Mathematical simulation of unidirectional tissue formation: in vitro transanastomotic endothelialization model

In vitro transanastomotic endothelialization was studied using a mathematical model with the Fisher equation. The Fisher equation is a nonlinear parabolic equation which has a cell migration term and a population growth term. The mathematical model was used to simulate recent experiments performed to investigate quantitatively the unidirectional formation of a bovine endothelial cell monolayer in vitro. The two parameters included in the equation were estimated using a trial and error method in which the calculated solutions of the various values of the two parameters are compared with the experimental data and the best fit pair is adopted: one parameter, D, which represents the unidirectional cell migration rate and the other, k, which represents the population growth rate. The calculated solutions fit the experimental data well. We also simulated the healing of a mechanically disrupted endothelial monolayer sheet. The significance of cellular biomechanics in tissue formation and design of tissue-engineered devices is discussed.