Mathematical modeling of airway epithelial wound closure during cyclic mechanical strain.

The repair of airway epithelium after injury is crucial in restoring epithelial barrier integrity. Because the airways are stretched and compressed due to changes in both circumferential and longitudinal dimensions during respiration and may be overdistended during mechanical ventilation, we investigated the effect of cyclic strain on the repair of epithelial wounds. Both cyclic elongation and compression significantly slowed repair, with compression having the greatest effect. We developed a mathematical model of the mechanisms involved in airway epithelial cell wound closure. The model focuses on the differences in spreading, migration, and proliferation with cyclic strain by using separate parameters for each process and incorporating a time delay for the mitotic component. Numerical solutions of model equations determine the shape of the diffusive wave solutions of cell density that correspond to the influx of cells into the wound during the initial phase of reepithelialization. Model simulations were compared with experimental measurements of cell density and the rate of wound closure, and parameters were determined based on measurements from airway epithelial cells from several different sources. The contributions of spreading, migration, and mitosis were investigated both numerically and experimentally by using cytochalasin D to inhibit cell motility and mitomycin C to inhibit proliferation.