Neuron
The neuron is the most common component in our brain, we have nearly 86 billion neurons and 1000 trillion synaptic connections, estimates to a computer with a 1 trillion bit per seconds processor
Computational Neuroscience
Is the field of study in which we measure and simulate the neurons process. Our brain is a complex machine and its behavior is non-linear.
We need previous knowledge of electronics, ODE’s, neurobiology, chemistry, and programming.
Integrate-and-fire model
We start with the easiest model that tries to interpret the neuronal behavior.
We can consider the neuron an electronic circuit:
Passive Membrane Model:
We solve the linear differential equation:
where
Time-dependent
In absence of (Green’s Function):
(1)
where is an input current.
Add threshold :
Let be the removing charge, every
time we hit the threshold.
the reset corresponds to a short current pulse.
(2)
Here we have the simulation of a neuron using a heavystep current input first equation and Leaky-integrate and fire (LIF)
The image below shows the different Leaky-integrate and fire methods and the input current gived for the neuron.
Given an aleatory input for the neuron, we obtain the next simulation for voltage potential (, time-scale constant, , ):