How Frequency Affects Fatigue Testing of an Artificial Disc With a Viscoelastic Polymer Core

Abstract

The purpose of this study was to determine the highest appropriate test frequency for a viscoelastic total disc replacement (VTDR). Natural intervertebral discs display viscoelastic behavior. Viscoelasticity is the time-dependent property of a material to show sensitivity to the rate of loading or deformation, having stress and strain reactions that are out of phase. If frequency is too high during mechanical testing of a viscoelastic polymer or medical device, the specimen is unable to recover fully before the next load application. Polymers absorb energy with each cycle. Since work (or energy utilized) is defined as the area under the force–displacement curve [Giordano, N. J., College Physics: Reasoning and Relationships, Brooks/Cole Publishing, Pacific Grove, CA, 2010], a frequency increase which decreases displacement will by definition also decrease the energy the polymer is using to achieve that decreased displacement. By reducing both total displacement and energy, a high test frequency would “protect” a viscoelastic device. A frequency of 2 Hz was used to determine the expected response of the VTDR during axial compression testing between 400 and 4000N. The response was defined as mean peak-to-peak displacement of five test cycles after 1000 cycles of preconditioning. Comparative data was collected at test frequencies of 3, 6, and 10 Hz. Displacement and energy utilized decreased with increasing test frequency. There were no significant differences between the viscoelastic responses in tests at 2 and 3 Hz. However, there were significant decreases in displacement and energy utilized at 6 and 10 Hz compared to 2 Hz. Over a 10 × 106 million cycle fatigue test, for this device, the total displacement would be 548 000mm less at 6 Hz and 988 000mm less at 10 Hz compared to 2 Hz. By decreasing the displacement, by definition it decreases the amount of overall work the disc has done when tested at these high frequencies [Giordano, N. J., College Physics: Reasoning and Relationships, Brooks/Cole Publishing, Pacific Grove, CA, 2010]. Viscoelastic devices should not be tested at high frequencies which “protect” the device by reducing the energy the device has to use overall by decreasing the total displacement it sees. To accurately evaluate in vivo behavior, fatigue testing should utilize test frequencies which do not significantly change the device’s viscoelastic response from that experienced at a physiologic loading frequency.