A tool for the quantitative spatial analysis of complex cellular systems.

Spatial events largely determine the biology of cells, tissues, and organs. In this paper, we present a tool for the quantitative spatial analysis of heterogeneous cell populations, and we show experimental validation of this tool using both artificial and real (mammary gland tissue) data, in two and three dimensions. We present the refined relative neighborhood graph as a means to establish neighborhood between cells in an image while modeling the topology of the tissue. Then, we introduce the M function as a method to quantitatively evaluate the existence of spatial patterns within one cell population or the relationship between the spatial distributions of multiple cell populations. Finally, we show a number of examples that demonstrate the feasibility of our approach.