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,.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 , 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 of bursts in the brain which are: 1) bursts are needed to overcome the synaptic transmission failure and reduce neuronal noise ; 2) Bursts can transmit saliency of the input, because the effect of a burst on the postsynaptic neuron is stronger than the effect of a single spike; and 3) bursts can be used for selective communication between neurons , where the interspike frequency within the bursts encodes the channel of communication. A good model of a cortical neuronal network cannot neglect bursting neurons. E. Mixed Model (Bursting Then Spiking) Intrinsically bursting (IB) excitatory neurons in mammalian neocortex  can exhibit a mixed type of spiking activity depicted in Fig. 1(e). They ﬁre a phasic burst at the onset of stimulation and then switch to the tonic spiking mode. It is not clear what kind of computation such a neuron can do in addition to detecting the onset and reporting the extent of stimulation.
URING last few years we have witnessed a shift of the emphasis in the artiﬁcial neural network community toward spiking neural networks. Motivated by biological discoveries, many studies (see this volume) consider pulse-coupled neural networks with spike-timing as an essential component in information processing by the brain. In any study of network dynamics, there are two crucial issues which are: 1) what model describes spiking dynamics of each neuron and 2) how the neurons are connected. Inappropriate choice of the spiking model or the connectivity may lead to results having nothing to do with the information processing by the brain. In this paper, we consider the ﬁrst issue, i.e., we compare and contrast various models of spiking neurons. In Section II and Fig. 1, we review important neuro-computational features of real neurons and their contribution to temporal coding and spike-timing information processing. In Section III, we consider various models of spiking neurons and rank them according to: 1) the number of...