A new non targeted bone remodeling model combined with an interpolation meshless method

Abstract

Regardless of the bone remodeling type (i.e. targeted or non targeted), disturbances in this process can have serious repercussions in bone diseases’ progression. Therefore, research in this field has been continuous in recent decades, producing clinically relevant results. Regarding non targeted remodeling, distinct computational models were developed to describe the process. However, they only offer a time analysis, lacking mathematical models able to simulate the process in space. Thus, this work combines, for the first time, advanced numerical discretization techniques with non targeted remodeling models. The mathematical formulation used is based on Komarova’s model, correlating the remodeling activity of osteoclasts and osteoblasts with their autocrine and paracrine signaling pathways. For the numerical example, a two-dimensional bone patch was studied, allowing a spatio-temporal analysis of bone mass, cell density of osteoclasts and osteoblasts during an event of bone remodeling. A biological stimulus was applied to trigger remodeling and the obtained bone mass variation is consistent with the applied stimulus. Also, results are supported by the histomorphometric data available in the literature. The numerical methods used in this work are the Finite Element Method (FEM) and the Radial Point Interpolation Method (RPIM). The inclusion of the meshless method RPIM conveys a great advantage for future work since the model will be combined with medical images obtained with CT scans and MRI.