2 A model on the dynamics of odontogenic cyst growth

Odontogenic cysts are non-neoplastic lesions that form as a consequence of the proliferation of epithelial residues that remain embedded in the maxillary bones after formation of dental tissues. The epithelial rests proliferate in response to activating cell mediator signals released during inflammatory processes (for example as a consequence of a tooth infection). In this report we discuss the pathogenesis of odontogenic cysts based on current knowledge and formulate a simple mathematical model of cystic growth. The aim of the modelling is to establish the dynamics (i.e. the long term behaviour) of cyst enlargement based on osmotic pressure differences between the cyst contents and the stomal extracellular fluid. Such osmotic gradient results in water movement into the cyst across the epithelium lining which acts as a semi-permeable membrane. The modelling assumes a (spherical) cyst with a semi-permeable shell of living cells and a core consisting of water and a generic osmotic material (fed by the continuous death of epithelial cells in the shell). The lining cells are assumed to behave like a Maxwell fluid, reflecting the action of physical stresses by the surrounding cyst capsule formed by fibroblasts and collagen fibres. The model couples the cyst radius and the osmotic pressure differences resulting in a system of two nonlinear ordinary differential equations. Using the combination of asymptotic and numerical techniques it is shown that in all parameter regimes the long time behaviour of the cyst is the same and that linear radial expansion is predicted. Moreover, the model predicts that in the early and intermediate stages of cystic growth, osmotic pressure differences play an important role; however, for very large cysts, this role is negligible as cell birth dominates growth.