Estimation of the in-plane ultimate stress of lamellar tissue as a function of bone mineral density and osteocyte lacunae porosity

Abstract

Background and objective: Detailed finite element models based on medical images (μ-CT) are commonly used to analyze the mechanical behavior of bone at microscale. In order to simulate the tissue failure onset, isotropic failure criteria of lamellar tissue are often used, despite its non-isotropic and heterogeneous nature. The main goal of the present work is to estimate the in-plane ultimate stress of lamellar bone, considering the influence of mineral content and the porosity due to the osteocyte lacunae concentration.

Methods: To this aim, a representative volume cell of lamellar tissue is modeled numerically, including: (1) non-isotropic elastic properties of tissue as a function of the bone mineral density and (2) explicit modeling of the osteocyte lacunae, considering the range of porosity content, size and orientation of ellipsoid-shaped lacunae. Firstly, the element size for the finite element models have been defined from a preliminary convergence analysis. Bounds on the ultimate stress of non-porous lamellar tissue are estimated for two values of bone mineral density, considering the results of tensile and compressive tests of wet osteons from the literature. Subsequently, the ultimate stress of lamellar tissue considering several values of micro-porosity is addressed.

Results: Results obtained in this work show that the strength of lamellar bone decreases exponentially with the increase of lacunae porosity concentration. Ultimate stress of non-porous tissue (p=0%) increases with high mineral content, reaching a value of S¯_trans^c=355.40±39.80 MPa for compression in the transversal direction of the fiber bundles, being BMD=1.246g/cm³. The mean value for the longitudinal to transverse strength ratio evaluated for porosity p=0%,1% and 5% and a mineral content BMD=1.2g/cm³, is 2.47:1 for tension and 1.55:1 for compression. These values are in agreement with literature.

Conclusions: Osteocyte lacunae act as stress concentrators, acting as potential stimulus for the bone regeneration process. A novel micromechanical model for the in-plane ultimate stress of lamellar tissue as a function of mineral content and lacunae concentration is presented. Additional considerations about the intralamellar shear stress evolution are also given.

Keywords: Bone mineral density; Finite element analysis; In-plane ultimate stress; Lamellar bone; Micro-porosity; Osteocyte lacunae; Strength micromechanical model.