An ionised/non-ionised dual porosity model of intervertebral disc tissue

Abstract

The volume of the intrafibrillar water space – i.e. the water contained inside the collagen fibres – is a key parameter that is relevant to concepts of connective tissue structure and function. Confined compression and swelling experiments on annulus fibrosus samples are interpreted in terms of a dual porosity model that distinguishes between a non-ionised intrafibrillar porosity and an ionised extrafibrillar porosity. Both porosities intercommunicate and are saturated with a monovalent ionic solution, i.c. NaCl. The extrafibrillar fixed charge density of the samples is assessed using radiotracer techniques and the collagen content is evaluated by measurement of hydroxyproline concentration. The interpretation of the experimental data yields values for the intrafibrillar water content, the average activity coefficient of the ions, the Donnan osmotic coefficient, the fraction of intrafibrillar water, the stress-free deformation state, and an effective stress–strain relationship as a function of the radial position in the disc. A linear fit between the second Piola–Kirchhoff effective stress and Green–Lagrange strain yielded an effective stiffness: H _e=1.087 ± 0.657 MPa. The average fraction of intrafibrillar water was 1.16 g/g collagen. The results were sensitive to changes in the activity and osmotic coefficients and the fraction of intrafibrillar water. The fixed charge density increased with distance from the outer edge of the annulus, whereas the hydroxyproline decreased.