  In silico testing of implant materials is a research area of high interest,
as cost- and labour-intensive experiments may be omitted. However, assessing
the tissue-material interaction mathematically and computationally can be very
complex, in particular when functional, such as biodegradable, implant
materials are investigated. In this work, we expand and refine suitable
existing mathematical models of bone growth and magnesium-based implant
degradation based on ordinary differential equations. We show that we can
simulate the implant degradation, as well as the osseointegration in terms of
relative bone volume fraction and changes in bone ultrastructure when applying
the model to experimental data from titanium and magnesium-gadolinium implants
for healing times up to 32 weeks. By conducting a parameter study we further
show that a lack of data at early time points has little influence on the
simulation outcome. Moreover, we show that the model is predictive in terms of
relative bone volume fraction with mean absolute errors below 6%
