A model for the change of cancellous bone volume and structure over time

A model is presented for characterizing the process by which cancellous bone changes in volume and structure over time. The model comprises simulations of local changes resulting from individual remodelling events, known as bone multicellular units (BMU), and an ordinary differential equation for connecting the number of remodelling events to real time. The model is validated on micro-CT scans of tibiae of normal rats, estrogen deprived rats and estrogen deprived rats treated with bisphosphonates. The model explains the asymptotic trends seen in changes of bone volume over time resulting from estrogen deprivation as well as trends seen subsequent to treatment. The model demonstrates that both bone volume and structure changes can be explained in terms of resetting remodelling parameters. The model also shows that either current understanding of the effects of bisphosphonates is not correct or that the simplest description of remodelling does not suffice to explain both the change in bone volume and structure of rats treated with bisphosphonates.