A phase field approach to trabecular bone remodeling

TL;DR

This paper presents a novel phase field modeling approach for trabecular bone remodeling that combines mechanical, biochemical, and morphological factors, offering computational efficiency and realistic simulations.

Contribution

It adapts phase field methods from materials science to simulate trabecular bone remodeling, integrating shape changes, signaling, and mechanical responses.

Findings

The phase field approach reduces computational costs compared to micro finite element methods.

Quantitative comparisons show good agreement with established methods.

Application to real sheep vertebra data demonstrates model realism.

Abstract

We introduce a continuous modeling approach which combines elastic responds of the trabecular bone structure, the concentration of signaling molecules within the bone and a mechanism how this concentration at the bone surface is used for local bone formation and resorption. In an abstract setting bone can be considered as a shape changing structure. For similar problems in materials science phase field approximations have been established as an efficient computational tool. We adapt such an approach for trabecular bone remodeling. It allows for a smooth representation of the trabecular bone structure and drastically reduces computational costs if compared with traditional micro finite element approaches. We demonstrate the advantage of the approach within a minimal model. We quantitatively compare the results with established micro finite element approaches on simple geometries and consider the bone morphology within a bone segment obtained from $\mu$CT data of a sheep vertebra with realistic parameters.