A framework to reconcile frequency scaling measurements, from intracellular recordings, local-field potentials, up to EEG and MEG signals.

In this viewpoint article, we discuss the electric properties of the medium around neurons, which are important to correctly interpret extracellular potentials or electric field effects in neural tissue. We focus on how these electric properties shape the frequency scaling of brain signals at different scales, such as intracellular recordings, the local field potential (LFP), the electroencephalogram (EEG) or the magnetoencephalogram (MEG). These signals display frequency-scaling properties which are not consistent with resistive media. The medium appears to exert a frequency filtering scaling as 1/f, which is the typical frequency scaling of ionic diffusion. Such a scaling was also found recently by impedance measurements in physiological conditions. Ionic diffusion appears to be the only possible explanation to reconcile these measurements and the frequency-scaling properties found in different brain signals. However, other measurements suggest that the extracellular medium is essentially resistive. To resolve this discrepancy, we show new evidence that metal-electrode measurements can be perturbed by shunt currents going through the surface of the brain. Such a shunt may explain the contradictory measurements, and together with ionic diffusion, provides a framework where all observations can be reconciled. Finally, we propose a method to perform measurements avoiding shunting effects, thus enabling to test the predictions of this framework.

[1]  J. B. Ranck,et al.  Analysis of specific impedance of rabbit cerebral cortex. , 1963, Experimental neurology.

[2]  Claude Bédard,et al.  Generalized cable theory for neurons in complex and heterogeneous media. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  R. W. Lau,et al.  The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. , 1996, Physics in medicine and biology.

[4]  W. Rall Electrophysiology of a dendritic neuron model. , 1962, Biophysical journal.

[5]  J. Diard,et al.  Linear diffusion impedance. General expression and applications , 1999 .

[6]  Henrik Jeldtoft Jensen,et al.  Self-Organized Criticality , 1998 .

[7]  H. Petsche,et al.  Universality in the brain while listening to music , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[8]  Claude Bédard,et al.  Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media , 2010, Journal of Computational Neuroscience.

[9]  Claude Bédard,et al.  Generalized theory for current-source-density analysis in brain tissue. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Claude Bédard,et al.  Evidence for frequency-dependent extracellular impedance from the transfer function between extracellular and intracellular potentials , 2009, Journal of Computational Neuroscience.

[11]  Christof Koch,et al.  Dynamic Moment Analysis of the Extracellular Electric Field of a Biologically Realistic Spiking Neuron , 2007, Neural Computation.

[12]  C. Bédard,et al.  Macroscopic models of local field potentials and the apparent 1/f noise in brain activity. , 2008, Biophysical journal.

[13]  C. Bédard,et al.  Does the 1/f frequency scaling of brain signals reflect self-organized critical states? , 2006, Physical review letters.

[14]  Alain Destexhe,et al.  Generalized cable formalism to calculate the magnetic field of single neurons and neuronal populations. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  C. Bédard,et al.  Model of low-pass filtering of local field potentials in brain tissue. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Laurent Venance,et al.  Microscale Inhomogeneity of Brain Tissue Distorts Electrical Signal Propagation , 2013, The Journal of Neuroscience.

[17]  John M. Beggs,et al.  Neuronal Avalanches in Neocortical Circuits , 2003, The Journal of Neuroscience.

[18]  Klas H. Pettersen,et al.  Amplitude variability and extracellular low-pass filtering of neuronal spikes. , 2008, Biophysical journal.

[19]  V. Smirnov,et al.  A course of higher mathematics , 1964 .

[20]  Claude Bédard,et al.  Modeling local field potentials and their interaction with the extracellular medium , 2012 .

[21]  S. R. Taylor,et al.  Physical Interpretation of the Warburg Impedance , 1995 .

[22]  Zach D. Haga,et al.  Avalanche Analysis from Multielectrode Ensemble Recordings in Cat, Monkey, and Human Cerebral Cortex during Wakefulness and Sleep , 2012, Front. Physio..

[23]  J. B. Ranck,et al.  Specific impedance of rabbit cerebral cortex. , 1963, Experimental neurology.

[24]  Henrik Jeldtoft Jensen,et al.  Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems , 1998 .

[25]  U. Mitzdorf Current source-density method and application in cat cerebral cortex: investigation of evoked potentials and EEG phenomena. , 1985, Physiological reviews.

[26]  Nicholas G. Hatsopoulos,et al.  Avalanche analysis from multi-electrode ensemble recordings in cat, monkey and human cerebral cortex during wakefulness and sleep , 2012 .

[27]  E. Novikov,et al.  Scale-similar activity in the brain , 1997 .

[28]  D. Turcotte,et al.  Self-organized criticality , 1999 .

[29]  H. Tuckwell Introduction to Theoretical Neurobiology: Linear Cable Theory and Dendritic Structure , 1988 .

[30]  Claude Bédard,et al.  Handbook of Neural Activity Measurement: Local field potentials , 2012 .

[31]  R. Keynes The ionic channels in excitable membranes. , 1975, Ciba Foundation symposium.

[32]  Claude Bédard,et al.  Mean-Field Formulation of Maxwell Equations to Model Electrically Inhomogeneous and Isotropic Media , 2014 .

[33]  H P Schwan,et al.  ELECTRODE POLARIZATION IMPEDANCE AND MEASUREMENTS IN BIOLOGICAL MATERIALS * , 1968, Annals of the New York Academy of Sciences.

[34]  N. Logothetis,et al.  In Vivo Measurement of Cortical Impedance Spectrum in Monkeys: Implications for Signal Propagation , 2007, Neuron.

[35]  C. Bédard,et al.  Modeling extracellular field potentials and the frequency-filtering properties of extracellular space. , 2003, Biophysical journal.

[36]  R. W. Lau,et al.  The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. , 1996, Physics in medicine and biology.

[37]  W. Pritchard,et al.  The brain in fractal time: 1/f-like power spectrum scaling of the human electroencephalogram. , 1992, The International journal of neuroscience.

[38]  Claude Bédard,et al.  Intracellular Impedance Measurements Reveal Non-ohmic Properties of the Extracellular Medium around Neurons. , 2015, Biophysical journal.