Understanding the Mathematical and Geometric Language of Endothelial Progenitor Cells

Stem cell activities also depend of mathematical principles and physical laws and tissue engineering has originated new methods to understand cell behaviors. Using mathematical and computational modeling facilitates the understanding of tissue growth process. This study focuses on the reactions of endothelial progenitor cells to fluid frictional stress by utilizing a mathematical and morphological analysis. A flow system was built where cultures of endothelial progenitor cells were exposed. We identified that the establishment of lamellipodia networks was related with a 103^o angle, which could be the mathematical expression of Rac proteins. The cell morphology of these cells in culture submitted to fluid frictional stress was determined by the flow strength. An original vectorial approach to identify cell migration direction was used. We concluded that endothelial progenitor cells under flow conditions adopt different morphologies to optimize their hydrodynamic capacities. Geometric factors and surface dynamics conduct are significant features of endothelial coverage and angiogenesis.