Structural Constitutive Models for Knee Ligaments

It has been estimated that approximately 375,000 people experience knee injuries every year in the United States. The majority of the pathologies affect the anterior cruciate ligament (ACL) and the medial collateral ligament (MCL). Thus, a thorough characterization of the mechanical properties of the ligaments is needed to understand the etiology of their injuries and to improve the strategies of their treatment. The first chapter of this dissertation offers a brief overview of the morphology and mechanics of the ligaments.

Since injuries are estimated to occur at strain rates that range from 50%/s to 150, 000%/s, studying the mechanical behavior of ligaments at various strain rates is imperative. In the second chapter, a structural constitutive model is formulated by taking into account the non-linearity, anisotropy, incompressibility, and strain rate-related properties of the ligaments. The collagen fibers, which comprise the ligament, are assumed to be the only load-bearing component of the tissue. They are oriented in various directions, undulated in the stress-free configuration, and they gradually become straight upon deformation. Moreover, the collagen fibers are characterized by a Kelvin-Voigt-type viscoelastic behavior. The fiber spatial orientation and gradual recruitment are represented statistically by probability density functions. Published experimental data on the ACLs are used to assess the constitutive model.

The most severe of the knee ligament injuries are partial and complete tears. Thus, there is a compelling need to understand the mechanical failure behavior of ligaments. In the third chapter, a structural constitutive model for the description of the ligament tensile properties is proposed. The model reproduces the three-regions of the nonlinear stress-strain relationship of ligaments. The collagen fibers contribute to the overall tissue’s response after becoming taut and before failing and they are assumed to behave as a linear elastic material. The fiber recruitment and failure processes are stochastically defined. Available experimental data for the MCLs are employed to validate the constitutive relation. Furthermore, the generalization to a three-dimensional model is also given.

Future research directions toward the development of a structural constitutive model for the subfailure behavior of ligaments are indicated in the fourth chapter and conclusions are drawn in the fifth chapter.

Year	Entry
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1980	Kastelic J, Palley I, Baer E. A structural mechanical model for tendon crimping. J Biomech. 1980;13(10):887-893.
2001	Provenzano P, Lakes R, Keenan T, Vanderby R Jr. Nonlinear ligament viscoelasticity. Ann Biomed Eng. October 2001;29(10):908-914.
1982	Sanjeevi R. A viscoelastic model for the mechanical properties of biological materials. J Biomech. 1982;15(2):107-109.
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.
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.
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Year

Entry

1976

Crowninshield RD, Pope MH. The strength and failure characteristics of rat medial collateral ligaments. J Trauma. February 1976;16(2):99-105.

1980

Kastelic J, Palley I, Baer E. A structural mechanical model for tendon crimping. J Biomech. 1980;13(10):887-893.

2001

Provenzano P, Lakes R, Keenan T, Vanderby R Jr. Nonlinear ligament viscoelasticity. Ann Biomed Eng. October 2001;29(10):908-914.

1982

Sanjeevi R. A viscoelastic model for the mechanical properties of biological materials. J Biomech. 1982;15(2):107-109.

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.