The role of mathematical models in prediction of osteoarthritis development

In the paper we presented the review of mathematical and numerical models of osteoarthritis (OA). As angiogenesis seems to be the most principal factor in OA mathematical and numerical modelling, we focused on the models that consider the process. The spectrum of the presented models is wide. They were divided in the scale of the simulated phenomena, i.e., micro- or macro-scale. A part of them considers only damage of tissue without paying attention to its remodeling. Others consider loss of tissue, new tissue formulation and remodeling of bone, both in micro- and macro-scale. What is worth mentioning is that most of the models were confirmed by comparing results to data available in literature. Only a few of them were experimentally validated. As the conclusion, we stated that the most accurate models are those that take into consideration mechanical stimulation, biological signaling and their nonlocal effects. Also, an important feature of an OA model is the ability to adapt it to various cases to be able to simulate OA in any joint.