A tool for solving bone growth related problems using finite elements adaptive meshes

Abstract

Long bones geometry changes in response to longitudinal growth in the epiphyseal plates and hydroxyapatite apposition in the periosteum. Due to its relevance for growth modulation and orthotics performance, researchers have extensively modeled these phenomena, using the finite elements method for it almost since the introduction of modern computers. This is a rather complex task that, besides the inherent difficulty of solving the models equations, requires considering a moving boundary. Here, the development of a new computational tool for its resolution is described. A generalized formulation of these problems is established based on the most common approaches taken in the literature and a novel finite elements algorithm is proposed for its resolution. The later allows a significant reduction of the spatial discretization requirements, the computational cost and the numerical errors associated with more classical approaches. The potentiality of the method is demonstrated by its application to three cases of practical interest, namely, hemiepiphysiodesis treatment, growth in the distal femur and bone remodeling around hip prosthesis. Eight relevant cases of study and an open source implementation of the proposed algorithm are also provided as supplementary material.

Keywords: Bone; FEM; Mechanobiology; Moving boundary; Prosthetic.