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

Abstract

Visual Abstract

Kramers-Kronig Relations and the Properties of Conductivity and Permittivity in Heterogeneous Media

“…We showed here that these measurements are consistent with Kramers-Kronig relations, and the principle of causality. However, other measurements suggesting resistive media [2,4], are also consistent with Kramers-Kronig relations. All these experimental measurements are thus physically plausible and self-consistent.…”

“…For example, let us consider the model examined by Miceli et al [4] of a medium in which the electric conductivity is frequency-dependent, but the permittivity is constant. According to above, such a medium is physically impossible, because it would violate the principle of causality.…”

LFPy – multimodal modeling of extracellular neuronal recordings in Python

“…This numerical scheme has been applied to predictions of the local field potential (LFP), that is, the low-frequency part of the extracellular potential Lindén et al, 2010Lindén et al, , 2011Gratiy et al, 2011;Makarova et al, 2011;Schomburg et al, 2012;Łęski et al, 2013;Reimann et al, 2013;Martín-Vázquez et al, 2013Głąbska et al, 2014;Mazzoni et al, 2015;Tomsett et al, 2015;Sinha and Narayanan, 2015;Taxidis et al, 2015;Hagen et al, 2016;Głąbska et al, 2016;Ness et al, 2016Ness et al, , 2018Hagen et al, 2017;McColgan et al, 2017), as well as extracellular spike waveforms which carry more power at high frequencies (Holt and Koch, 1999;Gold et al, 2006Gold et al, , 2007Franke et al, 2010;Schomburg et al, 2012;Thorbergsson et al, 2012;Reimann et al, 2013;Ness et al, 2015;Hagen et al, 2015;Miceli et al, 2017;Cserpán et al, 2017;Luo et al, 2018;Buccino et al, 2018Buccino et al, , 2019.…”

“…At frequencies relevant for neuronal processes (below ten thousand hertz or so), the derivation of the volume conductor theory from first principles is simplified by application of the so-called quasistatic approximation to Maxwell's equations (Hämäläinen et al, 1993, p. 426). The extracellular medium is in all cases assumed to be ohmic, which implies a linear and frequency-independent relation between currents and electric potentials (Pettersen et al, 2012;Einevoll et al, 2013;Miceli et al, 2017). Then, the simplest possible case is that of an infinite homogeneous (same in all locations) and isotropic (same in all directions) volume conductor (see e.g., Hagen et al (2018, Sec. 2.2.1)).…”

“…In a similar manner, current dipole moments computed using LFPy can be used with detailed head models constructed from MRI data (Bangera et al, 2010;DeMunck et al, 2012;Vorwerk et al, 2014;Huang et al, 2016). Frequency dependent conductive media may be accounted for by treating each Fourier component of recorded signals independently as pursued in Miceli et al (2017).…”