title: Detection and spatial characterization of minicolumnarity in the human cerebral cortex.
abstract: BACKGROUND
  Spatial characterization of vertical organization of neurons in human cerebral cortex, cortical columnarity or minicolumns, and its possible association with various psychiatric and neurological diseases has been investigated for many years.
  
  
  METHODS
  In this study, we obtained 3D coordinates of disector sampled cells from layer III of Brodmann area 4 of the human cerebral cortex using light microscopy and 140-μm-thick glycolmethacrylate sections. A new analytical tool called cylindrical K-function was applied for spatial point pattern analysis of 3D datasets to see whether there is a spatially organized columnar structure. In order to demonstrate the behaviour of the cylindrical K-function, the result from brain tissues was compared with two models: A homogeneous Poisson process exhibiting complete spatial randomness, and a Poisson line cluster point process. The latter is a point process model in 3D space, which exhibits spatial structure of points similar to minicolumns.
  
  
  RESULTS
  The data show in three out of four samples nonrandom patterns in the 3D neuronal positions with the direction of minicolumns perpendicular to the pial surface of the brain - without a priori assuming the existence of minicolumns.
  
  
  METHODS
  Studies on columnarity are difficult and have mainly been based on two-dimensional images analysis of thin sections of the cerebral cortex with the a priori assumption that minicolumns existed.
  
  
  CONCLUSIONS
  A clear difference from complete spatial randomness in the data could be detected with the new tool, the cylindrical K-function, although classical functional summary statistics are less useful in this connection.
authors.affiliation: Stereology and Electron Microscopy Laboratory, Department of Clinical Medicine, Aarhus University, Aarhus, Denmark.|Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University, Aarhus, Denmark.|Translational Neuropsychiatry Unit, Department of Clinical Medicine, Aarhus University, Risskov, Denmark.
authors.forename: A H
authors.initials: AH
authors.lastname: Rafati
authors.affiliation: Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University, Aarhus, Denmark.|Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark.
authors.forename: F
authors.initials: F
authors.lastname: Safavimanesh
authors.affiliation: Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University, Aarhus, Denmark.|Translational Neuropsychiatry Unit, Department of Clinical Medicine, Aarhus University, Risskov, Denmark.|Translational Neuroscience Program, Department of Psychiatry, University of Pittsburgh, Pittsburgh, Pennsylvania, U.S.A.
authors.forename: K-A
authors.initials: KA
authors.lastname: Dorph-Petersen
authors.affiliation: Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University, Aarhus, Denmark.|Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark.
authors.forename: J G
authors.initials: JG
authors.lastname: Rasmussen
authors.affiliation: Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University, Aarhus, Denmark.|Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark.
authors.forename: J
authors.initials: J
authors.lastname: Møller
authors.affiliation: Stereology and Electron Microscopy Laboratory, Department of Clinical Medicine, Aarhus University, Aarhus, Denmark.|Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University, Aarhus, Denmark.
authors.forename: J R
authors.initials: JR
authors.lastname: Nyengaard
mesh_terms: D000368:Aged; D002540:Cerebral Cortex / Q000033:anatomy & histology*; D005260:Female; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008875:Middle Aged; D009474:Neurons / Q000166:cytology / Q000502:physiology*
keywords: Cerebral cortex; cylindrical K-function; minicolumns