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On the Theories and Numerics of Continuum Models for Adaptation Processes in Biological Tissues

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Abstract

Computational continuum mechanics have been used for a long time to deal with the mechanics of materials. During the last decades researches have been using many of the theoretical models and numerical approaches of classical materials to deal with biological tissue which, in many senses, are a much more sophisticated material. We aim to review the last achievements of continuum models and numerical approaches on adaptation processes in biological tissues. In this review, we are looking, in particular, at growth in terms of changes of density and/or volume as, e.g., in collagen remodeling, wound healing, arterial thickening, etc. Furthermore, we point out some of the most relevant limitations of the current state-of-the-art in terms of these well established computational continuum models. In connection with these limitations, we will finish by discussing the trend lines of future work in the field of modeling biological adaptation, focusing on the computational approaches and mechanics that could overcome the current drawbacks. We would also like to attract the attention of all those researchers in classical materials (metal, alloys, composites, etc), to point out how similar the continuum and computational models between our fields are. We hope we can motivate them for getting their expertize in this challenging field of research.

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Acknowledgments

P. Saez acknowledges support from the Spanish Ministry of Research and Innovation through the Grant BES-009-028593 through which part of the research was conducted. P.S. also acknowledge Prof. Martinez and Prof. Pena for discussion and supervision. A special acknowledge also for Prof. Kuhl for many discussions and help during the last years.

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Saez, P. On the Theories and Numerics of Continuum Models for Adaptation Processes in Biological Tissues. Arch Computat Methods Eng 23, 301–322 (2016). https://doi.org/10.1007/s11831-014-9142-8

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