Novel nano-scale communications techniques are inspired by some naturally existing phenomena such as the molecular communication, neuro spike communication and controlling cellular signaling mechanisms. Among these, neuro-spike communication, which governs the communications between neurons, is a vastly unexplored area. It can be divided into three main blocks, i.e., the axonal transmission, the synaptic transmission and the spike generation. In this paper, we focus on the axonal transmission part as a separate channel. We model the input of this channel by a doubly Poisson process which is a Poisson process with a random intensity. Moreover, we consider an axonal noise modeled by a Poisson process. Then, we derive the capacity of Single-Input Single-Output (SISO) and Multiple-Input Single-Output (MISO) axonal channels, analytically. In the MISO channel case, we investigate the effect of the correlation among inputs on the channel capacity. Moreover, we derive a closed form description for the optimum value of input power to maximize the capacity of axonal channels in different cases. Furthermore, we verify the accuracy of the derived capacity of axonal transmission channels in different scenarios by simulation, i.e., it is shown that less than 10% mismatch exists in average between the analytical and simulation results.