Table 1.
List of abbreviations.
Fig 1.
Cartilage degeneration algorithm.
Outline of the proposed proteoglycan degeneration algorithm based on the loss of fixed charge density (FCD) via A) diffusion of pro-inflammatory cytokine interleukin-1 into the tissue and subsequent biochemical degradation of cartilage matrix, B) excessive levels of the maximum shear strain especially near lesions and C) combination of these cartilage-degrading mechanisms. In the combined degradation model, both mechanisms are in effect simultaneously during each simulation iteration, followed by an update of non-fibrillar matrix contents for the next iteration. Experimental biomechanical degradation images modified with permission from Orozco et al. [49].
Fig 2.
Workflow for creation of A) biochemical, B) biomechanical and C) combined biochemical and biomechanical degradation models. Lesion geometry was based on histological findings after injurious loading. All of the mechanobiological models estimated fixed charge density (FCD) loss near and away from the lesion over time. Histology image obtained with permission from Orozco et al. [49].
Fig 3.
Previous experimental findings.
A) In vitro experiments with exogenous pro-inflammatory cytokine interleukin-1 (IL-1) challenge (10 ng/ml in culture medium) show marked matrix degradation near the sample surface and edges [40]. B) In vitro experiments with injurious loading (50% at rate 100%/s) following a dynamic loading period (15% strain amplitude, haversine waveform, 1 Hz, 1h on and 5h off cycles) in unconfined compression show lower optical density (~lower fixed charge density, FCD) especially near lesions. The numbers [%] show the average localized FCD loss compared to the day when cartilage was mechanically injured. Biomechanical degradation images modified with permission from Orozco et al. [49].
Fig 4.
Simulated biochemical cartilage degradation.
Predicted biochemical fixed charge density (FCD) losses in A) intact reference model and B) injury model. Biochemical degradation shown at time t = 4 d was simulated with 1 ng/ml of exogenous interleukin-1.
Fig 5.
Simulated biomechanical cartilage degradation.
Predicted biomechanical fixed charge density (FCD) losses in A) intact reference model and B) injury model. Biomechanical degradation shown at time t = 12 d was simulated with the degeneration threshold of = 50% of the maximum shear strain. This threshold was chosen to match model predictions and experimental findings.
Fig 6.
Simulated combined biochemical and biomechanical cartilage degradation.
Predicted combined biochemical and biomechanical fixed charge density (FCD) losses in A) intact reference model and B) injury model. Combined biochemical and biomechanical degradation shown at time t = 4 d was simulated with 1 ng/ml of exogenous interleukin-1 and with the degeneration threshold of = 50% of the maximum shear strain. This threshold was chosen to match model predictions and experimental findings.
Fig 7.
Temporal estimations of cartilage degradation.
Average and maximum fixed charge density (FCD) losses over time predicted by A) biochemical, B) biomechanical, and C) combined biochemical and biomechanical model. The dashed line in biomechanical model includes the base degeneration rate parameter, which was chosen according to the experimental FCD loss in freely-swollen cartilage disks (see S1 Supplementary Material, Subsection S1.8). The blue and black errorbars (with 95% confidence intervals) at days 7 and 12 represent the experimental average FCD loss near lesions after dynamic loading and in freely-swollen samples, respectively. The FCD concentration was not allowed to decrease below 10% of the initial minimum FCD concentration in the model due to computational stability.
Fig 8.
Simulation of degraded cartilage area.
Temporal estimations of degraded cartilage area with A) biochemical and combined biochemical and biomechanical degradation and B) biomechanical degradation. In these simulations, cartilage was considered”degraded” when FCD loss in elements was equal or greater than 20%. See S1 Supplementary Material (Subsection S2.4, S5 Fig, S1–S4 Animation) for animations showing the propagation of the degraded area over time.