title: A multiscale modelling of bone ultrastructure elastic proprieties using finite elements simulation and neural network method.
abstract: Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties, including high fracture toughness, specific stiffness and strength. Bone tissue is essentially composed by two phases distributed in approximately 30-70%: an organic phase (mainly type I collagen and cells) and an inorganic phase (hydroxyapatite-HA-and water). The nanostructure of bone can be represented throughout three scale levels where different repetitive structural units or building blocks are found: at the first level, collagen molecules are arranged in a pentameric structure where mineral crystals grow in specific sites. This primary bone structure constitutes the mineralized collagen microfibril. A structural organization of inter-digitating microfibrils forms the mineralized collagen fibril which represents the second scale level. The third scale level corresponds to the mineralized collagen fibre which is composed by the binding of fibrils. The hierarchical nature of the bone tissue is largely responsible of their significant mechanical properties; consequently, this is a current outstanding research topic. Scarce works in literature correlates the elastic properties in the three scale levels at the bone nanoscale. The main goal of this work is to estimate the elastic properties of the bone tissue in a multiscale approach including a sensitivity analysis of the elastic behaviour at each length scale. This proposal is achieved by means of a novel hybrid multiscale modelling that involves neural network (NN) computations and finite elements method (FEM) analysis. The elastic properties are estimated using a neural network simulation that previously has been trained with the database results of the finite element models. In the results of this work, parametric analysis and averaged elastic constants for each length scale are provided. Likewise, the influence of the elastic constants of the tissue constituents is also depicted. Results highlight that intelligent numerical methods are powerful and accurate procedures to deal with the complex multiscale problem in the bone tissue with results in agreement with values found in literature for specific scale levels.
authors.affiliation: Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie (LR-MAI), 1002 Tunis, Tunisie; Université de Tunis El Manar, Institut Préparatoire aux Etudes d'Ingénieurs d'El Manar, B.P 244, 2092 Tunis, Tunisie. Electronic address: aabarkaoui@gmail.com.
authors.forename: Abdelwahed
authors.initials: A
authors.lastname: Barkaoui
authors.affiliation: Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis, LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie (LR-MAI), 1002 Tunis, Tunisie; Université de Tunis El Manar, Institut Préparatoire aux Etudes d'Ingénieurs d'El Manar, B.P 244, 2092 Tunis, Tunisie.
authors.forename: Brahim
authors.initials: B
authors.lastname: Tlili
authors.affiliation: Depto. de Ingeniería Mecánica y de Materiales, Centro de Investigación de Tecnología de Vehículos-CITV, Universitat Politècnica de València, Camino de Vera, 46022 Valencia, Spain.
authors.forename: Ana
authors.initials: A
authors.lastname: Vercher-Martínez
authors.affiliation: PRISME Laboratory, EA4229, University of Orleans Polytech' Orléans, 8, Rue Léonard de Vinci, 45072 Orléans, France.
authors.forename: Ridha
authors.initials: R
authors.lastname: Hambli
mesh_terms: D001842:Bone and Bones / Q000648:ultrastructure*; D004548:Elasticity; D020342:Finite Element Analysis; D006801:Humans; D008855:Microscopy, Electron, Scanning; D008962:Models, Theoretical; D016571:Neural Networks, Computer
keywords: Bone ultrastructure; Elastics properties; Finite element method; Multiscale modelling; Neural network computation