Assessing the effective elastic properties of the tendon-to-bone insertion: a multiscale modeling approach
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ORIGINAL PAPER
Assessing the effective elastic properties of the tendon‑to‑bone insertion: a multiscale modeling approach A. Aghaei1,2 · N. Bochud1,2 · G. Rosi1,2 · S. Naili1,2 Received: 4 May 2020 / Accepted: 20 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The interphase joining tendon to bone plays the crucial role of integrating soft to hard tissues, by effectively transferring stresses across two tissues displaying a mismatch in mechanical properties of nearly two orders of magnitude. The outstanding mechanical properties of this interphase are attributed to its complex hierarchical structure, especially by means of competing gradients in mineral content and collagen fibers organization at different length scales. The goal of this study is to develop a multiscale model to describe how the tendon-to-bone insertion derives its overall mechanical behavior. To this end, the effective anisotropic stiffness tensor of the interphase is predicted by modeling its elastic response at different scales, spanning from the nanostructural to the mesostructural levels, using continuum micromechanics methods. The results obtained at a lower scale serve as inputs for the modeling at a higher scale. The obtained predictions are in good agreement with stochastic finite element simulations and experimental trends reported in literature. Such model has implication for the design of bioinspired bi-materials that display the functionally graded properties of the tendon-to-bone insertion. Keywords Tendon-to-bone insertion · Homogenization · Continuum micromechanics · Biological interphase · Functionally graded material · Partially mineralized tissue
1 Introduction The interaction between soft and hard tissues is essential to ensure good mobility to the musculoskeletal system. Specifically, the integration between tendon (or ligament) and bone occurs through a particular tissue interphase called enthesis, which derives from the ancient Greek word referring to the insertion. According to their musculoskeletal site of insertion, entheses can be characterized as fibrous or fibrocartilaginous (Benjamin et al. 2002). Fibrous (or indirect) insertions are usually found where tendons and ligaments attach to the shaft of long bones, such as the insertion of the deltoid tendon into the humerus or the tibial insertion of the medial collateral ligament. Fibrocartilaginous (or direct) insertions are more common and present at the bony attachments of the rotator cuff, the anterior cruciate ligament * N. Bochud nicolas.bochud@u‑pec.fr 1
Univ Paris Est Creteil, CNRS, MSME, F‑94010 Creteil, France
Univ Gustave Eiffel, MSME, F‑77454 Marne‑la‑Vallée, France
2
and the Achilles tendons. Fibrocartilaginous insertions are generally divided into four distinct regions with different compositions, functions and biomechanical properties: (1) the tendon, which consists of aligned type I collagen fibers with a small amount of non-collagenous proteins (NCPs), including proteoglycans and the remaining volume fil
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