An Investigation into the Fluid-Structure Interactions of Articular Cartilage Based on the Theory of Poroelasticity

An important area in orthopaedic biomechanics is understanding the stress-strain behaviour of porous, soft tissues filled with interstitial fluid, such as articular cartilage (AC). Studying AC under load improves understanding of how healthy tissues operate within natural joints and of the physical mechanisms responsible for their load-bearing behaviour. The underlying mechanisms that impart transient stress-strain behaviour to AC were initially characterised by the well-established biphasic theory. Subsequent constitutive models have attempted to describe additional behaviours, including intrinsic viscoelasticity, permeability, and swelling related to fixed charge density (FCD). However, this has led to increasingly complex and sometimes conflated modelling approaches, resulting in limited characterisation of the underlying poroelastic theory and the individual physical interactions on which these formulations are based.
This thesis presents a novel poroelastic framework for investigating the biomechanical behaviour of AC at a macroscopic scale. The framework further develops Biot’s linear theory of poroelasticity through the derivation of the governing solid and fluid equations from first-principles conservation laws. The novelty of this work lies in the systematic recovery, retention and evaluation of additional coupling, compressibility and dynamic terms that are commonly simplified or neglected within conventional formulations. These equations are implemented within custom-built numerical solvers based on the Finite Volume Method (FVM), enabling the individual solid and fluid contributions to the poroelastic response to be quantified. The framework is initially formulated under infinitesimal-strain assumptions before being extended to finite-strain deformation and subsequently to account for hygroscopic swelling through species transport. The developed solvers are verified and validated using analytical solutions and published experimental data for an idealised three-dimensional cartilage plug subjected to confined compression.
The results demonstrate that the developed framework reproduces the characteristic biphasic response of AC under infinitesimal strain while providing direct assessment of fluid-solid load partitioning. Retention of the additional coupling terms does not substantially alter the qualitative small-strain response, indicating that classical biphasic behaviour is recovered within this more general poroelastic formulation. Permeability is identified as the dominant parameter governing transient pore-pressure dissipation and stress relaxation, while the Biot-Willis coefficient and drained porosity primarily influence the magnitude of the mechanical response. Extension to finite strain preserves these fundamental behavioural trends but amplifies reaction force, pore pressure and parameter sensitivity under larger deformation. Incorporation of hygroscopic swelling predominantly influences the post-drainage response, while short-term load support remains governed by poroelastic fluid pressurisation.
Collectively, the novelty and technical contribution of this work lies in establishing a consistent, conservation-law-based poroelastic framework through which fluid-solid interactions can be independently interrogated across infinitesimal-strain, finite-strain and swelling regimes. The framework provides a foundation for the systematic incorporation of additional physical mechanisms and the further development of predictive constitutive models for cartilage and other fluid-saturated biological tissues.