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

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 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.