A model on the dynamics of odontogenic cyst growth

Objective: To formulate a mathematical model of odontogenic cyst growth and establish the dynamics of cyst enlargement and the role of osmotic pressure forces throughout its growth. Study design: The model assumed a spherical cyst with a semi-permeable lining of living cells and a core consisting of degraded cellular material, including a generic osmotic material, fed by the continuous death of epithelial cells in the lining. The lining cells are assumed to have both elastic and viscous properties, reflecting the action of physical stresses by the surrounding cyst capsule composed of 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. Results: The model predicts that in all parameter regimes the long time behaviour of the cyst is the same and that linear radial expansion results. Conclusions: In the early and intermediate stages of cystic growth, osmotic pressure differences play an important role; however, for very large cysts, this role becomes negligible and cell birth in the lining dominates growth.