Fig 1.
Intact porcine tibial plateau sample used for indentation and histological tests.
The red circle indicates the area of interest where indentation tests were performed.
Fig 2.
Axial view of the topographical map of the joint surface and the specific points selected for indentation.
Fig 3.
Schematic representation of the transient free swelling experiment (bottom right) and the boundary conditions of the cartilage sample applied to the computational simulation.
A cartilage sample of 3 mm thickness and 30 mm diameter is immersed in a NaCl solution with an initial concentration of 0.15 M. The sample is confined in an impermeable chamber.
Table 1.
3D Model parameters for healthy cartilage considered as homogeneous material.
Table 2.
Initial permeability (k) introduced in the 3D computational model for healthy cartilage considered as through-the-thickness heterogeneous material.
Table 3.
Initial fixed charged density () introduced in the 3D computational model for healthy cartilage considered as heterogeneous material based on the work of Lai et al. [25] as well as following our GAG-histological results.
Property distribution similar to Young´s modulus represented in the zone of the sample shown in Fig 5. To clarify Table 3–Fig 5 correspondence, note that, for instance, first value in the first line and first column of table 3, 0.150, corresponds to the superficial layer and the point 13 of Fig 5. Values collected in table 3 are obtained in discrete material regions.
Fig 4.
Schematic representation of the experimental tests carried out to obtain the Young´s modulus and GAG distribution (phase 1) for the 3D computational simulation (phase 2) of articular cartilage behaviour.
Note that four random points were chosen to measure (qualitatively) the GAGs distribution.
Fig 5.
Young´s modulus experimentally obtained from the indentation test for the superficial layer (blue columns), and mathematically obtained for the middle zone (green columns) and deep zone (red columns) [19].
Fig 6.
Panoramic view of a longitudinal section of the cartilage sample extracted from porcine tibial plateaus.
Light microscopy of cartilage and subchondral bone, Safranin O staining, 100X.
Fig 7.
Comparison of the upper surface displacement in the free swelling test from the model considering articular cartilage as homogeneous material (green line) and through-the-thickness heterogeneous material (range marked by blue line, maximum value, and red line, minimum value).
The dark area represents the saturation phase.
Fig 8.
Range of cation concentration (c+) distribution in sample depth for the free swelling test considering cartilage through-the-thickness heterogeneity.
Fig 9.
z-displacement of the upper surface of the cartilage, and the flux of water and cations obtained with the model after 1650 seconds (coincident with the maximum swelling of the sample) of the free swelling simulation for through-the-thickness heterogeneous materials and homogeneous materials.
Note that the positive flux refers to the entrance of water or cations into the sample and the negative flux indicates the outflow of the substance.