Quantifying Spatial Heterogeneity of Syncytial Cells using Alpha Shapes

We introduce a structural method used for quantifying the spatial heterogeneity(or clumpiness) of viral syncytial cells in a transfected bioassay. The solution lies in an inter-disciplinary process based on simplicial topology being applied to a biological system. Our method revolves around using topological theories including Delaunay Tessellations and Voronoi Graphs to signify cell-cell interaction probability. The main emphasis is the subset of Delaunay Tessellation called Alpha Shapes. By applying a filtration to the overall Delaunay Tessellation, we can obtain unique Alpha Shapes that have cell-cell interactions removed. The emphasis of the filtration is to find the correct shape where there were no connection crossing syncytia, only between healthy neighborhoods of cells. The process allows for the associated alpha number to be assigned to the clumpiness. Alpha numbers can then be used to separate different bioassays, or quantify temporal changes found in a single viral transfection due to syncytia.