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Intrinsic Dendritic Filtering Gives Low-Pass Power Spectra of Local Field Potentials

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Intrinsic Dendritic Filtering Gives Low-Pass Power Spectra of Local Field Potentials J Comput Neurosci DOI 10.1007/s10827-010-0245-4 Intrinsic dendritic filtering gives low-pass power spectra of local field potentials Henrik Lindén · Klas H. Pettersen · Gaute T. Einevoll Received: 31 August 2009 / Revised: 30 March 2010 / Accepted: 6 May 2010 © Springer Science+Business Media, LLC 2010 Abstract The local field potential (LFP) is among the the LFP. The frequency dependence of the properties most important experimental measures when probing of the current dipole moment set up by the synaptic in- neural population activity, but a proper understanding put current is found to qualitatively account for several of the link between the underlying neural activity and salient features of the observed LFP. Two approximate the LFP signal is still missing. Here we investigate this schemes for calculating the LFP, the dipole approxima- link by mathematical modeling of contributions to the tion and the two-monopole approximation, are tested LFP from a single layer-5 pyramidal neuron and a and found to be potentially useful for translating results single layer-4 stellate neuron receiving synaptic input. from large-scale neural network models into predic- An intrinsic dendritic low-pass filtering effect of the tions for results from electroencephalographic (EEG) LFP signal, previously demonstrated for extracellular or electrocorticographic (ECoG) recordings. signatures of action potentials, is seen to strongly affect the LFP power spectra, even for frequencies as low as Keywords Local field potential · Single neuron · 10 Hz for the example pyramidal neuron. Further, the Forward modeling · Frequency dependence · EEG LFP signal is found to depend sensitively on both the recording position and the position of the synaptic in- put: the LFP power spectra recorded close to the active synapse are typically found to be less low-pass filtered 1 Introduction than spectra recorded further away. Some recording positions display striking band-pass characteristics of Extracellular recordings have been, and still are, among the most used methods for probing neural activity. This popularity mainly stems from the spike-counting abilities of sharp electrodes: when placed sufficiently Action Editor: Abraham Zvi Snyder close to a particular neuronal soma, such electrodes H. Lindén · K. H. Pettersen · G. T. Einevoll will measure a sequence of standardized extracellular Department of Mathematical Sciences and Technology, potential signatures, each signalling the presence of an Norwegian University of Life Sciences, PO Box 5003, 1432, Ås, Norway action potential in that particular neuron. Information about spiking is commonly extracted from the high H. Lindén e-mail: [email protected] frequency band ( 500 Hz) of the recorded extracel- lular potentials. The interpretation of the local f ield K. H. Pettersen e-mail: [email protected] potential (LFP), i.e., the low-frequency part ( 500 Hz) of extracellular potentials, is generally not so straight- G. T. Einevoll (B) forward. The LFP appears to be dominated by dendritic Center for Integrative Genetics, processing of synaptic inputs, not firing of action poten- Norwegian University of Life Sciences, Ås, Norway tials (Nunez and Srinavasan 2006; Einevoll et al. 2007; e-mail: [email protected] Pettersen et al. 2008), and the LFP measured at any J Comput Neurosci point will have sizable contributions from neurons tory (Plonsey 1969; Plonsey and Barr 2007). The cur- located many hundred micrometers away (Kreiman rent dipole concept has been particularly important et al. 2006; Liu and Newsome 2006; Berens et al. 2008; in the interpretation of EEG signals, but there one Lindén et al. 2008, 2009a; Katzner et al. 2009;Xing has typically considered ‘mesoscopic’ current dipoles et al. 2009). representing the collective effect from large number The advent of new silicon-based multicontact electri- of activated neurons (Nunez and Srinavasan 2006). cal probes in various geometrical arrangements, such as In a recent study, however, we found the current di- ‘multi-shank’ (Buzsáki 2004) or ‘needlepad’ (Normann pole momentfrom a single neuron to be a very use- et al. 1999), offers new exciting opportunities for mas- ful concept for gaining thorough understanding of the sively parallel recordings of LFP. Thus LFP certainly characteristics of extracellular signatures of action po- has the potential of becoming one of the most im- tentials (Pettersen and Einevoll 2008). Likewise, we portant experimental measures when probing neural here find the concept to be very useful for obtaining population activity (Mitzdorf 1985;Arieli1992;Dietal. better understanding of the results from our numeri- 1990; Einevoll et al. 2007; Kreiman et al. 2006; Nauhaus cally comprehensive calculations of LFPs generated by et al. 2009). This will require, however, a substantial synaptic activation of individual neurons with complex improvement in our understanding of the link between dendritic morphologies. Further, used in combination the underlying activity in neurons and the recorded with the standard far-field dipole approximation from LFP signal. The present model study aims to add to this electrostatics (Jackson 1998; Plonsey and Barr 2007), understanding by investigating the contribution to the this quantity is even found to provide quantitatively LFP signal from individual neurons receiving synaptic accurate predictions of the LFP a millimeter or more stimulation. Due to the linearity of electromagnetism, a away from the neuron. This dipole approximation, as recorded LFP signal will be built up by a linear sum of well as a two-monopole approximation also explored such contributions from individual neurons located in here (Freeman 1980), may even find its use in ambitious the vicinity of the electrode contact. The insight gained large-scale neural network modeling schemes aspir- by studying the LFP signals generated by individual ing to predict results from EEG recordings or ECoG neurons will thus be of great help when embarking on recordings, i.e., recordings done at the cortical surface. the larger project of linking measured LFPs to activity Preliminary results from this project were presented in populations of neurons or comprehensive neural earlier in poster format (Lindén et al. 2008). networks (Lindén et al. 2009a, b). In the present study we particularly address the question on the origin of observed frequency spectra 2 Methods in LFP and EEG (electroencephalography) recordings (Pritchard 1992; Freeman et al. 2003; Bedard et al. 2.1 Forward modeling of extracellular potentials 2006b; Buzsaki 2006; Bedard and Destexhe 2009; Milstein et al. 2009; Miller et al. 2009). In Pettersen and Extracellular potentials are generated by transmem- Einevoll (2008) we described an unavoidable low-pass brane currents, and in the presently used volume frequency-filtering effect of the extracellular action- conductor theory the system is envisioned as a 3- potential signature due to the electrical cable properties dimensional smooth extracellular continuum with the of the neuronal dendrites. In the present paper we find transmembrane currents represented as volume current for our example layer-5 pyramidal neuron that the same sources (Nunez and Srinavasan 2006). In volume con- intrinsic dendritic filtering effect also strongly affects ductor theory the fundamental formula for the contri- frequencies down to about 10 Hz, i.e., well into the typ- bution to the extracellular potential φ(r, t) from the ical LFP and EEG frequency bands. Moreover, we find activity in an N-compartment neuron model is given the detailed frequency-filtering effects to vary strongly by (Nicholson and Freeman 1975; Holt and Koch 1999; with recording position: for apical synaptic stimulation Pettersen and Einevoll 2008; Pettersen et al. 2008) the low-pass filtering effects are most prominent for recording positions near the soma, and vice versa. We 1 N I (t) φ(r, t) = n . (1) also consider a spatially more compact layer-4 stellate πσ | − | 4 = r rn neuron. The same low-pass filtering effect is observed, n 1 although with a higher cut-off frequency than for the Here In(t) denotes the transmembrane current in com- spatially more extended layer-5 pyramidal neuron. partment n positioned at rn,andσ is the extracellular The use of dipole and other multipole moments conductivity. This formula relies on a set of assump- in the modeling of bioelectric signals has a long his- tions and approximations: The first is the use of the J Comput Neurosci quasistatic approximation of Maxwell’s equations. This 4 stellate cell from cat visual cortex (Mainen and amounts to neglecting the terms with time derivatives Sejnowski 1996), both downloaded from ModelDB at of the electric field E and magnetic field B from the http://senselab.med.yale.edu/. To assure sufficient nu- original Maxwell’s equations so that the electromag- merical precision the length of each compartment of the netic field effectively decouples into separate ‘quasi- model neurons was chosen to be maximum one tenth static’ electric and magnetic fields (Hämäläinen et al. of the electrotonic length at 100 Hz. This gave a total 1993). Then the electric field E in the extracellular of 1,072 compartments for the layer-5 cell and 343 com- medium is related to the extracellular potential φ via partments for the layer-4 cell for our default choice of E =−∇φ. For frequencies inherent in neural activity, passive membrane parameters (see below). Simulations i.e., less than a few thousand hertz, the quasistatic in NEURON were performed
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