On the Active Response of Soft Living Tissues

Nardinocchi, Paola; Teresi, Luciano

doi:10.1007/s10659-007-9111-7

Cited by 104 publications

(99 citation statements)

References 23 publications

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“…The elastic deformations result from the multiplicative decomposition once the compatibility of the global bending deformation has been ensured; they deliver internal stresses within the gel beam corresponding, in the absence of external forces, to null forces and torques on each cross section of the beam. Importantly, we note that both the components of the deformation have an elastic nature, which is different from what happens when a similar multiplicative decomposition is used to describe growth or thermal processes [8][9][10]; hence, both the components of the multiplicative decomposition depend on the elastic properties of the gel. We have shown that our simple bending model predicts material responsiveness in excellent agreement with the outcomes of our pilot study.…”

Section: Introductionmentioning

confidence: 81%

Swelling-induced and controlled curving in layered gel beams

2014

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We describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swellinginduced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method.

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Section: Introductionmentioning

confidence: 81%

Swelling-induced and controlled curving in layered gel beams

2014

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“…Such a decomposition accounts for introducing an intermediate frame between the reference and the deformed configurations. The microscopic part of the deformation gradient takes the form [27] …”

Section: Dislocation Approachmentioning

confidence: 99%

“…The upscaling strategy is incorporated in the model following an anisotropic active strain formalism [27,41], where the force balance determining the motion of the tissue depends on local distortion of the microstructure followed by a macroscopic rearrangement of the material recovering compatibility of the deformation. Mathematically, this corresponds to a decomposition of strains.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics

Rossi

Lassila

Ruiz–Baier

et al. 2014

European Journal of Mechanics - A/Solids

175

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The complex phenomena underlying mechanical contraction of cardiac cells and their influence in the dynamics of ventricular contraction are extremely important in understanding the overall function of the heart. In this paper we generalize previous contributions on the active strain formulation and propose a new model for the excitation-contraction coupling process. We derive an evolution equation for the active fiber contraction based on configurational forces, which is thermodynamically consistent. Geometrically, we link microscopic and macroscopic deformations giving rise to an orthotropic contraction mechanism that is able to represent physiologically correct thickening of the ventricular wall. A series of numerical tests highlights the importance of considering orthotropic mechanical activation in the heart and illustrates the main features of the proposed model.

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“…In order to account for the activation of the cardiac contraction, we follow a model of active strain (Nardinocchi & Teresi, 2007;Cherubini et al, 2009;Rossi et al, 2012), where we assume a multiplicative decomposition of the deformation gradient into a passive and an active component, F = F E F A . This assumption means that the energy is not stored as strain energy, rather it corresponds to an internal rearrangement of the material that does not produce macroscopic deformation.…”

Section: Kinematicsmentioning

confidence: 99%

Mathematical modelling of active contraction in isolated cardiomyocytes

Ruiz–Baier

Gizzi

Rossi

et al. 2013

Mathematical Medicine and Biology

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We investigate the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A consistent mathematical model is presented considering a hyperelastic description of the passive mechanical properties of the cell, combined with an active-strain framework to explain the active shortening of myocytes and its coupling with cytosolic and sarcoplasmic calcium dynamics. A finite element method based on a Taylor-Hood discretization is employed to approximate the nonlinear elasticity equations, whereas the calcium concentration and mechanical activation variables are discretized by piecewise linear finite elements. Several numerical tests illustrate the ability of the model in predicting key experimentally established characteristics including: (i) calcium propagation patterns and contractility, (ii) the influence of boundary conditions and cell shape on the onset of structural and active anisotropy and (iii) the high localized stress distributions at the focal adhesions. Besides, they also highlight the potential of the method in elucidating some important subcellular mechanisms affecting, e.g. cardiac repolarization.Keywords: cardiomyocyte modelling; active-strain contraction; nonlinear elasticity; calcium propagation; finite element formulation; coupled multiphysics.

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On the Active Response of Soft Living Tissues

Cited by 104 publications

References 23 publications

Swelling-induced and controlled curving in layered gel beams

Swelling-induced and controlled curving in layered gel beams

Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics

Mathematical modelling of active contraction in isolated cardiomyocytes

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