David Dahmen

Hybrid Scheme for Modeling Local Field Potentials from Point-Neuron Networks

With rapidly advancing multi-electrode recording technology, the local field potential (LFP) has again become a popular measure of neuronal activity in both research and clinical applications. Proper understanding of the LFP requires detailed mathematical modeling incorporating the anatomical and electrophysiological features of neurons near the recording electrode, as well as synaptic inputs from the entire network. Here we propose a hybrid modeling scheme combining efficient point-neuron network models with biophysical principles underlying LFP generation by real neurons. The LFP predictions rely on populations of network-equivalent multicompartment neuron models with layer-specific synaptic connectivity, can be used with an arbitrary number of point-neuron network populations, and allows for a full separation of simulated network dynamics and LFPs. We apply the scheme to a full-scale cortical network model for a ∼1 mm2 patch of primary visual cortex, predict laminar LFPs for different network states, assess the relative LFP contribution from different laminar populations, and investigate effects of input correlations and neuron density on the LFP. The generic nature of the hybrid scheme and its public implementation in hybridLFPy form the basis for LFP predictions from other and larger point-neuron network models, as well as extensions of the current application with additional biological detail.

Correlated Fluctuations in Strongly Coupled Binary Networks Beyond Equilibrium

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics. The phase diagram of these systems is obtained in the thermodynamic limit by averaging over the quenched randomness of the couplings. However, many applications require the statistics of activity for a single realization of the possibly asymmetric couplings in finite-sized networks. Examples include reconstruction of couplings from the observed dynamics, learning in the central nervous system by correlation-sensitive synaptic plasticity, and representation of probability distributions for sampling-based inference. The systematic cumulant expansion for kinetic binary (Ising) threshold units with strong, random and asymmetric couplings presented here goes beyond mean-field theory and is applicable outside thermodynamic equilibrium; a system of approximate non-linear equations predicts average activities and pairwise covariances in quantitative agreement with full simulations down to hundreds of units. The linearized theory yields an expansion of the correlation- and response functions in collective eigenmodes, leads to an efficient algorithm solving the inverse problem, and shows that correlations are invariant under scaling of the interaction strengths.

Integration of Continuous-Time Dynamics in a Spiking Neural Network Simulator

Contemporary modeling approaches to the dynamics of neural networks include two important classes of models: biologically grounded spiking neuron models and functionally inspired rate-based units. We present a unified simulation framework that supports the combination of the two for multi-scale modeling, enables the quantitative validation of mean-field approaches by spiking network simulations, and provides an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most spiking simulations rely on the communication of discrete events, rate models require time-continuous interactions between neurons. Exploiting the conceptual similarity to the inclusion of gap junctions in spiking network simulations, we arrive at a reference implementation of instantaneous and delayed interactions between rate-based models in a spiking network simulator. The separation of rate dynamics from the general connection and communication infrastructure ensures flexibility of the framework. In addition to the standard implementation we present an iterative approach based on waveform-relaxation techniques to reduce communication and increase performance for large-scale simulations of rate-based models with instantaneous interactions. Finally we demonstrate the broad applicability of the framework by considering various examples from the literature, ranging from random networks to neural-field models. The study provides the prerequisite for interactions between rate-based and spiking models in a joint simulation.

Hybrid scheme for modeling local field potentials from point-neuron networks

Measurement of the local field potential (LFP) has become routine for assessment of neuronal activity in neuroscientific and clinical applications, but its interpretation remains nontrivial. Understanding the LFP requires accounting for both anatomical and electrophysiological features of neurons near the recording electrode as well as the entire large-scale neuronal circuitry generating synaptic input to these cells. The direct simulation of LFPs in biophysically detailed network models is computationally daunting. Here, we instead propose a hybrid modeling scheme combining the efficiency of simplified point-neuron network models (Fig. ​(Fig.1A)1A) with the biophysical principles underlying LFP generation by multicompartment neurons [1] (Fig ​(Fig1C).1C). We apply this scheme to a model representing a full-scale cortical network under about 1 square millimeter surface of cat primary visual cortex [2] (Fig. 1A,B) with layer-specific connectivity [3] to predict laminar LFPs (Fig. ​(Fig.1D)1D) for different network states, assess the relative contribution of local neuron populations to the LFP, investigate the role of input correlations and neuron density, and validate linear LFP predictions based on population firing rates. The hybrid scheme is accompanied by our open-source software, hybridLFPy (github.com/espenhgn/hybridLFPy). Figure 1 Overview of the hybrid scheme for modeling LFP generated by a cortical network model. A Sketch of point-neuron network model [1]. B Spikes of point neurons in the network for spontaneous and evoked activity. C Populations of multi-compartment neurons ...

Hybrid scheme for modeling LFPs from spiking cortical network models

While recordings of extracellular potentials (EP) remain a common method for experimentally measuring neural activity, the interpretation of the low-frequency part, the local field potential (LFP), is not straightforward. Cortical LFPs seem to mainly stem from synaptic inputs, but the net LFP signal from several contributing laminar populations is difficult to assess, as the individual contributions will depend on their locations, the morphologies of the postsynaptic neurons, the spatial distribution of active synapses, and the level of correlations in synaptic inputs [1]. While most comprehensive cortical-network simulations are done with single-compartment models [2], multicompartmental neuronal modeling is in general required to calculate LFPs [1]. Here we present a hybrid LFP modeling approach where a network of single-compartment LIF neurons generates the spiking activity (Figure ​(Figure1A),1A), while detailed multicompartment neuronal models are used to calculate the accompanying LFP (Figure 1B-C). Our model describes a 1mm2 patch of cat V1, and we incorporate spatially specific pre- to post-synaptic inter- and intra-layer connectivity constrained by experimental observations [3] using reconstructed neuron morphologies of excitatory and inhibitory neurons in layers L2/3-L6 with passive membrane properties. Model specifications of neuron and synapse numbers within populations are taken from [2], while spatial connectivity profiles are based on [3]. Our hybrid simulation framework allows detailed analysis of how the LFP correlates with network activity and connectivity, and how spatially specific synapse distributions influence the LFP. Spiking network simulations [2] were implemented in NEST (http://www.nest-initiative.org), while simulations of LFPs from morphologically realistic neurons used LFPy (compneuro.umb.no/LFPy) along with NEURON [4]. Figure 1 Schematic illustration of the hybrid scheme. (A) Spiking activity generated in network simulations using single-compartment neurons [2] are used as input to multicompartmental neuron models to generate LFPs (B). LFP contributions from each postsynaptic ...