Electric phenomena in brain tissue can be measured using extracellular potentials, such as the local field potential, or the electro-encephalogram. The interpretation of these signals depends on the electric structure and properties of extra cellular media, but the measurements of these electric properties are still debated. Some measurements point to a model in which the extracellular medium is purely resistive, and thus parameters such as electric conductivity and permittivity should be independent of frequency. Other measurements point to a pronounced frequency dependence of these parameters, with scaling laws that are consistent with capacitive or diffusive effects. However, these experiments correspond to different preparations, and it is unclear how to correctly compare them. Here, we provide for the first time, impedance measurements (in the 1-10 kHz frequency range) using the same setup in various preparations, from primary cell cultures to acute brain slices, and a comparison with similar measurements performed in artificial cerebrospinal fluid with no biological material. The measurements show that when the current flows across a cell membrane, the frequency dependence of the macroscopic impedance between intracellular and extracellular electrodes is significant, and cannot be captured by a model with resistive media. Fitting a mean field model to the data shows that this frequency dependence could be explained by the ionic diffusion mainly associated with Debye layers surrounding the membranes. We conclude that neuronal membranes and their ionic environment induce strong deviations to resistivity that should be taken into account to correctly interpret extracellular potentials generated by neurons.

Extracellular electric potentials, such as local field potentials (LFPs) or the elec-troencephalogram (EEG), are routinely measured in electrophysiological experiments. LFPs are recorded using micrometer-size electrodes, and sample relatively localized populations of neurons, as these signals can be very different for electrodes separated by 1 mm (Destexhe et al., 1999a) or by a few hundred micrometers (Katzner et al., 2009). In contrast, the EEG is recorded from the surface of the scalp using millimeter-scale electrodes and samples much larger populations of neurons (Niedermeyer and Lopes da Silva, 1998). LFPs are subject to much less filtering compared to EEG, because EEG signals must propagate through various media, such as cerebrospinal fluid, dura mater, cranium, muscle and skin. LFP signals are also filtered, because the recording electrode is separated from the neuronal sources by portions of cortical tissue. Besides these differences, EEG and LFP signals display the same characteristics during wake and sleep states (Steriade, 2003). The observation that action potentials have a limited participation in the gen-esis of the EEG or LFPs dates from early studies. Bremer (1938, 1949) was the first to propose that the EEG is not generated by action potentials, based on the mismatch of the time course of EEG waves with action potentials. Eccles (1951) proposed that LFP and EEG activities are generated by summated postsynaptic potentials arising from the synchronized excitation of cortical neurons. Intracel-lular recordings from cortical neurons later demonstrated a close correspondence between EEG/LFP activity and synaptic potentials (Klee et al., 1965; Creutzfeldt et al., 1966a, 1966b). The current view is that EEG and LFPs are generated by synchronized synaptic currents arising on cortical neurons, possibly through the The fact that action potentials have little participation in EEG-related activities indicates strong frequency-filtering properties of cortical tissue. High frequencies

The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an analogous paradigm applies to the macroscopic electric conductivity. If the causality principle is taken into account, there exists Kramers-Kronig relations for conductivity, which are mathematically equivalent to the Hilbert transform. These relations impose strong constraints that models of heterogeneous media should satisfy to have a physically plausible frequency dependence of the conductivity and permittivity. We illustrate these relations and constraints by a few examples of known physical media. These extended relations constitute important constraints to test the consistency of past and future experimental measurements of the electric properties of heterogeneous media.

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.

A recent commentary to Biophysical Journal criticized a previous study published in the same journal by Gomes et al. in 2016, and an alternative interpretation of the measurements was proposed. We reply here to these criticisms and provide some additional clarification, in particular, about a possible misinterpretation of the electrical circuit corresponding to these experiments. We suggest that, indeed, the extracellular impedance in cerebral cortex could be high and non-resistive, and we propose further experiments to settle this issue.

Determining the electrical properties of the extracellular space around neurons is important for understanding the genesis of extracellular potentials, as well as for localizing neuronal activity from extracellular recordings. However, the exact nature of these extracellular properties is still uncertain. Here, we introduce a method to measure the impedance of the tissue, one that preserves the intact cell-medium interface using whole-cell patch-clamp recordings in vivo and in vitro. We find that neural tissue has marked non-ohmic and frequency-filtering properties, which are not consistent with a resistive (ohmic) medium, as often assumed. The amplitude and phase profiles of the measured impedance are consistent with the contribution of ionic diffusion. We also show that the impact of such frequency-filtering properties is possibly important on the genesis of local field potentials, as well as on the cable properties of neurons. These results show non-ohmic properties of the extracellular medium around neurons, and suggest that source estimation methods, as well as the cable properties of neurons, which all assume ohmic extracellular medium, may need to be reevaluated.

Cable theory was introduced for neurons by Wilfrid Rall more than half a century ago and is widely used today for modeling the voltage and current flow in neuronal and dendritic structures. This theory was derived assuming that the extracellular medium is either inexistent or modeled as a resistor. For modeling neurons in more realistic situations, where the extracellular medium has more complex electric properties, it is necessary to generalize Rall's cable equations. We summarize here such generalized cable equations and show that the nature of the surrounding extracellular medium can exert nonnegligible influences on the cable properties of neurons.

Neurons generate fields which can be recorded with macroscopic techniques such as magneto-encephalography. The theory that accounts for the genesis of neuronal fields involves macroscopic dipole structures in homogeneous resistive extracellular media. Here, we study this problem at the microscopic level using a variant of cable theory which accounts for the genesis of fields, in extracellular media with arbitrarily complex electric properties. The cable formalism, initially introduced by Rall [1], has been recently generalized to include the influence of the extracellular medium [2]. We use here this generalized cable formalism to calculate the field generated by neurons. We show that the induction generally depends on the impedance of the extracellular and intracellular media. Therefore, like the electric field, the electric properties of these media can influence the field, contrary to what is usually assumed. Next, we use this formalism to calculate the magnetic signature of different neuronal morphologies, such as pyramidal cells and basket cells. We show that the strongest fields correspond to media which are non-resistive, such as diffusive media, although they exert low-pass filtering properties. Recent measurements (see companion poster by Bedard et al.) suggest that the extracellular medium is best described by a diffusive impedance. We therefore predict that this will also affect neuronal fields. In conclusion, we show here that the generalized cable formalism is an important tool to calculate the extracellular electric and fields generated by neurons. The nature of the medium influences both types of fields, and should be measurable by appropriate measurements. Given the fact that the nature of the medium influences the field, inverse methods should consider this important parameter.

The genesis of the Local Field Potential (LFP) highly depends on the electric properties of the extracellular medium, but such properties are still subject to a controversy because of contradictory measurements. One possibility is that the use of metal electrodes as current sources in previous studies provides non-physiological results. We tested this possibility by performing impedance measurements in conditions as close as possible to physiological conditions. We generated single-cell LFPs by injecting subthreshold inputs in single neurons using patch-clamp recordings, combined with extracellular recordings with micropipettes. Various measurement configurations show that (1) the extracellular medium has strong low-pass filtering properties and cannot be accounted by a resistive medium; (2) the frequency scaling of the filtering, as well as its phase, show that the system seems intermediate between resistive and capacitive. The extracellular impedance was also measured from in vivo experiments in rats under anesthesia. In this case, recording with intracellular (whole-cell) electrodes, together with extracellular LFP, showed results consistent with the in vitro experiments. Finally, we developed a theoretical model based on Maxwell equations, which shows that all measurements can be explained if the extracellular medium is of diffusive type (Warburg impedance). This model predicts that the phase difference between intracellular and extracellular signals should provide a signature of the physical nature of the impedance, with 45 degrees phase difference for purely diffusive type. The experiments show that indeed, the phase is that of a RC soma in series with a diffusive impedance (between 0 and -45 degrees), therefore confirming the diffusive nature of the extracellular impedance. These findings have potentially important consequences for interpreting LFP measurements and source estimation such as CSD analysis.

Neurons generate magnetic fields which can be recorded with macroscopic techniques such as magnetoencephalography. The theory that accounts for the genesis of neuronal magnetic fields involves dendritic cable structures in homogeneous resistive extracellular media. Here we generalize this model by considering dendritic cables in extracellular media with arbitrarily complex electric properties. This method is based on a multiscale mean-field theory where the neuron is considered in interaction with a "mean" extracellular medium (characterized by a specific impedance). We first show that, as expected, the generalized cable equation and the standard cable generate magnetic fields that mostly depend on the axial current in the cable, with a moderate contribution of extracellular currents. Less expected, we also show that the nature of the extracellular and intracellular media influence the axial current, and thus also influence neuronal magnetic fields. We illustrate these properties by numerical simulations and suggest experiments to test these findings.

Maxwell equations were originally designed to describe classic electromagnetic phenomena in any type of medium. In particular, to describe electromagnetic phenomena under the quasistatic electric approximation in media that are electrically inhomogeneous and isotropic, such as for example when there are strong spatial variations of conductivity, the formalism must be adapted according to the problem considered. We review here two approaches to this problem, first a “microscopic” model, where the spatial variations of conductivity and permittivity are explicitly taken into account. In a second “macroscopic” model, these spatial variations are taken on average by using a mean-field formulation of Maxwell equations. Both of these models can describe the electromagnetic behavior of inhomogeneous media. We illustrate this formalism to describe the electric behavior of biological media, such as brain tissue, which is typically very inhomogeneous. We show that the theory predicts that for the typical frequency range of biological phenomena (lower than about 1000 Hz), the inhomogeneous nature of the medium has a determinant influence.

Cable theory has been developed over the last decade, usually assuming that the extracellular space around membranes is a perfect resistor. However, extracellular media may display more complex electrical properties due to various phenomena, such as polarization, ionic diffusion, or capacitive effects, but their impact on cable properties is not known. In this paper, we generalize cable theory for membranes embedded in arbitrarily complex extracellular media. We outline the generalized cable equations, then consider specific cases. The simplest case is a resistive medium, in which case the equations recover the traditional cable equations. We show that for more complex media, for example, in the presence of ionic diffusion, the impact on cable properties such as voltage attenuation can be significant. We illustrate this numerically, always by comparing the generalized cable to the traditional cable. We conclude that the nature of intracellular and extracellular media may have a strong influence on cable filtering as well as on the passive integrative properties of neurons.

Cable theory has been developed over the last decades, usually assuming that the extracellular space around membranes is a perfect resistor. However, extracellular media may display more complex electrical properties due to various phenomena, such as polarization, ionic diffusion or capacitive effects, but their impact on cable properties is not known. Here, we generalize cable theory for membranes embedded in arbitrarily complex extracellular media. We outline the generalized cable equations, then consider specific cases. The simplest case is a resistive medium, in which case the equations recover the traditional cable equations. We show that for more complex media, for example in the presence of ionic diffusion, or polarization, the impact on cable properties such as voltage attenuation can be significant. We illustrate this numerically always by comparing the generalized cable to the traditional cable. We conclude that the nature of intracellular and extracellular media may have a strong influence on cable filtering as well as on the passive integrative properties of neurons.

Editorial FocusDo neurons generate monopolar current sources?Alain Destexhe, and Claude BedardAlain DestexheUnité de Neurosciences, Information and Complexité, Centre National de la Recherche Scientifique, Gif sur Yvette, France, and Claude BedardUnité de Neurosciences, Information and Complexité, Centre National de la Recherche Scientifique, Gif sur Yvette, FrancePublished Online:15 Aug 2012https://doi.org/10.1152/jn.00357.2012This is the final version - click for previous versionMoreSectionsPDF (76 KB)Download PDF ToolsExport citationAdd to favoritesGet permissionsTrack citations ShareShare onFacebookTwitterLinkedInEmailWeChat According to the “standard model,” electric potentials such as the local field potential (LFP) or the electroencephalogram (EEG) are generated by current dipoles made by cerebral cortex neurons arranged in parallel. In this issue of Journal of Neurophysiology, Riera et al. (2012) present experimental evidence that this standard model may be insufficient to account for LFP and EEG signals in the rat brain. The authors have designed a set of technically impressive experiments that question the validity of the dipole model. We briefly summarize these findings and then speculate on possible physical mechanisms to explain these surprising results.According to the standard model, a given current source (for example due to the opening of a postsynaptic conductance as in Fig. 1A) will be instantaneously balanced by an extracellular current and a “return current”, which will enter the neuron at another location (for example the soma; see Fig. 1B). This configuration implies that a dipole will instantaneously appear in the neuron, as illustrated in Fig. 1. In these conditions, the system is described by Kirchhoff's laws, similar to an electronic circuit (see Fig. 1, bottom, for an example of equivalent circuit).1Fig. 1.Illustration of the flow of ions following the activation of a synaptic conductance. A: activation of a synaptic conductance at a given position in the dendrite of a neuron The conductance is assumed in this example to be associated to a net entry of positive ions. B: according to the “standard model,” the synaptic current (downward arrow) is instantaneously balanced by a return current in another region of the neuron, resulting in a dipole. The equivalent electrical circuit corresponding to this situation is shown at bottom.Download figureDownload PowerPointAccording to this model, the instantaneous dipole that appears in asymmetric neurons (such as pyramidal cells) will be responsible for the production of an electric field outside of the neurons. If these cellular dipoles are oriented in parallel, a situation which is called “open field” configuration (Lorente de No 1947; such as typically in cerebral cortex), the field generated by the different dipoles will summate and create a signal strong enough to be recorded with extracellular microelectrodes, the LFP, or even give rise to potentials recordable at the surface of the scalp, such as the EEG. Motivated by this standard model, a number of methods have appeared to estimate the dipolar sources from LFP or EEG recordings (Jones et al. 2007; Pascual-Marqui et al. 1994; Ramirez 2008). These methods are quite popular in the EEG literature, and there exists several commercial or open-source programs to perform this estimate of underlying dipolar sources from the EEG (Pascual-Marqui et al. 2002; http://www.uzh.ch/keyinst/loreta.htm) and/or from magnetoencephalographic (MEG) recordings. These estimates are of course entirely dependent on the standard dipole model.In their study, Riera et al. (2012), investigated the validity of this model in several ways. They first recorded local neuronal activity in three dimensions, using a set of multicontact electrodes inserted in the rat barrel cortex (spanning several barrels). The system records both units and LFPs at all locations, thereby providing a dense three-dimensional coverage of this area of cerebral cortex. By applying variants of the current-source density (CSD) analysis (Nicholson and Freeman 1975), which estimates current sources (without making dipole assumptions), they demonstrate that, following whisker activation, there appears current sources and sinks, which are not necessarily balanced. Most interestingly, they designed a procedure to estimate the different multipolar components of the current profiles and quantified their respective importance.2 Surprisingly, while there were significant dipolar and multipolar components as expected, they also found an unexpected strong monopolar component. This component was necessary to explain the data.In a second series of experiments, Riera et al. (2012) directly tested the dipolar assumption in the rat brain. They conceived a high-resolution EEG cap for the rat brain, specifically designed for this purpose (a quite impressive achievement in itself), and used standard dipolar source estimation techniques to estimate the underlying dipoles in cerebral cortex. This estimate was aided by a three-dimensional reconstruction of the rat cerebral cortex and electrode position using magnetic resonance imaging (MRI). The MRI images were used to constrain the location of the dipoles in cerebral cortex, as is routinely done in human EEG (Dehghani et al. 2010b). In addition, the laminar LFPs were simultaneously recorded using microelectrodes. By using an approach that takes into account different multipolar configurations, the same result as above was obtained, namely that dipolar and higher order multipolar components were observed, but there was also a strong monopolar component in the data, thus confirming the estimates using microelectrodes.Thus, using these two independent methods, which are both technically impressive, the authors succeeded in bringing decisive data that put into question the standard dipolar model of the EEG. More importantly, they inferred that the estimation of sources, if uniquely based on dipoles, can be flawed because the monopolar components are erroneously “absorbed” in the dipoles. If confirmed, this finding has potentially devastating consequences for the estimates of dipolar sources from the EEG or MEG. Indeed, there is evidence that the dipolar model cannot predict simultaneously recorded EEG and MEG signals, either during interictal activity (Huiskamp et al. 2004; Fernandes et al. 2005) or during normal rhythms such as sleep spindle oscillations (Dehghani et al. 2010a,b).Where to go from there? It is of course imperative to seek for confirmation of these results. An important property is that monopolar sources have a very different distance dependence than dipolar sources, fields generated by electric monopoles decay with the inverse of distance (1/r), while dipolar fields vary as the inverse of the squared distance (1/r2) and thus attenuate much more steeply. As a consequence, estimates at different distances from the sources should reveal differences. Indeed, recent measurements seem to confirm that in some cases the distance decay of LFP amplitude unexpectedly follows 1/r profiles (Hunt et al. 2011), consistent with electric monopoles. This is important because if a given method to estimate neuronal activity from LFP and EEG assumes the wrong distance dependence, then this method will evidently provide wrong estimates.Another way to test the presence of monopolar sources would be to use coregistered surface EEG and electrocorticogram to determine whether a unique set of dipolar sources can account for both signals, or if monopolar contributions should be assumed. It is also possible to estimate monopolar contributions from CSD profiles, as proposed recently (Bédard and Destexhe 2011).Even more critical is how to explain the genesis of electric monopoles. If the neuron strictly obeys Kirchhoff's laws, then monopoles are impossible, because as soon as there is a current source, a dipole instantaneously appears (Fig. 1). Since in theory they are impossible but seem to be observed, what plausible physical explanations can be given?A first possible cause of monopolar contribution is that neurons may not strictly obey Kirchhoff's laws.3 According to the standard model, the charges are assumed to move instantaneously (infinitely fast), which gives rise to the fact that the return current appears immediately. However, in reality, there is an inertia time to charge movement, because the mobility of ions in a homogeneous electrolyte is finite and is considerably slower compared to electrons in a metal. For example, the mobility of Na+ in sea water is of 5.19 × 10−8 m2 = sV (Hille 2001) and is of the same order for other ions such as K+, Ca2+, and Cl− (Hille 2001). In contrast, the mobility of electrons in copper is of 4.45 × 10−3 m2 = sV for a temperature of 298.15°K (Philip and Bolton 2002), which is ∼105 times larger than ion mobilities.As a consequence, when ionic channels open (such as the postsynaptic currents indicated in Fig. 1), the setting of extracellular current and return current will not be instantaneous, and there will be a transient time during which charges will accumulate in the postsynaptic region. During this transient time, Kirchhoff's current rule does not apply (the local charge accumulation is contrary to Kirchhoff's current law), and the postsynaptic region may act as a monopole. After this transient time, the charge movement settles into a stationary regime, in which the currents are balanced, there is no charge accumulation, and the system obeys Kirchoff's laws. Thus, the dipole model would only apply to this stationary regime.4Another possible contribution to monopolar effects is the resistance to the lateral movement of charges in the membrane. While this movement is also considered as instantaneous (charges are usually assumed to instantaneously reequilibrate), there is evidence that in fact, charges do not move instantaneously but take some time due to residual friction tangential to the membrane (Bédard and Destexhe 2008). This effect will also cause an inertia of charge movement, as above, and will contribute to the transient regime in which the currents are not balanced. Moreover, the complex morphology of neurons (dendrites, spines, and axons) will further reduce ionic mobility. Consequently, if a membrane current suddenly appears in a given region of cerebral cortex, it is not instantaneously equilibrated by an opposite current. There is a transient time in which the system is outside of equilibrium and during which Kirchoff's rules do not apply. During this transient time, it is possible that the extracellular electric field is dominated by monopolar components.Further work is obviously necessary to first confirm the experimental observation of a strong monopolar component in neurons. Second, work is needed to develop in detail the theory to account for the genesis of monopolar current sources by neurons. One may need to profoundly revise the current theories, both at the level of single neuron cable theory, which entirely depends on Kirchhoff's laws, and at the level of population activity. If confirmed, the presence of monopolar sources in neurons will require to reevaluate electric field interactions between neurons (which may be stronger than expected), as well as methods to estimate neuronal sources from EEG or LFP data.FOOTNOTES1According to Kirchhoff's current law, the sum of the currents at any node of a circuit is zero, which implies that there cannot be any charge accumulation at any node of the circuit.2Note that this estimate of the different multipolar contributions is made based on a very simplified model of the LFP, and this estimate could be different with a more realistic model.3More generally, that for a given region of the neuron, the current entering is not equal to the current exiting that region, therefore causing accumulation of charges (positive or negative) in that region.4The duration of this transient time depends on the diffusion time of charges in the dendrite. For a 1-nA current in a dendrite of 5-μm diameter, the mean drift velocity is ∼1 mm/s, so this transient time may indeed be significant.REFERENCES Bédard C , Destexhe A. A modified cable formalism for modeling neuronal membranes at high frequencies. Biophys J 94: 1133–1143, 2008.Crossref | PubMed | ISI | Google Scholar Bédard C , Destexhe A. Generalized theory for current-source density analysis in brain tissue. Phys Rev E Stat Nonlin Soft Matter Phys 84: 041909, 2011.Crossref | PubMed | ISI | Google Scholar Dehghani N , Cash SS , Rossetti AO , Chen CC , Halgren E. Magnetoencephalography demonstrates multiple asynchronous generators during human sleep spindles. J Neurophysiol 104: 179–188, 2010a.Link | ISI | Google Scholar Dehghani N , Cash SS , Chen CC , Hagler DJ , Huang M , Dale AM , Halgren E. Divergent cortical generators of MEG and EEG during human sleep spindles suggested by distributed source modeling. 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Int J Psychophysiol 18: 49–65, 1994.Crossref | PubMed | ISI | Google Scholar Pascual-Marqui RD , Esslen M , Kochi K , Lehmann D. Functional imaging with low resolution brain electromagnetic tomography (LORETA): a review. Methods Find Exp Clin Pharmacol 108: 953–955, 2002.Google Scholar Ramirez RR. Source localization. In: Scholarpedia. http://www.scholarpedia.org/article/Source_Localization, 2008, p. 1733.Google Scholar Riera J , Ogawa T , Goto T , Sumiyoshi A , Nonaka H , Evans A , Miyakawa H , Kawashima R. Pitfalls in the dipolar model for the neocortical EEG sources. J Neurophysiol; published ahead of print April 25, 2012, doi: 10.1152/jn.00098.2011.ISI | Google ScholarAUTHOR NOTESAddress for reprint requests and other correspondence: A. Destexhe, Unité de Neurosciences, Information and Complexité, Centre National de la Recherche Scientifique, 1 Ave. de la Terrasse (BAT 33) 91190, Gif sur Yvette, France. Download PDF Back to Top Next FiguresReferencesRelatedInformationCited 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. 307Functional roles of three cues that provide nonsynaptic modes of communication in the brain: electromagnetic field, oxygen, and carbon dioxideLuigi F. Agnati,* Diego Guidolin,* Guido Maura, and Manuela Marcoli16 January 2018 | Journal of Neurophysiology, Vol. 119, No. 1Ion 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. 11Simplest relationship between local field potential and intracellular signals in layered neural tissue7 December 2015 | Physical Review E, Vol. 92, No. 6Are Heptodes Better than Tetrodes for Spike Sorting?IFAC-PapersOnLine, Vol. 48, No. 20The origins of the brain's endogenous electromagnetic field and its relationship to provision of consciousnessJournal of Integrative Neuroscience, Vol. 13, No. 02Generalized cable theory for neurons in complex and heterogeneous media13 August 2013 | Physical Review E, Vol. 88, No. 2A Detailed and Fast Model of Extracellular RecordingsNeural Computation, Vol. 25, No. 5Pitfalls in the interpretation of multielectrode data: on the infeasibility of the neuronal current-source monopolesSergey L. Gratiy, Klas H. Pettersen, Gaute T. Einevoll, and Anders M. Dale15 March 2013 | Journal of Neurophysiology, Vol. 109, No. 6Reply to Gratiy et al.Claude Bedard, and Alain Destexhe15 March 2013 | Journal of Neurophysiology, Vol. 109, No. 6 More from this issue > Volume 108Issue 4August 2012Pages 953-955 Copyright & PermissionsCopyright © 2012 the American Physiological Societyhttps://doi.org/10.1152/jn.00357.2012PubMed22572946History Published online 15 August 2012 Published in print 15 August 2012 Metrics

Extracellular electric potentials, such as local field potentials (LFPs) or the electroencephalogram (EEG), are routinely measured in electrophysiological experiments. LFPs are recorded using micrometer-size electrodes, and sample relatively localized populations of neurons, as these signals can be very different for electrodes separated by 1 mm (Destexhe et al., 1999a) or by a few hundred micrometers (Katzner et al., 2009). In contrast, the EEG is recorded from the surface of the scalp using millimeter-scale electrodes and samples much larger populations of neurons (Niedermeyer and Lopes da Silva, 1998). LFPs are subject to much less filtering compared to EEG, because EEG signals must propagate through various media, such as cerebrospinal fluid, dura mater, cranium, muscle and skin. LFP signals are also filtered, because the recording electrode is separated from the neuronal sources by portions of cortical tissue. Besides these differences, EEG and LFP signals display the same characteristics during wake and sleep states (Steriade, 2003).

The process of designing buildings presents characteristics that set it apart from the design process in other engineering fields. Traditionally, computers have been assigned the number-crunching and bookkeeping tasks in building design activities. Also, few participants in the design team have used computers on a regular basis. However, many changes are taking place which will affect the way a building design is carried out and the contribution computers could make in the process. All factors appear to advocate greater use of computers to achieve better designs. Three active areas of development are finally presented to illustrate new roles computers could assume in future building design projects. Key words: building design process, algorithm, synthesis/analysis, preliminary design, integration.