Mathematical Model of Age-Specific Tendon Healing

Tendons perform unique functions in the body-transmit muscle generated force to bones for joint motion. However, decreased mechanical response is observed post-injury and during aging, which in turn limits functional capacity. While there are many strategies aimed at restoration of pre-injury mechanical properties, they fail typically because of lack of understanding of tendon healing mechanisms, particularly at the extracellular matrix level. Toward this end, mathematical models, especially those with microstructural details can be insightful. In prior study, we evaluated the ability of three constitutive models to describe uniaxial mechanical test data from murine patellar tendons excised pre- and post-injury from multiple age groups. The chosen models range from simple i.e. the Freed-Rajagopal (FR) model, to complex i.e. the Gasser-Ogden-Holzapfel (GOH) and Shearer (SHR) models. Least-squares optimization was performed to obtain model parameter values, while the models fitted the experimental data adequately, the relatively complex models exhibited low parameter identifiability evidenced by high correlation. To address the limitations observed in the prior study, we adopted a Bayesian approach using an adaptive Markov chain Monte Carlo (MCMC) to compute the posterior distribution of model parameters. Agreement of two approaches was observed only in the FR model parameters. This study highlights the trade-off between model complexity and confidence level of inferred parameters, the critical need for structural data to motivate clinical relevance of mathematical model for tendons. Addressing these needs would enhance translational research and motivate the rational design of tissue engineering strategies for better treatment outcomes.