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Research Papers

# Characterization of the Fatigue Behavior of the Medial Collateral Ligament Utilizing Traditional and Novel Mechanical Variables for the Assessment of Damage Accumulation

[+] Author and Article Information
Michelle L. Zec

Department of Orthopaedics, Faculty of Medicine, University of British Columbia, 3415-910 West 10th Avenue, Vancouver, BC, V5Z 4E3, Canadazec@interchange.ubc.ca

Paul Thistlethwaite

ARTORG Center for Biomedical Engineering Research, University of Bern, Staufacherstrasse 78, Bern 3014, Switzerlandpaul_t@bluewin.ch

Cyril B. Frank

Department of Surgery, McCaig Institute for Bone and Joint Health, University of Calgary, 3330 Hospital Drive Northwest, Calgary, AB, T2N 4N1, Canadacfrank@ucalgary.ca

Nigel G. Shrive

Department of Civil Engineering, McCaig Institute for Bone and Joint Health, University of Calgary, 2500 University Drive Northwest, Calgary, AB, T2N 1N4, Canadangshrive@ucalgary.ca

J Biomech Eng 132(1), 011001 (Dec 01, 2009) (8 pages) doi:10.1115/1.4000108 History: Received June 15, 2008; Revised June 26, 2009; Posted September 01, 2009; Published December 01, 2009; Online December 01, 2009

## Abstract

Ligaments are regularly subjected to repetitive loading in vivo. Typically, mechanical studies focus on repetitive loading protocols of short duration, while those characterizing damage accumulation over a longer duration (i.e., fatigue studies) are lacking. The aims of this study were as follows: (a) to demonstrate that damage does accumulate in ligament tissue subjected to repetitive loading and (b) to evaluate existing and new methods for characterizing fatigue damage accumulation. It was hypothesized that ligaments would accumulate damage with repetitive loading as evidenced by failure at stresses well below ultimate tensile strength, creep curve discontinuities, and by reductions in stiffness during loading. Eight normal medial collateral ligaments from female New Zealand white rabbits were cycled in tension, between 0 MPa and 28 MPa, to failure or until 259,200 cycles, whichever came first. Medial collateral ligaments that did not fail were subsequently loaded to failure. Displacement rates $(dlmax/dt)$ as well as primary, secondary, and tertiary creeps were monitored as indices of damage accumulation and impending mechanical failure. Additionally, the relative utilities of tangent, secant, and chord stiffness parameters were critically evaluated. Finally, new uses for the second derivative of force-displacement data were explored. Three out of eight ligaments failed during testing, demonstrating that ligaments can fail in fatigue under moderate tensile stress in vitro. The evaluation of displacement rates $(dlmax/dt)$, as well as primary through tertiary creep patterns, were not well suited to predicting failure in normal ligaments until rupture was all but imminent. Tangent stiffness, which was calculated from a mathematically defined start of the “linear region,” was surprisingly constant throughout testing. Secant stiffness dropped in a predictable fashion, providing a global indicator of tissue stiffness, but did not provide any insight into fiber mechanics. Chord stiffness, on the other hand, appeared to be sensitive to fiber recruitment patterns. The second derivative of force-displacement data proved to be a useful means of (a) objectively defining the start of the linear region and (b) inferring changes in fiber recruitment patterns within ligament tissue. Tangent, secant, and chord stiffnesses highlight different attributes of ligament responses to loading; hence these parameters cannot be used interchangeably. Additionally, the second derivative of the force-displacement curve was introduced as a useful descriptive and analytical tool.

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## Figures

Figure 1

Plot of force versus displacement and the second derivative versus displacement. A spline curve of force versus time is depicted by the darker line and its second derivative (d2F/dl2) is depicted by the lighter (hatched) line. Data for one sample are shown. Note: Y-axes not to the same scale.

Figure 2

Schematics depicting the calculation of secant stiffness from 0 mm and chord stiffness from lmin, where C1 is the first cycle of loading, Ci is the ith cycle of loading, and lmin,i is the minimum displacement on the ith cycle of loading.

Figure 3

Peak cyclic displacement: mean values for six samples are depicted. Standard deviations (SDs) ranged initially from ±0.2 mm/s to ±0.5 mm/s for cycle 104,400. Data were fit to the regression line shown (solid line). Lower right: equation of regression line.

Figure 4

Second derivative of the peak displacement versus time curve for one representative sample. Inset (lower left): first 300 s of loading. Inset (upper right): last 300 s of loading. Sample failed after 114,326 load cycles. A creep curve discontinuity occurred during early loading (∼475 s) and is denoted by the larger blue arrow. Note: Noise is amplified with differentiation, hence the small scatter in values in the vicinity of zero.

Figure 5

Tangent, secant, and chord stiffnesses versus time. Standard deviations for these plots ranged from a minimum value of ±11 N/mm to a maximum value of ±20 N/mm. Note: Y-axis begins at 20 N/mm.

Figure 6

Plots of d2F/dl2 versus displacement. Maximum mean values for d2F/dl2 are shown in chronological order (from left to right). ‘†’ denotes a statistically significant difference between intervals. SDs for d2F/dl2max ranged from ±33 N/mm2 to ±42 N/mm2(n=6).

Figure 7

Plot of d2F/dl2 versus displacement for a ligament cycled in iso-osmotic solution (C30). The bars represent an estimate of recruitment obtained by calculating Δk/Δkmax for the one hundred intervals shown. The summation of all of the values is 100%. The simplest interpretation of this presupposes that fibers have a relatively uniform cross-sectional areas and similar values of tensile modulus.

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