In the simulation of whole brains, we face a tradeoff. Hodgkin-Huxley models are biologically accurate but computationally expensive (hundreds of floating-point operations per step). Integrate-and-Fire models are cheap but biologically unrealistic (they cannot burst or chatter).

In 2003, Eugene Izhikevich published Simple Model of Spiking Neurons, proposing a third way. This model powers the interactive visualiser on this website.

The Quadratic Integrate-and-Fire Model

The Izhikevich model reduces the complex ion channel dynamics of a neuron to two differential equations:

1. v’ = 0.04v² + 5v + 140 - u + I
   • v is the membrane potential.
   • The quadratic term (v²) allows the spike to initiate sharply, mimicking the sodium channel activation.
2. u’ = a(bv - u)
   • u is a recovery variable. It lumps together all slow currents (like Potassium or Calcium) that bring the neuron back to rest.

Rich Dynamics from Four Parameters

By tuning just four parameters (a, b, c, d), this simple math can reproduce 20 known neuro-computational behaviors seen in the mammalian cortex:

• RS (Regular Spiking): The standard pyramidal cell behavior.
• IB (Intrinsically Bursting): Neurons that fire clusters of spikes.
• CH (Chattering): High-frequency bursting (40 Hz), often found in the visual cortex.
• FS (Fast Spiking): Inhibitory interneurons that fire rapidly without tiring.
• LTS (Low-Threshold Spiking): Neurons that fire rebound spikes when released from inhibition.

Why This Matters for Emulation

The Izhikevich model proved that we do not need to simulate every protein to get realistic network dynamics. We can simulate the behavior of the neuron rather than its constituent parts. This abstraction reduces the computational load by orders of magnitude, making it possible to simulate millions of neurons on standard hardware—a critical step toward whole brain emulation.

Official Sources

• Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14(6), 1569-1572.
• Izhikevich.org