Three-dimensional constitutive finite element modeling of the Achilles tendon

Tendons connect muscles to bones enabling efficient locomotion. This study focuses on the Achilles tendon, which is the strongest tendon in the body and fundamental for activities like walking, running and jumping. The Achilles tendon is the most frequently subjected tendon when it comes to injuries and ruptures. The best treatment is still debated, because the biomechanics of the tendons is not yet well understood. Tendons consist of a complex structure of highly organized collagen fibers embedded in a hydrated matrix. Various material models have tried to represent the viscoelastic and highly non-linear behaviour of tendons. By using accurate material models, computer simulations can be used to predict the behaviour of materials under different loading conditions and to provide extensive information about the mechanical response. This study further develops an existing two-dimensional fiber- reinforced poroviscoelastic model of the Achilles tendon. The model considered that the tendon was a material consisting of collagen fibers, a non fibrillar matrix and fluid flow. All three components were contributing to the total stresses in the tendon. The existing model gave good representations of the stresses, but did not predict physiological direction of the fluid flow. Moreover, for an accurate analysis of the stresses and the fluid flow inside the tendon, the model should be able to be applied to the realistic three-dimensional geometry of the Achilles tendon. Therefore, this study aimed to modify the existing model to make it suitable for three-dimensional geometries and to substitute the isotropic constitutive model of the fibrillar matrix with an orthotropic constitutive model to predict a physiological direction of the fluid flow. The new model was validated against experimental data from rat Achilles tendons subjected to cyclic tensile loading tests by optimizing the material parameters of the model. Comparing the developed model with the previous one, the results showed that the three-dimensional finite element formulation generally behaves very similarly to the two-dimensional model. However, it predicts slightly lower hydrostatic pressure, but higher fluid flux. The introduction of an orthotropic matrix influenced the predictions more significantly. The stresses were higher, especially in the matrix, and the prediction of the direction of fluid flow resembled physiological flow. Hence, the flux and the hydrostatic pressure also assumed a physiological behaviour. The ability of the new model to fit the experimental data remained nearly unchanged. Therefore, the ability of the model to provide information about the mechanics of the Achilles tendon under cyclic loading has been improved. Future work could improve also the mechanics of the fibrillar part and model the interaction between the different components.Three-dimensional constitutive finite elementmodelling of the Achilles tendon The Achilles tendon is the largest tendon in the human body and it is commonly injured. However, the efficiency of todays treatments is not well established, because the biomechanical behaviour of tendons is not entirely understood. Computational modeling can provide useful information about tendon mechanics