MODELING & SIMULATION OF BIOLOGICAL NEURAL NETWORKS USING KOCH MODEL

Abstract

Neurons are of essential importance in biology and its applications. Neurons are the simplest unit of data (information) processing in the nervous system of humans and other animals. Besides their importance for biology and medicine, networks of neurons (the human brain) are the most complex and advanced computational devices known, and the study of neurons individually and working in concert is seen as a step toward understanding consciousness and cognition. A.L. Hodgkin and A.F. Huxley in 1950’s developed a system of nonlinear ordinary differential equations to explain the behavior of a neuron found of a giant squid. These nonlinear equations have since been used to model the behavior of a host of neurons and other excitable cells like heart muscles. Hodgkin-Huxley category models take a set of parameters as input and produce data relating the electrical behavior of the neuron as a function of time. The cornerstone of modern neurobiology is the analysis by Hodgkin and Huxley of the initiation and propagation of the action potential in the squid giant axon. Their description accounted for two ionic currents: the fast sodium current INa and a delayed potassium current, IK. However, while the Hodgkin-Huxley formula has been singularly important to biophysics, their equations do not describe a number of important phenomena such as adaptation to long-lasting stimuli or the dependency of some conductance on various ionic concentrations The Koch model is the extension of the famous Hodgkin-Huxley model which is based on the fast sodium and delayed potassium currents, while the Koch xii model incorporates numerous ionic membrane currents and also takes into account the calcium dynamics of a neuron. Spike Timing Dependent Plasticity (STDP) is a temporally asymmetric form of Hebbian learning encouraged by constricted temporal correlations between the spikes of pre- and postsynaptic neurons. As with additional forms of synaptic plasticity, it is broadly believed that it inspires learning and information storage in the brain, as well as the progress and improvement of neuronal circuits during brain development. In STDP, frequent presynaptic spike arrival a few milliseconds before postsynaptic action potentials points in many synapse types to long-term potentiation (LTP) of the synapses, whereas recurring spike arrival after postsynaptic spikes points to long-term depression (LTD) of the same synapse. We for the first time have combined KOCH neuron model and Spike Timing Dependent Plasticity (STDP). In the model we have also incorporated delays due to the length and diameter of a neuron. This study helps in understanding the working of neural networks and learning behaviors. The approach is not only adaptable, but it is also scalable to very large network (billions of neurons). Different neural diseases affect the conductance of nerves such as peripheral neuropathy and mononeuritis multiplex.