Tendon-to-bone insertion provides a gradual transition from soft tendon to hard bone tissue, functioning to alleviate stress concentrations at the junction of these tissues. Such macroscopic mechanical properties are achieved due to the internal structure in which collagen fibers and mineralization levels are key ingredients. We develop a structural-based model of tendon-to-bone insertion incorporating such details as fiber preferred orientation, fiber directional dispersion, mineralization level, and their inhomogeneous spatial distribution. A python script is developed to alter the tapered tendon-bone transition zone and to provide spatial grading of material properties, which may be rather complex as experiments suggest. A simple linear interpolation between tendon and bone material properties is first used to describe the graded property within the insertion region. Stress distributions are obtained and compared for spatially graded and various piece-wise materials properties. It is observed that spatial grading results in more smooth stress distributions and significantly reduces maximum stresses. The geometry of the tissue model is optimized by minimizing the peak stress to mimic in-vivo tissue remodeling. The in-silico elastic models constructed in this work are verified and modified by comparing to our in-situ biaxial mechanical testing results, thereby serving as translational tools for accurately predicting the material behavior of the tendon-to-bone insertions. This model will be useful for understanding how tendon-to-bone insertion develops during tissue remodeling, as well as for developing orthopedic implants.
Keywords: Biaxial mechanical testing; Constitutive model; Fiber dispersion; Functionally graded materials; Graded microstructure; Shape optimization.
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