# 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, , ):