Bone Remodeling Process: Mechanics, Biology, and Numerical Modeling

By Rabeb Ben Kahla and Abdelwahed Barkaoui

Bone Remodeling Process: Mechanics, Biology, and Numerical Modeling provides a literature review. The first part of the book discusses bones in a normal physiological condition, bringing together the involved actors and factors reported over the past two decades, and the second discusses pathological conditions, highlighting the attack vectors of each bone disease. The third part is devoted to the mathematical descriptions of bone remodeling, formulated to develop models able to provide information that is not amenable to direct measurement, while the last part focuses on models using the finite element method in investigating bone biomechanics.This book creates an overall image of the complex communication network established between the diverse remodeling actors, based on overwhelming control evidence revealed over recent years, as well as visualizes the remodeling defects and possible treatments in each case. It also regroups the models allowing readers to analyze and assess bone mechanical and biological properties. This book details the cellular mechanisms allowing the bone to adapt its microarchitecture to the requirements of the human body, which is the main issue in bone biology and presents the evolution of mathematical modeling used in a bone computer simulation.

• Each chapter covers a core topic in bone biomechanics
• Provides a multidisciplinary view that effectively links orthopaedics, cellular biology, mechanics, and computer simulation
• Draws an overall image about bone biology and cell interactions, for identifying cell populations that are crucial for the remodeling process

• Language: English
• Publisher: Academic Press
• Release date: Aug 14, 2021
• ISBN: 9780323902052

Rabeb Ben Kahla

Rabeb BEN KAHLA is a Mechanical Engineering PhD student at the National Engineering School of Tunis, Tunisia. She conducts research at LASMAP (Research Laboratory of Systems and Applied Mechanics) of Tunisia Polytechnic School. Currently assistant teacher at Ecole d'Ingénieurs Généraliste du Numérique (Efrei PARIS), France, she is the author of the book “Finite element method and medical imaging techniques in bone biomechanics” (Wiley ISBN: 978-1-786-30518-3) and three publications in well-known journals in the field of biomechanics (Journal of the Mechanical Behavior of Biomedical Materials, Biomechanics and Modeling in Mechanobiology , Journal of Mechanics in Medicine and Biology).

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Chapter 1

Bone multiscale mechanics

Abstract

Bones represent about 15% of the body’s weight, a figure which doesn’t deserve any interpretation of consequence. Most importantly, ambulation, ventilation, and protection of the human body is bone dependent for a start, highlighting the mechanical function of the bones making them a structural material with mechanical characteristics like any other mineral building material even if the process of discovery and study of the linkage between micro-components and bulk material is opposite for the two types of material. After more than 2000 years of improvements, we know the right components to make a very good steel but we don’t know yet how to fight osteoporosis efficiently in its natural occurrence with age. Following the Wolff’s law: bone remodels stronger where external stress goes higher. Literature shows many studies try and give probable cause of this tenet without the actual key of the phenomenon, which might hopefully be tantamount to unlock the osteoporosis treatment stalemate. Bone cells are no different from the other body cells (at the notable exception of neurons) with constant renewing until the process dramatically seizes up. So, characterization of bone mechanical behavior is not dependent on the bone age, as bone is always young, but the age of the individual and biological disorders and mechanical disturbances fall upon it. Beside shape and appearance, bone is classified into two main types: cortical, hard and dense and trabecular, porous and where plentiful biological processes, with some not yet deciphered, are taking place. Following characterization concerns cortical and trabecular separately then the composite of both. The objective of this first chapter is to better understand all the complexity of human bones related to: its structure, its composition, its histology, and its mechanical behavior at different levels of scales.

Keywords

Bone; bone mechanics; bone remodeling; multiscale hierarchical; bone proprieties

Abbreviations

ACP amorphous calcium phosphate

ARC arcuate nucleus

ATP adenosine triphosphate

BMP bone morphogenetic protein

BMU basic multicellular unit

BRC bone remodeling compartment

CLB circumferential lamellar bone

CRISPR clustered regularly interspaced short palindromic repeats

GAGs proteoglycans

HA hydroxyapatite

HCs Haversian canals

HRpQCT high resolution peripheral quantitative computed tomography

HSCs hematopoietic stem cells

IR infrared

M-CSF macrophage colony stimulating factor

MSCs mesenchymal stem cells

NCPs noncollagenous proteins

OPG osteoprotegerin

pQCT peripheral quantitative computed tomography

QCT quantitative computed tomography

PTH parathyroid hormone

NPY neuropeptide Y

RANK receptor activator of nuclear factor kappa beta

RGD arginine-glycine-aspartic

RPI reference point indentation

SERT serotonin transporter

SEM scanning electron microscopy

SSI strain stress index

VC Volkman canals

VMH ventromedial hypothalamus

µCT microcomputed tomography

1.1 Bone multiscale and hierarchical organization

Following the hierarchical scheme proposed by Weiner and Wagner (1998), representing seven hierarchical organization levels of the lamellar bone, Reznikov et al. (2014) adapted the same scheme while taking into account the existence of ordered and disordered materials (Fig. 1.1). The new resulting scheme is mainly related to the lamellar bone, as the latter is the most abundant structural type found in the adult skeleton. According to this figure, bone is arbitrarily subdivided into nine hierarchical levels, which only applies to lamellar bone. Some other types of bone materials, such as woven bone, could well be divided into fewer hierarchical levels. Still, more work is definitely required to confirm the existence of both ordered and disordered materials in other bone types. Besides, levels 1, 2 and 3 are assumed to be common to all bone types, which also requires further investigations.

Figure 1.1 Hierarchical organization levels of the lamellar bone.

Fig. 1.1 illustrates the classification proposed by Reznikov et al. (2014), that describes the set of bone scale levels, taking a human femur as an example: (I) longitudinally cut femur, (II) SEM of trabecular and cortical tissue, (III) a single trabeculae and osteon, (IV) lamella, (V) fibular organizations, (VI) mineralized collagen fibril (VII) collagen molecules and mineral nanostructure and (VIII) atomic structure of the main bone components.

Table 1.1 summarizes different classifications of the multiscale structure of the bone.

Table 1.1

Each of the multiscale structure nine levels proposed by Reznikov et al. (2014) is elaborated separately below.

1.1.1 Bone elementary components

At this coarse description level, the mineral and biomolecular components of both the ordered and disordered materials are similar. The ordered material mainly comprises type I collagen, mineral carbonated HA and water, in addition to minor amounts of other collagen types, NCPs and GAGs. The disordered material mainly contains type I collagen and carbonated HA, in addition to relatively large amounts of NCPs, GAGs and water, forming what can be loosely called ground mass. Yet, the specific molecular components of the disordered material should be the subject of deeper studies (Reznikov et al., 2014).

Mineral phase: The mineral phase of mature bone is made up of carbonated HA in the form of thin (Fig. 1.2) plate-shaped crystals. At the atomic level, the mature carbonated HA crystals are relatively disordered, in part because of the highly disordered precursor phase, from which the crystals form, the several included additives, such as carbonate, that these crystals contain, and the very thin thickness characterizing the mature crystals, resulting in a large surface-to-bulk ratios. The crystal surface is known to be relatively disordered compared to the bulk (Reznikov et al., 2014).

Figure 1.2 Plate-shaped crystals of bone HA: (A) SEM scanning electron microscopy of HA particles showing the diversity of their shapes and sizes, (B) SEM of HA particles showing their porous structure, (C) The arrangement of the different atoms of HA ( Peccati et al., 2018), (D) A medium height is accepted for almost all researchers: 50 nm *25 nm *3 nm.

The size and shape of HA crystals were observed using transmission electron microscopy (TEM) (Landis et al., 1996; Weiner & Traub, 1992) and small angle X-ray scattering (SAXS) (Fratzl et al., 1992; Paris et al., 2000). The majority of research studies considered that the HA molecules were gathered in the form of plaques (Fratzl et al., 2004; Jackson et al., 1978; Landis et al., 1993; Rubin et al., 2003). A range of geometric dimensions is given to HA crystals. The thickness varies from 2 to 7 nm, the length from 15 to 200 nm and the width from 10 to 80 nm (Eppell et al., 2001). An average size is accepted for almost all researchers, taking its dimensions as follows: 50 nm *25 nm *3 nm (Rho et al., 1998). The largest dimension of the mineral is oriented along the mineralized collagen fibril axis (Rubin et al., 2003).

Several experimental and numerical studies have been carried out to define the mechanical behavior of HA and to determine its mechanical properties (Barkaoui et al., 2015; Katz & Ukraincik, 1971; Lees & Rollins, 1972; Zamiri & De, 2011). Table 1.2 groups the elastic mechanical properties of the mineral reported in the literature. The modulus of elasticity of HA crystals varies from 111 to 170 GPa and its Poisson’s ratio from 0.23 to 0.45.

Table 1.2

Collagen: Type I collagen, made up of the triple helical molecules (Fig. 1.3), is the most abundant protein in mature bone, despite the existence of other collagen types, such as types III, VI and V. The staggered array structure of the triple helical molecules generates the formation of spaces, often referred to as holes, within the fibril. In bone, these holes are aligned to form thin extended slots, named grooves, in which the intrafibrillar crystals form. Based on the presence of the characteristic repeat structure in the collagen fibrils from both ordered and disordered materials, type I collagen is assumed to be a major component of both of these material types (Kraiem et al., 2018; Reznikov et al., 2014).

Figure 1.3 Collagen triple helix structure: (A) crystal structure of a collagen triple helix, (B) ball-and-stick image of a segment of collagen triple helix, (C) stagger of the three strands in the segment in panel ( Bella et al., 1994).

Several studies on mechanical behavior (Buehler & Wong, 2007; Buehler et al., 2008) and mechanical properties (An et al., 2004; Sun et al., 2004) of collagen molecules have been realized. Sasaki and Odajima (1996) studied the stress-strain behavior of collagen in the case of tensile loading, using the X-ray diffraction technique. They deduced that in its hydrated state, collagen has a linear behavior and its Young’s modulus has been estimated to be between 2.8 and 3.0 GPa. Sun et al. (2004) studied its behavior using an optical technique, finding that the modulus of elasticity of collagen ranges from 0.35 to 12. Buehler and Wong (2007) isolated and tested a single molecule of collagen under tensile loading and suggested that the collagen behaves nonlinearly following four regimes (Fig. 1.4).

Figure 1.4 Mechanical behavior of collagen: (A) Force displacement curve of a collagen molecule (B) enlargement of the first regime of the displacement force curve characterized by entropic elasticity (Buehler & Wong, 2007).

Water: Water is an essential component of bone and is present in various types that should also be integrated into the different hierarchical organizational levels. At level I, designating the crystal level, water bounds to the crystal surface. This is particularly prevalent when this surface comprises a disordered ACP-like layer. The absence or the partial presence of mineral is associated to the presence of water molecules between the collagen triple helical molecules. Interestingly, dehydration of lamellar bone causes a more pronounced contraction of the lamellae in the direction perpendicular to the lamellar boundary compared to the orthogonal direction, which indicates the presence of liquid water in the collagen channels, even in mineralized bone. Unbound water is likely to be present in the canaliculi, lacunae, and blood vessels (Reznikov et al., 2014).

Noncollagenous proteins and proteoglycans: Numerous noncollagenous proteins are present in bone, but most of them are not unique to it. However, several bone-related GAGs, such as decorin and biglycan, and a series of bone-related NCPs, such as osteocalcin, osteonectin, matrix gla protein, alkaline phosphatase, RGD and BAG-75 containing proteins, including bone sialoprotein and osteopontin, are thought to be crucial factors in bone formation. Surprisingly, little is known about the precise specific NCP macromolecule locations in bone and their specific functions (Reznikov et al., 2014).

1.1.2 Structural components level

The collagen molecules are organized into fibrils and may well be oval shaped. Crystals of carbonated HA nucleate from a disordered precursor phase within the gaps inside the fibril, and extend into the overlap zones while growing. This leads to the production of the mineralized collagen fibril that contains layers of plate-shaped crystals that span the fibril cross-section. Therefore, the fibril has no radial symmetry, but holds an essentially orthotropic crystalline structure (Fig. 1.5).

Figure 1.5 Mineralized collagen fibril: (A) TEM illustrating the collagen fibrils seen in the longitudinal section, (B) collagen molecules and mineral HA structural organization ( Facca et al., 2010).

Mineralized collagen fibrils represent the major ordered material component. The crystal c-axes are well aligned with the collagen fibril axis. Mineralized collagen fibrils are also present in the disordered material, and together with the abundant ground mass and the canaliculi, these fibrils contain only one of the major constituents. In the ordered material, the collagen fibrils are intimately associated with most of the crystals, whether in the interior or on the surface. In the disordered material, crystals were observed both within and between the collagen fibrils. Other studies also concluded the existence of crystals within and between the collagen fibrils, but did not notice the existence of the disordered material, which led to assume that this intrafibrillar and extrafibrillar crystal motif characterizes all lamellar bone types (Reznikov et al.,