A triphasic model of transversely isotropic biological tissue with applications to stress and biologically induced growth

Ricken, Tim; Schwarz, Alexander; Bluhm, Joachim

doi:10.1016/j.commatsci.2006.03.025

Cited by 40 publications

(38 citation statements)

References 24 publications

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“…[3], i.e. for the overall mixture stress using the concept of effective stresses with T = α T α = α n α λ I + T α E where λ is the pore pressure and T α E defines the so-called extra stress, the interaction forcep β acting between ϕ β where β ∈ {S, F, N} with the constriction βp β = 0 and the mass supply term between the solid and fluid phaseρ α with the constriction αρ α = 0 with…”

Section: Modelmentioning

confidence: 99%

An Enriched Biphasic Model for Solute Driven Degradation

Ricken

Bluhm

Epple

et al. 2009

Proc Appl Math and Mech

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Transport of solutes in porous materials plays an important role in many kinds of materials such as biological tissues, porous implants or even soils. In most of the cases the liquid phase in the pores acts as a solvent for one or more solutions. The motion of the solutions is driven by both, the advective and convective transport. The former is related to the fluid phase velocity whereas the letter follows the concentration gradient. The interactions between the solutes and the solid and liquid phase may influence the overall material behavior. Although the solutes often carry electrical charges this paper is focused on neutrally charged solutions. In this contribution the model to describe the solute transport in a fluid saturated porous material is based on the well founded Theory of Porous Media. We will present the basic framework and the governing equations. Finally, we will show a three dimensional numerical example of the solute driven degradation of a skull implant.

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Section: Modelmentioning

confidence: 99%

An Enriched Biphasic Model for Solute Driven Degradation

Ricken

Bluhm

Epple

et al. 2009

Proc Appl Math and Mech

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“…Ricken et al [70] proposed a triphasic model composed of solid, liquid, and nutrition for transversely isotropic saturated tissues. The growth is assumed to be governed by the stress state and the local proportion of nutrients.…”

Section: Recent Work Papers On Soft Tissuementioning

confidence: 99%

Remodeling of soft tissues due to cell activity

Stoffel

Weichert

et al. 2014

Proc Appl Math and Mech

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The continuum mechanical modeling of collagenous biological tissues is of interest in the field of biomedical engineering. Particularly, the change of material properties as a result of cell activity is of great interest, as chondrocyte (cartilage cell) implantation yields significant functional improvement. The aim of the contribution is to present the remodeling phenomenon of a cellular material due to cell activity, which results in synthesis of collagen type‐II fibers. For the experimental study, cellular condensed gel is mechanically stimulated in a bioreactor for four weeks. The change of the stiffness of the gel is measured in a compression test. The remodeling process is theoretically derived by an appropriate evolution law in the framework of continuum mechanics. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…Therein, the interaction between the fluid pressure, strain-dependent pores and solid matrix stress will be considered. Moreover, the transversely isotropic behavior of the solid impacts both the stress response and the internal fluid permeability, which is modeled by using an invariant formulation of the Helmholtz free energy and a transverse isotropic permeability function [2,3]. To work within material objectivity the difference velocity is given by…”

Section: Mechanical Descriptionmentioning

confidence: 99%