||Tendon-to-bone insertions are functionally-graded connective tissues whose anisotropic biomechanical functions depend intimately on the regional biochemical composition and structure . The insertion site provides a gradual transition from soft tendon tissue to hard bone tissue, functioning to alleviate stress concentration at the junction of these tissues . Specifically, dense and highly aligned collagen fibers are characteristic of the tendon side of the junction, and a high density of the mineral hydroxyapatite with randomly distributed collagen fibers is characteristic at the bone side. Inhomogeneity and discontinuities in tissue-level properties at the insertion site manifest in the unique, stress concentration-reducing material behavior at the macro-scale.
To better understand how tendon-to-bone insertion performs its function, we developed a computational model of tendon-to-bone insertion implemented in commercial finite element software ABAQUS. We adopted linear elastic and nonlinear anisotropic Gasser-Ogden-Holzapfel model  to incorporate collagen fiber dispersion and mineralization concentration. We started with a simplified geometry of tendon-to-bone insertion . A python script was 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 was 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 was observed that spatial grading results in more smooth stress distributions and significantly reduces maximum stresses. The geometry of the tissue model could be 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 functions and may be also useful to planning surgical interventions and developing orthopedic implants.
 G. M. Genin et al, Functional Grading of Mineral and Collagen in the Attachment of Tendon to Bone(2009), Biophysical Journal, Vol.97, 976-986.
 Y. Liu et al, Mechanisms of Bimaterial Attachment at the Interface of Tendon to Bone(2011), J. Eng. Mater. Technol., Vol.133.  T. C. Gasser et al, Hyperelastic Modeling of Arterial Layers with Distributed Collagen Fibre Orientations(2006), J. R. Soc. Interface, Vol.3, 15-35.