A Mathematical Approach to Chondrocyte Data Collection and Columnar Organization

The chondrocytic primary cilium has been hypothesized to act as a mechanosensor similar to the primary cilium of epithelial cells. However, the function of the primary cilium and its connection with cellular organization is unknown. In this paper we present a mathematical approach to automatically collect, analyze, and simulate the process of pattern formation of ciliated chondrocytes in the growth plate cartilage. High-resolution confocal microscopy images of the growth plate of Smad1/5 genetically mutated mouse and its wild type mouse show different spatial and geometric pattern formation. Wild type mouse show strong chondrocyte columnar pattern formation in the proliferative zone, while Smad 1/5 show distorted spatial and geometrical distributions. The goals of this paper are: to (1) present new methodologies to automatically collect and analyze geometric and spatial information of cellular organization; (2) present an algorithmic approach to recreate patterns formed by ciliated chondrocytes; (3) provide new spatial statistics to quantitatively describe and detect columnar organization.