Modelling columnarity of pyramidal cells in the human cerebral cortex

For modelling the location of pyramidal cells in the human cerebral cortex we suggest a hierarchical point process in $\mathbb{R}^3$ that exhibits anisotropy in the form of cylinders extending along the $z$-axis. The model consists first of a generalised shot noise Cox process for the $xy$-coordinates, providing cylindrical clusters, and next of a Markov random field model for the $z$-coordinates conditioned on the $xy$-coordinates, 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 final model allowing for both repulsion and attraction between the points seem adequate. We discuss how the final model relates to the so-called minicolumn hypothesis in neuroscience.