Most organs and biological tissues are soft viscoelastic materials with elastic moduli ranging from on the order of 100 Pa for the brain to 100 000 Pa for soft cartilage. Biocompatible synthetic materials already have many applications, but combining chemical compatibility with physiologically appropriate mechanical properties will increase their potential for use both as implants and as substrates for tissue engineering. Understanding and controlling mechanical properties, specifically softness, is important for appropriate physiological function in numerous contexts. The mechanical properties of the substrate on which, or within which, cells are placed can have as large an impact as chemical stimuli on cell morphology, differentiation, motility, and commitment to live or die.

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Soft biological materials and their impact on cell function

Hydrodynamics and phases of flocks

Substantial research over the past two decades has established that extracellular matrix (ECM) elasticity, or stiffness, affects fundamental cellular processes, including spreading, growth, proliferation, migration, differentiation and organoid formation. Linearly elastic polyacrylamide hydrogels and polydimethylsiloxane (PDMS) elastomers coated with ECM proteins are widely used to assess the role of stiffness, and results from such experiments are often assumed to reproduce the effect of the mechanical environment experienced by cells in vivo. However, tissues and ECMs are not linearly elastic materials-they exhibit far more complex mechanical behaviours, including viscoelasticity (a time-dependent response to loading or deformation), as well as mechanical plasticity and nonlinear elasticity. Here we review the complex mechanical behaviours of tissues and ECMs, discuss the effect of ECM viscoelasticity on cells, and describe the potential use of viscoelastic biomaterials in regenerative medicine. Recent work has revealed that matrix viscoelasticity regulates these same fundamental cell processes, and can promote behaviours that are not observed with elastic hydrogels in both two- and three-dimensional culture microenvironments. These findings have provided insights into cell-matrix interactions and how these interactions differentially modulate mechano-sensitive molecular pathways in cells. Moreover, these results suggest design guidelines for the next generation of biomaterials, with the goal of matching tissue and ECM mechanics for in vitro tissue models and applications in regenerative medicine.

Effects of extracellular matrix viscoelasticity on cellular behaviour.

Bacterial processes ranging from gene expression to motility and biofilm formation are constantly challenged by internal and external noise. While the importance of stochastic fluctuations has been appreciated for chemotaxis, it is currently believed that deterministic long-range fluid dynamical effects govern cell–cell and cell–surface scattering—the elementary events that lead to swarming and collective swimming in active suspensions and to the formation of biofilms. Here, we report direct measurements of the bacterial flow field generated by individual swimming Escherichia coli both far from and near to a solid surface. These experiments allowed us to examine the relative importance of fluid dynamics and rotational diffusion for bacteria. For cell–cell interactions it is shown that thermal and intrinsic stochasticity drown the effects of long-range fluid dynamics, implying that physical interactions between bacteria are determined by steric collisions and near-field lubrication forces. This dominance of short-range forces closely links collective motion in bacterial suspensions to self-organization in driven granular systems, assemblages of biofilaments, and animal flocks. For the scattering of bacteria with surfaces, long-range fluid dynamical interactions are also shown to be negligible before collisions; however, once the bacterium swims along the surface within a few microns after an aligning collision, hydrodynamic effects can contribute to the experimentally observed, long residence times. Because these results are based on purely mechanical properties, they apply to a wide range of microorganisms.

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Fluid dynamics and noise in bacterial cell–cell and cell–surface scattering

In this review, we compare the reported values of Young's modulus (YM) obtained from indentation and tensile deformations of soft biological tissues. When the method of deformation is ignored, YM values for any given tissue typically span several orders of magnitude. If the method of deformation is considered, then a consistent and less ambiguous result emerges. On average, YM values for soft tissues are consistently lower when obtained by indentation deformations. We discuss the implications and potential impact of this finding.

http://chemotaxis.semmelweis.hu/CHTXhpg/Durotaxis/DT2/McKeeCT_TissueEng_2011.pdf

Indentation versus tensile measurements of Young's modulus for soft biological tissues.

In this paper, the results from a series of rheological tests of fresh pig kidney have been reported. Using a standard strain-controlled rheometer, the oscillation strain sweep experiment showed a linear viscoelastic strain limit of the order of 0.2% strain. To determine the components of dynamic moduli in terms of frequency, shear oscillation tests were done at strain 0.2% using a stress-controlled rheometer. Shear stress relaxation tests were carried out with a fixed strain of 0.2% and 0.02 s rise time. The model we have developed uses a multi-mode upper convected Maxwell (UCM) model with variable viscosities and time constants, to which we have added a Mooney hyper-elastic response, both multiplied by a damping function. Different forms of damping functions that control the non-linearity of strain-stress profile have been tested. The model was fitted to our experimental data, and matched the entire test data reasonably well with a single set of parameters.

Viscoelastic properties of pig kidney in shear, experimental results and modelling

It is shown that several (single-mode) models (PTT, XPP) are basically special cases of the general network model. The XPP model [J. Rheol. 45 (2001) 823] is shown to give an identical response to a PTT model at high elongational rates, but the models differ in shear flow at high shear rates. The Giesekus term in the XPP model has practically no effect at any deformation rate except the generation of a second normal stress difference at small shear rates. The possibility of tailoring the shear flow response at high shear rates is explored. The results for the models are also given to show the effect of branching on the response in both transient and steady flows—elongation, shear, planar elongation and biaxial deformation. Finally, the fitting of data with multi-mode models is investigated.

Simple constitutive models for linear and branched polymers

Numerical results for two nearby swimming micromachines, obtained by the boundary element method (BEM), are reported in this paper. Two neighbouring configurations, side by side and in tandem, are considered and the translational and rotational velocities together with the force exerted on the micromachines are given. It is demonstrated that, for both configurations, the approximate reflection method gives comparable results to the full solutions. In the side by side configuration, hydrodynamic interaction is significant when the separation distance is less than about 1.5 of the total length of the machine. A propulsion advantage in the tandem configuration is found, where the leading machine acquires a higher velocity and the results obtained by the reflection method agree well with the full BEM solution.

Hydrodynamic interaction between two nearby swimming micromachines

Large-amplitude oscillatory squeezing flow data are reported for a complex biological material, which is highly shear-thinning in oscillatory shear flow This soft tissue has a linear viscoelastic limit at a strain of approximately 02% The oscillatory squeezing flow data at large strain are analyzed using two constitutive models: a bi-viscosity Newtonian model, and a non-linear Maxwell model It is found that although both models may have the same response in shape, the later matches with our non-linear experimental data better It is also concluded that the non-linear response of the material in large amplitude oscillatory flow is mainly due to the shear thinning of the material

Oscillatory squeezing flow of a biological material

This paper reports on the results of the numerical simulation of the motion of solid spherical particles in shear Stokes flows. Using the completed double layer boundary element method (CDLBEM) via distributed computing under Parallel Virtual Machine (PVM), the effective viscosity of suspension has been calculated for a finite number of spheres in a cubic array, or in a random configuration. In the simulation presented here, the short range interactions via lubrication forces are also taken into account, via the range completer in the formulation, whenever the gap between two neighbouring particles is closer than a critical gap. The results for particles in a simple cubic array agree with the results of Nunan and Keller (1984) and Stoksian Dynamics of Brady et al. (1988). To evaluate the lubrication forces between particles in a random configuration, a critical gap of 0.2 of particle's radius is suggested and the results are tested against the experimental data of Thomas (1965) and empirical equation of Krieger-Dougherty (Krieger, 1972). Finally, the quasi-steady trajectories are obtained for time-varying configuration of 125 particles.

Simin Nasseri

Papers

Viscoelastic properties of pig kidney in shear, experimental results and modelling

Simple constitutive models for linear and branched polymers

Hydrodynamic interaction between two nearby swimming micromachines

Oscillatory squeezing flow of a biological material

Lubrication approximation in completed double layer boundary element method