Simulating Neuron

Simple Neuron visualization using the Leaky Integrate-and-Fire Model. Objectives to Simulate the behavior of a single neuron using the leaky integrate-and-fire (LIF) model.

This project introduces basic neuroscience concepts and computational modeling.

What You'll required

• Python basics: variables, loops, and functions.
• Plotting with Matplotlib.
• Using numerical libraries like NumPy.
• Simple differential equations in neuroscience.

Description

The LIF model describes how the membrane potential (𝑉) of a neuron evolves over time, integrating inputs and "firing" (spiking) when the potential reaches a threshold. The membrane potential decays over time due to a "leak."

The governing equation is:

[ \tau_m \frac{dV}{dt} = -V + R \cdot I ]

Where:

• ( V ): Membrane potential (mV)
• ( \tau_m ): Membrane time constant (ms)
• ( R ): Membrane resistance (( \Omega ))
• ( I ): Input current (( \mu A ))
• Threshold (( V_{th} )): When ( V \geq V_{th} ), the neuron "spikes."

Steps

1. Set Up the Environment

Install Python and required libraries:

pip install numpy matplotlib

2. Execute the Simulation

Write the Python script to simulate over time, given constant or varying input current. Use Euler's method for numerical integration.

3. Visualize Results

Plot the membrane potential over time to see spiking behavior.

4. Experiment with Parameters

Explore how changing , , or affects the neuron’s firing.