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Spatial Point Pattern Analysis of Neurons Using Ripley's K-Function in 3D

By Mehrdad Jafari-Mamaghani, Mikael Andersson and Patrik Krieger


The aim of this paper is to apply a non-parametric statistical tool, Ripley's K-function, to analyze the 3-dimensional distribution of pyramidal neurons. Ripley's K-function is a widely used tool in spatial point pattern analysis. There are several approaches in 2D domains in which this function is executed and analyzed. Drawing consistent inferences on the underlying 3D point pattern distributions in various applications is of great importance as the acquisition of 3D biological data now poses lesser of a challenge due to technological progress. As of now, most of the applications of Ripley's K-function in 3D domains do not focus on the phenomenon of edge correction, which is discussed thoroughly in this paper. The main goal is to extend the theoretical and practical utilization of Ripley's K-function and corresponding tests based on bootstrap resampling from 2D to 3D domains

Topics: Neuroscience
Publisher: Frontiers Research Foundation
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Provided by: PubMed Central

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  8. (1986). Displaced amacrine cells in the retina of a rabbit: analysis of a bivariate spatial point pattern.
  9. (1988). Edge-corrected estimators for the reduced second moment measure of point processes.
  10. (1994). Evaluation of neuronal numerical density by Dirichlet tessellation.
  11. (1994). Fractals, Random Shapes and Point Fields.
  12. (2000). Improving ratio estimators of second order point process characteristics.
  13. (1999). New derivation reduces bias and increases power of Ripley’s L index.
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  20. (2008). Statistical Analysis and Modelling of Spatial Point Patterns. (Wiley-Interscience). tion of neurons and dendritic bundles in primary somatosensory cortex of the rat.
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  22. (2005). Statistical analysis of the threedimensional structure of centromeric heterochromatin in interphase nuclei.
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