# Modelling brain-wide neuronal morphology via rooted Cayley trees

arXiv: https://arxiv.org/abs/1810.03262 · HTML: https://mlsanity.com/paper/1810.03262/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2018.

## Built on by (most cited first, 1 of 1)

- [Elastic Shape Analysis of Tree-like 3D Objects using Extended SRVF Representation](https://mlsanity.com/paper/2110.08693/) (2021)

## Abstract (arXiv)

Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide neuron topology. Based on estimated order-dependent branching probability from actual axonal and dendritic trees, our inhomogeneous model quantitatively captures a number of topological features including size and shape of both axons and dendrites. This sheds lights on a universal mechanism behind the topological formation of brain-wide axonal and dendritic trees.