Modelling living tissues. Mechanical and mechanobiological aspects
Manuel Doblaré
Group of Structural Mechanics and Materials Modelling (GEMM)
Aragón Institute of Engineering Research (I3A). University of Zaragoza
Centro de Investigación en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN)
Campus Rio Ebro, Agustín de Betancourt Bldg
María de Luna, s/n. Zaragoza 50018 (Spain)
Email: mdoblare@unizar.es
Summary
Modelling biological tissues is multiphysical in nature, with a strong dependence on the underlying microstructure that leads to complex constitutive behaviours. The main goal of this work is to show the principal differences and similarities between standard engineering materials and living tissues from a structural point of view, with special emphasis on modelling aspects and the associated computational implementation. Both hard and soft tissues are addressed.
With respect to the former, bone is a multiphasic, heterogeneous, anisotropic and self-adaptive material. It is able to modify its microstructure and properties according to the specific mechanical environment. This adaptative process, known as bone remodelling, has a key role in calcium homeostasis and prevention of stress fractures. Finally, once a fracture occurs, healing is activated. Fracture healing is a complex biological phenomenon involving several cellular process partially controlled by the applied load and the stability of the fracture site. Modelling these mechanobiological problems follows the classical theory of multiphasic continuous media, including the influence of extracellular matrix composition and cell population bahaviour. Ssimplified formulations have been implemented into a finite element context that allow predicting the evolution of the factors such as growth, cellular proliferation, migration, differentiation or death, and tissue pattern formation.
On the other hand, soft tissues like ligament, cartilage or arteries among others, as structural materials, 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 fibres. In addition, they are non-linearly elastic, viscoelastic, subjected to non-negligible initial stresses and susceptible to be damaged. All these aspects should be considered for a full description of these materials which leads to a complex formulation that needs appropriate mathematical approaches and finite element implementation to get efficient simulations. The effect of each of these aspects on the overall response of soft tissues is commented and different applications of clinical interest are discussed.
References
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