Modeling tendon viscoelastic properties using a system identification approach

Viscoelasticity is characteristic of tendon mechanical behavior and is thought to reflect underlying structure, which can change with exercise, aging and pathology. We used ramp stretch experiments to measure the stress-relaxation response of rat tail tendon fascicles. System identification methods were applied to fit viscoelastic models to these measurements, enabling exploration of several possible viscoelastic model structures and quantification of the models' viscoelastic parameters. While tendons have been modeled as springs or quasi-linear viscoelastic materials, we found that tendons are well fit by a viscoelastic model consisting of a single Kelvin-Voigt (KV) element in series with a spring. From the viscoelastic model structure, we can predict tendon behavior beyond experimental measurements, providing insight into muscle-tendon interactions. The model comprising a series KV element and spring exhibits a force-frequency relationship that may protect muscles from high frequency damage and implies that most of the energy storage and power amplification of tendons is provided by the extracellular matrix rather than collagen fibers. The elastic modulus of the KV element was similar to that of single collagen fibers and increased with genipin treatment but not age. The elastic modulus of the series spring increased with age but not genipin treatment. The time constant of stress-relaxation increased over time, suggesting that rat tail tendon fascicles are more like amorphous polymers than quasi-linear viscoelastic materials. This approach revealed previously unknown properties of tendons which demonstrate that they are exquisitely designed to protect muscles and recover elastic energy across timescales.