Evolutional growth and remodeling in multiphase living tissue T. Ricken a, * , J. Bluhm b a Computational Mechanics, University of Duisburg-Essen, Campus Essen, 45117 Essen, Universitätsstr. 15, Germany b Institute of Mechanics, University of Duisburg-Essen, Campus Essen, 45117 Essen, Universitätsstr. 15, Germany article info Article history: Received 30 November 2007 Received in revised form 20 October 2008 Accepted 21 October 2008 Available online 17 December 2008 PACS: 05.70.Fh 87.19.R 87.85.G 81.10.Jt Keywords: Multiphase model Phase transition Growth Remodeling Porous Media Living tissue abstract It is well-known that biological systems have the capacity to change their inner structure and shape for an optimized load transfer. This paper deals with the development of a multiphase model to describe the growth and remodeling phenomenon in biological systems in order to learn more about the biological optimization mechanisms. A continuum triphasic model (i.e., a solid having interstitial space filled with water containing nutrients) based on the multiphase Theory of Porous Media (TPM) is proposed to pro- vide a thermodynamically consistent description of the growth and remodeling phenomenon. The con- stitutive modeling of stress–strain- or nutrient-driven growth and remodeling phenomena is discussed. Finally, the influence of different driving mechanisms for growth is demonstrated by three illustrative exemplary problems. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Living tissue consists of different phases and components in solutions. Even in the case that all interactions between these ingredients are known, and that is by far not the case, the solution of the coupled system of equation is not feasible. From this we di- vide the tissue into three different main groups; a solid phase, a fluid phase and a nutrient phase. All existing phases and compo- nents are subgroups of the defined main groups. Although the divi- sion is coarse, the model allows a deeper understanding in the functionality of the tissue, especially in contrast to a one-compo- nent approach. Fist of all, the apparent viscoelasticity of tissue is a combination of a fluid flow-dependent and a fluid flow-indepen- dent mechanism, see i.e., DiSilvestro and Suh [12], and that is obvi- ously not describable using a one-component approach. Secondly, the remodeling and growth processes underly the restriction of mass transfer and phase transition. It is impossible to balance the mass exchange and control the phase transition by using an open system approach with a one-component material. Although the proposed three phase model is far from capturing all the mechanisms that occur during the phase transition, it provides a more detailed insight into the functionality of living tissue. In general, growth and remodeling in living tissue are continu- ous processes and the results of a time dependent phase-conver- sion between tissue cells and nutrients, by which the nutrients themselves can be transported through the tissue. Overall, we con- sider that biological tissues consist mostly of multi-component materials, frequently exhibiting an anisotropic internal structure plus reaction to changing load cases with internal biological and/ or chemical activities. Growth processes in living tissues are driven by mechanical, chemical, genetic, metabolic, and hormonal influences. Due to the lack of detailed knowledge and specific parameters with which to quantify all these influences, a holistic numerical simulation cannot currently be provided. However, the capability of tissue to remodel its structure and density due to a changing stress state has been well-known for over a century. The precondition for tis- sue growth is the existence of growth material like nutrients. Therefore, a triphasic calculation concept for the description of stress and nutrient induced growth based on the well established Theory of Porous Media will be presented in this paper. In terms of comprehensive overviews of the experimental find- ings of the growth phenomenon, the reader refers to, e.g., Fung 0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.10.016 * Corresponding author. Tel.: +49 201 1832681; fax: +49 201 1832680. E-mail address: tim.ricken@uni-due.de (T. Ricken). Computational Materials Science 45 (2009) 806–811 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci