title: A mathematical model of the dynamics of odontogenic cyst growth.
abstract: OBJECTIVE
  To formulate a mathematical model of odontogenic cyst growth and establish the dynamics of cyst enlargement and role of osmotic pressure forces throughout its growth.
  
  
  METHODS
  The model assumed a spherical cyst with a semipermeable lining of living cells and a core consisting of degraded cellular material, including generic osmotic material, fed by the continuous death of epithelial cells in the lining. The lining cells were assumed to have both elastic and viscous properties, reflecting the action of physical stresses by the surrounding cyst capsule, composed of fibroblasts and collagen fibers. The model couples the cyst radius and osmotic pressure differences resulting in a system of 2 nonlinear ordinary differential equations.
  
  
  RESULTS
  The model predicts that in all parameter regimens the long-time behavior 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, in very large cysts, this role becomes negligible, and cell birth in the lining dominates growth.
authors.affiliation: Department of Mathematical Sciences, Loughborough University, Loughborough, Leictershire, U.K.
authors.forename: John P
authors.initials: JP
authors.lastname: Ward
authors.forename: Vanesa
authors.initials: V
authors.lastname: Magar
authors.forename: Susan J
authors.initials: SJ
authors.lastname: Franks
authors.forename: Gabriel
authors.initials: G
authors.lastname: Landini
mesh_terms: D000465:Algorithms; D016923:Cell Death; D002455:Cell Division; D003198:Computer Simulation; D003238:Connective Tissue / Q000473:pathology; D004548:Elasticity; D004847:Epithelial Cells / Q000473:pathology; D004848:Epithelium / Q000473:pathology; D006801:Humans; D006874:Hydrostatic Pressure; D006965:Hyperplasia / Q000473:pathology; D008954:Models, Biological; D008962:Models, Theoretical; D009807:Odontogenic Cysts / Q000473:pathology*; D009997:Osmotic Pressure; D013314:Stress, Mechanical