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Fundamental Aspects in Modelling the Constitutive Behaviour of Fibered Soft Tissues

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Abstract

Fibered soft tissues like ligament, tendons, cartilage or those composing the cardiovascular system among others are characterized by a complex behaviour derived from their specific internal composition and architecture that has 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 essential in predicting possible failure (i.e., aneurisms, atherosclerotic plaques, ligaments rupture) or the evolution of their microstructure under changing mechanical environment (i.e. cardiac aging, atherosclerosis, ligament remodeling). As structural materials, fibered soft tissues undergo large deformations even under physiological loads and are almost incompressible and highly anisotropic, mainly due to the directional distribution of the different composing families of collagen fibers. In addition, they are non-linearly elastic under slowly-acting loads, viscoelastic, due both to the moving internal fluid in some tissues (i.e. cartilage) or to the inherent viscoelasticity of the solid matrix. They are also subjected to non-negligible initial stresses due to the growth and remodeling processes that act along their whole live. Finally, they are susceptible to suffer damage induced by the rupture of the fibers or tearing of the surrounding matrix. All these aspects should be considered for a full description of the constitutive behaviour of these materials, requiring an appropriate mathematical formulation and finite element implementation to get efficient simulations useful for a better understanding of their phsyiological function, the effect of pathologies or surgery as well as for surgery planning and design of implants among many other usual applications. In this work, formulations of all the different phenomena commented above in fibered soft tissues are presented. The effect of each of these aspects is analyzed in simplified examples to demonstrate the applicability of the models. Finally, different applications of clinical interest are discussed.

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Notes

  1. 1.

    Notice that x is a dummy variable used for integration purposes.

  2. 2.

    Note that, thinking about the numerical implementation of this procedure, the elastic strain tensor \(\boldsymbol{F}_{\mbox{ cp}}\) corresponds to the strain field associated to the displacement needed to make ℬ rs to satisfy the equilibrium equations. Thus, it constitutes an output of the Finite Element Method.

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Acknowledgements

The authors gratefully acknowledge research support from the Spanish Ministry of Science and Technology through the research projects DPI2011-27939-C02-01, DPI2011-15551-E and DPI2010-20746-C03-01, and the CIBER-BBN initiative.

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Authors and Affiliations

  1. Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain

    Begoña Calvo & Estefanía Peña

  2. Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Barcelona, Spain

    Begoña Calvo & Estefanía Peña

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  1. Begoña Calvo
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  2. Estefanía Peña
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Correspondence to Estefanía Peña .

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Editors and Affiliations

  1. Facultad de Ciencias, Universidad de Málaga, Málaga, Málaga, Spain

    Carlos Parés

  2. Facultad de Informática, Universidade da Coruña, A Coruña, La Coruña, Spain

    Carlos Vázquez

  3. Centre de Mathématiques Appliquées, CNRS and Ecole Polytechnique, Paris, Paris, France

    Frédéric Coquel

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Calvo, B., Peña, E. (2014). Fundamental Aspects in Modelling the Constitutive Behaviour of Fibered Soft Tissues. In: Parés, C., Vázquez, C., Coquel, F. (eds) Advances in Numerical Simulation in Physics and Engineering. SEMA SIMAI Springer Series, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-02839-2_1

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