A mathematical model for viscoelastic properties of biological soft tissue

A quaternary viscoelastic structure model with two characteristic times is presented to describe the viscoelastic properties of parallel-fibered collagen tissue. The comparison results of model prediction and experimental data of rabbit medial collateral ligaments show that the model could accurately describe viscoelastic behavior such as stress-relaxation, strain-strengthening and creep of bio-soft-tissue within a small scope of errors. To study the biomechanical mechanism of viscoelasticity that biological soft tissue shows, the influence of model parameters on viscoelastic behavior of bio-soft-tissue is analyzed and researched, which indicated that the major influential elements of stress-relaxation in bio-soft-tissue are elastic modulus, relaxation time and strain rate of proteoglycan-rich matrix. The influence of elastic modulus of collagen fibers on stress-relaxation is not significant. However, the nonlinearity of stress–strain curve and viscoelastic behavior of bio-soft-tissue mostly depends on recruitment and reorientation of collagen fibers under external loading.