# Exponential distance distribution of connected neurons in simulations of two-dimensional in vitro neural network development

## TL;DR

This study uses simulations to investigate the distribution of distances between connected neurons in 2D in vitro neural networks, finding an exponential distribution contrary to previous power-law predictions.

## Contribution

It provides the first simulation-based verification of the distance distribution in neural networks, challenging prior theoretical power-law assumptions.

## Key findings

- Simulations show an exponential distance distribution in 2D neural networks.
- Karbowski's power-law decay distribution is not supported by simulation data.
- Results suggest different underlying principles for neural connectivity in vitro.

## Abstract

The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brain\'s dynamic properties at the ground level. Karbowski derived a power-law decay distribution that has not yet been verified by experiment. In this work, we check its validity using simulations with a phenomenological model. Based on the in vitro two-dimensional development of neural networks in culture vessels by Ito, we match the synapse number saturation time to obtain suitable parameters for the development process, then determine the distribution of distances between connected neurons under such conditions. Our simulations obtain a clear exponential distribution instead of a power-law one, which indicates that Karbowski's conclusion is invalid, at least for the case of in vitro neural network development in two-dimensional culture vessels.