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Reply to Gratiy et al.

2013; American Physiological Society; Volume: 109; Issue: 6 Linguagem: Inglês

10.1152/jn.00014.2013

1522-1598

Jorge Riera, Alejandro Cabo Montes de,

EEG and Brain-Computer Interfaces

Letters to the EditorReply to Gratiy et al.Jorge Riera, and Alejandro CaboJorge RieraDepartment of Biomedical Engineering, Florida International University, Miami, Florida; and , and Alejandro CaboThe Institute of Cybernetics and Mathematics Applied to Physics (ICIMAF), Havana, CubaPublished Online:15 Mar 2013https://doi.org/10.1152/jn.00014.2013MoreSectionsPDF (105 KB)Download PDF ToolsExport citationAdd to favoritesGet permissionsTrack citations ShareShare onFacebookTwitterLinkedInWeChat INSTANTANEOUS CHARGE UNBALANCE IN THE BRAIN: A RESULT FROM PROCEDURAL ERRORS OR AN AUTHENTIC PHYSICAL PHENOMENON?to the editor: Gratiy et al. (2013) proposed two alternative explanations for the nonbalanced current source density (CSD) estimates in Riera et al. (2012). Their commentary was based on a particular interpretation of the role played by the Ampere-Maxwell Law in the genesis of the electric fields for macroscopic media. In this Reply, we will provide further information to stimulate the debate in the community.Plausible Procedural ErrorsWe believe that partial inclusion of the cell membrane is not a conceivable situation in the particular case of CSD volumetric distributions of back-propagating action potentials. Riera et al. (2012) carefully selected spiking neurons (i.e., pyramidal and spine stellate cells) with somas around the center of the 3D probe. Based on the morphology of these neurons (Elston and Rosa 1998; Romand et al. 2011; Staiger et al. 2004), it is unlikely that significant parts of their dendrites were outside the region covered by the probe. In addition, it is well known that the amplitude of back-propagating action potentials, and consequently of the associated transmembrane currents, tends to decay rapidly from the soma to the dendrites, with experimental (Bar-Yehuda et al. 2008; Gulledge and Stuart 2003) and theoretical (Wang et al. 2013) estimations available for pyramidal cells. As discussed by Riera el al. (2012), vessels and axons in the neocortex could have caused a shunting of electric currents to remote locations and hence could have brought about an apparent unbalance in the estimated current sources. For the analysis of volumetric extracellular potentials, the authors employed a method that does not make assumptions on the lateral distributions of neuronal activity (Goto et al. 2011) and used accurate values of the extracellular conductivity and electrode positions (Goto et al. 2010). Using simulations, we demonstrated that such a CSD method does not introduce charge unbalances (data not shown, unpublished observations). However, methods for CSD analysis were all based on the validity of quasi-stationarity of the Maxwell equations. We would expect strong bias in the estimated CSD distributions if this approach were no longer valid (Wang et al. 2013). Finally, extracellular electrical potentials were recorded using filters with cut-off frequency larger than 8 kHz. Riera et al. (2012) provided an explanation for the CSD unbalance based on both sampling limitations and particular characteristics of brain tissues (i.e., anisotropy and inhomogeneity). In any of the cases discussed above, modeling and methods used today to interpret CSD distributions must be revisited as a consequence of the experimental data presented by Riera et al. (2012).An Authentic Physical PhenomenonThe question of this debate is whether or not the net electric charge crossing an imaginary closed surface at any time instant needs to be necessarily zero. The answer to this question is not in the Ampere-Maxwell Law, but in the charge continuity principle, which also comprises the Poisson's Law. ∇·J→T=j→f+∂ρf∂t=0J→T=J→M+J→DIt states that if there are variations in the total charge inside any imaginary surface, then the total electric current (e.g., migration J→M, diffusion J→D)1 across its surface will be not null. Then, the problem is reduced to determine whether or not a charge can be temporally retained inside that imaginary surface before it is screened by the medium. In the frequency range of electrophysiological recordings, mean values for the electric conductivity and permittivity are σ = 0.28 S m−1 (Goto et al. 2010) and ε = 5×106ε0 (Gabriel et al. 1996), respectively. Assuming that extracellular ionic contributions are predominant at this macroscopic level, and that, as a first approach, the tissue could be considered homogeneous, then the ionic strength will be I ∼ 150 mmoll−1. Therefore, the decay time constant τ =ε/σ and the Debye length RD=εRT/2F2I will not be small enough (i.e., τ = 0.16 ms and RD = 0.21 μm) as to assume a perfect electric field screening out at this particular scale. The decay time constant determines the volatility of any free electric charge (ρf) in the medium ρ(t) = ρfe−t/τ and the Debye length determines the shielding of the electric field ϕ(r→)=ρf4πϵ|r→|e−|r→|/RD produced by such a charge. Alternatively, assuming that the screening is instantaneous and that the “s” variable is nonvanishing outside the membrane, it follows that a monopole for it will be exactly canceled by the also nonvanishing monopole of the assumed volumetric ohmic currents.DISCLOSURESNo conflicts of interest, financial or otherwise, are declared by the author(s).AUTHOR CONTRIBUTIONSJ.J.R. and A.C. conception and design of research; J.J.R. drafted manuscript.FOOTNOTES1We assumed that there is no convection current, i.e., J→C=0REFERENCES Bar-Yehuda D , Ben-Porat H , Korngreen A . Dendritic excitability during increased synaptic activity in rat neocortical L5 pyramidal neurons. Eur J Neurosci 28: 2183–2194, 2008.Crossref | PubMed | ISI | Google Scholar Elston GN , Rosa MGP . Morphological variation of layer III pyramidal neurones in the occipitotemporal pathway of the macaque monkey visual cortex. Cereb Cortex 8: 278–294, 1998.Crossref | PubMed | ISI | Google Scholar Gabriel S , Lau RW , Gabriel C . 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Cereb Cortex 14: 690–701, 2004.Crossref | PubMed | ISI | Google Scholar Wang K , Riera J , Enjieu-Kadji H , Kawashima R . The role of extracellular conductivity profiles in compartmental models for neurons: particulars for layer 5 pyramidal cells. Neural Comp. In press.ISI | Google ScholarAUTHOR NOTESAddress for reprint requests and other correspondence: J. Riera, Dept. of Biomedical Engineering, Florida International Univ., 10555 West Flagler St., Miami, FL 33174 (e-mail: [email protected]edu). Download PDF Previous Back to Top FiguresReferencesRelatedInformationRelated ArticlesPitfalls in the interpretation of multielectrode data: on the infeasibility of the neuronal current-source monopoles 15 Mar 2013Journal of NeurophysiologyCited BywaveCSD: A method for estimating transmembrane currents originated from propagating neuronal activity in the neocortex: Application to study cortical spreading depressionJournal of Neuroscience Methods, Vol. 307Ion diffusion may introduce spurious current sources in current-source density (CSD) analysisGeir Halnes, Tuomo Mäki-Marttunen, Klas H. Pettersen, Ole A. Andreassen, and Gaute T. Einevoll1 July 2017 | Journal of Neurophysiology, Vol. 118, No. 1Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue7 November 2016 | PLOS Computational Biology, Vol. 12, No. 11Modelling and analysis of local field potentials for studying the function of cortical circuits1 November 2013 | Nature Reviews Neuroscience, Vol. 14, No. 11 More from this issue > Volume 109Issue 6March 2013Pages 1684-1685 Copyright & PermissionsCopyright © 2013 the American Physiological Societyhttps://doi.org/10.1152/jn.00014.2013PubMed23503558History Published online 15 March 2013 Published in print 15 March 2013 Metrics