This article describes the concepts and strategies that have guided the design and implementation of this simulator, with emphasis on those features that are particularly relevant to its most efficient use. 1.1 The problem domain

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

This article describes a program, NEURON, developed in collaboration with John W. Moore, written in C, and with source code freely available to any interested person. With NEURON, nerve properties are specified, the simulation controlled, and the results graphed by writing procedural statements to an interpreter. This has the advantage of generality but the disadvantage that it is more difficult to learn than a menu driven interface. The usefulness of NEURON degrades very slowly with increased complexity of morphology and ANALYSIS AND MODELING OF NEURAL SYSTEMS II membrane mechanisms. NEURON is best suited, in terms of efficiency, for problems ranging from parts of single cells to small numbers of cells in which cable properties play a crucial role. It is best suited, in terms of conceptual control, for stylized morphologies represented as connected cable sections and where membrane channel parameters are conveniently represented as piece-wise linear functions of position within each section. Two special classes of problems for which it is well suited are those in which it is important to calculate ionic concentrations and those where one needs to compute the extracellular potential just next to the nerve membrane. It is well suited for investigating new kinds of membrane channels since they are described using a high level model description language which allows the expression of models in terms of kinetic schemes or sets of simultaneous equations. B A barrier Extracellular Membrane Membrane Node Segment Section v(1.5/nseg) v(1) v(1) vext(1)

Introduction In this chapter we will discuss some practical and technical aspects of numerical methods that can be used to solve the equations that neuronal modelers frequently encounter. We will consider numerical methods for ordinary differential equations (ODEs) and for partial differential equations (PDEs) through examples. A typical case where ODEs arise in neuronal modeling is when one uses a single lumped-soma compartmental model to describe a neuron. Arguably the most famous PDE system in neuronal modeling is the phenomenological model of the squid giant axon due to Hodgkin and Huxley. The difference between ODEs and PDEs is that ODEs are equations in which the rate of change of an unknown function of a single variable is prescribed, usually the derivative with respect to time. In contrast, PDEs involve the rates of change of the solution with respect to two or more independent variables, such as time and space. The numerical methods we will discuss for both ODEs and

Neuronal function involves the interaction of electrical and chemical signals that are distributed in time and space. ...

NEURON is a simulation environment for models of individual neurons and networks of neurons that are closely linked to experimental data. NEURON provides tools for conveniently constructing, exercising, and managing models, so that special expertise in numerical methods or programming is not required for its productive use. This paper describes two tools that address the problem of how to achieve computational efficiency and accuracy.

Biophysically detailed models of single neurons which draw on a wide variety of experimental and theoretical foundations are increasingly important in the understanding of the functional role of various cellular mechanisms. In this paper, such an approach is detailed for pyramidal neurons of the hippocampus. Included is a review of the experimental literature, descriptions of biophysical models appropriate for the analysis of single cell behaviour, a comparative review of several published models, and parameters for an updated model of this cell type.

Computer simulation is an important tool for investigating the propagation behaviour of electrical excitation in cardiac tissue. When ionic models of cell membrane excitation are combined with the bidomain model of macroscopic tissue properties, numerical solution of the resulting partial differential equations requires a substantial amount of computation. Thus more efficient numerical methods are needed. One aspect of the computational complexity of this problem is the need for detailed spatial and temporal resolution while the depolarizing front of excitation propagates through the domain. During the subsequent, and more protracted, repolarization phase, the solution changes more slowly and a much coarser discretization would be adequate. Previous approaches have incorporated explicit integration methods whose stability limitations have prevented exploitation of this change in time scales. This study applies a stable implicit integration method which allows the time-step to be contro...

ABSTRACT Axonal trees are typically morphologically and physiologically complicated structures. Because of this complexity, axonal trees show a large repertoire of behavior: from transmission lines with delay, to frequency filtering devices in both temporal and spatial domains. Detailed theoretical exploration of the electrical behavior of realistically complex axonal trees is notably lacking, mainly because of the absence of a simple modeling tool. AXONTREE is an attempt to provide such a simulator. It is written in C for the SUN workstation and implements both a detailed compartmental modeling of Hodgkin and Huxley-like kinetics, and a more abstract, event-driven, modeling approach. The computing module of AXONTREE is introduced together with its input/output features. These features allow graphical construction of arbitrary trees directly on the computer screen, and superimposition of the results on the simulated structure. Several numerical improvements that increase the computational efficiency by a factor of 5-10 are presented; most notable is a novel method of dynamic lumping of the modeled tree into simpler representations ("equivalent cables"). AXONTREE's performance is examined using a reconstructed terminal of an axon from a Y cell in cat visual cortex. It is demonstrated that realistically complicated axonal trees can be handled efficiently. The application ofAXONTREE for the study of propagation delays along axonal trees is presented in the companion paper (Manor et al., 1991).

We demonstrate that a biphasic shock is more effective than a monophasic shock at eliminating reentrant electrical activity in an ionic model of cardiac ventricular electrical activity. This effectiveness results from early hyperpolarization that enhances the recovery of sodium inactivation, thereby enabling earlier activation of recovering cells. The effect can be seen easily in a model of a single cell and also in a cable model with a ring of excitable cells. Finally, we demonstrate the phenomenon in a two-dimensional model of cardiac tissue.