scholarly journals Stress-dependent amplification of active forces in nonlinear elastic media

Soft Matter ◽  
2019 ◽  
Vol 15 (2) ◽  
pp. 331-338 ◽  
Author(s):  
Pierre Ronceray ◽  
Chase P. Broedersz ◽  
Martin Lenz
Keyword(s):  
Nonlinear Elasticity ◽  
Molecular Motors ◽  
Surrounding Medium ◽  
Elastic Media ◽  
Stress Dependent ◽  
Nonlinear Elastic ◽  
Contractile Cells

Forces generated by molecular motors and contractile cells can be dramatically amplified by the nonlinear elasticity of the surrounding medium.

Self-Similarity Problems in Nonlinear Elastic Media

2020 ◽  
pp. 2211-2219
Author(s):  
Anatoliy A. Burenin ◽  
Dmitrii A. Potianikhin ◽  
Marina V. Shitikova
Keyword(s):  
Elastic Media ◽  
Self Similarity ◽  
Nonlinear Elastic

Surface solitons in nonlinear elastic media

1996 ◽  
Vol 346 (1-3) ◽  
pp. 337-345 ◽  
Author(s):  
Alexander S Kovalev ◽  
Eugen S Syrkin
Keyword(s):  
Elastic Media ◽  
Nonlinear Elastic

Self-Similarity Problems in Nonlinear Elastic Media

2019 ◽  
pp. 1-9
Author(s):  
Anatoliy A. Burenin ◽  
Dmitrii A. Potianikhin ◽  
Marina V. Shitikova
Keyword(s):  
Elastic Media ◽  
Self Similarity ◽  
Nonlinear Elastic

Bubble dynamics in a viscoelastic medium with nonlinear elasticity

2015 ◽  
Vol 766 ◽  
pp. 54-75 ◽  
Author(s):  
R. Gaudron ◽  
M. T. Warnez ◽  
E. Johnsen
Keyword(s):  
Soft Tissue ◽  
Nonlinear Elasticity ◽  
Viscoelastic Medium ◽  
Strain Energy ◽  
Bubble Dynamics ◽  
Surrounding Medium ◽  
Viscoelastic Model ◽  
Energy Functions ◽  
Newtonian Liquids ◽  
Strain Energy Functions

AbstractIn a variety of recently developed medical procedures, bubbles are formed directly in soft tissue and may cause damage. While cavitation in Newtonian liquids has received significant attention, bubble dynamics in tissue, a viscoelastic medium, remains poorly understood. To model tissue, most previous studies have focused on Maxwell-based viscoelastic fluids. However, soft tissue generally possesses an original configuration to which it relaxes after deformation. Thus, a Kelvin–Voigt-based viscoelastic model is expected to be a more appropriate representation. Furthermore, large oscillations may occur, thus violating the infinitesimal strain assumption and requiring a nonlinear/finite-strain elasticity description. In this article, we develop a theoretical framework to simulate spherical bubble dynamics in a viscoelastic medium with nonlinear elasticity. Following modern continuum mechanics formalism, we derive the form of the elastic forces acting on a bubble for common strain-energy functions (e.g. neo-Hookean, Mooney–Rivlin) and incorporate them into Rayleigh–Plesset-like equations. The main effects of nonlinear elasticity are to reduce the violence of the collapse and rebound for large departures from the equilibrium radius, and increase the oscillation frequency. The present approach can readily be extended to other strain-energy functions and used to compute the stress/deformation fields in the surrounding medium.

scholarly journals A chemo-mechanical free-energy-based approach to model durotaxis and extracellular stiffness-dependent contraction and polarization of cells

2016 ◽  
Vol 6 (1) ◽  
pp. 20150067 ◽  
Author(s):  
Vivek B. Shenoy ◽  
Hailong Wang ◽  
Xiao Wang
Keyword(s):  
Free Energy ◽  
Molecular Motors ◽  
Mechanical Energy ◽  
Second Law Of Thermodynamics ◽  
Mechanical Coupling ◽  
Coupling Parameters ◽  
Chemical Free Energy ◽  
Myosin Motors ◽  
Stress Dependent ◽  
Extracellular Environment

We propose a chemo-mechanical model based on stress-dependent recruitment of myosin motors to describe how the contractility, polarization and strain in cells vary with the stiffness of their surroundings and their shape. A contractility tensor, which depends on the distribution of myosin motors, is introduced to describe the chemical free energy of the cell due to myosin recruitment. We explicitly include the contributions to the free energy that arise from mechanosensitive signalling pathways (such as the SFX, Rho-Rock and MLCK pathways) through chemo-mechanical coupling parameters. Taking the variations of the total free energy, which consists of the chemical and mechanical components, in accordance with the second law of thermodynamics provides equations for the temporal evolution of the active stress and the contractility tensor. Following this approach, we are able to recover the well-known Hill relation for active stresses, based on the fundamental principles of irreversible thermodynamics rather than phenomenology. We have numerically implemented our free energy-based approach to model spatial distribution of strain and contractility in (i) cells supported by flexible microposts, (ii) cells on two-dimensional substrates, and (iii) cells in three-dimensional matrices. We demonstrate how the polarization of the cells and the orientation of stress fibres can be deduced from the eigenvalues and eigenvectors of the contractility tensor. Our calculations suggest that the chemical free energy of the cell decreases with the stiffness of the extracellular environment as the cytoskeleton polarizes in response to stress-dependent recruitment of molecular motors. The mechanical energy, which includes the strain energy and motor potential energy, however, increases with stiffness, but the overall energy is lower for cells in stiffer environments. This provides a thermodynamic basis for durotaxis, whereby cells preferentially migrate towards stiffer regions of the extracellular environment. Our models also explain, from an energetic perspective, why the shape of the cells can change in response to stiffness of the surroundings. The effect of the stiffness of the nucleus on its shape and the orientation of the stress fibres is also studied for all the above geometries. Along with making testable predictions, we have estimated the magnitudes of the chemo-mechanical coupling parameters for myofibroblasts based on data reported in the literature.

Boosted kink-type solitary waves in nonlinear elastic media

1992 ◽  
Vol 55 (3-4) ◽  
pp. 251-258 ◽  
Author(s):  
R.J. Gooding ◽  
G.S. Bales
Keyword(s):  
Solitary Waves ◽  
Elastic Media ◽  
Nonlinear Elastic
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