Finite element analysis of strain-stiffening behaviors of tendons: Compared with shear wave elasticity imaging

The strain-stiffening property of tendons is a key feature to prevent muscle from damage during vigorous contraction. Tendon injuries are usually associated with declination of such property. Shear wave elasticity imaging (SWEI) has emerged as a promising tool to non-invasively evaluate this property in injured tendons and monitor its deterioration or recovery after treatment. In our previous work, we found that the shear wave velocities increase linearly when tendons subjected to increasing loads. However, the Young´s modulus derived from shear wave velocities (i.e. E=3ρv₂²) can´t be coincided with the Young´s modulus measured by uniaxial tensile test. In other words, there are few quantitative models available to interpret the SWEI results measured in tendons due to their complex architecture and nonlinear mechanical behaviors. In this study, we developed a numerical model using ABAQUS to characterize the non-linear and strain-stiffening properties of tendons measured from SWEI and mechanical stretching tests. Normal and injured tendons were modeled based on the material properties measured from experiments. An anisotropic hyperelastic model was employed and shear wave propagation was simulated in the modeled tendons when they were pre-stretched by loads varying from 0 to 3 N. Our preliminary results successfully recapitulated the trend of changes of shear wave velocities with respect to different pre-stretches observed in SWEI. The simulated velocity of shear waves propagating along the longitudinal axis of the control tendons increased from 15.9 to 23.61 m/s. On the other hand, the simulated velocity of shear waves propagating along the longitudinal axis of the injured tendons increased from 14.26 to 16.43 m/s. In addition, both the shear wave velocities and tensile moduli of the normal/injured tendons increased as the pre-stretches increased. Our work provides a quantitative basis to explain the strain-stiffening behaviors of t- ndons measured by SWEI and highlights the potential of applying SWEI to quantitatively assess mechanical dysfunction of injured tendons.