Hierarchical Biomechanics: Concepts, Bone as Prominent Example, and Perspectives Beyond

Abstract

Biological materials and systems are hierarchically organized.The main motivation for hierarchical biomechanics is that the wide variability of mechanical properties encountered at the macroscopic scale may be traced back to just a few universal. i.e. tissue-invariant, mechanical properties of elementary components at a sufficiently small scale (such as collagen, elastin, and water in case of soft tissues; complemented by hydroxyapatite in case of hard tissues), and to the nano and microstructures which the latter build up. This challenging task requires a physically rigorous and mathematically sound basis, as provided by Finite Element and Fast Fourier Transform methods, as well as by continuum micromechanics resting on (semi-)analytical solutions for Eshelby-type matrix-inclusion problems. Corresponding numerical and analytical mathematical models have undergone diligent experimental validation, by means of data stemming from a variety of biophysical, biochemical, and biomechanical testing methods, such as light and electron microscopy, ultrasonic testing and scanning acoustic microscopy, as well as physico-chemical tests associated with dehydration, demineralization, decollagenization, ashing, and weighing in air and fluid. While elastic scale transition and homogenization methods have attained a high maturity level, the hierarchical nature of dissipative (i.e. viscous or strength) properties is still a vibrant field of research. This applies even more to hierarchical approaches elucidating the interface between biological cells and extracellular matrices, and to the highly undiscovered mechanics unfolding within biological cells.

A coarse-grained molecular dynamics investigation of the role of mineral arrangement on the mechanical properties of mineralized collagen fibrils

“…Furthermore, in this study, we only consider a single MCF and do not consider other components of the ultrastructural arrangement. In particular, the extrafibrillar matrix and non-collagenous proteins, which are shown to significantly affect the bone mechanical properties [40][41][42][43]76,77], have not been considered. Several other studies have explicitly considered the important role of extrafibrillar mineralization on the effective properties of the tissue [40][41][42][43][44], and these have shown excellent agreement with experimental observations in the elastic regime.…”

“…In particular, the extrafibrillar matrix and non-collagenous proteins, which are shown to significantly affect the bone mechanical properties [40][41][42][43]76,77], have not been considered. Several other studies have explicitly considered the important role of extrafibrillar mineralization on the effective properties of the tissue [40][41][42][43][44], and these have shown excellent agreement with experimental observations in the elastic regime. However, the model presented here is an idealized MCF model, which is more difficult to validate as it cannot be physically isolated from the tissue in the absence of an extrafibrillar mineral.…”

“…Several theoretical [26,[30][31][32][33][34] and computational models [28,[35][36][37][38][39][40][41][42][43][44] have been developed to predict the effective properties of mineralized tissues. These models have considered a range of configurations, but have generally assumed a staggered composite model of HAp minerals and collagen to predict the effective properties of the tissue through theoretical or numerical means.…”

Research progress on the regulatory mechanism of integrin‐mediated mechanical stress in cells involved in bone metabolism

“…Previous studies have shown that this process is influenced by the following main factors: (1) cell shrinkage, leading to cytoskeleton rearrangement in response to applied mechanical stimuli; 29 (2) ECM properties, 30 such as matrix stiffness and matrix roughness of the surface; and (3) the spatiotemporal characteristics of the applied stimulus 31,32 . Previous research has indicated that mechanical loading is applied and measured based on the consideration of length scale‐related factors 33 . Mechanical stress, whether defined as the force per unit area in a one‐dimensional analysis or through the Cauchy stress tensor in a three‐dimensional context, is highly dependent on the size of the area being measured.…”

Triple Function of Amelogenin Peptide-Chitosan Hydrogel for Dentin Repair

“…The highly oriented apatite crystals grown on the DD surface in the presence of the peptide-CS hydrogels formed a robust mineralized layer with organized structures, dictating its mechanical strength (Hellmich et al 2022). The newly formed apatitic layer bound tightly to the remineralized dentin and could withstand rigorous ultrasonication challenges.…”