Simple Model of Spiking Neurons

As I wrote in my last post on neural modeling there are several things that I like about the model of spiking neurons proposed by Eugene Izhikevich (see also Which Model to Use for Cortical Spiking Neurons? for comprehensive comparison with other available models):

  1. It's fast: only 13 FLOPS versus 5 FLOPS for Integrate-and-Fire and 1200 FLOPS for the Hodgkin-Huxley model
  2. It's biologically plausible: it exhibits the same neuro-computational properties as the most complex, Hodgkin-Huxley model
  3. It allows to model various types of neurons by changing four (seven in the latest revision) parameters
  4. It has no fixed threshold or absolute refractory period: these are properties rather than parameters of the model and depend on the type of a neuron. Based on the history of the membrane potential prior to the spike, the threshold potential can be as low as -55 mV or as high as -40 mV.

Izhikevich proposes classification of all neuron types as resonator/integrator (based on presence of subthreshold oscillations) and as being bistable/monostable (based on co-existance of resting and spiking states), which, in combination, make four groups. By using this classification he is able to derive several neuro-computational properties of those types of neurons:

  • Inhibition impedes spiking in integrators, but can promote it in resonators (this came as news to me; I was under the impression that inhibition always inhibit spiking)
  • Integrators have all-or-none spikes while resonators may not
  • Integrators have well-defined threshold while resonators may not
  • Integrators integrate, resonators resonate. This means integrators prefer high-frequency inputs; the higher the frequency, the sooner they fire. By contrast, the response of the resonator neuron depends on the frequency content of the input

Most cortical pyramidal neurons (including regular spiking (RS), and chattering (CH) neurons shown in the previous post) are integrators. Most cortical inhibitory neurons are resonators. According to the author of the model, a good neuronal model must reproduce not only electrophysiology but also bifurcaiton dynamics of neurons.

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