Computational and experimental study of articular cartilage under free swelling

  • Kinga Czerbak

Student thesis: Doctoral ThesisPhD


Articular cartilage is abundant in the human body and is vital for the health of our joints. It allows for relative, frictionless movement of the contacting bones and distribution of the joint loads over the joint surface. The biomechanical functions of cartilage are closely related to its specialised internal structure that is divided into 3 distinctive layers mainly composed of water and a solid matrix made out of collagen and proteoglycans. This distinct layered structure gives the cartilage its specific mechanical properties. When this structure is disrupted, it can lead to the first signs of cartilage damage and Osteoarthritis (OA). The damage is believed to be initiated by non-physiological stresses and strains. Therefore, the major motivation for studying the biomechanical behaviour of articular cartilage is to understand the development of tissue damage and OA and underpinning future opportunities for treatment approaches.

The early experimental investigations into cartilage behaviour used measuring techniques based on indentation and confined and unconfined compression. The researchers employed numerical theories such as linear elastic and viscoelastic at an arbitrary point in time to describe the tissue behaviour. However, due to cartilage's complex time-dependent response to load, it became evident that a better theory was needed to fully underpin the tissue's behaviour. This led to the emergence of biphasic and multiphasic theories that divided cartilage into a number of distinct phases and highlighted the role of interstitial fluid and ions on the tissue response. The complexity of both of these theories facilitated the development of computational approaches such as the Finite Element (FE) method for calculating the behaviour of cartilage. The use of FE allowed the creation of more accurate cartilage models and was underpinned by the combination of complex materials theories coupled with finite element models validated through experimental behaviour. Such validated computational models allow the exploration of cartilage geometry and loading conditions which are too complex or too expensive to explore experimentally. Therefore, this thesis aimed to use numerical and experimental approaches to measure and predict the strain response of articular cartilage under free swelling experiments.

Digital Image Correlation was used to obtain full-thickness strain maps of articular cartilage during free swelling experiments. The experiments were performed on porcine samples from two different joints. The approach was challenging and to gain confidence in the obtained results, the method was calibrated using a Virtual Strain Gauge study, followed by validation using Linear Variable Transducer physically connected to the swelling cartilage samples. The developed experimental methodology was novel and allowed for successful analysis of glenohumeral and femoral cartilage samples highlighting the high strain localisation at the surface of the cartilage during the experiments. Such strain localisation in free swelling was not evident in any known previous studies.

The experimental portion of the thesis was followed by the first FE study of cartilage based on examples found in the literature. This first study aimed to create a biofidelic finite element model of cartilage employing two different FE software - ANSYS and FEbio. The investigation produced several poroelastic, biphasic and biphasic-solute cartilage models that were validated through literature examples. This approach allowed to gain sufficient knowledge in cartilage FE modelling approaches to begin recreating the cartilage swelling experiment.

Informed by the literature it was evident that the chosen material model used in the FE investigations of cartilage had the potential to influence the agreement between the experimental results and numerical predictions. As a consequence, the biphasic-solute modelling framework was generated and validated by comparing the generated computational predictions to relevant examples from literature, as well as to ensure that the complexity of the FE representation was sufficient to replicate the experimental behaviour. The strain predicted by the generated biphasic-solute model compared well to the experimental results at the later time points, as quantified by the Lin’s Concordance Coefficient (LCC) but differed significantly at the earlier stages of the simulation, and these inaccuracies led to the development of a multiphasic modelling approach.

The multiphasic formulation is an extension to a biphasic-solute theory as alongside the same material features it allows to separately model a number of solutes within the cartilage structure. Therefore, the aim was to generate a multiphasic model and compare its predictions to the experimental behaviour obtained from DIC during the swelling experiments. The investigation into the swelling of this type of material highlighted the need to employ fibre reinforcement of the cartilage porous matrix to strengthen the response of the deeper layers of cartilage. This addition proved crucial to the improvement of the models as it produced an almost perfect agreement with the experimental result, further assisted by the near-perfect LCC coefficient (LCC>0.9 at all times). The developed approach highlights the role of the fibres and the layered microstructure of articular cartilage. It allows for exploring the cartilage behaviour in free-swelling in much more detail which was not possible in the challenging experimental study. The level of agreement demonstrated by the multiphasic fibre-reinforced model opens the possibilities for future investigations into more physiological experimental conditions.

Looking into the future, improvements in the experimental methodology would be beneficial, mainly involving the creation of a speckle pattern of controlled size and density, as well as using samples from the same joint and joint location. Furthermore, it would be of great interest to perform a histological analysis of the cartilage samples used in the DIC experiments as it would allow correlating the findings of this thesis to the true microscopic structure of the tissue. Finally, using the developed experimental and computational methodologies to further cartilage investigations such as prediction of the response of damaged samples and using different experimental conditions.
Date of Award29 Mar 2023
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorSabina Gheduzzi (Supervisor) & Sally Clift (Supervisor)


  • articular cartilage
  • free swelling
  • osmotic swelling
  • multiphasic material
  • biphasic-solute material
  • Digital Image Correlation
  • full-field strain
  • through-thickness strain
  • validated computational model

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