Objectives

 

1. To understand how Integrate and Fire Neuron (IFN) can be modeled into electronic circuits.
2. To generate and study output spikes generation of Integrate and Fire Neuron using remotely triggered equipment.

 

Theory

 

Human brain known to consist of 10¹¹ neurons or so are capable of transmitting signals in the form of action potential to long distances. Non-neural cells such as glia, though exist in major proportion than neurons seemed to lack the typical action potential generation capability. The input capability of these neurons depends on the extensive dendritic characterization, which can vary from 1 to 10000 synaptic contacts. Neurons with complex dendritic tree morphology such as Purkinje neurons receive highest synaptic contacts while simple neuron morphology structures such as pyramidal neuron receive fewer synaptic contacts comparatively (Figure 1). Current generated by these synaptic contacts induce post-synaptic potentials (PSP) which change the membrane potential of the neuron. Voltage-sensitive channels modulate the firing of an action potential depending on the magnitude of the current. Smaller currents lead to smaller PSP’s while larger currents lead to significant PSP’s thereby generating an action potential. As the line from the book “Dynamical Systems in Neuroscience” supports this idea ‘Neurons do not fire, they get fired’.

 

                    

        

                                                                                                                  

 Figure 1. Purkinje Neuron (left) , Pyramidal Neuron (right)

 

Image source: http://en.wikipedia.org/

 

Most of the neurons work like integrators: receive inputs from multiple neurons, sum up and compare the result with a fixed threshold. If the summed up result is greater than threshold, exponential rise in the membrane potential is observed, a typical analogous Na+ channel influx behavior. Otherwise it will generate a small PSP, which can be EPSP (Excitatory post synaptic potential) or IPSP (Inhibitory post synaptic potential) depending on the kind of input it receives. On the other hand, Hodgkin-Huxley model behaves like an oscillator rather than an integrator. It would oscillate according to the input frequency it receives. Electrical circuit idioms are often used to model these different types of neurons. Integrate and fire neuron is the most popular and one of the oldest neural models, widely used for analyzing the behavior of neural systems.Basic structure of a neuron is shown in Figure 2. 

 

 

 Figure 2. Basic structure of neuron (Image source: http://en.wikipedia.org/)

 

Integrate and fire neuron is a prime example of describing a neuron based on its membrane potential. Here the entire neuron is reduced to a simple electronic circuit. These neurons fire action potentials that are separated by time intervals that are of the same orders of magnitude. Here the shape of the action potentials is more or less the same. Random fluctuations in the membrane potential cause neuron to fire and generate output. IFN helps in the analysis of the dynamical behaviors of single neuron. Also it improves speed/space of modeling. In IFN the pulsed nature of the neuronal signal is taken into account and considered as potentially relevant for coding and information processing.

 

 

Neurons are enclosed by a membrane separating interior from extra cellular space. The concentration of ions inside is different to that in the surrounding liquid.

 

The difference in concentration generates an electrical potential (membrane potential) which plays an important role in neuronal dynamics. Cell membrane is impermeable to most charged molecules and so acts as a capacitor, Cm by separating the charges lying on either side of the membrane. Membrane time constant tm = R_mC_m sets the basic time-scale for changes in the membrane potential (typically between 10 and 100ms). Rm and Cm are the membrane resistance and capacitance.

 

Each neuron has a different threshold level that needs to be reached in order for that neuron to fire. Reaching or exceeding this threshold level is what must be accomplished to successfully produce an output signal. When a cell reaches its threshold and fires, its signal is passed onto the next neuron, which may or may not cause it to fire. If the neuron does not fire, its potential will be raised so that if it receives another input signals within a certain time frame, it will be more likely to fire. Producing regular output pulses at a rate depending on the input current.

 

No biophysical states (channel dynamics) are involve in the mechanism of IFN. These models (Figure 3) basically assume that action potentials are simply spikes occurring when the membrane potential reaches a threshold Vth . After firing membrane potential is reset to a Vreset

 

ie, Membrane Voltage                             if   v > V_th

                                                             →v = V_reset

 

                                                                                                                    

                    Figure 3. Shows a simple IFN using resistor, capacitor and a Schmitt trigger

 

The IF neuron circuit (Figure 4) is designed using RC components and a Schmitt trigger. In electronics, Schmitt trigger is a name of threshold circuits. The Schmitt trigger action uses a comparator to produce stable level-crossing switches in contrast to the action of a straight reference comparison. It has two modes of operation: Inverting and non-inverting.

 

In the non-inverting configuration Schmitt trigger output retains its value until the input changes sufficiently to trigger a change, when the input is higher than a certain chosen threshold, the output is high. When the input is below a chosen threshold, the output is low and when the input is between the two, the output retains its value. In inverting configuration the output negative when the input passes upward through a positive reference voltage and when the input is below threshold output is low. Here for our circuit we use non inverting mode

 

When we apply in put to the RC circuits capacitor begins to charge. When the capacitor voltage exceeds the threshold voltage maintained by the Schmitt trigger circuits generates the output. The circuit will not fire until the input square pulse exceed the high threshold V_Th (here it is 1.5 Volts ) maintained by the Schmitt trigger. After this V_Th , the IF neuron circuit generates spikes as in Figure 5.

 

                                  

                            Figure 4. Input signals with 1V_pp amplitude                              

 

 

 

              

 Figure 5. Input signals with 4V_pp amplitude

Compare to other single-Cell models they offer several advantages. In IFN the pulsed nature of the neuronal signal is taken into account and considered as potentially relevant for coding and information processing. Moreover dynamics in networks of IFN can be analyzed mathematically. Integrate-and-fire neuron models have found widespread applications in computational neuroscience. This model can be used for robotics signal processing. IFN circuits are the basic building blocks for many robotic circuits.