Articles in PresS. J Neurophysiol (October 1, 2014). doi:10.1152/jn.00914.2013

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Generation of field potentials and modulation of their dynamics through volume integration of cortical activity Yoshinao Kajikawa1 & Charles E. Schroeder1,2 1. Cognitive Neuroscience and Schizophrenia Program, Nathan S. Kline Institute for Psychiatric Research, Orangeburg, NY. 2. Department of Psychiatry, Columbia University College of Physicians and Surgeons, New York, NY Running Head: Generation

and modulation of cortical field potentials

Corresponding author: Yoshinao Kajikawa Nathan Kline Institute 140 Old Orangeburg Rd Orangeburg, NY10965 Phones: +1 (845) 398-6630 Fax: +1 (845) 398-6545 E-mail: [email protected] Abstract: Field potentials (FPs) recorded within the brain, often called “local field potentials” (LFPs), are useful measures of net synaptic activity in a neuronal ensemble. However, due to volume conduction, FPs spread beyond regions of underlying synaptic activity, and thus, an “LFP” signal may not accurately reflect the temporal patterns of synaptic activity in the immediately surrounding neuron population. To better understand the physiological processes reflected in FPs, we explored the relationship between the FP and its membrane current generators using current source density (CSD) analysis in conjunction with a volume conductor model. The model provides a quantitative description of the spatiotemporal summation of immediate local and more distant membrane currents to produce the FP. By applying the model to FPs in the macaque auditory cortex, we investigate a critical issue that has broad implications for FP research. We show that FP responses in particular cortical layers are differentially susceptible to activity in other layers. Activity in the supragranular layers has the strongest contribution to FPs in other cortical layers, and infragranular FPs were most susceptible to contributions from other layers. In order to define the physiological processes generating FPs recorded in loci of relatively weak synaptic activity, stronger synaptic events in the vicinity have to be taken into account. While outlining limitations and caveats inherent to FP measurements, our results also suggest specific peak and frequency band components of FPs can be related to activity in specific cortical layers. These results may help improving the interpretability of FPs. Keywords: Field potential, Current source density, Volume conduction, LFP.

Copyright © 2014 by the American Physiological Society.

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Abstract

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Field potentials (FPs) recorded within the brain, often called “local field potentials” (LFPs), are

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useful measures of net synaptic activity in a neuronal ensemble. However, due to volume

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conduction, FPs spread beyond regions of underlying synaptic activity, and thus, an “LFP” signal

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may not accurately reflect the temporal patterns of synaptic activity in the immediately

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surrounding neuron population. To better understand the physiological processes reflected in

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FPs, we explored the relationship between the FP and its membrane current generators using

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current source density (CSD) analysis in conjunction with a volume conductor model. The model

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provides a quantitative description of the spatiotemporal summation of immediate local and more

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distant membrane currents to produce the FP. By applying the model to FPs in the macaque

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auditory cortex, we investigate a critical issue that has broad implications for FP research. We

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show that FP responses in particular cortical layers are differentially susceptible to activity in

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other layers. Activity in the supragranular layers has the strongest contribution to FPs in other

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cortical layers, and infragranular FPs were most susceptible to contributions from other layers.

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In order to define the physiological processes generating FPs recorded in loci of relatively weak

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synaptic activity, stronger synaptic events in the vicinity have to be taken into account. While

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outlining limitations and caveats inherent to FP measurements, our results also suggest specific

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peak and frequency band components of FPs can be related to activity in specific cortical layers.

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These results may help improving the interpretability of FPs.

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Introduction

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The field potential (FP) recorded within active neural tissue is an information-rich measure that

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arises mainly from synaptically-driven transmembrane currents related to excitability

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fluctuations in ensembles of neurons (Buzsaki et al. 2012; Mitzdorf 1985). Decoding of FPs can

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extract information about motor commands (Bansal et al. 2012; Ince et al. 2010), sensory stimuli

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(Belitski et al. 2010; Kayser et al. 2007) and current behavioral and cognitive state (Fries et al.

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2001; Lakatos et al. 2009, 2013; Scherberger et al. 2005; Steriade et al. 1993). This is true

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whether the FP is tightly or loosely phase-locked to an identified stimulus [so-called “evoked”

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and “induced” FPs (Makeig et al. 2004; Shah et al. 2004)], and it also holds for “spontaneous”

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activity, whose immediate antecedents are obscure (Fukushima et al. 2012; Lakatos et al. 2005).

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Despite its strengths, the interpretation of FPs is complicated by volume conduction, the

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spread of electric field generated by current sources in a conductive medium. As FPs are

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typically recorded with an active recording electrode amplified against a reference signal from a

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distant electrode, the exact point of origin of the signal is unknown due to volume conduction

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(Einevoll et al. 2013; Nunez and Srinivasan 2006). The signal could in theory arise anywhere

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within the conductive medium housing the electrodes. Understanding of the principles of volume

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conduction allows one to track down the brain sources of electroencephalographic (EEG) and

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event related potential (ERP) components (Godlove et al. 2011; Schroeder et al. 1995). This

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same understanding also prompts the use of techniques that isolate relatively local activity like

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current source density (CSD) (Einevoll et al. 2013; Kajikawa and Schroeder 2011; Mitzdorf

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1985; Nicholson and Freeman 1975, Pettersen et al. 2006) or the surface Laplacian, a 2-

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dimensional approximation of the second derivative of potential, used to derive scalp current

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density (Nunez and Srinivasan 2006; Tenke and Kayser 2012). CSD analysis estimates the

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laminar profile and magnitude of current sources (net local outward currents) and sinks (net local

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inward currents) that produce fluctuation of voltage in the conductive medium of the

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extracellular space (Nicholson and Freeman 1975), and is in most experimental cases explored

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by analyzing the one-dimensional spatial pattern of FPs (but see Riera et al. 2012). Previous

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ERP/EEG studies have shown that ERP peak components and EEG frequency components

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(bands) have distinct scalp topographies and source localizations. The same conditions apply to

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the laminar-spatial patterns of FP and CSD signals within a cortical area. This is a critical

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problem for LFP studies, as it limits their ability to attribute experimental effects to specific cell

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populations (e.g., supragranular pyramidal cells) or input types (e.g., top-down vs. bottom-up)

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Effects of volume conduction at a macro (>1 mm) scale are recognized as essential to the

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formation of the spatiotemporal profile of electromagnetic signals that can be measured in ERP

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and EEG recordings at the scalp (Nunez 1998; Nunez and Srinivasan 2006; Pascual-Marqui

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1999), but these effects at a micro (< 1 mm) scale are poorly understood (Bédard and Destexhe

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2011, Buzsaki et al. 2012, Einevoll et al. 2013, Riera et al. 2012). Recent papers on the related

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topic of the “spatial spread of the LFP” have outlined several variables that likely affect volume

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conduction beyond the boundaries of active (generator) tissue. Some have emphasized spatial

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variables, such as the size and shape of the generator substrate that is the population of neurons

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whose transmembrane currents are reflected in an FP, and the magnitude of the activation

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(Kajikawa and Schroeder 2011), while others have emphasized temporal variables, such as the

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synchrony of local cellular activity (Lindén et al. 2011; Reimann et al. 2013). Critically, in most

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circumstances, synchrony and strength of activation are confounded. On one hand, a given

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ensemble of neurons is expected to produce a stronger net response, as reflected by a larger FP

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signal magnitude, when they are activated simultaneously than when they are activated

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asynchronously (e.g. Reimann et al. 2013). On the other hand, we cannot directly relate the

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magnitude of FP signal, to the degree of synchronous firing in a given neuron population

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because, as discussed above, synchrony is not a sole factor that determines spatial spread of the

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FP. In the present study, we deal with the spread of FP activity within hot spots of highly

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synchronized activation; i.e., we examine local neuronal responses to preferred stimuli that

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excite massive and synchronous activation of local neuron ensembles. In this circumstance, high

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synchrony can be assumed. Interestingly, such strong, synchronous, responses, likely

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encompassing multiple cortical layers, are reported in many papers. However, investigation of

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how local (i.e., sub-millimeter scale), well-correlated (i.e. sensory-evoked response) activity

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patterns of neuron populations in different layers of cerebral cortex, contribute to the

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construction of a local FP began only recently.

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A simulation study investigated the contributions of electrical activity of neurons and

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their compartments to LFP at such scales and suggested the potential role of the active

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membrane conductance that generates action potentials in shaping the spatiotemporal patterns of

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FP (Reimann et al. 2013). Regardless of types of membrane conductance and difference in

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patterns of constituent neurons, transmembrane currents of neuronal population can be translated

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to CSD features. In sensory systems, sensory stimuli effective in driving strong neuronal firing

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responses also evoked larger CSD responses (Fishman and Steinschneider 2006, Kajikawa and

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Schroeder 2011) and larger postsynaptic currents (Tan et al. 2004), that corroborate the close

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correspondence between CSD components and transmembrane currents.

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Detailed understanding of the contribution of local activity to local FP is particularly

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important at this time, as studies are beginning to investigate laminar and sublaminar

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distributions of FPs in different frequency bands in order to help to sort out influences of

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feedforward and feedback projections (Buffalo et al. 2011; Spaak et al 2012; Sundberg et al.

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2012). Importantly in this regard, distinct frequency bands can be dissociated by their differential

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behavior in both event-related responses (Fries et al. 2011; Khayat et al. 2010; Ray and Maunsell

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2011; Wilke et al. 2006) and ongoing activity (Lakatos et al. 2005; Magri et al. 2012). However,

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the spatiotemporal summation by which these microprocesses combine to form a local FP has

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not been directly investigated in physiological data. In an effort to advance the understanding

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and physiological interpretation of FP measures this study examined the contribution of volume

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conduction to the generation of FPs at a sub-millimeter scale. We used a volume conductor

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model constructed on physical principles to spatially integrate “observed” CSD activity

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distributed across cortical depths, in order to calculate a “predicted” spatiotemporal pattern of

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intracortical FPs, and evaluated the similarity between the originally observed and model-derived

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FP patterns. Our results indicate that volume conduction integrates distributed activity across

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layers to shape the temporal pattern of an FP in any given layer. Our results also suggest that

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particularly in the infragranular layers where local FP generation is relatively weak, the form and

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frequency content of the locally-recorded FP may largely reflect activity in other cortical layers.

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Materials and Methods

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All experimental procedures were approved by the Institutional Animal Care and Use Committee

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of the Nathan Kline Institute.

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Subjects. Six macaque monkeys were implanted with a headpost and one or two recording

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chambers during aseptic surgeries. The chambers were oriented to make penetrations

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perpendicular to the lateral sulcus.

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Stimuli. Calibrated binaural tone stimuli were delivered through two free field speakers directed

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to ears (TDT). Tones ranged from 353.55 Hz to 32 kHz with 0.5 octave intervals (14

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frequencies) were presented at 60 dB SPL (duration: 100 ms, SOA: 625 ms).

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Recordings. All recordings were done while monkeys were awake. We used electrodes of linear-

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arrays of 23 electrical contacts spaced either 100 or 200 m apart (0.3-0.5M at 1.0 kHz) to

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record signals at different cortical depths. FP (0.1Hz-500Hz) were recorded from all contacts

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simultaneously and sampled at 2 kHz. As a reference (or indifferent) electrode, a metal pin

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immersed in saline filling the recording chamber was used. The best frequency (BF) of multiunit

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activity responses to tones was identified in each recording site (Kajikawa and Schroeder 2011).

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In the present study, responses to BF tones were analyzed.

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Current source density. CSD was calculated from FPs recorded from 3 adjacent electrode

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contacts by the second order finite differences:

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CSDz   FPz  dz   2FPz   FPz  dz  dz 2 ,

(Eq. 1)

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as the one dimensional approximation of the second order spatial derivative of the FP (Mitzdorf

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1985), with an assumption of homogeneous conductivity (see Discussion):

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2 2 2     2         r    2r     2  2  2     y z  z 2  x 

,

(Eq. 2)

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The generality of this method of CSD approximation (Eq. 1) has been questioned recently

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because of generator “edge” effects in rodent barrel cortex (Einevoll et al. 2013), with regard to

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traditional assumption of “trans-positional invariance” to validate Eq. 1 performed only in

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vertical dimension across cortex (Mitzdorf 1985). However, the solution proposed by Einevoll

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and colleagues “iCSD,” (discussed below) was devised for the unique structure of rodent barrel

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cortex, and does not generalize to the neocortex as a whole. Here, to support the last equality in

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Eq. (2) as an approximation, “trans-positional invariance” is only a special case of generally

V V V  , z x y

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required conditions that satisfy the inequality:

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electrodes (see Discussion). As Figure 2D will show, the condition is usually met when

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suprathreshold stimulation excites extensive regions of cortex (see also Reimann et al. 2013).

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Thereby, it is appropriate for a wide range of neocortical applications, including the present case.

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In the present study we used this standard approximation for compatibility with the vast majority

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of prior studies.

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Spectral analyses of FP and CSD. To derive the spectrotemporal patterns and frequency bands of

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those FP and CSD ( FP(t ) and CSD(t ) respectively), we used the complex Morlet wavelet

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 t '  4

1



e

i0t '



, along the vertical path of array

t' 2

e , 0  6 ,

to calculate the wavelet transforms of those signals (Torrence and Compo 1998):

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WTLFP (t , f ) 

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WT CSD(t , f ) 

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f 

t

FP(t 't )  s

t

*

 t 't   dt ' ,  s 

CSD(t 't )  s

*

 t 't   dt ' ,  s 

(Eq. 3),

0  2  02 , 4s

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in which t is the sampling interval. The complex Morlet wavelets were scaled to conserve the

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energy relationship between frequency components. The translation step was 1 ms. Center

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frequencies of the wavelet stepped from 1 to 256 Hz with 0.1 octave intervals. This dense

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frequency sampling leaves high redundancy between neighboring frequency bands of the

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wavelet transform and allows reconstruction of the original signal as (Farge 1992)

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256 FP(t )  Re   WTFP ( f , t )df  . 1 

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Power and phase spectrotemporal distributions were derived as the absolute values and phase

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angles of WTFP (t , f ) and WTCSD (t , f ) .

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Frequency band signals of FP and CSD were calculated as the sums of 16 center

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frequencies (delta: 1.0~2.9 Hz, theta: 3.0~8.8 Hz, gamma1: 27.7~81 Hz, gamma2: 83.9~256 Hz)

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or 8 center frequencies (alpha: 9.1~15.9 Hz, beta: 17.0~25.8 Hz,) of WTFP (t , f ) and WTCSD (t , f )

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along the frequency axis (Kajikawa and Schroeder 2011). Derived signals were approximately

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1.6 or 0.8 octaves wide with small overlaps between frequency bands, and were complex-valued,

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same as WT (t , f ) . The real part of signals (e.g. WT (t, f ) ) was identical to the transform with

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real part of wavelet (e.g. replacing  t ' in Eq. 2 with  t ' ). As the original signals were of

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real-valued, real parts of derived signals corresponded to the filtered signals and were used as

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frequency band-limited signals (Farge 1992). Absolute amplitudes of the complex transforms

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were used as the power of signals.

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Volume conductor model. The volume conductor model assumed that CSD at different depths

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contributed to the FP by volume conduction. Under the assumption of homogeneous tissue

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conductivity, volume conducted signals decay in proportion to the inverse of distance with no

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assumption of frequency dependent gain change; this predicted decay is matched by empirical

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findings (Schroeder et al. 1992; 1998; Kajikawa and Schroeder 2011). We calculated FP at a

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certain depth d k that could be generated by a given spatial distribution of CSD at every moment

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as

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vcFP k , t   A j

CSDd j , t  h  d j  dk 2

2

, h  rh 2d  d

(Eq. 4),

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in which d  d k 1  d k  is the spatial distance between neighboring contacts of array electrode.

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The parameter h represents a displacement distance of the center of mass of CSD from the array

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electrode assuming all CSD components were vertically aligned across cortical depths. The idea

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behind the displacement is as follows.

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In general, there are many possible solutions of sources that could generate topographic

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or depth patterns of FP in solving Eq. (2). In the present case, the only boundary was the line of

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the array electrodes with depth-distributed signals with surrounding open space. It was not

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definitive in finding particular CSD solutions as there are many possible configurations of CSD.

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However, to be consistent with the columnar structure of cortex, one constraint we could

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presume was that CSD distributed vertically across cortical layers. That reduced the problem to

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one of determination of the finite horizontal spread. However, again, any horizontal spread of

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CSD could be replaced by a variety of other CSD to create the same spatial pattern of FP. Thus,

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it would be an ideal approach to reduce the arbitrariness of horizontal spread and model it as

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simply as possible, since at this time, we cannot realize more complex (parametric) models in

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detail or justify them.

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Responses to suprathreshold pure tones in auditory cortex must distribute as medial-

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lateral stripes defined by iso-frequency contours. The shapes of stripes were kept similar across

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cortical layers and horizontally finite, constrained by the anterior-posterior extent of an iso-

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frequency domain. Any such spatial distributions of sources may be substituted by one or several

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charge densities located at a horizontal point somewhere inside of responsive zones to generate

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same field potential patterns. That is equivalent to what is done at a different spatial scale in

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source estimation for EEG/MEG. The anchoring point around which spread is estimated is single

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point at the center of mass in a horizontal distribution of sources. Its exact position may remain

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unknown. Only its distance from electrodes is needed in deriving FP at the electrodes. Thus, we

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included the horizontal displacement parameter h to represent the horizontally delimited

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distribution of activity in the simplest way. While such a simplified model can introduce error

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(uncertainty), it is preferable to a model with more unknown parameters, unless they can be

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empirically validated.

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The output of the resultant model becomes equivalent to that generated by a dipole-like

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substrate (i.e., having a vertical distribution), horizontally displaced at an average distance h

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from the recording electrode array across depths (Kajikawa and Schroeder 2011; Somogyvari et

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al. 2012). In Eq. 3, rh 2 d was the sole free parameter that could influence the shape of vcFP (k , t ) .

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Its values were chosen to maximize the similarity (see below) of spatiotemporal patterns between

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the calculated and the observed LFP. The parameter h  rh 2d  d may be considered to be the

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distance to the center of horizontally distributed sources generating FP from the electrodes. Note

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that, due to the linearity of both wavelet decomposition and volume conduction, the order of

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calculating them is interchangeable. However, once the power or phase of wavelet-decomposed

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signals is derived, these values cannot be entered into the volume conductor model due to the

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non-linearity of power/phase calculations.

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Within a “column,” vertical profiles of CSD that contributed to the FP at a given depth

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were derived as follows. The spatiotemporal CSD profiles were weighted along the depth axis by

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their distances from the origins of CSD with an additional displacement h . Wavelet-derived

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frequency band signals were derived in a similar manner. The spatiotemporal profiles of CSD

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power were derived after distance-weighing.

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Depth distributions of the power of CSD contributions to granular FP responses and

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phase differences of CSD from granular FP responses were derived as follows. The mean of the

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CSD power over a150 ms period post-onset of tone was calculated for each CSD and subtracted

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by mean power during a 150 ms period prior to the tone onset. For data sampled with 200 m

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intervals, missing data points were linearly interpolated. For each frequency band, such

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distribution was normalized by the power at the depth of the granular sink. Since depths of

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cortical layers relative to electrode positions differed between penetration sites, depths of

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granular sinks were aligned to zero. Median and confidence intervals at each depth were derived

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after alignment.

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While the field generated by dipoles decays with the inverse of the square of distances, 2

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1 r , the volume conductor model treated individual poles of multi-poles as separate monopoles

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whose field decayed with the inverse of the distance, 1 r , not squared. However, it should be

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noted that superimposition of electric fields generated by two monopoles of opposite signs

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decaying with 1 r becomes same as an electric field that decays with 1 r

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relatively larger than the dimension of the dipole. Therefore, while the model treats CSD features

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as spatially distributed monopoles, it can generate the field potentials generated by dipoles as

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well.

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This implementation was preferred, because recordings in the present study were done within the

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zones of active generators or dipoles, where the dipole field approximation’s relevance is

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questionable.

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Similarity score. To quantify the similarity between temporal patterns of FP and CSD, and the

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similarity between the spatiotemporal patterns of the observed FP and CSD or model-derived FP,

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we calculated the similarity score as described below. Temporal patterns of FP, CSD, and model-

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   derived FP at individual recording channels were expressed as vectors, vFP , vCSD and v vcFP of nT

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independent samples, where nT = sample duration x sampling rate. Spatiotemporal profiles were

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expressed as matrices, M FP , M CSD , and M vcFP , whose number of rows corresponded to the

2

at distances

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number of recording contacts of electrodes - 23 and 21 for FP and CSD, respectively.

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Spectrotemporal patterns of signals at each channel were expressed similarly in matrices

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WTFP , WTCSD , and WTvcFP ; whose number of rows corresponded to the number of wavelet

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center frequencies. Before calculation of the similarity, these vectors and matrices were

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 normalized by the root of mean squared values (e.g. v

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compensate for their difference in the signal power and to analyze shapes in isolation. For

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matrices, the mean was calculated across both rows and columns. Similarity between those

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patterns was calculated as the inner product between vectors or the Frobenius inner products of

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matrices after normalization. The similarity value ranged from –1 for completely mirrored

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shapes of opposite polarities to 1 for identical shapes of same polarities regardless of

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magnitudes. While similarity could depend on the periods of FP, CSD, or their wavelet

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transforms, values were derived using signals between -30 and 170 ms from the onset of sound.

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However, the similarity score is model-free in that it can be evaluated for any models or analysis

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that creates spatiotemporal patterns as long as it keeps dimensions (the number of depth channels

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and time bins) constant.

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Statistics. All statistical tests were done non-parametrically with a criterion level of p = 0.01,

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except for ad hoc comparisons at p = 0.05. 95% Confidence intervals were derived by bootstrap

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using the Matlab function, bootstrp, with 1000 re-sampling (Figs. 4, 6A and B).

 

2 mean v or M

 ) to

mean M

2

309 310

Results

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Sensory-evoked FP and CSD signals at a given location in the brain often differ in temporal

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pattern even though both signals are considered to reflect local synaptic activity. We first

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elaborate the difference between these signals in both temporal and spectral domains. We then

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describe how the volume conductor model bridges the gap between the two signals. We further

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show that the FP integrates local and distant activity in individual frequency bands independently

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of the spatial distributions of the CSD activity of other frequency bands.

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Differences between co-located FP and CSD signals.

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First, we show the difference in temporal patterns between FP and CSD. Figure 1 shows

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examples of FP and co-located CSD responses recorded simultaneously from (i) supragranular

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(Sg), (ii) granular (Gr), and (iii) infragranular (Ig) layers in an A1 penetration, along with

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spectrotemporal patterns of signal power (C,D) and phase difference (E). FPs in the different

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layers share similar patterns starting with onset negativity (Fig. 1A), but after this point

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waveforms diverge between Sg and other layers. This is not surprising because FP patterns are

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expected to change systematically as recordings traverse an active FP generator region (Mitzdorf

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1985, Schroeder et al. 1995) and the strongest CSD activity was found in the Sg layer. The point

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of interest here, however, is the contrast between co-located FP and CSD signals as it reveals

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effects of volume conduction. The FP - CSD contrast is described systematically by comparison

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of their temporal patterns (B), low frequency power plots (C vs. D) and phase differences (E). In

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Sg layers, both FP and CSD signals maintained negative deflections after the onset until 100 ms.

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Low frequency power had similar peaks. In Gr layers, though temporal patterns looked similar,

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the onset negativity occurred earlier in CSD than FP and had a nearly 90 degrees phase

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difference in high frequency bands. In Ig layer, the larger positive/negative fluctuations in FP

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were more rapid than the source/sink fluctuations in the CSD signal. Thus, the peak FP power

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was higher in a higher frequency band than peak CSD power.

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To assess the dissimilarity between FP and CSD across penetration sites, we quantified

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the similarity score as an inner product of vectors representing temporal patterns of 2 signals in 3

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cortical layers (Fig. 1E). The score changes from 1 when FP and CSD had identical temporal

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patterns to -1 when two patterns were of opposite polarity and mirror images of one another. The

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scores for 3 pairs in Fig. 1B were 0.85 (i), 0.44 (ii), and -0.08 (iii), respectively. The distributions

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of the score were skewed towards 1 in all cortical layers. Median scores were 0.81, 0.75, and

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0.33 for Sg, Gr, and Ig layers respectively (n=130), with significant difference (Friedman’s non-

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parametric repeated measures ANOVA, 2(df=2, n=116) = 30.4, p < 0.01, excluding penetration

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sites missing Ig layer). This difference was attributable to the lower scores of Ig layer when

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compared to other layers (Tukey's HSD test, p < 0.05). Thus, temporal patterns of FP and CSD were

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more dissimilar in Ig layers than Gr and Sg layers. However, even in Gr and Sg layers, the scores

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distributed over wide ranges. These results suggested the generality of the differences in

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spectrotemporal patterns between co-located FP and CSD signals. Below, we show how the

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discrepancies between the two signals are explained by volume conduction, and evaluated the

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effect by the similarity score.

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Volume conductor model Here, we explain the volume conductor model first, and then fill the gap between FP and

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CSD by applying the model to experimental data. CSD signals reflect transmembrane current

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flow patterns that are localized to the spatial extent of neuronal processes (1). The local 1-

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dimensional CSD profile is customarily derived from a laminar FP profile using Eq. 1 by

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approximating  2 (r )  qr  , in which  is the tissue conductivity (assumed to be spatially

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   uniform), (r ) is the FP, and qr  is CSD. FP reflects spatially distributed events qr  through









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volume conduction. When the boundary condition of ()  0 is met,  2 (r )  qr  can be

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solved as    1 qr  r   ( r )    dr  . 4  r  r 

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(Eq. 4)

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Since auditory cortical FP responses to best frequency tones are several hundreds of microvolts

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and scalp ERPs centimeters away from the auditory cortex are generally on the order of 1

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microvolts, we used this solution as an approximate model of a local volume conductor. There is

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 no constraint on the spatial distribution of qr  within a body. The volume conductor model

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summates spatially distributed CSD signals after weighing them with the inverse of their

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distances from the point of measurement as in Eq. (4), which weakens distant CSD to some

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degree.

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Figure 2 shows how Eq. (4) governs volume conduction when there are two different FP

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generators, each consisting of sink and source, operating in isolation (one strong source/sink -

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Fig. 2A; one weak sink/source - Fig. 2B), or together (Fig, 2C). Sink sand sources modeled here

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have round shapes delimited to two parallel flat planes spread horizontally (xy, Fig. 2Ai and Bi).

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FP profiles were calculated based on Eq. 4. Due to symmetry of sink and source shapes around

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their centers, FP profiles formed in planes that contain x-y centers of sink and source are

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identical. When there is one FP generator, inversion of FP polarity occurs at the mid z position

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between sink and source (Fig. 2Aii and Bii). Above and below the inversion, the FP spreads with

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constant polarity with amplitude peak positions aligned vertically to sink and source (Fig. 2Aiii

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and Biii). However, when two FP generators co-exist, FP distributions from single generators

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superimpose, and an FP distribution reflecting an interaction of the two generators emerges.

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Ventral spread of the negative FP below the inversion of the single strong generator (Fig. 2A) is

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reduced in the combined case (Fig. 2C) and is interrupted by small positivity due to the lower

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generator’s source. Compared to the positive peak below the inversion in Fig. 2B, the positive

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peak at the corresponding z-position is smaller in Fig. 2C. Thus, within the cortex where activity

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spreads over cortical layers through volume conduction, the FP in any one layer is

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‘contaminated’ by signals of activity generated in other layers. We utilized the volume conductor

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model to specify this effect quantitatively.

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Figure 3 shows how the volume conductor model links sensory-evoked FP and CSD

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responses. At all penetration sites, we simultaneously recorded FP at 23 depths spanning the

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superficial to deep layers of auditory cortex, as illustrated by the representative FP profile in Fig.

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3C, from which the spatiotemporal CSD profile in Fig. 3A was derived. The volume conductor

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model-derived FP profile for these signals (described below) is shown in Fig. 3B. Fig. 3D

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illustrates the gradual change in the FP produced by the systematically increasing spatial range of

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the CSD profile that is incorporated into the volume conductor model to derive Gr layer FP

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waveform. This is shown in increasing order from top to bottom, starting from a summation of

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one channel that corresponds to Gr layer CSD itself. While temporal patterns of the observed FP

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and CSD (bottom red and top green traces in Fig. 3D) differed in their temporal patterns, the FP

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generated by the model (traces between the top and bottom in Fig. 3D) became successively

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closer approximations of the observed FP as the spatial range of CSD estimates (incorporated by

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the model) is increased. In this example, the model broadened the onset negativity and delayed

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the timing of the following positive peak (asterisks in Fig. 3D) from 38 to 62 ms. This effect

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indicates that the Gr layer FP was influenced by current generators (indexed by CSD) in other

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layers. By performing the same model calculation over all depths of FP recording, we calculated

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a model-derived spatiotemporal FP profile (Fig. 3B), which resembles the profile of the observed

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FP (Fig. 3C) more closely than it does the CSD profile. Accordingly, the spectrotemporal pattern

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of the model-derived FP for the Gr layer also bears greater similarity to that of the observed FP

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than that of the CSD signal (Figs. 3E-G).

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For the example shown in Fig. 3, the similarity score of the observed FP with the co-

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located CSD signal was 0.38 and increased to 0.95 when computed using the model-derived FP.

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Also, across penetration sites (n=130), the similarity over the 150 ms long temporal patterns

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between the observed FP in Gr layer and the model-derived FP increased as a function of the

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number of proximal CSD signals (Fig. 4B). Improvement of the score through use of the model

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waveform was also observed for FP in Sg and Ig layers (Fig. 4A and C).

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In all layers, the score reached asymptote by integrating signals within less than 1 mm.

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This suggested that FP responses to the best frequency tones within the auditory cortex are

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shaped by activity of variable temporal patterns occurring in the gray matter over the range of a

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millimeter where strong activation is spread. It may be also noted that the model-derived FP in

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Sg layer, where local CSD activity was stronger than other layers (Fig. 6C), still increased its

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similarity to the observed FP by integrating activity over several hundreds of micrometers. These

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results suggested that even at loci where the CSD signals were strong, the effect of volume

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conduction would not be negligible due to activity in their vicinity.

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Notably, the FPs in Ig layers (which are farthest from Sg layers) had the lowest similarity

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scores. FPs in these layers required the widening of spatial coverage in the model to include CSD

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in the Sg layers in order for the similarity score to asymptote. We estimated the channel

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increments needed for the scores to reach 90% of the net changes, for all 3 layers in each

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penetration site (Fig 4D). Those channel increments differed significantly between layers

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(Friedman’s nonparametric repeated-measures ANOVA, 2(df=2, n=116) = 38.2, p < 0.01,

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excluding sites missing Ig layer data). This difference was attributable to the channel increments

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needed significantly more in Ig layer than other layers (Tukey's HSD test, p < 0.05). Thus, in

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order to define the physiological processes generating FPs recorded in loci of relatively weak

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synaptic activity (e.g., the Ig layers), stronger synaptic events in the vicinity (e.g., those in the Sg

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layers) have to be taken into account.

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Contributions of different frequency bands to volume conducted signals Below, we expand the consideration of volume conduction to the relationships between

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components of FP and CSD. Sensory cortical responses are not only distributed across layers but

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 also transient and of broad spectral content. A CSD signal qr , t  can be considered as a linear

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summation of the CSD frequency bands q f r , t  as q r , t    q f r , t  . By incorporating this into







f

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440

Eq. 4, FP signals decomposed into frequency bands in the volume conductor model is  1 (r , t )  4 

   q r  r , t  f

f

  r  r

 dr  .

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Due to linearity of both volume conduction for spatially distributed CSD signals and spectral

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transforms for frequency bands in each CSD signal, those operations are interchangeable. Thus,

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the FP due to volume conduction can be derived separately for different frequency bands as

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   1 q f r  r , t    f (r , t )  dr  .   4  r  r 

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Figure 5 illustrates how spatiotemporal patterns of CSD activity in the different

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frequency bands contribute to the infragranular FP response. Fig. 5A and B show the

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spatiotemporal profiles of CSD responses and their power over a wide frequency range (,

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1~256 Hz) and in five 1.6 octave- (, ,  and ) and 0.8 octave-wide ( and ) frequency

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bands. Due to division by the distance from the point of interest, the volume conductor model

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weakens distant CSD before summation. Therefore, actual signals in the Sg layer CSD

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components were stronger than what is plotted in Fig. 5A and B, regardless of frequency band.

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In each frequency band, summation of CSD responses weighted inversely by the distance from

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the Ig layer along depth reflects the Ig layer FP response derived by the volume conductor model

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(orange traces in Fig. 5C).

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In the example shown in Fig. 5, the Ig layer CSD response (green in Fig. 5C, ) was

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negative from 10 to 100 ms after the onset of sound and had a negative peak at 50 ms followed

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by a positive peak at 130 ms. The FP response (red in Fig. 5C, ) had a positive peak at 50 ms

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followed by a negative peak around 130 ms. Temporal pattern differences between CSD and FP

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signals were reflected in opposite polarities essentially throughout the response time course

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across frequency bands (, ,  and ). Beta band CSD and FP signals also differed in

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frequency.

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These temporal pattern discrepancies between CSD and FP signals across frequency

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bands were due to volume conduction. In most frequency bands, powers of signals in Gr and Sg

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layers were comparable to or even stronger than the power in the Ig layer (Fig. 5B, , , ,  and

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). In each band, by spatially summating the CSD signals across depths, the volume conductor

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model reproduced an FP response that greatly resembled the observed FP, but with a polarity

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opposite to that of the co-located Ig layer CSD signal (orange in Fig. 5C). Thus, the temporal

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pattern of the Ig layer FP response reflected not the local generator currents, but rather those in

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other cortical layers via volume conduction.

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We quantified the relative contributions of CSD signals across depths to the granular FP

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for all experiments (penetration sites). In each penetration site, the depth distributions of CSD

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response power, weighted by the inverse of distances from the Gr layer sink were calculated

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separately for the same 6 frequency bands as done for Fig. 5. In general, sensory evoked CSD

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signals are distributed across cortical layers in sensory cortices and have broad frequency content

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(Kajikawa and Schroeder 2011; Lakatos et al. 2005, Maier et al. 2011).

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Figure 6A illustrates the laminar distribution of CSD power by frequency band that

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contributed to the Gr layer FP response. As the power of the Gr layer CSD responses differed

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significantly between frequency bands (median values from low to high frequency bands: 0.49,

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0.41, 0.076, 0.032, 0.012 and 0.86x10-3 mV/mm2, Friedman's test, 2(df=5, n=130) = 621, p