This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

At the molecular scale, bone is mainly constituted of type-I collagen, hydroxyapatite, and water. Different fractions of these constituents compose different composite materials that exhibit different mechanical properties at the nanoscale, where the bone is characterized as a fiber, i.e., a bundle of mineralized collagen fibrils surrounded by water and hydroxyapatite in the extra-fibrillar volume. The literature presents only models that resemble mineralized collagen fibrils, including hydroxyapatite in the intra-fibrillar volume only, and lacks a detailed prescription on how to devise such models. Here, we present all-atom bone molecular models at the nanoscale, which, differently from previous bone models, include hydroxyapatite both in the intra-fibrillar volume and in the extra-fibrillar volume, resembling fibers in bones. Our main goal is to provide a detailed prescription on how to devise such models with different fractions of the constituents, and for that reason, we have made step-by-step scripts and files for reproducing these models available. To validate the models, we assessed their elastic properties by performing molecular dynamics simulations that resemble tensile tests, and compared the computed values against the literature (both experimental and computational results). Our results corroborate previous findings, as Young’s Modulus values increase with higher fractions of hydroxyapatite, revealing all-atom bone models that include hydroxyapatite in both the intra-fibrillar volume and in the extra-fibrillar volume as a path towards realistic bone modeling at the nanoscale.

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Bones are responsible for body support, structure, motion, and several other functions that enable and facilitate life for many different animal species. They exhibit a complex network of distinct physical structures and mechanical properties, which ultimately depend on the fraction of their primary constituents at the molecular scale. However, the relationship between structure and mechanical properties in bones are still not fully understood. Here, we investigate structural and mechanical properties of all-atom bone molecular models composed of type-I collagen, hydroxyapatite (HA), and water by means of fully atomistic molecular dynamics simulations. Our models encompass an extrafibrillar volume (EFV) and consider mineral content in both the EFV and intrafibrillar volume (IFV), consistent with experimental observations. We investigate solvation structures and elastic properties of bone microfibril models with different degrees of mineralization, ranging from highly mineralized to weakly mineralized and nonmineralized models. We find that the local tetrahedral order of water is lost in similar ways in the EFV and IFV regions for all HA containing models, as calcium and phosphate ions are strongly coordinated with water molecules. We also subject our models to tensile loads and analyze the spatial stress distribution over the nanostructure of the material. Our results show that both mineral and water contents accumulate significantly higher stress levels, most notably in the EFV, thus revealing that this region, which has been only recently incorporated in all-atom molecular models, is fundamental for studying the mechanical properties of bones at the nanoscale. Furthermore, our results corroborate the well-established finding that high mineral content makes bone stiffer.

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