Generalization of the event-based Carnevale-Hines integration scheme for integrate-and-fire models

Perfect Detection of Spikes in the Linear Sub-threshold Dynamics of Point Neurons

Spiking neuronal networks are usually simulated with one of three main schemes: the classical time-driven and event-driven schemes, and the more recent hybrid scheme. All three schemes evolve the state of a neuron through a series of checkpoints: equally spaced in the first scheme and determined neuron-wise by spike events in the latter two. The time-driven and the hybrid scheme determine whether the membrane potential of a neuron crosses a threshold at the end of the time interval between consecutive checkpoints. Threshold crossing can, however, occur within the interval even if this test is negative. Spikes can therefore be missed. The present work offers an alternative geometric point of view on neuronal dynamics, and derives, implements, and benchmarks a method for perfect retrospective spike detection. This method can be applied to neuron models with affine or linear subthreshold dynamics. The idea behind the method is to propagate the threshold with a time-inverted dynamics, testing whether the threshold crosses the neuron state to be evolved, rather than vice versa. Algebraically this translates into a set of inequalities necessary and sufficient for threshold crossing. This test is slower than the imperfect one, but can be optimized in several ways. Comparison confirms earlier results that the imperfect tests rarely miss spikes (less than a fraction 1/10⁸ of missed spikes) in biologically relevant settings.

Toward unified hybrid simulation techniques for spiking neural networks

In the field of neural network simulation techniques, the common conception is that spiking neural network simulators can be divided in two categories: time-step-based and event-driven methods. In this letter, we look at state-of-the art simulation techniques in both categories and show that a clear distinction between both methods is increasingly difficult to define. In an attempt to improve the weak points of each simulation method, ideas of the alternative method are, sometimes unknowingly, incorporated in the simulation engine. Clearly the ideal simulation method is a mix of both methods. We formulate the key properties of such an efficient and generally applicable hybrid approach.

Fast recruitment of recurrent inhibition in the cat visual cortex

Neurons of the same column in L4 of the cat visual cortex are likely to share the same sensory input from the same region of the visual field. Using visually-guided patch clamp recordings we investigated the biophysical properties of the synapses of neighboring layer 4 neurons. We recorded synaptic connections between all types of excitatory and inhibitory neurons in L4. The E–E, E–I, and I–E connections had moderate CVs and failure rates. However, E–I connections had larger amplitudes, faster rise-times, and shorter latencies. Identification of the sites of putative synaptic contacts together with compartmental simulations on 3D reconstructed cells, suggested that E–I synapses tended to be located on proximal dendritic branches, which would explain their larger EPSP amplitudes and faster kinetics. Excitatory and inhibitory synapses were located at the same distance on distal dendrites of excitatory neurons. We hypothesize that this co-localization and the fast recruitment of local inhibition provides an efficient means of modulating excitation in a precisely timed way.

A general and efficient method for incorporating precise spike times in globally time-driven simulations

Traditionally, event-driven simulations have been limited to the very restricted class of neuronal models for which the timing of future spikes can be expressed in closed form. Recently, the class of models that is amenable to event-driven simulation has been extended by the development of techniques to accurately calculate firing times for some integrate-and-fire neuron models that do not enable the prediction of future spikes in closed form. The motivation of this development is the general perception that time-driven simulations are imprecise. Here, we demonstrate that a globally time-driven scheme can calculate firing times that cannot be discriminated from those calculated by an event-driven implementation of the same model; moreover, the time-driven scheme incurs lower computational costs. The key insight is that time-driven methods are based on identifying a threshold crossing in the recent past, which can be implemented by a much simpler algorithm than the techniques for predicting future threshold crossings that are necessary for event-driven approaches. As run time is dominated by the cost of the operations performed at each incoming spike, which includes spike prediction in the case of event-driven simulation and retrospective detection in the case of time-driven simulation, the simple time-driven algorithm outperforms the event-driven approaches. Additionally, our method is generally applicable to all commonly used integrate-and-fire neuronal models; we show that a non-linear model employing a standard adaptive solver can reproduce a reference spike train with a high degree of precision.

Fast and exact simulation methods applied on a broad range of neuron models

Recently van Elburg and van Ooyen (2009) published a generalization of the event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory currents and double exponential inhibitory synaptic currents, introduced by Carnevale and Hines. In the paper, it was shown that the constraints on the synaptic time constants imposed by the Newton-Raphson iteration scheme, can be relaxed. In this note, we show that according to the results published in D'Haene, Schrauwen, Van Campenhout, and Stroobandt (2009), a further generalization is possible, eliminating any constraint on the time constants. We also demonstrate that in fact, a wide range of linear neuron models can be efficiently simulated with this computation scheme, including neuron models mimicking complex neuronal behavior. These results can change the way complex neuronal spiking behavior is modeled: instead of highly nonlinear neuron models with few state variables, it is possible to efficiently simulate linear models with a large number of state variables.