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CHA PTE R

10

Determination of the Anisotropic

Mechanical Properties of Bone Tissue

Using a Homogenization Technique

Combined With Meshless Methods

§
,†
,‡
Marco Marques* , Jorge Belinha* , Anto ´nio F. Oliveira ,
Renato M. Natal Jorge* ,†
†
*Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), Porto, Portugal Faculty of
‡
Engineering of University of Porto (FEUP), Porto, Portugal School of Engineering, Polytechnic of Porto (ISEP), Porto,
§
Portugal ICBAS—Abel Salazar Institute of Biomedical Sciences, Porto, Portugal

10.1 INTRODUCTION

Bones are the main integrant of the skeletal system by which the body supports, protects, and moves itself as well as
stores and produces blood cells. Bone is a complex structure that consists of two different tissue types: the cortical bone,
a thin and stiff outer layer, and the trabecular bone, which is more flexible and has a foam-like inner structure [1–3].
Bone biomechanics are based on the idea that bone provides a high load-carrying capacity and that bone tissue is struc-
turally optimized for this mechanical function [4, 5]. Considering this purpose, bone has a mechanism, bone remodel-
ing, that allows its microstructural integrity to be continuously maintained. This process can lead to bone removal via
osteoclasts or bone regeneration via osteoblasts [6–11]. It also occurs in other biological processes such as growth, rein-
forcement, and resorption. Bone remodeling has been continuously studied, resulting in the development of semiem-
pirical mathematical descriptions. These models simulate and predict experimental results using, for example,
computer science methodologies such as finite element methods (FEM). The efforts to understand the bone remodeling
phenomenon have led to a continuous development of semiempirical mathematical descriptions, but also to better
comprehension of the bone structure. It was observed that bone has different functional requirements at different
scales. This is the reason why some authors start to classify bone as a hierarchical multiscale material, with different
structural levels from the macroscale (whole bone) to the subnanoscale (hydroxyapatite crystals, constituent of the
inorganic phase of bone) [12–17]. Because bone has different functional requirements at different scales, it was neces-
sary to investigate the mechanical properties of its distinct components and the structural relationships across different
scales [18, 19]. The evolution of the hierarchical bone classification also led to the evolution of models that allow study-
ing bone biological and mechanical processes by incorporating a multiscale approach.
Mechanoregulatory models are defined by laws that only consider the influence of mechanical factors in bone remo-
deling. In bioregulatory models, only the biochemical factors are considered while in the mechanobioregulatory
models, both mechanical and biochemical factors are considered. Despite being more representative in comparison
with mechanoregulatory and bioregulatory models, mechanobioregulatory models are more complicated due to
the higher number of assumptions and restrictions involved in their formulation. The mechanoregulatory was the
first to appear, in 1960 by Pauwels [20]. In 1999, Adam and coworkers [21] created one of the first bioregulatory
modes to characterize bone behavior. Later, the mechanobioregulatory models appear as a combination of the

Advances in Biomechanics and Tissue Regeneration 201 © 2019 Elsevier Inc. All rights reserved.
https://doi.org/10.1016/B978-0-12-816390-0.00010-8