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Models of Spiking Neurons

 find the fake
I develop a new class of models of spiking neurons that combines computational efficiency of integrate-and-fire and resonate-and-fire models and biological plausibility and versatility of Hodgkin-Huxley type models.

Find the fake!
In this figure, one column is an in vitro recording of rat pyramidal neuron (layer 5, motor cortex) in response to pulses of injected current of various amplitudes, the other column is a simulation of the simple model
100v'=0.7(v+60)(v+40)-u+I,
      u'=0.03(-2(v+60)-u),
if v>+35 mV (peak of spike),
then reset: v := -50 mV, u := u+100
Can you determine which is the real neuron which is the fake? (Hint: the real one is noisier.)

Examples of other neuronal types are in my book





Simulation of Large-Scale Brain Models
microcircuitry
 I develop large-scale models of the brain having microcircuitry of the mammalian thalamo-cortical system.

On October 27, 2005 I finished simulation of a model that has the size of the human brain. The model has 100,000,000,000 neurons (hundred billion or 10^11) and almost 1,000,000,000,000,000 (one quadrillion or 10^15) synapses. It represents 300x300 mm^2 of mammalian thalamo-cortical surface, specific, non-specific, and reticular thalamic nuclei, and spiking neurons with firing properties corresponding to those  recorded in the mammalian brain. (Even if the model had only 1000 neurons, it would still be one of the most detailed models ever simulated.)

The model exhibited alpha and gamma rhythms, moving clusters of neurons in up- and down-states, and other interesting phenomena (watch a 25M  .avi or .mov movie).
 
One second of simulation took 50 days on a beowulf cluster of 27 processors (3GHz each). Why did I do that?





Computer Model of the Human Brain

  Brain of Eugene Izhikevich
I developed a large-scale computer model of the human brain that connects three drastically different scales:
  • Single neurons with branching dendritic morphology (pyramidal, stellate, basket, non-basket, etc.); synaptic dynamics with GABA, AMPA, and NMDA kinetics, short-term and long-term synaptic plasticity (in the form of dendritic STDP); neuromodulation of plasticity by dopamine; firing patterns representing 21 basic types found in the rat cortex and thalamus (includes Regular Spiking, Intrinsically Bursting, Chattering, Fast Spiking, Late Spiking, Low-Threshold Spiking, Thamamic Bursting, etc., types); See my 2007 book.
  • 6-Layer thalamo-cortical microcircuitry based on quantitative anatomical studies of cat cortex (area 17) and on anatomical studies of thalamic circuitry in mammals; see above.
  • Large-scale white-matter anatomy using human DTI (diffusion tensor imaging) and fibertraking methods.


    • You can read more about this model in my 2008 PNAS paper and download some interesting (but long) movies of the spiking activity of the human brain model.

    This research has a more ambitious goal than the the Blue Brain Project conducted by IBM and EPFL (Lausanne, Switzerland). The Blue Brain Project builds a small part of the brain that represents a cortical column, though to a much greater detail than the models I develop. In contrast, my goal is a large-scale biologically acurate computer model of the whole human brain. At present, it has only cortex and thalamus; other subcortical structures, including hippocampus, cerebellum, basal ganglia, etc., will be added later. Spiking models of neurons in these structures have already being developed and fine-tuned.



      Scholarpedia articles: FitzHugh-Nagumo model, Bursting, Equilibrium, Phase space.

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