Efficient Implementation of Continuous-Time Spiking Neuron Models and Development of Heuristics to Study Effective Connectivity in Basal Ganglia  


Efficient Implementation of Continuous-Time Spiking Neuron Models

Two classical approaches to simulate neuronal networks are the time-driven and event-driven methods. Both methods describe the physical system in terms of a set of state variables representing the neurons and events that mediate their interaction, i.e. spikes.

In the discrete-time (on-grid mode) of the NEST simulator, the dynamics of each neuron is propagated by a pre-defined simulation step. Various pitfalls of this approach such as artificial synchronization have been addressed previously and the state-of-the-art method for spike handling embeds event-driven methods in a globally time-driven simulation. This method of processing spikes in continuous-time is applicable to a certain class of neuron models whose sub-threshold dynamics can be exactly integrated.

However, the accuracy of these continuous-time precise models (off-grid mode) of the NEST simulator has not been systematically investigated yet. One source of imprecision is the possibility to miss spikes caused by brief and unnoticed excursions of the membrane potential beyond threshold. We here develop a new spike detection algorithm based on state-space analysis of variables governing the linear system of a leaky integrate-and-fire neuron with exponential currents.

Conventional spike detection methods in time-driven simulations propagate the state of neuron forward and only check at the end of time interval whether there has been a threshold crossing. If the membrane voltage is below threshold at these check points and and supra-threshold between these points, this leads to a spike miss. The idea of this work is to understand whether such voltage excursions occur and if so, how frequent they are and what is their effect on accuracy the of the LIF model.

Instead of propagating the neuron state forward, we propagate the threshold plane backward in time to find the set of initial conditions (spiking states) that would cross threshold in the future. By doing so, we get two distinct regions in state-space: the initial states leading to a spike, and those not leading to a spike, within a propagation step.

This algorithm confirms that the precise LIF model in NEST rarely misses spikes. The reason is that frequently arriving synaptic impulses effectively induce a fine-grained grid of check points making brief excursions above threshold extremely unlikely.

Development of Heuristics to Study connectivity in Basal Ganglia in Pathological and Healthy States

The classical model of basal ganglia has been regularly updated with discovery of new types of sub-populations within a nucleus or new projections from existing nuclei in recent years. However, to systematically understand these developments it is integral to question how do these changes in structure affect the function in Basal Ganglia.

Using a dataset obtained from simulations of a firing rate model for basal ganglia from a previous study for healthy and pathological states, here we attempt to find a heuristic to classify these datasets. The effective connectivity for 20 areas of Basal ganglia contribute in some way to the state of the brain. First results show that PCA is good naive-classifier, however a more intelligent method is required to find an approximate distance matrix given any two clusters.