A comparsion of different bone remodelling simulation algorithms based on micro finite element analysis

Abstract

Bone remodelling algorithms are designed to simulate transformations in bone structures caused by changes in loading, physiological changes, diseases or treatments. The mechanical stimulus is usually the strain energy density (SED) of the loaded structure based on finite element analysis. The results of bone remodelling are dependent on the resolution and structure of the initial geometry, material properties, boundary conditions and the used remodelling algorithms. The subject of this work is the investigation of these factors based on simplified digitized geometries. Four bone remodelling algorithms from the in literature were implemented into the in-house script manager medtool. All Finite Element Analyses were performed with ParOsol. The algorithms were calibrated on a reference model by varying their respective input parameters so that a predefined SED and similar mean bone volume fraction (BV/TV) were reached. The parameters of the reference model were gradually changed afterwards and the influence on the SED distribution, the BV/TV, and the micro-structure of each algorithm was investigated. The varied parameters were the voxel size and the shape of the initial structure, the boundary conditions of the model, the elasticity modulus of the embedding and the maximum attainable elasticity modulus of the bone tissue. All algorithms could be successfully calibrated. Changes in the mean SED (target value of the optimization) could be detected only in few cases. Decreasing the maximum bone elasticity and increasing the applied loading resulted in an increase of BV/TV. Changing the stiffness of the embedding led to significant structural changes by the remodelling. SED based bone remodelling algorithms are robust in terms of reaching a target SED. In contrast, bone volume fraction and structure strongly depend on the choice of model parameters - especially the boundary conditions and the used algorithms. These facts severely limit the current use of such simulations.