Which Model to Use for Cortical Spiking Neurons?
IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 15, NO. 5, SEPTEMBER 2004
1063
Which Model to Use for Cortical Spiking Neurons?
Eugene M. Izhikevich
Abstract—We discuss the biological plausibility and computational efficiency of some of the most useful models of spiking and bursting neurons. We compare their applicability to large-scale simulations of cortical neural networks. Index Terms—Chaos, Hodgkin–Huxley, pulse-coupled neural network (PCNN), quadratic integrate-and-fire (I&F), spike-timing.
A. Tonic Spiking Most neurons are excitable, that is, they are quiescent but can fire spikes when stimulated. To test this property, neurophysiologists inject pulses of dc current via an electrode attached to the neuron and record its membrane potential. The input current and the neuronal response are usually plotted one beneath the other, as inFig.1(a).Whiletheinputison,theneuroncontinuestofireatrain of spikes. This kind of behavior, called tonic spiking, can be observed in the three types of cortical neurons: regular spiking (RS) excitatory neurons, low-threshold spiking (LTS), and fast spiking (FS)inhibitoryneurons[1],[6].Continuousfiringofsuchneurons indicate that there is a persistent input. B. Phasic Spiking A neuron may fire only a single spike at the onset of the input, as in Fig. 1(b), and remain quiescent afterwards. Such a response is called phasic spiking, and it is useful for detection of the beginning of stimulation. C. Tonic Bursting Some neurons, such as the chattering neurons in cat neocortex [7], fire periodic bursts of spikes when stimulated, as in Fig. 1(c). The interburst (i.e., between bursts) frequency may be as high as 50 Hz, and it is believed that such neurons contribute to the gamma-frequency oscillations in the brain. D. Phasic Bursting Similarly to the phasic spikers, some neurons are phasic bursters, as in Fig. 1(d). Such neurons report the beginning of the stimulation by transmitting a burst. There are three major hypothesis on the importance
1063
Which Model to Use for Cortical Spiking Neurons?
Eugene M. Izhikevich
Abstract—We discuss the biological plausibility and computational efficiency of some of the most useful models of spiking and bursting neurons. We compare their applicability to large-scale simulations of cortical neural networks. Index Terms—Chaos, Hodgkin–Huxley, pulse-coupled neural network (PCNN), quadratic integrate-and-fire (I&F), spike-timing.
A. Tonic Spiking Most neurons are excitable, that is, they are quiescent but can fire spikes when stimulated. To test this property, neurophysiologists inject pulses of dc current via an electrode attached to the neuron and record its membrane potential. The input current and the neuronal response are usually plotted one beneath the other, as inFig.1(a).Whiletheinputison,theneuroncontinuestofireatrain of spikes. This kind of behavior, called tonic spiking, can be observed in the three types of cortical neurons: regular spiking (RS) excitatory neurons, low-threshold spiking (LTS), and fast spiking (FS)inhibitoryneurons[1],[6].Continuousfiringofsuchneurons indicate that there is a persistent input. B. Phasic Spiking A neuron may fire only a single spike at the onset of the input, as in Fig. 1(b), and remain quiescent afterwards. Such a response is called phasic spiking, and it is useful for detection of the beginning of stimulation. C. Tonic Bursting Some neurons, such as the chattering neurons in cat neocortex [7], fire periodic bursts of spikes when stimulated, as in Fig. 1(c). The interburst (i.e., between bursts) frequency may be as high as 50 Hz, and it is believed that such neurons contribute to the gamma-frequency oscillations in the brain. D. Phasic Bursting Similarly to the phasic spikers, some neurons are phasic bursters, as in Fig. 1(d). Such neurons report the beginning of the stimulation by transmitting a burst. There are three major hypothesis on the importance
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