It has been experimentally proposed that the discrete regions of articular cartilage, along with different subchondral bone tissues, known as the bone-cartilage unit, are biomechanically altered during osteoarthritis degeneration. However, a computational framework capturing all of the dominant changes in the multiphasic parameters has not yet been developed. This article proposes a new finite element model of the bone-cartilage unit by combining several validated, nonlinear, depth-dependent, fibril-reinforced, and swelling models, which can computationally simulate the variations in the dominant parameters during osteoarthritis degeneration by indentation and unconfined compression tests. The mentioned dominant parameters include the proteoglycan depletion, collagen fibrillar softening, permeability, and fluid fraction increase for approximately non-advanced osteoarthritis. The results depict the importance of subchondral bone tissues in fluid distribution within the bone-cartilage units by decreasing the fluid permeation and pressure (up to a maximum of 100 kPa) during osteoarthritis, supporting the notion that subchondral bones might play a role in the pathogenesis of osteoarthritis. Furthermore, the osteoarthritis composition-based studies shed light on the significant biomechanical role of the calcified cartilage, which experienced a maximum change of 70 kPa in stress, together with relative load contributions of articular cartilage constituents during osteoarthritis, in which the osmotic pressure bore around 70% of the loads after degeneration. To conclude, the new insights provided by the results reveal the significance of the multiphasic osteoarthritis simulation and demonstrate the functionality of the proposed bone-cartilage unit model.

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Collagen network is one of the articular cartilage (AC) vital components, which contributes to the depth-dependent and anisotropic response of the tissue. As it is computationally expensive to simulate all the structural details of the AC network, they were typically simplified in numerical analysis. In particular, the so-called arcade-like structure, which has been widely used in the previous complex simulations, does not capture the rotations of the fibrillar bundles. In this study, we investigate the role of such possible rotations in the AC mechanical response by a set of advanced, biphasic, and parametric finite element (FE) simulations of indentation tests. Our results unveil the influence of fibrillar rotations (FR) on the mechanical response by increasing the fibrillar stress while regionally affecting the stress in the upper layers of the AC tissue. On the contrary, the FR did not significantly alter the tissue elasticity, and consequently might be ignored safely in pure contact mechanical problems. It is concluded that the excessive FR might regionally increase the stress, which can have a degenerative effect on the collagen constituent, and therefore, should not be neglected in the corresponding future studies, in which the upper AC layers resist high permanent shear strains.

Numerical simulation is widely used to study physical systems, although it can be computationally too expensive. To counter this limitation, a surrogate may be used, which is a high-performance model that replaces the main numerical model by using, e.g., a machine learning (ML) regressor that is trained on a previously generated subset of possible inputs and outputs of the numerical model. In this context, inspired by the definition of the mean squared error (MSE) metric, we introduce the pointwise MSE (PMSE) metric, which can give a better insight into the performance of such ML models over the test set, by focusing on every point that forms the physical system. To show the merits of the metric, we will create a dataset of a physics problem that will be used to train an ML surrogate, which will then be evaluated by the metrics. In our experiment, the PMSE contour demonstrates how the model learns the physics in different model regions and, in particular, the correlation between the characteristics of the numerical model and the learning progress can be observed. We therefore conclude that this simple and efficient metric can provide complementary and potentially interpretable information regarding the performance and functionality of the surrogate.