Multiscale finite element analysis of bone

Bone possesses a complex hierarchical architecture with characteristic arrangement of material structures at individual length levels. The unique morphological features at each length scale affect the mechanical properties both at each scale and interdependently, and must be taken into account when understanding the basic mechanics of bone. In this study, five hierarchical levels of bone structures are recognized from the nanoscale to the macroscale, namely: mineralised collagen fibrils (level 1), collagen fibres (level 2), lamellae (level 3), cortical bone (level 4) and whole bone (level 5). At each level, the geometric and material properties of the constituents vary due to a range of factors, such as age, disease, gender, species, exercise, nutrition and anatomical location. This makes it imperative to conduct a parametric study in order to determine the mechanical properties of the whole bone.This study utilises the Finite Element Analysis (FEA) to predict the mechanical properties of a whole bone for a range of geometrical and material parameters at the lower length scales. A representative volume element (RVE) is designed for each level to capture the structural and material characteristics of that level. The RVE is then loaded to six independent loads and the mechanical properties determined. Beginning with the nanoscale RVE, the predicted mechanical properties are used as input parameters for the next level and this process is repeated up to the macroscale. Finally, a whole femur bone is subjected to a three-point bend simulation and the results compared with available experiments.Thus, the study confirms the feasibility of a multiscale FEA modelling in closely predicting the mechanical properties of the bone structure. It also demonstrates that element design and appropriate boundary conditions influence the property predictions, and that certain geometric parameters are more influential than others. The FEA simulation of three-point bending of the whole femur bone provides good agreement with the experiment, validating the current multiscale model. In the future, this model can be used in the development of a bone model tailored to a patient’s bone condition and possibly serve as a non-invasive tool to accurately predict the likelihood of patient’s bone fractures