Keywords: soft tissues, finite element, anisotropic hyperelasticity, viscoelasticity, initial strains, blood vessels, ligaments, preoperative planning.

Fibrous soft tissues like ligament, cartilage or cardiovascular tissues among others are characterized by a complex behaviour derived from their specific internal composition and architecture that have to be considered when trying to simulate their response under physiological or pathological external loads, their interaction with external implants or during and after surgery. The evaluation of the acting stresses and strains on these tissues is also essential in predicting possible ruptures (i.e. aneurisms, atherosclerotic plaques, ligaments rupture) or the evolution of their microstructure under changing environments (i.e. cardiac aging, atherosclerosis).

As structural materials, fibrous soft tissues undergo large deformations even under physiological loads and are almost incompressible and anisotropic, mainly due to the directional distribution of the different composing families of fibers. In addition, they are non-linearly elastic under slowly-acting loads, viscoelastic, due to the moving internal fluid found in cartilage or to the inherent viscoelasticity of the solid matrix found in ligaments. They are also subjected to non-negligible initial stresses due to growth and remodelling that act throughout their whole life. Finally, they are susceptible to suffering damage induced by the rupture of the fibers or the tearing of the surrounding matrix. All these aspects should be considered during a full description of these materials which leads to a complex formulation that needs an appropriate mathematical formulation and finite element implementation to achieve efficient simulations of processes like balloon angioplasty, stenting, clamping, anastomosis or ligament repair.

In this chapter, formulations for all the different phenomena commented upon above in fibrous soft tissues are presented. The effect of each aspect is analysed in simplified examples to demonstrate the validity of the results. Finally, different applications of clinical interest are presented and discussed.

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