and ankle for automotive impact applications. Ann Biomed Eng. December 2012;40(12):2519-2531.
2017	Smolen C, Quenneville CE. A finite element model of the foot/ankle to evaluate injury risk in various postures. Ann Biomed Eng. August 2017;45(8):1993-2008.
2005	Holzapfel GA, Schulze-Bauer CAJ, Feigl G, Regitnig P. Single lamellar mechanics of the human lumbar anulus fibrosus. Biomech Model Mechanobiol. March 2005;3(3):125-140.
2009	Lucas SR, Bass CR, Crandall JR, Kent RW, Shen FH, Salzar RS. Viscoelastic and failure properties of spine ligament collagen fascicles. Biomech Model Mechanobiol. December 2009;8(6):487-498.
2014	Forestiero A, Carniel EL, Natali AN. Biomechanical behaviour of ankle ligaments: constitutive formulation and numerical modelling. Comput Methods Biomech Biomed Eng. March 12, 2014;17(4):395-404.
2015	Wei F, Fong DT-P, Chan K-M, Haut RC. Estimation of ligament strains and joint moments in the ankle during a supination sprain injury. Comput Methods Biomech Biomed Eng. February 17, 2015;18(3):243-248.
2020	Liu Y, Zhou Q, Gan S, Nie B. Influence of population variability in ligament material properties on the mechanical behavior of ankle: a computational investigation. Comput Methods Biomech Biomed Eng. February 2020;23(4):43-53.
2004	Bulter AM, Walsh WR. Mechanical response of ankle ligaments at low loads. Foot Ankle Int. January 2004;25(1):8-12.
2004	Gefen A, Margulies SS. Are in vivo and in situ brain tissues mechanically similar? J Biomech. September 2004;37(9):1339-1352.
2008	Imhauser CW, Siegler S, Udupa JK, Toy JR. Subject-specific models of the hindfoot reveal a relationship between morphology and passive mechanical properties. J Biomech. 2008;41(6):1341-1349.
2009	Kent RW, Woods WA, Salzar RS, Damon AM, Bass CR. The transient relationship between pressure and volume in the pediatric pulmonary system. J Biomech. August 7, 2009;42(11):1656-1663.
2004	Abramowitch SD, Woo SL-Y. An improved method to analyze the stress relaxation of ligaments following a finite ramp time based on the quasi-linear viscoelastic theory. J Biomech Eng. February 2004;126(1):92-97.
2004	Ledoux WR, Meaney DF, Hillstrom HJ. A quasi-linear, viscoelastic, structural model of the plantar soft tissue with frequency-sensitive damping properties. J Biomech Eng. 2004;126(6):831-837.
2017	Nie B, Panzer MB, Mane A, Mait AR, Donlon J-P, Forman JL, Kent RW. Determination of the in situ mechanical behavior of ankle ligaments. J Mech Behav Biomed Mater. January 2017;65:502-512.
2003	Gefen A. Plantar soft tissue loading under the medial metatarsals in the standing diabetic foot. Med Eng Phys. 2003;25(6):491-499.
2016	Ha CWS. A Subject-Specific Computational Model to Investigate an Ankle Inversion Ligamentous Sprain Injury and Evaluate the Intelligent Anti-Sprain System [PhD thesis]. The Chinese University of Hong Kong; October 2016.
2004	Imhauser CW. The Development and Evaluation of a 3-Dimensional, Image-Based, Patientspecific, Dynamic Model of the Hindfoot [PhD thesis]. Philadelphia, PA: Drexel University; August 2004.
2012	Luck JF. The Biomechanics of the Perinatal, Neonatal and Pediatric Cervical Spine: Investigation of the Tensile, Bending and Viscoelastic Response [PhD thesis]. Duke University; 2012.
2015	Wood GW. Interspecies Scaling in Blast Neurotrauma [PhD thesis]. Duke University; 2015.
2016	Grigoriadis G. Heel Biomechanics Under Blast Conditions [PhD thesis]. Imperial College London; June 2016.
2015	Smolen C. Evaluation of the Load Path Through the Foot/ankle Complex in Various Postures Through Cadaveric and Finite Element Model Testing [Master's thesis]. Hamilton, ON: McMaster University; September 2015.
2012	Wei F. Biomechanical Investigations and Computational Modeling of the Human Ankle [PhD thesis]. East Lansing, MI: Michigan State University; 2012.
2015	Button KD. Biomechanical Response of the Ankle to Excessive External Rotation [PhD thesis]. East Lansing, MI: Michigan State University; 2015.
2004	Abramowitch SD. An Evaluation of the Non-Linear Viscoelastic Properties of the Healing Medial Collateral Ligament [PhD thesis]. University of Pittsburgh; 2004.
2007	Papas NP. Potential of a Bioscaffold to Enhance the Healing of the MCL Following a Mop-End Tear: An Animal Model Study [Master's thesis]. University of Pittsburgh; 2007.
2001	Thomopoulos S. Supraspinatus Tendon to Bone Healing: Differences in Biomechanical, Structural, and Compositional Properties Due to a Range of Activity Levels [PhD thesis]. University of Michigan; 2001.
2011	Weber JF. Mechanical Property Quantification of Tendons Using Improved Methodologies [Master's thesis]. University of Guelph; February 2011.
2013	Kiapour A. Non-Contact ACL Injuries During Landing: Risk Factors and Mechanisms [PhD thesis]. University of Toledo; August 2013.
2008	Lucas SR. A Microstructural Viscoelastic Ligament Failure Model [PhD thesis]. Charlottesville, VA: University of Virginia; January 2008.
2009	Forman J. The Structural Characteristics of the Costal Cartilage: The Roles of Calcification and the Perichondrium, and the Representation of the Costal Cartilage in Finite Element Models of the Human Body [PhD thesis]. Charlottesville, VA: University of Virginia; August 2009.
2009	Parent DP. Scaling and Optimization of Thoracic Impact Response in Pediatric Subjects [Master's thesis]. Charlottesville, VA: University of Virginia; 2009.
2011	Shin J. Injury and Response of Human Ankle and Subtalar Joints Under Complex Loading [PhD thesis]. Charlottesville, VA: University of Virginia; December 2011.
2013	Lopez-Valdes FJ. Mechanics of the Pediatric Thoracic Spine and Its Role in the Kinematics of the Head in Automotive Frontal Impacts [PhD thesis]. Charlottesville, VA: University of Virginia; May 2013.
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.
2020	Giudice JS. Personalized Finite Element Modeling of the Brain: Understanding Subject-Specific Deformation Patterns [PhD thesis]. Charlottesville, VA: University of Virginia; December 2020.
2008	Manoogian SJ. Protecting the Pregnant Occupant: Dynamic Material Properties of Uterus and Placenta [PhD thesis]. Virginia Polytechnic Institute and State University; May 29, 2008.
2021	Rezvani SN. Novel Preclinical Approaches to the Understanding and Treatment of Achilles Tendinopathy [PhD thesis]. Virginia Polytechnic Institute and State University; May 2021.
2002	Mkandawire C. The Relationship Between Viscoelastic Relaxation and Ligament Morphometry [PhD thesis]. University of Washington; 2002.
2019	Berardo-Cates A. Development of Methods for Characterizing Ankle Ligament Viscoelastic Properties [Master's thesis]. University of Washington; 2019.
2002	Lee JB. Development of a Finite Element Model of the Human Abdomen [PhD thesis]. Detroit, MI: Wayne State University; 2002.
2011	Duenwald-Kuehl S. Characterization of Tendon Mechanics: Experiment, Modeling, and Noninvasive Methods [PhD thesis]. University of Wisconsin – Madison; 2011.