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A new constitutive model for hydration-dependent mechanical properties in biological soft tissues and hydrogels.

ABSTRACT: It is challenging to noninvasively determine the mechanical properties of biological soft tissues in vivo. In this study, based on the biphasic theory and the transport models, a new constitutive model for hydration-dependent mechanical properties in hydrated soft materials was derived: HA = An(1-f?)(f?)2-n/2(2-f?), where HA(=?+2 ?) is the aggregate modulus, ?(f) is the volume fraction of fluid (i.e., hydration), A and n (>2) are two parameters related to the transport properties of the biphasic materials. A linear model for hydration-dependent shear modulus in the literature was verified for hydrogels. The effects of tissue hydration on mechanical properties (aggregate modulus and Poisson's ratio) were investigated. It was found that the value of Poisson's ratio was very sensitive to the tissue hydration in soft materials with high water content. The predictions of the aggregate modulus and shear modulus for hydrogels by the model compared well with those from experimental results. This study is important for developing new techniques for noninvasively assessing the mechanical properties of biological soft tissues using quantitative MRI methods as well as for designing scaffolds with proper mechanical properties for tissue engineering applications.

SUBMITTER: Gao X

PROVIDER: S-EPMC4163069 | biostudies-literature | 2014 Sep

REPOSITORIES: biostudies-literature

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A new constitutive model for hydration-dependent mechanical properties in biological soft tissues and hydrogels.

Gao Xin X Gu Weiyong W

Journal of biomechanics 20140621 12

It is challenging to noninvasively determine the mechanical properties of biological soft tissues in vivo. In this study, based on the biphasic theory and the transport models, a new constitutive model for hydration-dependent mechanical properties in hydrated soft materials was derived: HA = An(1-fϕ)(fϕ)2-n/2(2-fϕ), where HA(=λ+2 μ) is the aggregate modulus, ϕ(f) is the volume fraction of fluid (i.e., hydration), A and n (>2) are two parameters related to the transport properties of the biphasic ...[more]

PMID: 25001202

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Project description:Mechanical and mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems, particularly in developmental biology, and describe the physical interactions between cells and their local surroundings. These models in their original form consist of a balance equation for the cell density, a balance equation for the density of the extracellular matrix (ECM), and a force-balance equation describing the mechanical equilibrium of the cell-ECM system. Under the assumption that the cell-ECM system can be regarded as an isotropic linear viscoelastic material, the force-balance equation is often defined using the Kelvin-Voigt model of linear viscoelasticity to represent the stress-strain relation of the ECM. However, due to the multifaceted bio-physical nature of the ECM constituents, there are rheological aspects that cannot be effectively captured by this model and, therefore, depending on the pattern formation process and the type of biological tissue considered, other constitutive models of linear viscoelasticity may be better suited. In this paper, we systematically assess the pattern formation potential of different stress-strain constitutive equations for the ECM within a mechanical model of pattern formation in biological tissues. The results obtained through linear stability analysis and the dispersion relations derived therefrom support the idea that fluid-like constitutive models, such as the Maxwell model and the Jeffrey model, have a pattern formation potential much higher than solid-like models, such as the Kelvin-Voigt model and the standard linear solid model. This is confirmed by the results of numerical simulations, which demonstrate that, all else being equal, spatial patterns emerge in the case where the Maxwell model is used to represent the stress-strain relation of the ECM, while no patterns are observed when the Kelvin-Voigt model is employed. Our findings suggest that further empirical work is required to acquire detailed quantitative information on the mechanical properties of components of the ECM in different biological tissues in order to furnish mechanical and mechanochemical models of pattern formation with stress-strain constitutive equations for the ECM that provide a more faithful representation of the underlying tissue rheology.

Dataset Information

A new constitutive model for hydration-dependent mechanical properties in biological soft tissues and hydrogels.

Publications

A new constitutive model for hydration-dependent mechanical properties in biological soft tissues and hydrogels.

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