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 , an open source Python package for numerical simulations of extracellular potentials. 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 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.

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.

Local field potentials (LFP), the low-frequency part of extracellular electric potential, reflect dendritic processing of synaptic inputs to neuronal populations. They are an invaluable tool in the studies of neural activity both in vivo and in vitro. With recent fast development of multielectrode technology one can easily record potentials in different geometries, including 3D setups, from multiple sites simultaneously. Due to the longrange nature of electric field each electrode may reflect activity of sources located millimeters away which complicates analysis of LFP. Whenever possible it is convenient to estimate the sources of measured potential, called current source density (CSD), which is the volume density of net transmembrane currents. CSD directly reflects the local neural activity and current source density analysis is often used to analyze LFP.In homogeneous and isotropic tissue CSD is given by the Laplacian of the potentials, so discrete differentiation is the simplest estimate for a set of potentials on a regular grid. Recently continuous methods for CSD estimation have been developed, called the inverse CSD (iCSD). These methods assume a specific parametric form of CSD generating potentials and calculate the LFP in a forward-modeling scheme to obtain the values of CSD parameters. The iCSD framework assumes CSD distributions parameterized with as many parameters as there are measurements.Here we present a nonparametric method for CSD estimation based on kernel techniques. Kernel Current Source Density method lets the user specify the family of allowed CSD distributions through a basis of dimensionality much larger than the number of measurements. Prior knowledge of the anatomy or physiology of the probed structure, such as laminarity, can be incorporated in the method. kCSD can be applied to recordings from electrodes distributed arbitrarily on one-, two-, and three-dimensional sets so one can consider experimental setups optimally adapted to a research problem of interest (Figure 1). We show that kCSD is a general non-parametric framework for CSD estimation including