We introduce a continuous modeling approach which combines elastic response of the trabecular bone structure with the concentration of signaling molecules within the bone and a mechanism for concentration dependent 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 μCT data of a sheep vertebra with realistic parameters.
|Journal||Frontiers in applied mathematics and statistics|
|Publication status||Published - 5 May 2020|