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TopIntroduction
The building block of the human brain is the neuron. A neuron in the human brain may be connected to about 10,000 other neurons. The neuron may receive signals from other neurons through their dendrites and may pass signals to other neurons through their axons. These signals are short electrical pulses of similar form and define the building blocks for information transmission between any neurons in the brain. It is a common belief that their form does not carry any information. The dendrites and axons are the channels of these pulses. The junction between an axon and a dendrite is called a synapse. See Figure 1. Most synapses are chemical which means that an electrical signal from a sending neuron leads to a release of certain molecules called neurotransmitters. These molecules are caught by receptors at the receiving side of the synaptic cleft. They lead to an ion influx which again changes the voltage of the membrane of the receiving neuron. Other synapses are electrical in which specialized membrane proteins make a direct electrical connection between the two neurons.
The potential difference between the interior of the cell and its surroundings is called the membrane potential. Without any activity, that means no signals, the membrane potential will have a constant value of about -65 mV. After the arrival of a signal (a spike), the potential changes. If the potential change is positive, we say the synapse is excitatory. In the opposite case the synapse is inhibitory. A negative potential change will after some time approach the resting potential. With a positive potential change there are two possibilities. If no or a few more spikes are received during a short time span, the potential will decay to its resting potential. However, if enough excitatory spikes arrive within this short time span, the membrane potential will reach a critical value, known as its firing threshold.
The membrane potential then exhibits a pulse-like excursion with an amplitude of about 100 mV and a duration of 1-2 milliseconds. This membrane potential is called the action potential or simply a spike. The action potential propagates along the axon of the neuron to the synapses (Figure 2) of other neurons. After a spike has been generated the resting potential after some time returns to its resting value (Gerstner & Kistler, 2002).
Figure 2. The structure of the synapse
TopSpiking Neuron Models
Engineers are interested to understand the mechanisms by which neurons interact witch each other including how this may be used to build complex neural systems. The prominent goal in the field of neural engineering is focused on increasing the knowledge about human functions via direct interactions between the nervous system and artificial devices. The main objective is to introduce a general and comprehensive overview of different spiking neuron models based on their neural action potential behavior. The Hodgkin Huxley model (H-H) is used in this paper to generate spikes (Kristensen & McNearey, 2013), but also the useful Leaky-Integrate-and-Fire model (LIF) is presented. The spiking neuron models presented here transmit information by pulses, also called action potentials or spikes. First the background knowledge necessary to understand the Hodgkin-Huxley and Leaky Integrate-and-fire models are described. Then the simulation of these neuron models will be performed in Java and graphical solutions of the action potentials is shown.