Second-harmonic generation image showing collagen fibers in a transversal section of the cartilage with calculated local 3D fiber directions projected onto the image (red lines).

Indentation experiment with an impermeable, plane-ended cylinder of diameter 1mm compressing a cartilage sample to 1% global strain in 150s. Top: stress distribution based on a model with patient-specific collagen fibers and inhomogeneous material properties; Bottom: stress distribution based on a model without collagen fibers and homogeneous material properties.

Cartilage tissue is a multi-phase material composed of fluid, electrolytes, chondrocytes, collagen fibers, proteoglycans and other glycoproteins, and it contains a fiber network of predominantly Type II collagen which provides tensile strength and stiffness to the solid phase, a proteoglycan gel.

Working with international collaborators, we proposed several 3D, large deformation constitutive models for articular cartilage to facilitate finite element (FE) simulation of cartilage morphology and material response. An initial phenomenological and patient-specific simulation approach focuses on incorporating the collagen fiber fabric in a 3D viscoelastic fiber-reinforced finite-strain setting, where each material parameter has a clear physical interpretation. A novel feature of the proposed method is 3D sample-specific numerical tracking of the fiber fabric deformation under general loading.

Next, we proposed an extended constitutive model for human articular cartilage that considers fiber dispersion, and demonstrated a numerical approach for incorporating DT-MRI (17.6 T) data by predicting collagen fiber fabric deformation for an indentation experiment. We developed a FE approach to determine the geometry, the meshing, and the fiber structural input (estimated principal fiber direction and dispersion). This approach allows the generation of fiber stretch plots and fiber tension/compression plots, providing new insight to fiber fabric deformation.

To further improve FE modeling fidelity, we quantified the 3D morphology of articular cartilage using second-harmonic imaging microscopy, and connected the imaging data to specific parameters of a new 3D large-strain constitutive model. Using representative numerical examples on the mechanical response of cartilage, we reproduced several features which have been demonstrated experimentally in the cartilage mechanics literature, e.g., solid and fluid anisotropy, tension-compression nonlinearity, creep displacement with significant fluid pressure load support, variable instantaneous and equilibrium Poisson's ratios, as well as inhomogeneous, depth-dependent strain.

Funding: Austrian Science Fund, Graz University of Technology