An Evaluation of the Quasi-Linear Viscoelastic Properties of the Healing Medial Collateral Ligament in a Goat Model

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Abstract
The viscoelastic properties of the healing medial collateral ligament (MCL) at 12 weeks after isolated injury were investigated in a goat model. The stress-strain relationships, static and cyclic stress-relaxation behaviors of the healing MCL up to 5% strain were determined experimentally using a femur-MCL-tibia complex. These experimental data were used in combination with the quasi-linear viscoelastic (QLV) theory of Fung (1972) to characterize the reduced relaxation function, G(t) (described by constants C, tau1, and tau2) and the elastic response, sigmae(epsilon) (described by constants A and B) of this tissue. It was found that the percentage of stress relaxation for the healing MCLs was significantly greater than those for sham-operated controls (49.0 +/- 12.1% vs. 26.5 +/- 8.1%, respectively; p < 0.05). The product of constants A x B, i.e. the initial slope of the stress-strain curves, was found to be significantly lower for healing MCLs compared to those for sham-operated controls (32.9 +/- 15.8 MPa vs. 118.8 +/- 48.3 MPa; p < 0.05). The dimensionless constant C, i.e. the magnitude of the viscous response, was nearly three times greater for healing MCLs, while constant tau1 was found to be similar between the two groups (0.80 +/- 0.43 s vs. 0.89 +/- 0.52 s, respectively). Constant tau2 for the healing MCL was significantly less than the controls (1269 +/- 38 s vs. 1845 +/- 431 s; p < 0.05) indicating that the stress relaxation reached a plateau earlier. These constants of the QLV theory used to describe the healing MCL were validated for the strain level utilized in this experiment (approximately equal to 4.5%) by predicting the peak stresses during a cyclic stress-relaxation experiment. The theoretically determined values closely matched the experimentally measured values. Thus, this study demonstrates that the QLV theory could be successfully used to describe the viscoelastic behavior of the MCL during the early phases of healing.
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