The Brian Simulator

“Brian” is a simulator for spiking neural networks (http://www.briansimulator.org). The focus is on making the writing of simulation code as quick and easy as possible for the user, and on flexibility: new and non-standard models are no more difficult to define than standard ones. This allows scientists to spend more time on the details of their models, and less on their implementation. Neuron models are defined by writing differential equations in standard mathematical notation, facilitating scientific communication. Brian is written in the Python programming language, and uses vector-based computation to allow for efficient simulations. It is particularly useful for neuroscientific modelling at the systems level, and for teaching computational neuroscience

Equation-oriented specification of neural models for simulations

Simulating biological neuronal networks is a core method of research in computational neuroscience. A full specification of such a network model includes a description of the dynamics and state changes of neurons and synapses, as well as the synaptic connectivity patterns and the initial values of all parameters. A standard approach in neuronal modeling software is to build network models based on a library of pre-defined components and mechanisms; if a model component does not yet exist, it has to be defined in a special-purpose or general low-level language and potentially be compiled and linked with the simulator. Here we propose an alternative approach that allows flexible definition of models by writing textual descriptions based on mathematical notation. We demonstrate that this approach allows the definition of a wide range of models with minimal syntax. Furthermore, such explicit model descriptions allow the generation of executable code for various target languages and devices, since the description is not tied to an implementation. Finally, this approach also has advantages for readability and reproducibility, because the model description is fully explicit, and because it can be automatically parsed and transformed into formatted descriptions. The presented approach has been implemented in the Brian2 simulator

Three-dimensional MRI assessment of regional wall stress after acute myocardial infarction predicts postdischarge cardiac events

PURPOSE: To determine the prognostic significance of systolic wall stress (SWS) after reperfused acute myocardial infarction (AMI) using MRI. MATERIALS AND METHODS: A total of 105 patients underwent MRI 7.8 +/- 4.2 days after AMI reperfusion. SWS was calculated by using a three-dimensional (3D) MRI approach to left ventricular (LV) wall thickness and to the radius of curvature. Between hospital discharge and the end of follow-up, an average of 4.1 +/- 1.7 years after AMI, 19 patients experienced a major cardiac event, including cardiac death, nonfatal reinfarction or heart failure (18.3%). RESULTS: The results were mainly driven by heart failure outcome. In univariate analysis the following factors were predictive of postdischarge major adverse cardiac events: 1) at the time of AMI: higher heart rate, previous calcium antagonist treatment, in-hospital congestive heart failure, proximal left anterior descending artery (LAD) occlusion, a lower ejection fraction, higher maximal ST segment elevation before reperfusion, and ST segment reduction lower than 50% after reperfusion; 2) MRI parameters: higher LV end-systolic volume, lower ejection fraction, higher global SWS, higher SWS in the infarcted area (SWS MI) and higher SWS in the remote myocardium (SWS remote). In the final multivariate model, only SWS MI (odds ratio [OR]: 1.62; 95% confidence interval [CI]: 1.01-2.60; P = 0.046) and SWS remote (OR: 2.17; 95% CI: 1.02-4.65; P = 0.046) were independent predictors. CONCLUSION: Regional SWS assessed by means of MRI a few days after AMI appears to be strong predictor of postdischarge cardiac events, identifying a subset of at risk patients who could qualify for more aggressive management

Numerical Solution of Differential Equations by the Parker-Sochacki Method

A tutorial is presented which demonstrates the theory and usage of the Parker-Sochacki method of numerically solving systems of differential equations. Solutions are demonstrated for the case of projectile motion in air, and for the classical Newtonian N-body problem with mutual gravitational attraction.Comment: Added in July 2010: This tutorial has been posted since 1998 on a university web site, but has now been cited and praised in one or more refereed journals. I am therefore submitting it to the Cornell arXiv so that it may be read in response to its citations. See "Spiking neural network simulation: numerical integration with the Parker-Sochacki method:" J. Comput Neurosci, Robert D. Stewart & Wyeth Bair and http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2717378

Resolution of hyposmotic stress in isolated mouse ventricular myocytes causes sealing of t‐tubules

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98789/1/expphysiol.2013.072470.pd

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

Numerical Analysis of Ca2+ Signaling in Rat Ventricular Myocytes with Realistic Transverse-Axial Tubular Geometry and Inhibited Sarcoplasmic Reticulum

The t-tubules of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca2+). To investigate how the t-tubule microanatomy and the distribution of membrane Ca2+ flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca2+ signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca2+ signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca2+ flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca2+ buffers, including the Ca2+ indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca2+ transients was found when the Ca2+ flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca2+ signals are predicted. Even at modest elevation of Ca2+, reached during Ca2+ influx, large and steep Ca2+ gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca2+ flux density along the cell membrane support initiation and propagation of Ca2+ waves in rat myocytes

Structural and thermodynamic analysis of a three-component assembly forming <i>ortho</i>-iminophenylboronate esters

Structural studies of a three-component assembly - a host and two distinct guests - were carried out using a combination of 11B and 1H NMR. In aprotic solvent, the imino group that forms ortho to the boronic acid or boronate ester group can form a dative N-B bond. In protic solvent, a molecule of solvent inserts between the nitrogen and boron atoms, partially ionizing the solvent molecule. Additionally, 11B NMR was used in combination with a seventh-order polynomial to calculate five binding constants for each of the individual steps in protic solvent. Comparison of these binding constants was used to establish positive cooperativity in the binding of the two guests.</p

How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation

This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks ? and; (ii) what are the effects of synaptic plasticity on these statistics ? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure