RipleyGUI: software for analyzing spatial patterns in 3D cell distributions

Abstract

The true revolution in the age of digital neuroanatomy is the ability to extensively quantify anatomical structures and thus investigate structure-function relationships in great detail. To facilitate the quantification of neuronal cell patterns we have developed RipleyGUI, a MATLAB-based software that can be used to detect patterns in the 3D distribution of cells. RipleyGUI uses Ripley's K-function to analyze spatial distributions. In addition the software contains statistical tools to determine quantitative statistical differences, and tools for spatial transformations that are useful for analyzing non-stationary point patterns. The software has a graphical user interface making it easy to use without programming experience, and an extensive user manual explaining the basic concepts underlying the different statistical tools used to analyze spatial point patterns. The described analysis tool can be used for determining the spatial organization of neurons that is important for a detailed study of structure-function relationships. For example, neocortex that can be subdivided into six layers based on cell density and cell types can also be analyzed in terms of organizational principles distinguishing the layers.

Keywords: Ripley's K-function; cell distribution; neuroanatomical method; software; spatial point pattern.

Figure 1

Screenshot of the opening screen of RipleyGUI. The upper left panel (Create a new distribution) is allocated for distribution simulations. Each of the four reference distributions (see section Reference distributions) can be tuned with intensity and other parameters. The simulated distributions are displayed in the upper center panel (Name). The lower left panel (Operations on this distribution) is designed for analysis of the distribution on display in the upper central panel (Name). The right panel (Operations on all distributions in a chosen set) is designed for saving, managing, and analyzing single or multiple data sets. The results of all the analysis can be viewed inside or outside of RipleyGUI depending on the user's preference. All analysis-related parameters are tunable in their corresponding panels.

Figure 2

Examples of simulated reference cell distributions. (A,D) The Homogenous Poisson Process [Complete spatial randomness (CSR)]. The difference $\widehat{K}$(t) – E[$\widehat{K}$(t)] is close to 0 and we cannot discard that the sample distribution is following CSR. (B,E) $\widehat{K}$(t) – E[$\widehat{K}$(t)] is positive indicating aggregation. (C,F) $\widehat{K}$(t) – E[$\widehat{K}$(t)] is negative indicating inhibition (dispersion). Data was generated using a t-value step 2, and max 30.

Figure 3

Cell count data. (A) Confocal image (z-projection) of a brain slice showing neurons (gray) labeled with Neuronal Nuclei (NeuN) antibodies, and genetically EGFP-labeled layer 5a corticostriatal pyramidal cells (green). Scale bar 50 μm. (B) 2D projection of manually placed markers indicating the position of NeuN-labeled cell bodies in a brain slice of the somatosensory mouse cortex cut in the coronal plane. Pia matter is at y = 0, and the y-axis is distance from pia matter; x-axis is the width of the tissue slice. The six cortical layers are labeled L1 (Layer 1), etc. The black box shows the approximate position of the image in (A) and the green box the approximate position of the EGFP-labeled cells. A sub-section of the image is plotted in 3D in (C).

Figure 4

Comparing a test distribution with a CSR distribution. Etv-pyramid distributions in visual cortex (vc) are not randomly distributed. The samples (n = 6) have been divided and rotated (using Divide and Station) to obtain stationarity. 200 CSR distributions were generated, and used to create a confidence interval for the CSR hypothesis. (A) The estimated K-function for etv-pyramids (blue lines) compared to simulated CSR distributions (red lines). The K-function is estimated for t-values between 4 and 50 μm with a 2 μm step size. (B) P-values from the hypothesis test of CSR. For t = 18 μm the etv-pyramid distributions differs from CSR with 95% significance. These types of graphs can be generated with the RipleyGUI.

Figure 5

Example of how RipleyGUI can be used to compare two different cell distributions. Etv-pyramids in visual cortex (red lines) and etv-pyramids in barrel cortex (blue lines). (A) The estimated K-function for etv-pyramids in visual (vc-etv) and barrel cortex (bc-etv). (B) Average of estimated K-function with 95% confidence interval for etv-pyramids in visual and barrel cortex. (C) The BTSS value for the experimental data (red square) is larger than the BTSS value at the 0.95 quantile of the accumulated probability distribution. The probability that the compared test distributions are from the same underlying distribution is thus less than 5%. These types of graphs can be generated with the RipleyGUI.