Review: Rheological properties of biological materials

Verdier, Claude; Etienne, J; Duperray, Alain; Preziosi, Luigi

doi:10.1016/j.crhy.2009.10.003

Cited by 91 publications

(74 citation statements)

References 199 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Considering that the living material can be macroscopically described by a Newtonian fluid moving at low Reynolds numbers [38][39][40], the classical Darcy's law gives the velocity of the living colony, v ¼ 2K p rp, where K p is the permeability coefficient describing the friction properties with the substrate and p is the pressure.…”

Section: Mathematical Modelmentioning

confidence: 99%

Branching instability in expanding bacterial colonies

Giverso

Verani

Ciarletta

2015

J. R. Soc. Interface.

View full text Add to dashboard Cite

Self-organization in developing living organisms relies on the capability of cells to duplicate and perform a collective motion inside the surrounding environment. Chemical and mechanical interactions coordinate such a cooperative behaviour, driving the dynamical evolution of the macroscopic system. In this work, we perform an analytical and computational analysis to study pattern formation during the spreading of an initially circular bacterial colony on a Petri dish. The continuous mathematical model addresses the growth and the chemotactic migration of the living monolayer, together with the diffusion and consumption of nutrients in the agar. The governing equations contain four dimensionless parameters, accounting for the interplay among the chemotactic response, the bacteria-substrate interaction and the experimental geometry. The spreading colony is found to be always linearly unstable to perturbations of the interface, whereas branching instability arises in finite-element numerical simulations. The typical length scales of such fingers, which align in the radial direction and later undergo further branching, are controlled by the size parameters of the problem, whereas the emergence of branching is favoured if the diffusion is dominant on the chemotaxis. The model is able to predict the experimental morphologies, confirming that compact (resp. branched) patterns arise for fast (resp. slow) expanding colonies. Such results, while providing new insights into pattern selection in bacterial colonies, may finally have important applications for designing controlled patterns.

show abstract

Section: Mathematical Modelmentioning

confidence: 99%

Branching instability in expanding bacterial colonies

Giverso

Verani

Ciarletta

2015

J. R. Soc. Interface.

View full text Add to dashboard Cite

show abstract

“…Most models explore the mechanical properties with perhaps an excessive simplification of the growth process itself. On the contrary, after several decades since the pioneering work of Greenspan [4], tumor growth models have explored all the facets of possible elementary biological processes known to date [5] with different modeling approaches at different scales: continuum models at the tissue scale, discrete models at the cells scale, and eventually hybrid continuum-discrete models [6]. The recent review by [6] reports more than 550 citations but few of them explore the possibility of shape instabilities except in simplified models [4,7].…”

mentioning

confidence: 99%

Curvature-Dependent Elastic Properties of Liquid-Ordered Domains Result in Inverted Domain Sorting on Uniaxially Compressed Vesicles

Risselada

Marrink²,

Mueller

2011

Phys. Rev. Lett.

View full text Add to dashboard Cite

Recent tumor growth models are often based on the multiphase mixture framework. Using bifurcation theory techniques, we show that such models can give contour instabilities. Restricting to a simplified but realistic version of such models, with an elastic cell-to-cell interaction and a growth rate dependent on diffusing nutrients, we prove that the tumor cell concentration at the border acts as a control parameter inducing a bifurcation with loss of the circular symmetry. We show that the finite wavelength at threshold has the size of the proliferating peritumoral zone. We apply our predictions to melanoma growth since contour instabilities are crucial for early diagnosis. Given the generality of the equations, other relevant applications can be envisaged for solving problems of tissue growth and remodeling. Introduction.-Soft tissue growth models in ideal geometries have shown shape instabilities with a special focus on morphogenesis of living systems [1][2][3]. Anisotropic or inhomogeneous growth and constraints due to boundaries are responsible for these shape instabilities. Most models explore the mechanical properties with perhaps an excessive simplification of the growth process itself. On the contrary, after several decades since the pioneering work of Greenspan [4], tumor growth models have explored all the facets of possible elementary biological processes known to date [5] with different modeling approaches at different scales: continuum models at the tissue scale, discrete models at the cells scale, and eventually hybrid continuum-discrete models [6]. The recent review by [6] reports more than 550 citations but few of them explore the possibility of shape instabilities except in simplified models [4,7]. However, models based on nonlinear coupled partial-differential equations (PDEs) require numerical investigations [8,9] with lack of understanding of the parameters at the origin of shape instabilities.Nevertheless, these instabilities are often correlated with the beginning of aggressive neoplasia: they are of utmost importance for melanoma where symmetry and regularity are key criteria in clinical methods [10]. Our aim is then to identify the main biophysical interactions at the origin of these contour instabilities. It has already been shown, both in vitro [11,12] and theoretically [13], that mechanical interactions between cells and their microenvironment are crucial for tumor evolution and can determine some macroscopic tumor properties [11].We discuss here how they can control tumor shape evolution as well, dictating the condition for the development of contour instabilities on a circular growing tumor, possibly giving rise to the patterns observed in vivo. We consider a continuous multiphase model describing the tumor as a two component mixture [6]. Although simplificative, such a model already contains the main

show abstract

“…The proposed theory has been applied to the study of pattern formation for either a fluid-like and a solid-like biological system model, using both theoretical methods and simulation tools. Nonetheless, it should be reminded that biological materials have a wide range of rheological properties in between such limiting ideal behaviors [115]. Furthermore, it has been recently highlighted that morphogenetic processes may involve microstructural rearrangement processes, such cell duplication and/or migration, which provoke fluid-like stress relaxation phenomena up to the timescale of days [96,97].…”

Section: Discussionmentioning

confidence: 99%

Mathematical Modeling of Morphogenesis in Living Materials

Balbi

Ciarletta

2016

Lecture Notes in Mathematics

View full text Add to dashboard Cite

From a mathematical viewpoint, the study of morphogenesis focuses on the description of all geometric and structural changes which locally orchestrate the underlying biological processes directing the formation of a macroscopic shape in living matter. In this chapter, we introduce a continuous chemo-mechanical approach of morphogenesis, deriving the balance principles and evolution laws for both volumetric and interfacial processes. The proposed theory is applied to the study of pattern formation for either a fluid-like and a solid-like biological system model, using both theoretical methods and simulation tools.

show abstract

Review: Rheological properties of biological materials

Cited by 91 publications

References 199 publications

Branching instability in expanding bacterial colonies

Branching instability in expanding bacterial colonies

Curvature-Dependent Elastic Properties of Liquid-Ordered Domains Result in Inverted Domain Sorting on Uniaxially Compressed Vesicles

Mathematical Modeling of Morphogenesis in Living Materials

Contact Info

Product

Resources

About