Computational geometry for modeling neural populations: From visualization to simulation

Virtual Intelligence: A Systematic Review of the Development of Neural Networks in Brain Simulation Units

The functioning of the brain has been a complex and enigmatic phenomenon. From the first approaches made by Descartes about this organism as the vehicle of the mind to contemporary studies that consider the brain as an organism with emergent activities of primary and higher order, this organism has been the object of continuous exploration. It has been possible to develop a more profound study of brain functions through imaging techniques, the implementation of digital platforms or simulators through different programming languages and the use of multiple processors to emulate the speed at which synaptic processes are executed in the brain. The use of various computational architectures raises innumerable questions about the possible scope of disciplines such as computational neurosciences in the study of the brain and the possibility of deep knowledge into different devices with the support that information technology (IT) brings. One of the main interests of cognitive science is the opportunity to develop human intelligence in a system or mechanism. This paper takes the principal articles of three databases oriented to computational sciences (EbscoHost Web, IEEE Xplore and Compendex Engineering Village) to understand the current objectives of neural networks in studying the brain. The possible use of this kind of technology is to develop artificial intelligence (AI) systems that can replicate more complex human brain tasks (such as those involving consciousness). The results show the principal findings in research and topics in developing studies about neural networks in computational neurosciences. One of the principal developments is the use of neural networks as the basis of much computational architecture using multiple techniques such as computational neuromorphic chips, MRI images and brain–computer interfaces (BCI) to enhance the capacity to simulate brain activities. This article aims to review and analyze those studies carried out on the development of different computational architectures that focus on affecting various brain activities through neural networks. The aim is to determine the orientation and the main lines of research on this topic and work in routes that allow interdisciplinary collaboration.

A numerical population density technique for N-dimensional neuron models

Population density techniques can be used to simulate the behavior of a population of neurons which adhere to a common underlying neuron model. They have previously been used for analyzing models of orientation tuning and decision making tasks. They produce a fully deterministic solution to neural simulations which often involve a non-deterministic or noise component. Until now, numerical population density techniques have been limited to only one- and two-dimensional models. For the first time, we demonstrate a method to take an N-dimensional underlying neuron model and simulate the behavior of a population. The technique enables so-called graceful degradation of the dynamics allowing a balance between accuracy and simulation speed while maintaining important behavioral features such as rate curves and bifurcations. It is an extension of the numerical population density technique implemented in the MIIND software framework that simulates networks of populations of neurons. Here, we describe the extension to N dimensions and simulate populations of leaky integrate-and-fire neurons with excitatory and inhibitory synaptic conductances then demonstrate the effect of degrading the accuracy on the solution. We also simulate two separate populations in an E-I configuration to demonstrate the technique's ability to capture complex behaviors of interacting populations. Finally, we simulate a population of four-dimensional Hodgkin-Huxley neurons under the influence of noise. Though the MIIND software has been used only for neural modeling up to this point, the technique can be used to simulate the behavior of a population of agents adhering to any system of ordinary differential equations under the influence of shot noise. MIIND has been modified to render a visualization of any three of an N-dimensional state space of a population which encourages fast model prototyping and debugging and could prove a useful educational tool for understanding dynamical systems.

MIIND : A Model-Agnostic Simulator of Neural Populations

MIIND is a software platform for easily and efficiently simulating the behaviour of interacting populations of point neurons governed by any 1D or 2D dynamical system. The simulator is entirely agnostic to the underlying neuron model of each population and provides an intuitive method for controlling the amount of noise which can significantly affect the overall behaviour. A network of populations can be set up quickly and easily using MIIND's XML-style simulation file format describing simulation parameters such as how populations interact, transmission delays, post-synaptic potentials, and what output to record. During simulation, a visual display of each population's state is provided for immediate feedback of the behaviour and population activity can be output to a file or passed to a Python script for further processing. The Python support also means that MIIND can be integrated into other software such as The Virtual Brain. MIIND's population density technique is a geometric and visual method for describing the activity of each neuron population which encourages a deep consideration of the dynamics of the neuron model and provides insight into how the behaviour of each population is affected by the behaviour of its neighbours in the network. For 1D neuron models, MIIND performs far better than direct simulation solutions for large populations. For 2D models, performance comparison is more nuanced but the population density approach still confers certain advantages over direct simulation. MIIND can be used to build neural systems that bridge the scales between an individual neuron model and a population network. This allows researchers to maintain a plausible path back from mesoscopic to microscopic scales while minimising the complexity of managing large numbers of interconnected neurons. In this paper, we introduce the MIIND system, its usage, and provide implementation details where appropriate.

Mind the last spike - firing rate models for mesoscopic populations of spiking neurons

The dominant modeling framework for understanding cortical computations are heuristic firing rate models. Despite their success, these models fall short to capture spike synchronization effects, to link to biophysical parameters and to describe finite-size fluctuations. In this opinion article, we propose that the refractory density method (RDM), also known as age-structured population dynamics or quasi-renewal theory, yields a powerful theoretical framework to build rate-based models for mesoscopic neural populations from realistic neuron dynamics at the microscopic level. We review recent advances achieved by the RDM to obtain efficient population density equations for networks of generalized integrate-and-fire (GIF) neurons - a class of neuron models that has been successfully fitted to various cell types. The theory not only predicts the nonstationary dynamics of large populations of neurons but also permits an extension to finite-size populations and a systematic reduction to low-dimensional rate dynamics. The new types of rate models will allow a re-examination of models of cortical computations under biological constraints.