Computational geometry for modeling neural populations: From visualization to simulation

Abstract

The importance of a mesoscopic description level of the brain has now been well established. Rate based models are widely used, but have limitations. Recently, several extremely efficient population-level methods have been proposed that go beyond the characterization of a population in terms of a single variable. Here, we present a method for simulating neural populations based on two dimensional (2D) point spiking neuron models that defines the state of the population in terms of a density function over the neural state space. Our method differs in that we do not make the diffusion approximation, nor do we reduce the state space to a single dimension (1D). We do not hard code the neural model, but read in a grid describing its state space in the relevant simulation region. Novel models can be studied without even recompiling the code. The method is highly modular: variations of the deterministic neural dynamics and the stochastic process can be investigated independently. Currently, there is a trend to reduce complex high dimensional neuron models to 2D ones as they offer a rich dynamical repertoire that is not available in 1D, such as limit cycles. We will demonstrate that our method is ideally suited to investigate noise in such systems, replicating results obtained in the diffusion limit and generalizing them to a regime of large jumps. The joint probability density function is much more informative than 1D marginals, and we will argue that the study of 2D systems subject to noise is important complementary to 1D systems.

MIIND : A Model-Agnostic Simulator of Neural Populations

“…For example, to approximate adaptive behaviour where the post synaptic efficacy lowers as the membrane potential increases. Jump files have been used in MIIND to simulate the Tsodyks-Markram (Tsodyks and Markram, 1997) synapse model as described in De Kamps et al (2019). In the model, one variable/dimension is required to represent the membrane potential, V, of the post-synaptic neuron and the second to represent the synaptic contribution, G. G and V are then used to derive the post-synaptic potential caused by an incoming spike.…”

“…Using the "Group" algorithms is recommended if possible as it provides a significant performance increase. As shown in De Kamps et al (2019), with the use of the GPGPU, a population of conductance based neurons in MIIND performs comparably to a NEST simulation of 10,000 individual neurons but using an order of magnitude less memory. This allows MIIND to simulate many thousands of populations on a single PC.…”

“…If multiple cores are available, the OpenMP implementation significantly improves performance of the master process step. More information covering this technique can be found in de Kamps ( 2013 ), De Kamps et al ( 2019 ).…”

“…A mesh is constructed from strips which follow the trajectories of neurons in state space ( Figure 8 ). The trajectories form so-called characteristic curves of the neuron model from which this method is inspired (de Kamps, 2013 ; De Kamps et al, 2019 ).…”

“…Why use this technique? Nykamp and Tranchina ( 2000 ), Omurtag et al ( 2000 ), Kamps ( 2003 ), Iyer et al ( 2013 ) have demonstrated that PDTs are much faster than Monte Carlo simulation for 1D models; De Kamps et al ( 2019 ) have shown that while speed is comparable between 2D models and Monte Carlo, memory usage is orders of magnitude lower because no spikes need to be buffered, which accounts for significant memory use in large-scale simulations. In practice, this may make the difference between running a simulation on an HPC cluster or a single PC equipped with a general purpose graphics processing unit (GPGPU).…”