Mathematics as a conduit for translational research in post-traumatic osteoarthritis.

Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients. In this sense, we refer to the mathematics as a "conduit of translation." The new in silico framework presented in this paper involves a biomathematical model for the cellular and biochemical response to strains computed using finite element analysis. The model predicts qualitative responses presently, utilizing system parameter values largely taken from the literature. To contribute to accurate predictions, models need to be accurately parameterized with values that are based on solid science. We discuss a parameter identification protocol that will enable us to make increasingly accurate predictions of PTOA progression using additional data from smaller scale explant and small animal assays as they become available. By distilling the data from the explant and animal assays into parameters for biomathematical models, mathematics can translate experimental data to clinically relevant knowledge.