Irregular bone remodeling is associated with a number of bone diseases such
as osteoporosis and multiple myeloma.
Computational and mathematical modeling can aid in therapy and treatment as
well as understanding fundamental biology. Different approaches to modeling
give insight into different aspects of a phenomena so it is useful to have an
arsenal of various computational and mathematical models.
Here we develop a mathematical representation of bone remodeling that can
effectively describe many aspects of the complicated geometries and spatial
behavior observed.
There is a sharp interface between bone and marrow regions. Also the surface
of bone moves in and out, i.e. in the normal direction, due to remodeling.
Based on these observations we employ the use of a level-set function to
represent the spatial behavior of remodeling. We elaborate on a temporal model
for osteoclast and osteoblast population dynamics to determine the change in
bone mass which influences how the interface between bone and marrow changes.
We exhibit simulations based on our computational model that show the motion
of the interface between bone and marrow as a consequence of bone remodeling.
The simulations show that it is possible to capture spatial behavior of bone
remodeling in complicated geometries as they occur \emph{in vitro} and \emph{in
vivo}.
By employing the level set approach it is possible to develop computational
and mathematical representations of the spatial behavior of bone remodeling. By
including in this formalism further details, such as more complex cytokine
interactions and accurate parameter values, it is possible to obtain
simulations of phenomena related to bone remodeling with spatial behavior much
as \emph{in vitro} and \emph{in vivo}. This makes it possible to perform
\emph{in silica} experiments more closely resembling experimental observations.Comment: Math. Biosci. Eng., 9(2), 201
