Limits of Applicability of the Voronoi Tessellation Determined by Centers of Cell Nuclei to Epithelium Morphology

Abstract

It is well accepted that cells in the tissue can be regarded as tiles tessellating space. A number of approaches were developed to find an appropriate mathematical description of such cell tiling. A particularly useful approach is the so called Voronoi tessellation, built from centers of mass of the cell nuclei (CMVT), which is commonly used for estimating the morphology of cells in epithelial tissues. However, a study providing a statistically sound analysis of this method's accuracy is not available in the literature. We addressed this issue here by comparing a number of morphological measures of the cells, including area, perimeter, and elongation obtained from such a tessellation with identical measures extracted from direct imaging acquired by staining the cell membranes. After analyzing the shapes of 15,000 MDCK II epithelial cells under several conditions, we find that CMVT reasonably well reproduces many of the morphological properties of the tissue with an error that is between 10 and 15%. Moreover, cross-correlations between different morphological measures are reproduced qualitatively correctly by this method. However, all of the properties including the cell perimeters, number of neighbors, and anisotropy measures often suffer from systematic or size dependent errors. These discrepancies originate from the polygonal nature of the tessellation which sets the limits of the applicability of CMVT.

Three-dimensional cell neighbourhood impacts differentiation in the inner mass cells of the mouse blastocyst

“…1A (III-IV), 29 ). Implementing a Delaunay cell graph allows an approximation of which cells (nuclei in this case) are in physical contact 29,31,32 .…”

“…The DCG graph is constructed based on a Delaunay triangulation. Delaunay triangulation and its dual, the Voronoi tessellation are routinely used to approximate which cells are in physical contact 29,31,32 . An edge ( , ) was created between two vertices and if the corresponding points are connected by a line in the Delaunay triangulation and the Euclidean distance between and was less than 30µm.…”

Active glasses

“…The purple and green circles represent the respective degrees of freedom in these models. Panel (c) shows the differences between the cell boundaries of MDCK cells obtained via imaging methods (blue) and a Voronoi tesselation of the cell nuclei (yellow).Figure (c)is reproduced from Ref [130]…”

Confluent and nonconfluent phases in a model of cell tissue

“…We now analyze the cubic polynomial inP G(P ) =P 3 g 1 ( q) + 23328K P g 2 ( q) −P 0 g 3 ( q) . (24) Since g 1 ( q) ≥ 0 and g 2 ( q) ≥ 0 for all q, the polynomial G is an increasing function ofP . Since atP = 0 the polynomial G is negative, and atP → ∞ the polynomial G goes to infinity, it must have a single root at some positiveP * ( q).…”