Strength Increase During Ceramic Biomaterial-Induced Bone Regeneration: A Micromechanical Study

Abstract

Bone tissue engineering materials must blend in the targeted physiological environment, in terms of both the materials' biocompatibility and mechanical properties. As for the latter, a well-adjusted stiffness ensures that the biomaterial's deformation behavior fits well to the deformation behavior of the surrounding biological tissue, whereas an appropriate strength provides sufficient load-carrying capacity of the biomaterial. Here, a mathematical modeling approach for estimating the macroscopic load that initiates failure of a hierarchically organized, granular, hydroxyapatite-based biomaterial is presented. For this purpose, a micromechanics model is developed for downscaling macroscopically prescribed stress (or strain) states to the level of the needle-shaped hydroxyapatite crystals. Presuming that the biomaterial fails due to the quasi-brittle failure of the most unfavorably stressed hydroxyapatite needle, the downscaled stress tensors are fed into a suitable, Mohr-Coulomb-

Mathematical and computational models for bone tissue engineering in bioreactor systems

“…55 Downscaling schemes can then be used to derive the stress and strain levels at the micro-scale from known mechanical loads at the macro-scale to model bone remodelling driven by pore-specific mechanosensation. 56,57 In contrast, some models exploit the separation of the micro- and macro-scales through asymptotic techniques and applying knowledge of the pore-scale, derive construct-level models, for example, to obtain Darcy-type description of mass transport 58 or poroelastic continuum formulations of tissue growth resulting from nutrient exchange with the liquid phase. 59…”