  We present a three dimensional, time dependent model for bone regeneration in
the presence of porous scaffolds to bridge critical size bone defects. Our
approach uses homogenized quantities, thus drastically reducing computational
cost compared to models resolving the microstructural scale of the scaffold.
Using abstract functional relationships instead of concrete effective material
properties, our model can incorporate the homogenized material tensors for a
large class of scaffold microstructure designs. We prove an existence and
uniqueness theorem for solutions based on a fixed point argument. We include
the cases of mixed boundary conditions and multiple, interacting signalling
molecules, both being important for application. Furthermore we present
numerical simulations showing good agreement with experimental findings.
