MATHEMATICAL SIMULATION OF UNIDIRECTIONAL TISSUE FORMATION - IN-VITROTRANSANASTOMOTIC ENDOTHELIALIZATION MODEL

In vitro transanastomotic endothelialization was studied using a mathe matical model with the Fisher equation. The Fisher equation is a nonli near parabolic equation which has a cell migration term and a populati on growth term The mathematical model was used to simulate recent expe riments performed to investigate quantitatively the unidirectional for mation of a bovine endothelial cell monolayer in vitro. The two parame ters included in the equation were estimated using a trial and error m ethod in which the calculated solutions of the various values of the t wo parameters are compared with the experimental data and the best fit pair is adopted: one parameter, D, which represents the unidirectiona l cell migration rate and the other, k, which represents the populatio n growth rate. The calculated solutions fit the experimental data well . We also simulated the healing of a mechanically disrupted endothelia l monolayer sheet. The significance of cellular biomechanics in tissue formation and design of tissue-engineered devices is discussed.