Poroelasticity of (bio)polymer networks during compression: theory and experiment

Abstract

Soft living tissues like cartilage can be considered as biphasic materials comprised of a fibrous complex biopolymer network and a viscous background liquid. Here, we show by a combination of experiment and theoretical analysis that both the hydraulic permeability and the elastic properties of (bio)polymer networks can be determined with simple ramp compression experiments in a commercial rheometer. In our approximate closed-form solution of the poroelastic equations of motion, we find the normal force response during compression as a combination of network stress and fluid pressure. Choosing fibrin as a biopolymer model system with controllable pore size, measurements of the full time-dependent normal force during compression are found to be in excellent agreement with the theoretical calculations. The inferred elastic response of large-pore (µm) fibrin networks depends on the strain rate, suggesting a strong interplay between network elasticity and fluid flow. Phenomenologically extending the calculated normal force into the regime of nonlinear elasticity, we find strain-stiffening of small-pore (sub-µm) fibrin networks to occur at an onset average tangential stress at the gel-plate interface that depends on the polymer concentration in a power-law fashion. The inferred permeability of small-pore fibrin networks scales approximately inverse squared with the fibrin concentration, implying with a microscopic cubic lattice model that the thickness of the fibrin fibers decreases with protein concentration. Our theoretical model provides a new method to obtain the hydraulic permeability and the elastic properties of biopolymer networks and hydrogels with simple compression experiments, and paves the way to study the relation between fluid flow and elasticity in biopolymer networks during dynamical compression.Soft biopolymer networks have essential functions in living cells 1,2 , the extracellular matrix 3,4 and the process of blood coagulation 5,6 . Their mechanical properties are determined by the network's hydraulic permeability and (visco)elastic properties.The permeability of biopolymer networks determines mass transport in soft tissues 7-9 , the dynamic behaviour of cells 10,11 * These authors contributed equally to this work.

Fibrous gels modelled as fluid-filled continua with double-well energy landscape

“…Finite difference techniques were used to solve the resulting partial differential equations and this gave results that were in qualitative agreement with experiments. In doing so, we have gone beyond analytically solvable problems that require assumptions of small strains [21], but have stopped short of writing a fully three-dimensional continuum theory for the compression of fibrous gels. A fully three-dimensional continuum calculation can be done using finite elements, but not without significant effort in developing appropriate elements to handle poro-elasticity with large deformations and phase transitions.…”

Microfluidic In-Situ Measurement of Poisson’s Ratio of Hydrogels

“…We presented a new technique for the measurement of Poisson's ratio of micrometric soft hydrogels with a very good measurement accuracy. The absolute measurement errors varying from 0.002 to 0.012 are comparable to what is obtainable using X-ray diffraction [12], and are much smaller than for measurements relying on the determination of two independent elastic moduli [7,30]. We successfully used this approach to measure Poisson's ratios of different hydrogels and showed that this Poisson ratio varied in a large range of values (0.165 to 0.5).…”

A method for measuring intra-tissue swelling pressure using a needle micro-osmometer

“…To make this calculation, membrane permeability was measured empirically, as described below. Meanwhile, tissue permeability, which is known to be influenced by the degree of tissue strain ( Holmes, 1985 ; Punter et al ., 2020 ), was approximated from an equation describing the relationship between the deformation and permeability of bovine NP tissue ( Heneghan and Riche 2008a ), This equation defines tissue permeability in terms of the stretch ratio, λ = h f / h o where h o denotes the initial height of the specimen and h f denotes the final height after confined compression. For the current study, pressure was applied isotropically to the tissue; therefore, it was assumed that tissue compression proceeded radially.…”