Simulation of networks of spiking neurons: A review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of Computational Neuroscience, in press (2007

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks

On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses

We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model where spikes are effective at times multiple of a characteristic time scale $\delta$, where $\delta$ can be \textit{arbitrary} small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and Integrate-and-Fire models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.Comment: 36 pages, 9 figure

KInNeSS: A Modular Framework for Computational Neuroscience

Making use of very detailed neurophysiological, anatomical, and behavioral data to build biological-realistic computational models of animal behavior is often a difficult task. Until recently, many software packages have tried to resolve this mismatched granularity with different approaches. This paper presents KInNeSS, the KDE Integrated NeuroSimulation Software environment, as an alternative solution to bridge the gap between data and model behavior. This open source neural simulation software package provides an expandable framework incorporating features such as ease of use, scalabiltiy, an XML based schema, and multiple levels of granularity within a modern object oriented programming design. KInNeSS is best suited to simulate networks of hundreds to thousands of branched multu-compartmental neurons with biophysical properties such as membrane potential, voltage-gated and ligand-gated channels, the presence of gap junctions of ionic diffusion, neuromodulation channel gating, the mechanism for habituative or depressive synapses, axonal delays, and synaptic plasticity. KInNeSS outputs include compartment membrane voltage, spikes, local-field potentials, and current source densities, as well as visualization of the behavior of a simulated agent. An explanation of the modeling philosophy and plug-in development is also presented. Further developement of KInNeSS is ongoing with the ultimate goal of creating a modular framework that will help researchers across different disciplines to effecitively collaborate using a modern neural simulation platform.Center for Excellence for Learning Education, Science, and Technology (SBE-0354378); Air Force Office of Scientific Research (F49620-01-1-0397); Office of Naval Research (N00014-01-1-0624

Event-driven simulation scheme for spiking neural networks using lookup tables to characterize neuronal dynamics

Nearly all neuronal information processing and interneuronal communication in the brain involves action potentials, or spikes, which drive the short-term synaptic dynamics of neurons, but also their long-term dynamics, via synaptic plasticity. In many brain structures, action potential activity is considered to be sparse. This sparseness of activity has been exploited to reduce the computational cost of large-scale network simulations, through the development of event-driven simulation schemes. However, existing event-driven simulations schemes use extremely simplified neuronal models. Here, we implement and evaluate critically an event-driven algorithm (ED-LUT) that uses precalculated look-up tables to characterize synaptic and neuronal dynamics. This approach enables the use of more complex (and realistic) neuronal models or data in representing the neurons, while retaining the advantage of high-speed simulation. We demonstrate the method's application for neurons containing exponential synaptic conductances, thereby implementing shunting inhibition, a phenomenon that is critical to cellular computation. We also introduce an improved two-stage event-queue algorithm, which allows the simulations to scale efficiently to highly connected networks with arbitrary propagation delays. Finally, the scheme readily accommodates implementation of synaptic plasticity mechanisms that depend on spike timing, enabling future simulations to explore issues of long-term learning and adaptation in large-scale networks.This work has been supported by the EU projects SpikeFORCE (IST-2001-35271), SENSOPAC (IST-028056) and the Spanish National Grant (DPI-2004-07032

Introducing numerical bounds to improve event-based neural network simulation

Although the spike-trains in neural networks are mainly constrained by the neural dynamics itself, global temporal constraints (refractoriness, time precision, propagation delays, ..) are also to be taken into account. These constraints are revisited in this paper in order to use them in event-based simulation paradigms. We first review these constraints, and discuss their consequences at the simulation level, showing how event-based simulation of time-constrained networks can be simplified in this context: the underlying data-structures are strongly simplified, while event-based and clock-based mechanisms can be easily mixed. These ideas are applied to punctual conductance-based generalized integrate-and-fire neural networks simulation, while spike-response model simulations are also revisited within this framework. As an outcome, a fast minimal complementary alternative with respect to existing simulation event-based methods, with the possibility to simulate interesting neuron models is implemented and experimented.Comment: submitte

Neuromorphic silicon neuron circuits

23 páginas, 21 figuras, 2 tablas.-- et al.Hardware implementations of spiking neurons can be extremely useful for a large variety of applications, ranging from high-speed modeling of large-scale neural systems to real-time behaving systems, to bidirectional brain–machine interfaces. The specific circuit solutions used to implement silicon neurons depend on the application requirements. In this paper we describe the most common building blocks and techniques used to implement these circuits, and present an overview of a wide range of neuromorphic silicon neurons, which implement different computational models, ranging from biophysically realistic and conductance-based Hodgkin–Huxley models to bi-dimensional generalized adaptive integrate and fire models. We compare the different design methodologies used for each silicon neuron design described, and demonstrate their features with experimental results, measured from a wide range of fabricated VLSI chips.This work was supported by the EU ERC grant 257219 (neuroP), the EU ICT FP7 grants 231467 (eMorph), 216777 (NABAB), 231168 (SCANDLE), 15879 (FACETS), by the Swiss National Science Foundation grant 119973 (SoundRec), by the UK EPSRC grant no. EP/C010841/1, by the Spanish grants (with support from the European Regional Development Fund) TEC2006-11730-C03-01 (SAMANTA2), TEC2009-10639-C04-01 (VULCANO) Andalusian grant num. P06TIC01417 (Brain System), and by the Australian Research Council grants num. DP0343654 and num. DP0881219.Peer Reviewe