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

Abstract

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, [Formula: see text], 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 [Formula: see text], 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 [Formula: see text] data of circumferential and interstitial tissue. The experimental and the model data compare very well for both tissue types (relative error 6-8 %).

The asymptotic homogenization elasticity tensor properties for composites with material discontinuities

“…We perform the three dimensional numerical simulations via the finite element software COMSOL Multiphysics and exploit the same computational setting described in detail in [33], in particular assuming a linear elastic isotropic and uniform behavior of both the matrix and the inclusion phases. The Young's moduli and Poisson's ratios, denoted by E A , E B and ν A , ν B , respectively, are consistent to those exploited in [33]; they refer to the realistic scenario reported in [42], so that, identifying our matrix Ω A and our inclusion Ω B with the collagen matrix and the (hydroxyapatite) mineral inclusion in the bone, we have…”

“…Further average field techniques involve the well-known results by Eshelby [12], i.e. the representative volume is identified with an infinite medium equipped with uniform strain condition at infinity (which also satisfies Hill's condition), and the different constituents are modeled as ellipsoidal inclusions; this way, the strain inside the inclusions turns out to be uniform, and further approximations (such as the Mori-Tanaka [27] and self-consistent [19] schemes) can be exploited to compute the effective elastic constants semi-analytically (see, e.g., [42], where these techniques are exploited to compute the mineralized turkey leg tendon elastic constants and validated against experimental data).…”

Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues

“…mineralized turkey leg tendon (MTLT) [23], human femur [24], human radius [25] and mice [26]. The lines show the upper and lower stiffness bounds predicted by the MTLT model proposed in [23]. The encircled data are predominantly from interstitial tissue regions and are clearly outside the range predicted by the MTLT model (reprinted from Tiburtius et al [23] with permission).…”

“…The experimental data have been obtained from various tissues and specimen, i.e. mineralized turkey leg tendon (MTLT) [23], human femur [24], human radius [25] and mice [26]. The lines show the upper and lower stiffness bounds predicted by the MTLT model proposed in [23].…”

“…In other words, for given phase volume fractions, mean field approaches do not distinguish between a fused end-to-end network of mineral crystals and a dense cloud of small (not connected) mineral crystals. In [23] we developed a multiscale Eshelby-based model for the hierarchical structure of the mineralized turkey leg tendon (MTLT). We exploited a sequence of nested models to compute the apparent stiffness of MTLT on the basis of (a) The MCF and ES compartments, represented as collagen-mineral and mineral-water composites, respectively (b) the mineralized collagen fibril bundle (MCFB), modeled as composite consisting of an ES and an MCF phase, and (d) the MTLT, comprising the MCFB and the (micro) pores phases.…”