Impedance Spectrum in Cortical Tissue: Implications for Propagation of LFP Signals on the Microscopic Level

Abstract

Brain research investigating electrical activity within neural tissue is producing an increasing amount of physiological data including local field potentials (LFPs) obtained via extracellular in vivo and in vitro recordings. In order to correctly interpret such electrophysiological data, it is vital to adequately understand the electrical properties of neural tissue itself. An ongoing controversy in the field of neuroscience is whether such frequency-dependent effects bias LFP recordings and affect the proper interpretation of the signal. On macroscopic scales and with large injected currents, previous studies have found various grades of frequency dependence of cortical tissue, ranging from negligible to strong, within the frequency band typically considered relevant for neuroscience (less than a few thousand hertz). Here, we performed a detailed investigation of the frequency dependence of the conductivity within cortical tissue at microscopic distances using small current amplitudes within the typical (neuro)physiological micrometer and sub-nanoampere range. We investigated the propagation of LFPs, induced by extracellular electrical current injections via patch-pipettes, in acute rat brain slice preparations containing the somatosensory cortex in vitro using multielectrode arrays. Based on our data, we determined the cortical tissue conductivity over a 100-fold increase in signal frequency (5-500 Hz). Our results imply at most very weak frequency-dependent effects within the frequency range of physiological LFPs. Using biophysical modeling, we estimated the impact of different putative impedance spectra. Our results indicate that frequency dependencies of the order measured here and in most other studies have negligible impact on the typical analysis and modeling of LFP signals from extracellular brain recordings.

Keywords: conductivity; cortex; local field potential; multielectrode array; neuronal tissue; signal frequency.

Graphical abstract

Figure 1.

Experimental setup. A, Current was injected by a patch electrode into the extracellular medium of a 200-µm-thick thalamocortical slice preparation immersed in ACSF (excitatory cells are represented in red, and inhibitory cells in gray). The extracellular potential was measured simultaneously by all electrodes of the MEA beneath. B, The recording setup can be represented as an equivalent circuit where current flows from the patch-clamp electrode toward the ground, while the electric potential is recorded by a voltmeter. Z_PC, Patch-clamp impedance; Z_T, tissue impedance; V, voltmeter (MEA electrodes); Z_EP, electrode polarization impedance. C, Schematic overview of the recording and analysis routine. C1, Picture photograph of the acute brain slice preparation during the current injection and LFP recording. Roman numbers indicate the position of layers I to VI of the somatosensory cortex. wm, White matter. Enlarged section zooming in on layer Vb shows neuron somata (asterisks), the positioning of the tip of the patch pipette (white arrow) and an illustration of the injection of sinusoidal current (red) into the cortical tissue. C2, LFP recording via the MEA. The array shows for each electrode the 50 recorded sweeps (gray) and, superimposed, the average LFP (black). C3, The LFP amplitude and phase at a given current injection frequency was extracted from the averaged LFPs using a Fast Fourier Transformation. The largest LFP amplitude was detected at the MEA electrode directly underneath the tip of the patch pipette. C4, With the amplitude and phase of the LFP and injected current, we can find the total impedance, Z(r) = Z_T(r) + Z_EP = φ₀(r)/I₀ e^{(j (β(r)- α))} (Eq. 8). The real part of Z (Re(Z); C4, left) shows a decay with distance toward a constant, from which we can find the tissue conductivity (black line, Eq. 2) and R_EP (blue line). The imaginary part of Z is constant (C4, right), implying Im(Z) ∼ X_EP (red line), and Im(Z_T) ∼ 0.

Figure 2.

Current amplitude, distance, and frequency dependence of conductivity within ACSF and neural tissue. Conductivities were determined for different current amplitudes (175, 300, and 500 pA), distances between injection and closest recording electrode (100 and 125 µm), and current injections of different frequencies (5, 60, 100, 300, and 500 Hz). A, conductivity (S/m) within ACSF (ACSF_R, amplitude n = 2, distance n = 3, light gray) and control ACSF (ACSF_C, amplitude n = 4, distance n = 6, black). Parameter-specific frequency dependence is shown for the pooled data of the remaining two parameters. Data are shown as the mean (diamonds) and individual data points (dots). B, conductivity of neural tissue (amplitude n = 18, distance n = 27 recorded in 9 brain slices, mean is plotted in red). C, Comparison of data recorded in ACSF and in cortical neural tissue based on data shown in A and B. Conductivity as a function of frequency for ACSF_R (light gray), ACSF_C, (dark gray), and neural tissue (red) as absolute values (left) and normalized to the value at 5 Hz (middle). Right, Difference between phases measured in ACSF and neural tissue. Data are reported as the mean ± SEM.

Figure 3.

Simulated effect of frequency-dependent conductivity on extracellular potential arising from dendritic synaptic input as well as a somatic spike. Middle, Somatodendritic reconstruction of a layer V pyramidal neuron and three representative simulated extracellular recording electrodes (black dots; I–III). Extracellular recording of a synaptic input was simulated to take place at the level of the distal apical dendrite (red star), an action potential (spike) was simulated to be induced at the soma (blue star). A1, Three different conductivity profiles, corresponding to a constant conductivity (red) or a linear increase in conductivity of 25% from 5 to 500 Hz that either stops increasing at 500 Hz (gray) or continues to rise linearly (black dashed). A2, A3, Normalized extracellular responses at electrodes I–III following the dendritic synaptic input (A2) or the somatic spike (A3) for the different conductivity profiles shown in A1. B1, Three different conductivity profiles similar to those in A1 but for a 50% increase in conductivity. B2, B3, Normalized extracellular responses at electrodes I–III following the dendritic synaptic input (B2) or the somatic spike (B3) for the different conductivity profiles shown in B1. Note that simulations of other extracellular recording positions led to different extracellular potentials but to a similar negligible impact of the frequency-dependent conductivity.

Figure 4.

Effect of frequency-dependent conductivity on extracellular potentials arising from white noise input. A, Somatodendritic reconstruction of a layer V pyramidal neuron and three simulated extracellular recording electrodes (black dots, layers I–III) and the location of simulated somatic white noise current input (red star). B, Three different conductivity profiles, corresponding to a constant conductivity (red), a linear increase in conductivity from 5 to 500 Hz of 25% (gray) and 50% (black dashed). C, Excerpts of normalized LFP signals recorded at the electrode points I–III for the different conductivity profiles in B and diagrams showing the respective normalized power spectral density of the LFPs. D, Amplitude of somatic membrane potential response as a function of frequency in response to the white noise current input.

Figure 5.

Literature review of reported conductivities in various species and experimental setups. Gabriel et al. (1996): data from bovine brains recorded with a two-electrode setup. Elbohouty (2013): data recorded in vitro in slices of mouse cerebral cortex with a two-electrode setup. Logothetis et al. (2007): data from monkey recorded with a four-electrode setup. The average conductivity value, 0.405 S/m, combined with the reported increase of ∼25%. Wagner et al. (2014): recordings from cat cerebral cortex with a two-electrode setup, which was similar to the setup used by Gabriel et al. (1996). Ranck (1963): data from rabbit brain.