Gaute T. Einevoll

Modelling and analysis of local field potentials for studying the function of cortical circuits

The past decade has witnessed a renewed interest in cortical local field potentials (LFPs) — that is, extracellularly recorded potentials with frequencies of up to ∼500 Hz. This is due to both the advent of multielectrodes, which has enabled recording of LFPs at tens to hundreds of sites simultaneously, and the insight that LFPs offer a unique window into key integrative synaptic processes in cortical populations. However, owing to its numerous potential neural sources, the LFP is more difficult to interpret than are spikes. Careful mathematical modelling and analysis are needed to take full advantage of the opportunities that this signal offers in understanding signal processing in cortical circuits and, ultimately, the neural basis of perception and cognition.

Current-source density estimation based on inversion of electrostatic forward solution : Effects of finite extent of neuronal activity and conductivity discontinuities

A new method for estimation of current-source density (CSD) from local field potentials is presented. This inverse CSD (iCSD) method is based on explicit inversion of the electrostatic forward solution and can be applied to data from multielectrode arrays with various geometries. Here, the method is applied to linear-array (laminar) electrode data. Three iCSD methods are considered: the CSD is assumed to have cylindrical symmetry and be (i) localized in infinitely thin discs, (ii) step-wise constant or (iii) continuous and smoothly varying (using cubic splines) in the vertical direction. For spatially confined CSD distributions the standard CSD method, involving a discrete double derivative, is seen in model calculations to give significant estimation errors when the lateral source dimension is comparable to the size of a cortical column (less than approximately 1 mm). Further, discontinuities in the extracellular conductivity are seen to potentially give sizable errors for even wider source distributions. The iCSD methods are seen to give excellent estimates when the correct lateral source dimension and spatial distribution of conductivity are incorporated. To illustrate the application to real data, iCSD estimates of stimulus-evoked responses measured with laminar electrodes in the rat somatosensory (barrel) cortex are compared to estimates from the standard CSD method.

In vivo Stimulus-Induced Vasodilation Occurs without IP3 Receptor Activation and May Precede Astrocytic Calcium Increase

Calcium-dependent release of vasoactive gliotransmitters is widely assumed to trigger vasodilation associated with rapid increases in neuronal activity. Inconsistent with this hypothesis, intact stimulus-induced vasodilation was observed in inositol 1,4,5-triphosphate (IP3) type-2 receptor (R2) knock-out (KO) mice, in which the primary mechanism of astrocytic calcium increase—the release of calcium from intracellular stores following activation of an IP3-dependent pathway—is lacking. Further, our results in wild-type (WT) mice indicate that in vivo onset of astrocytic calcium increase in response to sensory stimulus could be considerably delayed relative to the simultaneously measured onset of arteriolar dilation. Delayed calcium increases in WT mice were observed in both astrocytic cell bodies and perivascular endfeet. Thus, astrocytes may not play a role in the initiation of blood flow response, at least not via calcium-dependent mechanisms. Moreover, an increase in astrocytic intracellular calcium was not required for normal vasodilation in the IP3R2-KO animals.

Intrinsic dendritic filtering gives low-pass power spectra of local field potentials

The local field potential (LFP) is among the most important experimental measures when probing neural population activity, but a proper understanding of the link between the underlying neural activity and the LFP signal is still missing. Here we investigate this link by mathematical modeling of contributions to the LFP from a single layer-5 pyramidal neuron and a single layer-4 stellate neuron receiving synaptic input. An intrinsic dendritic low-pass filtering effect of the LFP signal, previously demonstrated for extracellular signatures of action potentials, is seen to strongly affect the LFP power spectra, even for frequencies as low as 10 Hz for the example pyramidal neuron. Further, the LFP signal is found to depend sensitively on both the recording position and the position of the synaptic input: the LFP power spectra recorded close to the active synapse are typically found to be less low-pass filtered than spectra recorded further away. Some recording positions display striking band-pass characteristics of the LFP. The frequency dependence of the properties of the current dipole moment set up by the synaptic input current is found to qualitatively account for several salient features of the observed LFP. Two approximate schemes for calculating the LFP, the dipole approximation and the two-monopole approximation, are tested and found to be potentially useful for translating results from large-scale neural network models into predictions for results from electroencephalographic (EEG) or electrocorticographic (ECoG) recordings.

Towards reliable spike-train recordings from thousands of neurons with multielectrodes.

The new generation of silicon-based multielectrodes comprising hundreds or more electrode contacts offers unprecedented possibilities for simultaneous recordings of spike trains from thousands of neurons. Such data will not only be invaluable for finding out how neural networks in the brain work, but will likely be important also for neural prosthesis applications. This opportunity can only be realized if efficient, accurate and validated methods for automatic spike sorting are provided. In this review we describe some of the challenges that must be met to achieve this goal, and in particular argue for the critical need of realistic model data to be used as ground truth in the validation of spike-sorting algorithms.

Decorrelation of neural-network activity by inhibitory feedback.

Correlations in spike-train ensembles can seriously impair the encoding of information by their spatio-temporal structure. An inevitable source of correlation in finite neural networks is common presynaptic input to pairs of neurons. Recent studies demonstrate that spike correlations in recurrent neural networks are considerably smaller than expected based on the amount of shared presynaptic input. Here, we explain this observation by means of a linear network model and simulations of networks of leaky integrate-and-fire neurons. We show that inhibitory feedback efficiently suppresses pairwise correlations and, hence, population-rate fluctuations, thereby assigning inhibitory neurons the new role of active decorrelation. We quantify this decorrelation by comparing the responses of the intact recurrent network (feedback system) and systems where the statistics of the feedback channel is perturbed (feedforward system). Manipulations of the feedback statistics can lead to a significant increase in the power and coherence of the population response. In particular, neglecting correlations within the ensemble of feedback channels or between the external stimulus and the feedback amplifies population-rate fluctuations by orders of magnitude. The fluctuation suppression in homogeneous inhibitory networks is explained by a negative feedback loop in the one-dimensional dynamics of the compound activity. Similarly, a change of coordinates exposes an effective negative feedback loop in the compound dynamics of stable excitatory-inhibitory networks. The suppression of input correlations in finite networks is explained by the population averaged correlations in the linear network model: In purely inhibitory networks, shared-input correlations are canceled by negative spike-train correlations. In excitatory-inhibitory networks, spike-train correlations are typically positive. Here, the suppression of input correlations is not a result of the mere existence of correlations between excitatory (E) and inhibitory (I) neurons, but a consequence of a particular structure of correlations among the three possible pairings (EE, EI, II).

Astrocytic Mechanisms Explaining Neural-Activity-Induced Shrinkage of Extraneuronal Space

Neuronal stimulation causes ∼30% shrinkage of the extracellular space (ECS) between neurons and surrounding astrocytes in grey and white matter under experimental conditions. Despite its possible implications for a proper understanding of basic aspects of potassium clearance and astrocyte function, the phenomenon remains unexplained. Here we present a dynamic model that accounts for current experimental data related to the shrinkage phenomenon in wild-type as well as in gene knockout individuals. We find that neuronal release of potassium and uptake of sodium during stimulation, astrocyte uptake of potassium, sodium, and chloride in passive channels, action of the Na/K/ATPase pump, and osmotically driven transport of water through the astrocyte membrane together seem sufficient for generating ECS shrinkage as such. However, when taking into account ECS and astrocyte ion concentrations observed in connection with neuronal stimulation, the actions of the Na+/K+/Cl− (NKCC1) and the Na+/HCO3 − (NBC) cotransporters appear to be critical determinants for achieving observed quantitative levels of ECS shrinkage. Considering the current state of knowledge, the model framework appears sufficiently detailed and constrained to guide future key experiments and pave the way for more comprehensive astroglia–neuron interaction models for normal as well as pathophysiological situations.

Frequency Dependence of Signal Power and Spatial Reach of the Local Field Potential

Despite its century-old use, the interpretation of local field potentials (LFPs), the low-frequency part of electrical signals recorded in the brain, is still debated. In cortex the LFP appears to mainly stem from transmembrane neuronal currents following synaptic input, and obvious questions regarding the ‘locality’ of the LFP are: What is the size of the signal-generating region, i.e., the spatial reach, around a recording contact? How far does the LFP signal extend outside a synaptically activated neuronal population? And how do the answers depend on the temporal frequency of the LFP signal? Experimental inquiries have given conflicting results, and we here pursue a modeling approach based on a well-established biophysical forward-modeling scheme incorporating detailed reconstructed neuronal morphologies in precise calculations of population LFPs including thousands of neurons. The two key factors determining the frequency dependence of LFP are the spatial decay of the single-neuron LFP contribution and the conversion of synaptic input correlations into correlations between single-neuron LFP contributions. Both factors are seen to give low-pass filtering of the LFP signal power. For uncorrelated input only the first factor is relevant, and here a modest reduction (<50%) in the spatial reach is observed for higher frequencies (>100 Hz) compared to the near-DC () value of about . Much larger frequency-dependent effects are seen when populations of pyramidal neurons receive correlated and spatially asymmetric inputs: the low-frequency () LFP power can here be an order of magnitude or more larger than at 60 Hz. Moreover, the low-frequency LFP components have larger spatial reach and extend further outside the active population than high-frequency components. Further, the spatial LFP profiles for such populations typically span the full vertical extent of the dendrites of neurons in the population. Our numerical findings are backed up by an intuitive simplified model for the generation of population LFP.

LFPy: a tool for biophysical simulation of extracellular potentials generated by detailed model neurons

Electrical extracellular recordings, i.e., recordings of the electrical potentials in the extracellular medium between cells, have been a main work-horse in electrophysiology for almost a century. The high-frequency part of the signal (≳500 Hz), i.e., the multi-unit activity (MUA), contains information about the firing of action potentials in surrounding neurons, while the low-frequency part, the local field potential (LFP), contains information about how these neurons integrate synaptic inputs. As the recorded extracellular signals arise from multiple neural processes, their interpretation is typically ambiguous and difficult. Fortunately, a precise biophysical modeling scheme linking activity at the cellular level and the recorded signal has been established: the extracellular potential can be calculated as a weighted sum of all transmembrane currents in all cells located in the vicinity of the electrode. This computational scheme can considerably aid the modeling and analysis of MUA and LFP signals. Here, we describe LFPy, an open source Python package for numerical simulations of extracellular potentials. LFPy consists of a set of easy-to-use classes for defining cells, synapses and recording electrodes as Python objects, implementing this biophysical modeling scheme. It runs on top of the widely used NEURON simulation environment, which allows for flexible usage of both new and existing cell models. Further, calculation of extracellular potentials using the line-source-method is efficiently implemented. We describe the theoretical framework underlying the extracellular potential calculations and illustrate by examples how LFPy can be used both for simulating LFPs, i.e., synaptic contributions from single cells as well a populations of cells, and MUAs, i.e., extracellular signatures of action potentials.

The Challenge of Connecting the Dots in the B.R.A.I.N.

The Brain Research through Advancing Innovative Neurotechnologies (BRAIN) Initiative has focused scientific attention on the necessary tools to understand the human brain and mind. Here, we outline our collective vision for what we can achieve within a decade with properly targeted efforts and discuss likely technological deliverables and neuroscience progress.