A theoretical model for tissue growth in confined geometries

Dunlop, John W. C.; Fischer, Franz Dieter; Gamsjäger, Ernst; Fratzl, Peter

doi:10.1016/j.jmps.2010.04.008

Cited by 46 publications

(46 citation statements)

References 53 publications

(69 reference statements)

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“…Tissue remodelling is the process by which cells can rearrange their orientation and position with respect to each other as well as to move, reorient and degrade the extracellular matrix in which they are sitting. The driving force for remodelling has its origin in the thermodynamics of the irreversible process controlled by the dissipation; for details, we refer to [36] and the contributions by Ambrosi et al [24,33,34]. With these assumptions, we show that the problem reduces to a single free parameter interpreted as a critical curvature for tissue growth.…”

Section: Introductionmentioning

confidence: 90%

“…We use the formalism for growth outlined in [35,36] but assume that the growing body behaves like an ideal fluid, with a defined surface stress, g (for details, see [14]). This relies on the assumption that there are three separable timescales, that of growth, remodelling and elasticity.…”

Section: Formulation Of the Model Hypothesesmentioning

confidence: 99%

“…[29][30][31]). We start with a simple approach fully compatible with thermodynamics [32][33][34][35][36] which considers both a biochemical driving force (in the form of a chemical potential) and a mechanical one (including volume stresses as well as surface stresses). Then we assume that local tissue remodelling is sufficiently rapid compared with the growth rate, so that the tissue can essentially be regarded as an ideal fluid on the timescale of growth.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Tissue growth controlled by geometric boundary conditions: a simple model recapitulating aspects of callus formation and bone healing

Fischer

Zickler

Dunlop

et al. 2015

J. R. Soc. Interface.

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The shape of tissues arises from a subtle interplay between biochemical driving forces, leading to cell growth, division and extracellular matrix formation, and the physical constraints of the surrounding environment, giving rise to mechanical signals for the cells. Despite the inherent complexity of such systems, much can still be learnt by treating tissues that constantly remodel as simple fluids. In this approach, remodelling relaxes all internal stresses except for the pressure which is counterbalanced by the surface stress. Our model is used to investigate how wettable substrates influence the stability of tissue nodules. It turns out for a growing tissue nodule in free space, the model predicts only two states: either the tissue shrinks and disappears, or it keeps growing indefinitely. However, as soon as the tissue wets a substrate, stable equilibrium configurations become possible. Furthermore, by investigating more complex substrate geometries, such as tissue growing at the end of a hollow cylinder, we see features reminiscent of healing processes in long bones, such as the existence of a critical gap size above which healing does not occur. Despite its simplicity, the model may be useful in describing various aspects related to tissue growth, including biofilm formation and cancer metastases.

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Section: Introductionmentioning

confidence: 90%

Section: Formulation Of the Model Hypothesesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Tissue growth controlled by geometric boundary conditions: a simple model recapitulating aspects of callus formation and bone healing

Fischer

Zickler

Dunlop

et al. 2015

J. R. Soc. Interface.

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show abstract

“…For instance, recent experiments indicate the existence of residual stresses in a normal esophageal mucosa (Liao et al, 2003;Lu and Gregersen, 2001;Yang et al, 2007). It is well recognized that residual stresses play an important role in various functions of living tissues (Dunlop et al, 2010;Fung, 1990;Holzapfel et al, 2000;Humphrey, 2003;Skalak et al, 1996). A sufficiently large residual stress can buckle the biological tissues (Ben Amar and Goriely, 2005;Ben Amar and Ciarletta, 2010;Liang and Mahadevan, 2009;Volokh, 2006).…”

Section: Introductionmentioning

confidence: 99%

Growth and surface folding of esophageal mucosa: A biomechanical model

Cao

Feng

2011

Journal of Biomechanics

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“…Boundary conditions confine the domain and therefore, the growth induces residual stresses in the body that trigger instabilities [4,29]. For further details on the continuum theory of growth and its implications see [12,13,[15][16][17]19,21,24,34,36,65] and references therein. Note that we formulate the theory of growth within the framework of open system thermodynamic where the body is allowed to constantly exchange energetic structures [28] with its environment through fluxes across its boundary [14,19].…”

Section: Introductionmentioning

confidence: 99%

Computational aspects of growth-induced instabilities through eigenvalue analysis

et al. 2015

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The objective of this contribution is to establish a computational framework to study growth-induced instabilities. The common approach towards growth-induced instabilities is to decompose the deformation multiplicatively into its growth and elastic part. Recently, this concept has been employed in computations of growing continua and has proven to be extremely useful to better understand the material behavior under growth. While finite element simulations seem to be capable of predicting the behavior of growing continua, they often cannot naturally capture the instabilities caused by growth. The accepted strategy to provoke growth-induced instabilities is therefore to perturb the solution of the problem, which indeed results in geometric instabilities in the form of wrinkles and folds. However, this strategy is intrinsically subjective as the user is prescribing the perturbations and the simulations are often highly perturbation-dependent. We propose a different strategy that is inherently suitable for this problem, namely eigenvalue analysis. The main advantages of eigenvalue analysis are that first, no arbitrary, artificial perturbations are needed and second, it is, in general, independent of the time step size. Therefore, the solution obtained by this methodology is not B C. Linder subjective and thus, is generic and reproducible. Equipped with eigenvalue analysis, we are able to compute precisely the critical growth to initiate instabilities. Furthermore, this strategy allows us to compare different finite elements for this family of problems. Our results demonstrate that linear elements perform strikingly poorly, as compared to quadratic elements.

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A theoretical model for tissue growth in confined geometries

Cited by 46 publications

References 53 publications

Tissue growth controlled by geometric boundary conditions: a simple model recapitulating aspects of callus formation and bone healing

Tissue growth controlled by geometric boundary conditions: a simple model recapitulating aspects of callus formation and bone healing

Growth and surface folding of esophageal mucosa: A biomechanical model

Computational aspects of growth-induced instabilities through eigenvalue analysis

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