| OCR Text |
Show Strain-And Rate-Dependent Viscoelastic Properties of Human MCL in Tension Introduction: Ligament viscoelasticity is an important determinant of tissue response to rapid loading and potential for injury, and may also play a role in tissue nutrition via fluid movement during loading/unloading. Small sinusoidal perturbations about an equilibrium strain value allow application of linear viscoelasticity theory for determination of dynamic stiffness and phase as a function of frequency and equilibrium strain level. With these data, one can assess the appropriateness of different viscoelastic and/or poroelastic models to describe time- and rate-dependent constitutive behavior. The objective of this study was to quantify the strain- and rate-dependent viscoelastic behavior of the human medial collateral ligament (MCL) in tension along its long axis. Our hypotheses were that the dynamic stiffness would increase modestly with strain rate and strain level, and that the phase would remain relatively constant with strain rate but decrease with increasing strain level. Methods: Five human MCLs were used in this study (44.6±20.8 yrs). The right or left MCL was chosen at random to be used for collecting a longitudinal tensile test specimen. A dumbbell-shaped steel punch (gauge dimensions 2x10 mm) was used to harvest a tensile test specimen from the MCL. Initial width and thickness were measured using digital calipers, and cross-sectional area was calculated assuming a rectangular shape. Tensile Specimens. After harvest, longitudinal tensile specimens were loaded into a pair of custom clamps attached to a servomotor/screw drive system. Load was measured with a 44 N load cell and elongation was monitored with an LVDT. The zero-load length was established by consecutively applying and removing a 0.5 N tare load. The test protocol consisted of incremental stress relaxation tests followed by cyclic loading at different frequencies using a sinusoidal displacement waveform. Specimens were first stretched to 2% strain at 1%/sec, allowed to stress relax for 25 minutes, and then subjected to sinusoidal oscillations about the 2% strain level (amplitude = ±0.5%) at rates of 0.01, 0.1, 1, 5, 10 and 15 Hz. Ten cycles were repeated at each frequency. After completion, the entire protocol was repeated for equilibrium strain levels of 4 and 6%. Relaxation times at 4 and 6% were increased to 35 and 45 minutes, respectively, to allow for the longer relaxation time constants at these strain levels. Specimens were kept continuously moist with sprays of 0.9% N saline during testing. Load and displacement profiles were converted to stress and strain, respectively. The peak and equilibrium stresses from the stress relaxation tests were determined at 2%, 4%, and 6% strain. The cyclic strain- and stress-time data were fit to a sine function to determine the amplitude (A) and phase (f). This was performed for each frequency at each equilibrium strain level. The dynamic stiffness M (MPa) and phase q (radians) were calculated as: Statistical Analysis: Two-way repeated measures ANOVAs were used to test for the effect of strain level and strain rate on the dynamic stiffness and phase. Statistical significance was set at p£0.05. When significance was detected, Tukey tests were performed between different levels of a factor. Results: The dynamic stiffness showed a mild positive slope on a log-log plot (Fig 2), indicating a stiffening effect with increasing frequency (p<0.001). There was a continuous increase in dynamic stiffness with equilibrium strain (p<0.001), indicating that the material is nonlinear viscoelastic. The phase was always small and positive. Lower positive values describe less material damping, indicative of solid behavior, while higher values indicate a more viscous behavior. The phase initially showed a drop with increasing frequency up to 1 Hz, but this was followed by a marked increase up to 15 Hz (Fig 2). This suggests that the material is more viscous at slow and fast strain rates. There was a significant effect of frequency on the phase (p<0.001) but no effect on strain level (p=0.263). Figure 1: Peak and equilibrium stress vs. applied strain (mean±std. err). Typical data for stress and strain vs. time for one sample. Figure 2: Dynamic stiffness and (Right) phase as a function of frequency for longitudinal tensile test specimens of the human MCL (mean±std. error). Discussion: The results of this study clearly demonstrate the nonlinear viscoelastic behavior of human MCL. Not only does the material stiffen with increasing strain rate and equilibrium strain level, but it also shows a highly nonlinear phase behavior with fluid-like behavior at both low and high frequencies. Future studies will examine the viscoelastic response in the transverse and shear modes of loading. These data will allow the formulation of three-dimensional viscoelastic constitutive models for the human MCL. Acknowledgements: Financial support from NIH grant #AR47369 is gratefully acknowledged. Thanks to Mike Small for help with data analysis. Spencer P. Lake Class Standing: Junior Major: Bioengineering E-mail: spencelake@hotmail.com Faculty Sponsor: Jeffrey A. Weiss, Assistant Professor Bioengineering E-mail: jeff.weiss@utah.edu |
