On the elastic properties of mineralized turkey leg tendon tissue: multiscale model and experiment

The key parameters influencing the elastic properties of the mineralized turkey leg tendon (MTLT) were investigated. Two structurally different tissue types appearing in the MTLT were considered: circumferential and interstitial tissue. These differ in their amount of micropores and their average diameter of the mineralized collagen fibril bundles. A multiscale model representing the apparent elastic stiffness tensor of MTLT tissue was developed using the Mori–Tanaka and the self-consistent homogenization schemes. The volume fraction of mineral (hydroxyapatite) in the fibril bundle, (hbox {vf}_{{text {ha}}}^{{text {MCFB}}}) , and the tissue microporosity are the variables of the model. The MTLT model was analyzed performing a global sensitivity analysis (Elementary Effects method) and a parametric study. The stiffnesses parallel (axial) and perpendicular (transverse) to the MTLT long axis were the only significantly sensitive components of the apparent stiffness tensor of MTLT tissue. The most important parameters influencing these apparent stiffnesses are (hbox {vf}_{{text {ha}}}^{{text {MCFB}}}) , tissue microporosity, as well as shape and distribution of the minerals in the fibril bundle (intra- vs. interfibrillar). The predicted apparent stiffness was converted to acoustic impedance for model validation. From measurements on embedded MTLT samples, including 50- and 200-MHz scanning acoustic microscopy as well as synchrotron radiation micro-computed tomography, we obtained site-matched acoustic impedance and (hbox {vf}_{{text {ha}}}^{{text {MCFB}}}) data of circumferential and interstitial tissue. The experimental and the model data compare very well for both tissue types (relative error 6–8 %).