Development of the deterministic and stochastic Markovian model of a dendritic neuron

In this study, we propose a model of the dendritic structure of the neuron (referred to as a neural network - NN), which can be viewed as an extension of the models that are currently used in the description of the potential on the neuron's membrane. The proposed extensions augment the generic model and offer a fuller description of the neuron's nature. The common assumption being used in most of the previous models stating a single channel (forming component of the neuron's membrane) can be positioned in only one of the two states (permissive - open and non-permissive - closed), is now relaxed by allowing the channel to be positioned in more states (five or eight states). The relationship between these states is expressed in terms of Markov kinetic schemes. In the paper, we demonstrate that the new approach is more suitable for a larger number of applications than the conventional Hodgkin-Huxley model. The study, by providing the mathematical background of the new extended model, forms a significant step towards a hardware implementation of the biologically realistic neural network (NN) of this type. To reduce the number of components required in such implementation, we propose a new optimization technique that significantly reduces the computational complexity of a single neuron. (C) 2017 Nalecz Institute of Biocybemetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.