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Elastic modeling of bone at nanostructural level

机译：在纳米结构水平上对骨骼进行弹性建模

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摘要

Bone is a connective tissue which gives body its support and stability. In mechanical terms, bone is a nanocomposite material with a complex hierarchical structure which contributes to bone's excellent mechanical properties, including high stiffness, strength and fracture toughness, and light weight. At nanoscale, cross-linked collagen molecules, hydroxyapatite (HA) nanocrystals, water, and a small amount of non-collagenous proteins (NCPs) form mineralized collagen fibrils (MCF). The MCF serves as the primary building block of bone, and, thus, its physical and mechanical characterization is critical for finding structure-property relations in bone and understanding bone's overall behavior. In this paper, we review the composition and structure of the MCF and summarize the existing models proposed in literature to predict its effective elastic response. These models can be classified into the following four categories: Ⅰ. Models based on strength of materials approach which are mainly variants of Voigt and Reuss bounds. Most of such models were originally proposed for characterization of composite materials; however, they are also applicable to model a MCF as a collagen-HA composite. Ⅱ. Models based on micromechanics theories. Ⅲ. Computational models, involving mostly a finite element method (FEM). Ⅳ. Atomistic simulations using molecular dynamics (MD). Each of these types of models has some advantages and disadvantages. The strength of materials models are simpler mathematically but they involve approximate solutions, while the micromechanics approaches usually involve simpler geometrical models which are solved more rigorously. Computational models, based mainly on the finite element method, can account more precisely for the structural features of bone including collagen-HA arrangement, collagen cross-links, and collagen-HA interphase. MD simulations, conducted at the atomic level and over very small regions, provide insights into properties of collagen molecules and fibrils, the effect of collagen cross-linking, and collagen-HA interphase, and can serve as inputs for continuum-based models. In this paper, we outline some representative models of bone at nanoscale (mineralized collagen fibril) and discuss the assumptions, limitations, and drawbacks of these models, present their comparison, and offer recommendations on the future work in this area. Such discussion will help to develop more complete models of MCF addressing physical, mechanical, and biological aspects of bone's behavior at the nanoscale. Furthermore, it will shed light on designs of collagen-HA nanocomposites with desired mechanical properties which can be used as biomaterials for orthopedic applications such as surface coatings for implant materials, as bone substitutes, and as scaffolds for bone tissue regeneration.
机译：骨是结缔组织，可为身体提供支撑和稳定性。用机械术语来说，骨骼是具有复杂层次结构的纳米复合材料，有助于形成骨骼的出色机械性能，包括高刚度，强度和断裂韧性以及重量轻。在纳米级，交联的胶原分子，羟基磷灰石（HA）纳米晶体，水和少量非胶原蛋白（NCP）形成矿化的胶原原纤维（MCF）。 MCF是骨骼的主要组成部分，因此，其物理和机械特性对于发现骨骼中的结构特性关系和了解骨骼的整体行为至关重要。在本文中，我们回顾了MCF的组成和结构，并总结了文献中提出的现有模型以预测其有效的弹性响应。这些模型可以分为以下四类：Ⅰ。基于材料强度方法的模型主要是Voigt和Reuss边界的变体。大多数此类模型最初是为表征复合材料而提出的。但是，它们也适用于将MCF建模为胶原HA复合材料。 Ⅱ。基于微力学理论的模型。 Ⅲ。计算模型，主要涉及有限元方法（FEM）。 Ⅳ。使用分子动力学（MD）的原子模拟。这些模型中的每一种都有一些优点和缺点。材料模型的强度在数学上比较简单，但是它们涉及近似解，而微力学方法通常涉及更简单的几何模型，这些模型需要更严格地求解。计算模型主要基于有限元方法，可以更精确地说明骨骼的结构特征，包括胶原蛋白HA排列，胶原蛋白交联和胶原蛋白HA间期。在原子水平和非常小的区域上进行的MD模拟可深入了解胶原蛋白分子和原纤维的特性，胶原蛋白交联的效果以及胶原蛋白HA的相间关系，并可作为基于连续谱的模型的输入。在本文中，我们概述了一些具有代表性的纳米级骨（矿化胶原蛋白原纤维）模型，并讨论了这些模型的假设，局限性和缺点，并进行了比较，并就此领域的未来工作提出了建议。这种讨论将有助于建立更完整的MCF模型，以解决纳米级骨骼行为的物理，机械和生物学方面的问题。此外，它将阐明具有所需机械性能的胶原-HA纳米复合材料的设计，这些材料可用作骨科应用的生物材料，例如植入材料的表面涂层，骨替代物以及骨组织再生的支架。

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