Visualization of cell flow by cell vertex and bubbly cell shape tracking

For clinical applications, researchers have paid attention to biological tissues and their multicellular mechanical structures. However, the mechanical aspect of morphological mechanisms remain unclear. So far, mathematical models have been developed to elucidate the mechanism: the vertex model (VM) by polygon approximation of cells, and the bubbly vertex model (BVM) with the curvature of cell boundaries, and so on. None of them leads to the basic equations for the migration and deformation of cell populations yet. The main reasons are that the physical properties of tissues differ among the morphogenetic stages, the cell boundary tensions are non-uniform, and the stress-strain relationship has not been clarified.In order to determine the physical properties for such basic equations, precise quantification of cell flow is necessary. However, conventional methods, such as PIV and PTV, do not fit naively to various cellular events: deformation, division, apoptosis, rearrangement, etc. Live-imaging techniques also limit the quality of experimental data.In this paper, we extract cell boundaries from the live data, fit them to the tissue shape defined by BVM, and perform vertex and edge (cell boundary) tracking similar to PTV. We also attempt to visualize and quantitatively evaluate the cell flow from real data.