It is unclear how neurons with variable response properties and stochastic failures can reliably transmit and process information. This article examines signal transmission and communication in the neural networks as an intermediate function of neural networks between artificial intelligence (AI) and each neuron functions, and derives multiplex signal transmission principle by spike waves in the neural networks. This article (Part 1) presents simulations of a two-dimensional (2D) mesh artificial neural network. If one of the transmitting neuron groups is stimulated, the signal is propagated in the form of spike waves with fluctuations. The corresponding receiving neuron group can identify the signal after learning to form an asynchronous multiplex communication channels such as 9:9 in the simulation. The communication channel is composed of many intermediate neurons working as relays. Each neuron can work as an input/output (I/O) and as a relay element, i.e., as a multiuse unit. Grouping and synchronic firing is often observed in real neuronal networks and appears to be effective for stable and robust spatial multiplex communication. This multiplex communication pattern is similar to that of sound identification by the ears and mobile adaptive communication systems. Some of the experimental results validating the simulation model and connecting it to wet experiments of the succeeding article (Part 2) using cultured neuronal network including spike code flow which shows part of spike waves, effects of using extracellular electrode, and an example of communication channels of 3:n in real cultured neuronal networks are also described. The results of both artificial neural network simulations (this Part 1) and multichannel recording of cultured neuronal networks (Part 2) support multiplex communication principle in the brain.