  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.
