Non-linear elasticity and relaxation in cells, tissues and biopolymer networks

The stiffness of tissues in which cells are embedded has effects on cell structure and function that can act independently of or override chemical stimuli. Most measurements of tissue stiffness report elastic moduli measured at a single frequency and at a low strain, but tissues and the cells within them are subjected to strains that often exceed the range of linear viscoelasticity.  Rheologic measurements of liver, brain, and adipose tissues over a range of shear, compressive, and elongational strains show that the viscoelastic response of these tissues differs from that of synthetic hydrogels that have similar elastic moduli when measured in the linear range. The shear moduli of soft tissues generally decrease with increasing shear or elongational strain, but they strongly increase under uniaxial compression.  In contrast, networks of crosslinked collagen or fibrin soften under compression, but strongly increase shear modulus when deformed in extension.  The mechanisms leading to the unusual strain-dependent rheology of soft tissues and fibrous networks do not appear to be explained by current models of polymer mechanics, but appear to relate to local and global volume conservation within the networks and tissues.