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Modelling columnarity of pyramidal cells in the human cerebral cortex

By Andreas Dyreborg Christoffersen, Jesper Møller and Heidi Søgaard Christensen
CSGB Research Reports
No. 08, August 2019
Abstract:

For modelling the location of pyramidal cells in the human cerebral cortex we suggest a hierarchical point process in $\mathbb{R}^3$. The model consists first of a generalised shot noise Cox process in the $xy$-plane, providing cylindrical clusters, and next of a Markov random field model on the $z$-axis, providing either repulsion, aggregation, or both within specified areas of interaction. Several cases of these hierarchical point processes are fitted to two pyramidal cell datasets, and of these a model allowing for both repulsion and attraction between the points seem adequate.

Keywords: Cylindrical $K$-function; Determinantal point process; Hierarchical point process model; Line cluster point process; Minicolumn hypothesis

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