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

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 distri-bution 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.