Statistical Comparison of Spatial Point Patterns in Biological Imaging

In biological systems, functions and spatial organizations are closely related. Spatial data in biology frequently consist of, or can be assimilated to, sets of points. An important goal in the quantitative analysis of such data is the evaluation and localization of differences in spatial distributions between groups. Because of experimental replications, achieving this goal requires comparing collections of point sets, a noticeably challenging issue for which no method has been proposed to date. We introduce a strategy to address this problem, based on the comparison of point intensities throughout space. Our method is based on a statistical test that determines whether local point intensities, estimated using replicated data, are significantly different or not. Repeating this test at different positions provides an intensity comparison map and reveals domains showing significant intensity differences. Simulated data were used to characterize and validate this approach. The method was then applied to two different neuroanatomical systems to evaluate its ability to reveal spatial differences in biological data sets. Applied to two distinct neuronal populations within the rat spinal cord, the method generated an objective representation of the spatial segregation established previously on a subjective visual basis. The method was also applied to analyze the spatial distribution of locus coeruleus neurons in control and mutant mice. The results objectively consolidated previous conclusions obtained from visual comparisons. Remarkably, they also provided new insights into the maturation of the locus coeruleus in mutant and control animals. Overall, the method introduced here is a new contribution to the quantitative analysis of biological organizations that provides meaningful spatial representations which are easy to understand and to interpret. Finally, because our approach is generic and punctual structures are widespread at the cellular and histological scales, it is potentially useful for a large spectrum of applications for the analysis of biological systems.