A Triphasic Theory for Growth in Biological Tissue – Basics and Applications

Ricken, Tim; Schwarz, Alexander; Bluhm, Joachim

doi:10.1002/mawe.200600018

Cited by 6 publications

(3 citation statements)

References 36 publications

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“…Thus, it is easily seen from ( 16) that the dehydration of the tissue cells is naturally included in (45) byρ S , also compare the similar ansatz by [52] dealing with porous materials with a growing (or shrinking) solid skeleton.…”

Section: Solid Skeletonmentioning

confidence: 98%

A thermodynamically consistent quasi-double-porosity thermo-hydro-mechanical model for cell dehydration of plant tissues at subzero temperatures

et al. 2021

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Many plant tissues exhibit the property of frost resistance. This is mainly due to two factors: one is related to metabolic effects, while the other stems from structural properties of plants leading to dehydration of their cells. The present contribution aims at assessing the impact of ice formation on frost-resistant plant tissues with a focus on structural properties specifically applied to Equisetum hyemale. In this particular case, there is an extracellular ice formation in so-called vallecular canals and the pith cavity, which leads to a dehydration of the tissue cells to avoid intracellular ice formation, what would be fatal for the cells and subsequently for the whole plant. To address the underlying phenomena in the plant, a coupled thermo-hydro-mechanical model based on the Theory of Porous Media is introduced as the modelling framework. The dehydration of the tissue cells is referred to as of quasi-double-porosity nature, since the water is mobile within the intercellular space, but confined to the cells in the intracellular space and consequently kinematically coupled to them. However, the mass exchange of water across the cell wall is considered. The presented numerical example shows the strong coupling of the underlying processes as well as the quasi-double-porosity feature. Finally, it supports the experimental finding of the vallecular canals as the main location of ice formation.

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Section: Solid Skeletonmentioning

confidence: 98%

A thermodynamically consistent quasi-double-porosity thermo-hydro-mechanical model for cell dehydration of plant tissues at subzero temperatures

et al. 2021

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“…Extending the idea of biphasic to triphasic mixture theory, Lai et al [33] developed mathematical models for soft tissues including the ion concentration as a third phase in addition to solid and fluid phase. Large numbers of papers [34][35][36][37] have been reported considering triphasic approach. Treating the ions in a mixture as a combination of cations and anions, a quardiphasic mixture theory for soft biological tissue was developed by Frijns et al [38].…”

Section: Further Applications Of Mixture Theorymentioning

confidence: 99%

A Review of Mixture Theory for Deformable Porous Media and Applications

et al. 2017

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Abstract:Mixture theory provides a continuum framework to model a multi-phase system. The basic assumption is, at any instant of time all phases are present at every material point and momentum and mass balance equations are postulated. This paper reviews the recent developments in mixture theory and focuses on the applications of the theory in particular areas of biomechanics, composite manufacturing and infiltration into deformable porous materials. The complexity based upon different permeability and stress functions is also addressed. The review covers the literature presented in the past fifty years and summarizes applications of mixture theory in specific areas of interest, for the sake of brevity, only necessary details are provided rather than complete modeling and simulation.

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“…Ricken et al [69] proposed a triphasic model for transversely isotropic saturated biological tissues including growth. They assumed that growth is determined by stress and local proportion of nutrients.…”

Section: Multiphasic Modelmentioning

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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A Triphasic Theory for Growth in Biological Tissue – Basics and Applications

Cited by 6 publications

References 36 publications

A thermodynamically consistent quasi-double-porosity thermo-hydro-mechanical model for cell dehydration of plant tissues at subzero temperatures

A thermodynamically consistent quasi-double-porosity thermo-hydro-mechanical model for cell dehydration of plant tissues at subzero temperatures

A Review of Mixture Theory for Deformable Porous Media and Applications

Remodeling of soft tissues due to cell activity

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