Understanding the effects of mineralization and structure on the mechanical properties of tendon-bone insertion using mesoscale computational modeling

Tendon-bone fibrocartilaginous insertion, or enthesis, is a specialized interfacial region that connects tendon and bone, effectively transferring forces while minimizing stress concentrations. Previous studies have shown that insertion features gradient mineralization and branching fiber structure, which are believed to play critical roles in its excellent function. However, the specific structure-function relationship, particularly the effects of mineralization and structure at the mesoscale fiber level on the properties and function of insertion, remains poorly understood. In this study, we develop mesoscale computational models of the distinct fiber organization at tendon-bone insertions, capturing the branching network from tendon to interface fibers and the different mineralization scales. We specifically analyze three key descriptors: the mineralization scale of interface fibers, the mean, and relative standard deviation of the local branching angles of interface fibers. Tensile test simulations on insertion models with varying mineralization scales of interface fibers and structures are performed to mimic the primary loading condition applied to the insertion. We measure and analyze five representative mechanical properties: Young's modulus, strength, toughness, resilience, and failure strain. Our results reveal that mechanical properties are significantly influenced by the three key descriptors, with tradeoffs observed between mutually exclusive properties. For instance, strength and resilience plateau beyond a certain mineralization scale, while failure strain and Young's modulus exhibit monotonic decreasing and increasing trends, respectively. Consequently, there exists an optimal mineralization scale for toughness due to these tradeoffs. By analyzing the mesoscale deformation and failure mechanisms from simulation trajectories, we identify three fracture regimes closely related to the trends in mechanical properties, supporting the observed tradeoffs. Additionally, we examine in detail the effects of the mean and relative standard deviation of local branching angles on mechanical properties and deformation mechanisms. Overall, our study enhances the fundamental understanding of the composition-structure-function relationships at the tendon-bone insertion, complementing recent experimental studies. The mechanical insights from our work have the potential to guide the future biomimetic design of fibrillar adhesives and interfaces for joining soft and hard materials.