A fibril-reinforced poroviscoelastic swelling model for articular cartilage

Abstract

From a mechanical point of view, the most relevant components of articular cartilage are the tight and highly organized collagen network together with the charged proteoglycans. Due to the fixed charges of the proteoglycans, the cation concentration inside the tissue is higher than in the surrounding synovial fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. The fibrillar collagen network resists straining and swelling pressures. This combination makes cartilage a unique, highly hydrated and pressurized tissue, enforced with a strained collagen network. Many theories to explain articular cartilage behavior under loading, expressed in computational models that either include the swelling behavior or the properties of the anisotropic collagen structure, can be found in the literature. The most common tests used to determine the mechanical quality of articular cartilage are those of confined compression, unconfined compression, indentation and swelling. All theories currently available in the literature can explain the cartilage response occurring in some of the above tests, but none of them can explain these for all of the tests. We hypothesized that a model including simultaneous mathematical descriptions of (1) the swelling properties due to the fixed-change densities of the proteoglycans and (2) the anisotropic viscoelastic collagen structure, can explain all these test simultaneously. To study this hypothesis we extended our fibril-reinforced poroviscoelastic finite element model with our biphasic swelling model. We have shown that the newly developed fibril-reinforced poroviscoelastic swelling (FPVES) model for articular cartilage can simultaneously account for the reaction force during swelling, confined compression, indentation and unconfined compression as well as the lateral deformation during unconfined compression. Using this theory it is possible to analyze the link between the collagen network and the swelling properties of articular cartilage.