  The maintenance of tissue and organ structures during dynamic homeostasis is
often not well understood. In order for a system to be stable, cell renewal,
cell migration and cell death must be finely balanced. Moreover, a tissue's
shape must remain relatively unchanged. Simple epithelial tissues occur in
various structures throughout the body, such as the endothelium, mesothelium,
linings of the lungs, saliva and thyroid glands, and gastrointestinal tract.
Despite the prevalence of simple epithelial tissues, there are few models which
accurately describe how these tissues maintain a stable structure.
  Here, we present a novel, 3D, deformable, multilayer, cell-centre model of a
simple epithelium. Cell movement is governed by the minimisation of a bending
potential across the epithelium, cell-cell adhesion, and viscous effects. We
show that the model is capable of maintaining a consistent tissue structure
while undergoing self renewal. We also demonstrate the model's robustness under
tissue renewal, cell migration and cell removal. The model presented here is a
valuable advancement towards the modelling of tissues and organs with complex
and generalised structures.
