Comparing the Feature Selectivity of the Gamma-Band of the Local Field Potential and the Underlying Spiking Activity in Primate Visual Cortex

The local field potential (LFP), comprised of low-frequency extra-cellular voltage fluctuations, has been used extensively to study the mechanisms of brain function. In particular, oscillations in the gamma-band (30–90 Hz) are ubiquitous in the cortex of many species during various cognitive processes. Surprisingly little is known about the underlying biophysical processes generating this signal. Here, we examine the relationship of the local field potential to the activity of localized populations of neurons by simultaneously recording spiking activity and LFP from the primary visual cortex (V1) of awake, behaving macaques. The spatial organization of orientation tuning and ocular dominance in this area provides an excellent opportunity to study this question, because orientation tuning is organized at a scale around one order of magnitude finer than the size of ocular dominance columns. While we find a surprisingly weak correlation between the preferred orientation of multi-unit activity and gamma-band LFP recorded on the same tetrode, there is a strong correlation between the ocular preferences of both signals. Given the spatial arrangement of orientation tuning and ocular dominance, this leads us to conclude that the gamma-band of the LFP seems to sample an area considerably larger than orientation columns. Rather, its spatial resolution lies at the scale of ocular dominance columns.


INTRODUCTION
Low frequency extracellular voltage fl uctuations, widely known as local fi eld potential (LFP), are abundant across species and brain regions. These signals are believed to primarily refl ect synchronized dendro-somatic components of synaptic signals (Mitzdorf, 1987), subthreshold membrane oscillations (Kamondi et al., 1998) and afterpotentials of somatodendritic action potentials originating from an area around the electrode tip (Buzsaki, 2002;Logothetis and Wandell, 2004). In recent years a growing number of studies have tried to link local fi eld potentials in cortical circuits to coding of sensory stimuli (Henrie and Shapley, 2005;Kayser and Konig, 2004;Kreiman et al., 2006;Kruse and Eckhorn, 1996;Liu and Newsome, 2006;Siegel and Konig, 2003) as well as cognitive processes like attention Taylor et al., 2005), memory (Lee et al., 2005;Pesaran et al., 2002) and perception (Fries et al., 2002;Gail et al., 2004;Womelsdorf et al., 2006). Recently, it has been suggested that LFPs can be useful for the control of cortical motor prostheses (Andersen et al., 2004;Mehring et al., 2003;Rickert et al., 2005). In addition, electroencephalography (EEG), the extracranial counterpart of the LFP signal, has been used in research and clinical application for decades. Much of the current resurgent interest also stems from the LFPs intricate relationship to the BOLD signal measured with fMRI (Logothetis et al., 2001).
Surprisingly little is known, however, about the mechanisms generating the LFP signal and its relationship to local cortical circuits. It has been established, for example, that the spectral coherence between local fi eld potentials from different recording sites falls of with increasing distance (Destexhe et al., 1999;Juergens et al., 1999;Leopold and Logothetis, 2003), where the falloff is steeper in higher frequency bands than in lower ones. But surprisingly strong correlation between the signals from different sites can typically be found up to a few millimeters. Under visual stimulation with gratings, Juergens et al. fi nd that up to a distance of 1.5 mm LFP coherence in the gamma-band remains very high at ∼0.7 (Juergens et al., 1999). This has been interpreted as a sign of synchronized activity between distant cortical populations measured via the LFP signal, which was taken to refl ect activity from local populations (Engel et al., 2001).
An alternative parsimonious interpretation, however, is that the LFP signal measures the extended network activity with poor spatial resolution, as it is not well understood how closely LFP activity refl ects physiological properties and local processing at the scale of cortical columns (Albright et al., 1984;Wiesel, 1968, 1974;Zeki, 1974). Functional properties of neurons in the cortex are often organized on a very fi ne spatial scale, such as orientation tuning in area V1 of the macaque. It is believed to be represented in orientation columns spanning a cortical distance of about 50 μm (Hubel and Wiesel, 1968, 1974, 1977 or to vary smoothly along the cortical surface with several changes in preferred orientation within one ocular dominance column (Bartfeld and Grinvald, 1992;Blasdel, 1992b;Horton and Adams, 2005;Vanduffel et al., 2002). In order to understand the relationship between the activity of localized populations of neurons and the gamma-band frequency range of the LFP, it is imperative to determine if LFP signals are in fact restricted enough to refl ect local activity at the scale of orientation columns.
We investigated this question by studying the relationship of the LFP, and in particular the gamma-band, to the spiking activity of local populations of neurons in the primary visual cortex of the macaque. We exploited the well known spatial organization of orientation tuning and ocular dominance columns and recorded multi-unit (MU) activity and LFP using arrays of multiple chronically implanted tetrodes. With this experimental setup we were able to record simultaneously from nearby sites with distinct MU preferences and compare the properties of the LFP to those of the MU at the same site. Previous studies established a power increase in the gamma-band as the most prominent feature of LFP activity under visual stimulation in V1, but did not systematically assess the relationship between LFP tuning and the tuning of MU activity, which refl ects the spiking activity of neurons close to the recording electrode tip Fries et al., 2001Fries et al., , 2002Gray and Singer, 1989;Siegel and Konig, 2003).
We fi nd that the preferred orientation of the LFP did not correlate well with the preferred orientation of the MU recorded at the same site. As expected, nearby MU recording sites (around 200 μm apart) had distinct orientation preferences, while LFP tuning was homogenous across adjacent tetrodes located up to 1 mm apart. This leads us to conclude that the LFP integrates the activity of neurons with diverse orientation preferences, sampling an area spanning several orientation columns (more than 50 μm). In contrast to orientation tuning, ocular dominance columns span about 450 μm (Bartfeld and Grinvald, 1992;Blasdel, 1992a;Wiesel, 1972, 1977). When we compared the ocular dominance tuning of the LFP and the MU at the same site, we did fi nd a much stronger correlation between LFP and MU preferences.

ELECTROPHYSIOLOGICAL RECORDINGS AND SURGICAL METHODS
Experiments were conducted in three healthy, adult monkeys (Macaca mulatta) weighing 16, 12, and 11 kg (monkeys A, B, and C). The studies were approved by the local authorities (Regierungspräsidium) and were in full compliance with the guidelines of the European Community (EUVD 86/609/EEC) for the care and use of laboratory animals. Recording chambers were positioned stereotactically with the aid of high-resolution magnetic resonance anatomical images. These methods have been described in detail previously (Logothetis et al., 1999). Inside the form-specifi c chambers built out of titanium (monkeys A and B) a custom-built array of tetrodes was chronically implanted over the left hemisphere operculum in area V1 (Tolias et al., 2007). In monkeys A and C we also recorded non-chronically from form-specifi c chambers implanted in the right hemispheres. All recordings were conducted with tetrodes attached to microdrives that could be manually adjusted independently. The initial impedances of the tetrodes after electroplating and before implantation were between 200 and 800 kΩ.
For the chronic recordings, the distance between nearby tetrodes was 200 and 500 μm for monkeys A and B, respectively, and the maximal distance between pairs of tetrodes was ∼750 μm in monkey A and 1 mm in monkey B. For the non-chronic recordings, manually adjustable microdrives were inserted into a custom-built grid and activity was recorded using tetrodes. No functional pre-selection criteria were applied for the neurons. Multi-unit (MU) activity and single unit (SU) activity was sampled at 32 kHz, digitized, and stored using the Cheetah data acquisition system (Neuralynx, Tuscon, AR). LFP signals were recorded by fi ltering (steepness of fi lters: 16 db/octave) the raw voltage signal from one of the tetrode channels using analogue band pass fi ltering (0.1-475 Hz) and digitized at 2 kHz (12 bits). Multi-unit activity was defi ned as the events that exceeded a predefi ned threshold (set at 25 μV for most recording sites and 30 μV for a few) of the fi ltered, digitized signal (analogue fi ltering, 0.6-6 kHz and digitized at 32 Hz, 12 bits). Single units were isolated using a custom-built offl ine clustering system working on features extracted from the recorded waveforms. Details of single units isolation have been described elsewhere (Tolias et al., 2007).
In the orientation tuning experiments, in monkey A two tetrodes were advanced deep into white matter and used for reference (142/160 recording sites for this experiment were recorded with these reference tetrodes). The remaining 18 sites and all the data from monkey B were recorded using the ground for referencing (a screw on the bone inside the chamber). We did not fi nd any signifi cant differences in the results we obtained from the two animals. Given the recording arrangement using a reference tetrode, it is possible that the increase in the gamma band (see Results) is dominated by electrical dipoles close to the reference. If this were the case, we expect nearby tetrodes to have nearly the same signal. However, re-referencing each recordingtetrode with an adjacent tetrode (by digital subtraction), we fi nd a 5% increase in the gamma-band power in the re-referenced signal compared to the original one. In contrast, if the increase in the gamma band was caused by dipoles close to the reference, this portion of the signal would be present on both tetrodes and re-referencing would lead to a strong decrease in gamma-band power. Therefore, it is very unlikely that the gamma power is dominated by dipoles close to the original reference. In the ocular dominance experiments, all sites were recorded using ground referencing.
In the orientation experiments, data from monkey A were recorded from 64 and 96 sites using static and moving gratings, respectively (datasets A1 and A2, recorded using the same chronic tetrode array 10 months apart). Data from monkey B were recorded from 36 sites (dataset B1). Due to our chronic recording setup, most recordings from each monkey come from a very similar part of the cortical map. The shape of the evoked potential of the LFP was suggestive that recordings were performed in layer 4 (Schroeder et al., 1995). In the ocular Comparing LFP and MU activity in V1 dominance experiments, data from monkey A were recorded from 199 sites using monocular static gratings (92 chronic, 107 non-chronic). All data from monkey C were recorded nonchronically from 210 sites using the same kind of stimuli.

VISUAL STIMULATION AND BEHAVIORAL PARADIGM
Visual stimuli were displayed using a dedicated graphics workstation (TDZ 2000; Intergraph Systems, Huntsville, AL) with a resolution of 1280 × 1024 pixels, and refresh rate of 85 Hz, running an OpenGL-based stimulation program. The behavioral aspects of the experiment were controlled using the QNX real-time operating system (QSSL, Ontario, Canada). In the orientation experiments, after the monkey acquired fi xation on a colored square target (0.2°) for 300 ms, a sine wave grating stimulus was presented. Typically the size of the grating was 5° in diameter and the spatial frequency 4 cycles per degree. We applied either static or moving gratings equally distributed at eight different orientations and typically high contrast (moving gratings: 100%, static gratings: 30-100%). For moving gratings the speed was 0.5 cycles per second. The grating stimuli were displayed for 500 ms and the animal was required to maintain fi xation for another 500 ms. At the end of each successful trial a drop of apple juice was used for reward. In the ocular dominance experiments, a similar stimulus presentation design was used, but gratings were presented monocularly using a custommade mirror-stereoscope and two LCD monitors on both sides running with a refresh rate of 60 Hz. The fi xation window was ±0.5°. The animals were implanted with a scleral search coil (Robinson, 1963) and their eye movements were monitored on-line. Data were also collected for off-line analysis using both the QNX-based data acquisition system at 200 Hz and the Cheetah data acquisition system at 2000 Hz.

STATISTICAL AND DATA ANALYSIS
We considered three different time periods. The baseline period ranged from 300 ms before the stimulus appeared to stimulus onset. We consider the fi rst 200 ms of the stimulation period as the evoked response period (ERP), where we observe a strong transient response dominated by low frequencies. Therefore, we treat this period separately. The stimulation period ranged from 200 to 500 ms after stimulus onset.
The power spectrum of the LFP was obtained by computing its multi-taper estimate (Thomson, 1982) using a time-bandwidth product of 2.5 (number of samples: N = 600, spectral concentration: W = 0.042, or ∼8 Hz). The power increase in the LFP during stimulation period relative to baseline was defi ned as 10⋅ − (log( ) log( )) P P stim base and is measured in db. To obtain a "response value" for the LFP at different frequencies, we used the mean power in a narrow band of 10 Hz around the center frequency. As a response value for the ERP we used the root mean square power in the respective time period.
We tested both MU and LFP responses for orientation tuning with an ANOVA (p < 0.05). Orientation tuning functions were fi tted using a standard least squares algorithm (lsqcurvefi t, Optimization Toolbox, Matlab, The Mathworks) and modifi ed a von Mises circular distribution function (Fisher, 1993) given by The parameter θ is the sites' preferred orientation, b determines the width of the orientation tuning function (the larger, the more sharply tuned, fl at if zero), f 0 and a determine the offset above zero and the peak fi ring rate.
To assess how well stimuli with different orientations can be discriminated at each site, we computed a tuning index d′ defi ned as Here μ pref and μ orth denote the mean response to the preferred and the orthogonal stimulus condition, respectively, and ˆ( ) / σ σ σ 2 2 = + pref orth 2 is the pooled variance of the two response distributions. This measure differs from those used in previous studies Kayser and Konig, 2004;Liu and Newsome, 2006) in that it takes explicitly into account the trial variability of the response (Siegel and Konig, 2003). We also investigated other tuning indices used in the above studies. Although they gave qualitatively similar results for the LFP tuning alone, they underestimate the effect of the variability of the LFP response compared to the MU response especially in low frequencies (data not shown). Therefore they lead to spuriously high estimates of LFP tuning strength compared to that of the MU signal. To obtain an estimate of the expected d′ assuming no structure in the LFP over conditions, we calculated the tuning index on shuffl ed datasets, where trials were randomly assigned to conditions.
The correlation between the preferred orientations of MU and LFP was assessed using the circular correlation coeffi cient (Jammalamadaka and SenGupta, 2001). Its sample estimate is given by Here α i and β i denote the respective sample angles and α and β the circular sample means. Ocular dominance of MU and LFP was tested using a t-test (p < 0.05) between the responses to stimuli presented to the left and the right eye. An ocular dominance index was computed where μ left and μ right denote the response value to stimuli presented to the left and right eye respectively. This index ranges between −1 (right preference) and 1 (left preference). To compute correlation coeffi cients between MU and LFP ocular dominance indices we used Spearman's ρ, a rank correlation measure appropriate for bounded data.

ORIENTATION TUNING: ELECTROPHYSIOLOGICAL SIGNALS
We recorded from 196 V1 recording sites from two monkeys (A and B) using chronically implanted tetrode arrays. From each site, we recorded local fi eld potentials (LFP) and multi-unit activity (MU, Figure 1). Orientation tuning functions were mapped using sinusoidal gratings. Figure 1A and B show exemplar local fi eld potential traces of a single recording site during stimulation with two gratings of orthogonal directions. During the stimulus period a dominant high-frequency oscillation can be observed. Visually, fast oscillations during the sustained period increase noticeably from A to B, while the signal shape during the evoked response period (ERP) does not change. Figure 1C and D show the multi-unit activity recorded simultaneously with the LFP from A and B, respectively. In contrast to the fast oscillations in the LFP, the MU fi ring rate is higher in C than in D. This indicates that oscillations in the local-fi eld potential are not always tightly coupled to the activity of local populations of neurons. In the remainder of the paper, we investigate the link between the LFP and spiking activity in local cortical circuits in more detail.
First, we computed the LFP power spectra separately for the baseline period (-300 ms to stimulus onset) and the stimulus period (200-500 ms after stimulus onset, excluding the ERP transient). Figure 2A and B show the power spectra of a recording site representative of our sample where visual stimulation induces a broad band increase in the LFP as compared to baseline (dashed line) located in a band centered around 55 Hz. Interestingly, the power increase is stronger for some stimulus orientations than for others: In the example, a grating at 22° led to a stronger power increase than one at 90° (dark grey and light grey line, respectively). At most recording sites (88%), visual stimulation induced at least a twofold increase of LFP power in the gamma band (40-70 Hz) of the frequency spectrum ( Figure 2C, dataset A2, all sites). While the precise position of the peak in the relative spectra was dependent on the type of stimulation and the monkey (median frequency of maximal increase: A1 66.1, A2 54.4, and B1 60.3 Hz), the increase of gamma-band power was prominent in all three datasets ( Figure 2D).

ORIENTATION TUNING OF THE LFP
We investigated the stimulus dependent modulation of the LFP gamma-band power quantitatively by computing an orientation tuning index for the power in different narrow frequency bands. This tuning index describes the strength of tuning as a function of the discriminability between the stimulus orientation evoking the strongest response and the response to the orthogonal condition (for details see Materials and Methods). To further control for spuriously high estimates of tuning strength induced by a large variability in the data, we also computed this tuning index on condition shuffl ed data (for details see Materials and Methods). We observe that tuning strength is signifi cantly increased from 40 up to 70 Hz with a maximum at 55 Hz for dataset A2 (Figure 3A). This effect was similar in all three datasets ( Figure 3D, A1 30-45 Hz, B1 58-75 Hz).
Therefore, as previously shown, the increase in power of the gamma-band is tuned to the orientation of the stimulus . This was the case in a large percentage of recording sites across all datasets ( Figure 3B, A1 99%, A2 87%, B1 67%). The power at frequencies over 100 Hz is also signifi cantly tuned, but not as strong as the gamma power ( Figure 3C and E, Sign test, p = 3.8 × 10 −8 ). Interestingly, in contrast to other studies in inferior temporal cortex (Kreiman et al., 2006), we did not observe a strong stimulus dependence of the evoked response power ( Figure 3F). The power of the ERP signal (see Materials and Methods) is signifi cantly less tuned than the power in the gamma-band (Sign test, p = 2.1 × 10 −10 ).

COMPARISON OF ORIENTATION TUNING OF LFP AND MU
To obtain a deeper insight into the relationship between the gamma band activity of the LFP signal and the underlying neural activity, we also computed the tuning index for all MU sites and compared it to the corresponding LFP sites (Figure 4). Although we used the most strongly tuned LFP band for each site (see above), the MU is on average signifi cantly more tuned than the LFP in this frequency band (Sign test, p = 3.1 × 10 −11 ) with a mean tuning strength (d′) of 2.46 ± 0.15 for MU and 1.01 ± 0.05 for the LFP (mean ± SEM, data pooled from all three datasets).
We also compared the preferred orientation of the LFP tuning function with that of the MU tuning function (Figure 5). We fi nd that the preferred orientations of signifi cantly tuned MU and LFP sites are not signifi cantly correlated (circular correlation coeffi cient for dataset A1 0.19, p = 0.12; A2 -0.07, p = 0.57; B1 0.39, p = 0.12) or at best only weakly correlated (circular correlation coeffi cient 0.21, p = 0.0094, dataset A1 and A2 pooled together). In Figure 6 we show two examples of orientation tuning functions. While at site A the tuning curves of MU activity and LFP gamma band are tightly correlated, the preferred directions of both signals at site B are separated by 90°. The two sites shown in A and B are representative of our sample of sites: While there is a considerable number of sites where MU activity and LFP have similar preferred orientations (within 20°), there are also many sites, at which the preferred orientations of the two signals are separated by over 60° (Figure 6C). The mean distance between the preferred orientations of MU and LFP was 34.1°. It is possible that the two groups of sites represent different recording locations on the orientation map: Due to signal integration properties, the preferred orientations might be better correlated at sites in linear zones than at sites near pinwheel centers (see Discussion). To test this hypothesis, we compared the LFP tuning strength as measured with d′ of sites with well matching preferred orientations (Δθ < 20°, n = 63) to sites with very different preferred orientations (Δθ > 60°, n = 35). Indeed, we fi nd the LFP gamma-band at sites where LFP and MU had closely matching preferred orientations to be significantly more tuned than sites where MU and LFP had very different preferred orientations (Figure 6D, Wilcoxon rank sum Comparison of the tuning index of the gamma-band (x-axis) with tuning index at frequencies over 100 Hz. The cross indicates the mean. Note that it lies well below the main diagonal. Therefore the gamma-band is on average more tuned than the frequencies over 100 Hz. (F) Comparison of the tuning index of the gamma-band (x-axis) with tuning index of the event-related potential. The cross indicates the mean. Note that it lies well below the main diagonal. Therefore the gamma-band is on average more tuned than the event-related potential.
The apparent lack of strong correlation could be due to the fact that the MU signal is dominated by interneurons with high mean fi ring rates and orientation preference differing from the local pyramidal neurons, that contribute little to the LFP power, as their absolute number is low (Beaulieu and Colonnier, 1983). Therefore, we studied the relationship between the preferred orientations of the LFP with that of well-isolated and signifi cantly tuned single neurons (SU), recorded from the same tetrode. It is likely that a large fraction (∼75-90%) of these are pyramidal neurons contributing to the MU (Bartho et al., 2004;Constantinidis and Goldman-Rakic, 2002). We fi nd that the preferred orientation of the LFP and the SU activity are not signifi cantly correlated as well (Figure 6E, circular correlation coeffi cient -0.07, p = 0.26). This provides strong evidence that the preferred orientation of the LFP gamma band indeed does not refl ect well the tuning properties of localized populations of neurons.

OCULAR DOMINANCE
In addition, we recorded from 409 sites from two monkeys (A and C) using chronically implanted and non-chronic tetrodes and mapped ocular dominance using static sinusoidal gratings, presented on each eye separately. As before, we recorded LFP and MU.
For each site, we computed an ocular dominance index (ODI), ranging between -1 for preferred right eye and +1 for preferred left eye (for details, see Materials and Methods). 56.7% of all MU sites had a signifi cant ocular dominance tuning (t-test, p < 0.05; Monkey A: 54.7%; Monkey B: 58.6%), 53.9% of which where preferably excited by stimulation to the left eye. The signifi cantly tuned sites had a mean absolute ODI of 0.22. For the LFP analysis we chose again a frequency band where ocular dominance was strongest. In both monkeys, this was in the lower gamma-band between 35 and 45 Hz, somewhat lower than the bands chosen for analysis in the orientation experiments. Here, 50.8% of all LFP recording sites had signifi cant ocular dominance (Monkey A: 55.3%; Monkey B: 46.7%), with 52.4% of which being preferably excited by the left eye. LFP sites had a mean absolute ODI of 0.13 in the most strongly modulated frequency band around 40 Hz. Therefore, the MU activity shows signifi cantly stronger ocular dominance tuning than the LFP (Sign test, p = 6.5 × 10 −25 ).
We compared the ODI of MU activity and LFP recorded from the same site for all sites, which showed signifi cant ocular dominance in both signals (Figure 8A, 35.7% of all sites). We fi nd a signifi cant correlation in both monkeys (All sites: Spearman's ρ = 0.61, p < 10 −20 ; Monkey A: ρ = 0.51, p = 5 × 10 −6 ; Monkey C, ρ = 0.65, p = 2.4 × 10 −9 ). Furthermore, if a site showed signifi cant ocular dominance for MU, it also exhibited signifi cant ocular modulation for the LFP in 62.1% of the cases. When MU activity did not show signifi cant ocular dominance, only 37.3% of the sites had signifi cant ocularity tuning for the LFP. Therefore, the LFP gamma-band signal was signifi cantly more likely to be tuned when the MU was (p = 1.2 × 10 −6 , Fisher exact test, right-tailed). We also analyzed how the correlation between LFP and MU ODIs  test, p = 0.0282). The mean tuning strength was 1.20 and 0.81 in the two groups, respectively. Interestingly, we observe that all preferred orientations of the LFP cluster around one value, −40.1° for monkey A and 3.8° for monkey B (Figure 5, lower panels, see Discussion). In contrast, the MU preferred orientations are uniformly distributed over the whole range of orientations ( Figure 5, left panels).  Figure 5, because not so many LFP sites are tuned in these frequency bands.
changes in higher frequency bands ( Figure 8B). We observe an increase of the correlation to values up to 0.7 in frequency bands ranging to 70 Hz. After that, the correlation remains constant for the entire range of analyzed frequency bands.

THE SPATIAL SCALE OF THE LOCAL FIELD POTENTIAL
In the present study we fi nd that in a large proportion of our recording sites the gamma-power of the LFP does not refl ect well the orientation tuning properties of local multi-unit activity. While the gamma-power of the LFP is in general less tuned than the MU, at sites where LFP and MU had similar orientation preferences the gamma-power of the LFP tends to be more strongly tuned than at other sites, where the two signals had strongly differing preferred orientations. Also, we observe a strong correlation between the LFP power in the gamma-band and the MU activity on the scale of ocular dominance columns (450 μm).
In addition, the correlation between LFP power and MU activity increases with frequency saturating around 40 Hz for ocular dominance and 120 Hz for orientation tuning. At least part of the increased correlation at high frequencies may refl ect contamination from low-frequency components of individual spikes. These results suggest that the gamma-band activity is generated by ensembles of neurons that are larger than local populations measured as multi-unit activity. More likely it resembles the activity of neurons from an area spanning several hundred micrometers, as indicated by the ocular dominance correlation between MU activity and LFP (Figure 8A). These conclusions are compatible with at least two hypotheses regarding the underlying mechanism generating the LFP: a. Based on modeling studies, it is possible that the brain acts like a capacitive fi lter and therefore lower frequencies are attenuated less than higher frequencies (Bedard et al., 2004). Assuming a fl at local LFP spectrum, in this case, one would expect an inverse relationship between the spatial scale of organization of the stimulus property under study and frequency bands tuned to it. A stimulus property represented at fi ne spatial scale like orientation tuning in V1 is refl ected only in higher frequency bands of the LFP signal, because the generating signals must be strongly attenuated to produce a measurement with high enough spatial resolution. In converse, when a stimulus property is organized on a much larger scale like ocular dominance columns, the attenuation at medium frequencies might suffi ce to capture the properties of local populations of neurons. However, there is direct experimental evidence against the capacitive fi ltering model. Studies in the rabbit cortex (Ranck, 1963) showing that the impedance spectrum of the cortex is rather fl at have recently been confi rmed by detailed measurements in monkey cortex . b. An alternative parsimonious explanation for our fi ndings which does not depend on the capacitive fi ltering model is the following: Oscillations in the local fi eld potential are generated by neural populations of distinct size and power acting as potential generators at different frequencies . Small, weak generators might oscillate at high frequencies, like small local groups of neurons, and strong, larger generators at low frequencies, possibly refl ecting coherent subcortical input Steriade, 2006). Locally, this would lead to a power spectrum with roughly exponential decay. If attenuation takes place independently of frequency Ranck, 1963), frequencies with more power generated by stronger neural generators will propagate farther through the tissue. This leads to higher correlations between LFP power and MU activity at higher frequencies, as these have less power and are therefore more local.
Under visual stimulation, the maximal power increase can be found in the gamma-range, as we and others have reported . Under the above model, oscillators of this particular frequency become stronger under visual stimulation, possibly refl ecting the coherent activity of local populations of neurons. Indeed, the gamma band of the LFP has been interpreted as the "working regime" of cortical neurons: the activity of neurons is temporally structured by a sub-threshold oscillatory process indicated by coherence between spike trains and the LFP at this frequency band (Siegel and Konig, 2003). As ). The black line shows the least square fi t to the data of both monkeys. LFPs are generally less tuned to ocularity than MU activity. Grey dots represent data from monkey A, black dots from monkey C. (B) Correlation of the ODI between MU activity and LFP as a function of frequency. The correlation increases to a maximal level of about 0.6, saturating for frequencies greater than 60 Hz. Also compare to Figure 7A. The different spatial scales seem to be refl ected in the saturation point as well. Comparing LFP and MU activity in V1 the power of the signal in this band is increased under visual stimulation, however, it spreads further and gets averaged over a wider area of cortical tissue.
Note that averaging over a larger area does not necessarily lead to no tuning at all: It has been shown that even 3 × 3 × 3 mm voxels in fMRI data can be used to decode orientation from human primary visual cortex (Haynes and Rees, 2005). This explains naturally why the preferred orientations of all our sites scatter around a single value per monkey ( Figure 5) and LFP tuning is weaker than MU tuning (Figure 4): As we record from a chronically implanted tetrode array with closely spaced tetrodes (maximal distance: ∼750-1000 μm) and the LFP integrates over a relatively large area of cortical tissue, this local average is seemingly insensitive to the tetrode location and is blurred compared to the MU (Figure 4).
At frequencies higher than the gamma-band, we observe a stronger correlation between preferred orientations of LFP and MU for tuned sites in contrast to the weak correlation between the preferred orientation of the gamma band of the LFP and MU. However, compared to the gamma-band we fi nd only a minority of the LFP sites to be tuned to the stimulus at these higher frequencies (compare Figure 3B and C). Under our second hypothesis, it is likely due to the fact that high-frequency generators are smaller and have less power, thereby creating a weaker, but more localized signal. As mentioned before, given that action potentials have power around this higher frequency range, it could also be the case that these high correlations result from low-frequency components of individual spikes leaking into the LFP measurement.
In contrast, ocular dominance properties of MU recordings are refl ected well in the gamma-band of the LFP, because neural populations generating a coherently oscillating dipole in response to the stimulation of one eye are large enough (i.e. about the size of ocular dominance columns of ∼450 μm) to be faithfully picked up using the LFP.

RECORDING LOCATION IN THE ORIENTATION MAP
Naturally, the exact position of the recording electrode within the orientation map has an important impact on the strength of the correlation between MU and LFP preferred orientations. For instance in the middle of a linear zone that can stretch out for several hundred micrometers, the two are likely to be well correlated, as the main signal generators for both signals all have the same preferred orientation, despite the fact that MU activity originates from ∼65-100 μm around the electrode tip (Gray et al., 1995) and LFP gamma-band under the above model from several hundred micrometers. This is different, however, close to a singularity or pinwheel. Although orientation preferences of single neurons are arranged in a highly ordered manner (Ohki et al., 2006), only the MU activity will refl ect the local processing structure well. The LFP power is in this case strongly modulated by groups of neurons with widely varying orientation preferences due to the pinwheel structure and possibly dominated by neurons with a completely different preferred orientation than the MU activity at the tetrode tip. Therefore, it should be less tuned than LFP signals in linear zones. In agreement with this line of thought, we fi nd that a group of sites with a small difference in orientation preference between LFP and MU has on average a more strongly tuned LFP gamma-band signal, than sites where orientation preferences differ a lot (Figure 6). It is tempting to speculate that this result indeed refl ects the recording location in the orientation map. Interestingly, a recent study has found that even single units in parts of the orientation map where many different orientations are represented are less tuned than in linear zones (Nauhaus et al., 2008), lending further support to this interpretation. We plan to investigate this further by combining tetrode recordings with optical imaging in the awake macaque.

RELATIONSHIP TO OTHER CORTICAL AREAS AND FUNCTIONAL PROPERTIES
In a recent study, the authors compared the speed and direction tuning properties of MU activity and LFP in area MT (Liu and Newsome, 2006). Comparable to our results from the ocular dominance analysis, they also fi nd a correlation on the scale of speed tuning [300-600 μm; (Liu and Newsome, 2003)]. In addition, they report a near perfect correlation between the two signals when looking at direction of motion tuning curves. Direction of motion is believed to be represented in MT on a similar spatial scale as orientation tuning in V1 (Albright et al., 1984). The major difference between our and their study is that we used a grating stimulus that was large compared to the typical receptive fi eld size in V1 and covered several degrees of the visual fi eld. On the contrary, Liu and Newsome optimized their stimulus size for maximal MU response Newsome, 2003, 2006). It has been shown that unlike the MU response the LFP response monotonically increases when a grating stimulus is enlarged (Gieselmann and Thiele, 2007), even beyond a point where MU activity decreases again because of possible centersurround effects. This naturally could explain the apparent difference: While in our study large neuronal ensembles with differing orientation tuning get simultaneously activated although the stimulus orientation might not be optimal for all of them, Liu and Newsome record more localized signals from groups of neurons around their electrode since these are the only ones excited. Thus, to assess the feature selectivity of the LFP and the related issue of its spatial resolution large stimuli relative to the receptive fi eld size are better suited than small stimuli. Furthermore, our fi ndings are in good agreement with a recent study in auditory cortex  which also fi nds a weak correlation between MU and LFP preferred frequencies in the gamma-range rising to a strong correlation at 80 Hz and higher.

THE ROLE OF SYNAPTIC INPUT AND INTERNEURONS
It is also conceivable that we fi nd differences in orientation preferences of the gamma-band LFP and the MU activity because the LFP does not measure spiking output but rather synaptic input to a local group of neurons. Therefore our results might not refl ect differences in spatial integration properties between the two signals but rather a difference in the orientation tuning of synaptic inputs and cortical outputs. In the macaque, however, orientation tuning is thought to be generated within V1 circuits in layer 4C, whereas the thalamic input is largely untuned (Hubel and Wiesel, 1968;Lund et al., 2003). While untuned synaptic input from the thalamus might contribute to the diminished tuning strength of the LFP signal compared to the MU activity (Figure 4), it is unlikely to be the source of the discrepancy in the preferred orientations of the two signals. As in addition to postsynaptic potentials, the local fi eld potential likely also measures several nonsynaptic events like spike afterpotentials or intrinsic neural currents across membranes (Buzsaki, 2002;Logothetis and Wandell, 2004;Logothetis et al., 2007) the feature tuning observed in the spiking responses should also be refl ected in the tuning of the LFP. It cannot be excluded, however, that synaptic input from lateral connections or feedback projections from other cortical areas that is tuned differently than the local spiking activity contributes to the observed difference in orientation tuning. Moreover, populations of inhibitory interneurons might dominate the increase in gamma power (Henrie and Shapley, 2005), as inhibitory postsynaptic currents have been shown to exhibit stronger gamma modulation and larger synchrony between neighboring cells than excitatory currents (Hasenstaub et al., 2005). Therefore, it is possible that differences between LFP and MU orientation tuning could refl ect differences between the tuning of interneurons and pyramidal neurons.

LFP FOR CORTICAL MOTOR PROSTHESES
Recently the use of LFP signals for the decoding of movement directions has become popular (Andersen et al., 2004;Rickert et al., 2005) for it is comparably easy to obtain and can be used without need for complex post-processing like single-unit isolation. One study shows the LFP to be superior to the MU activity for decoding movement direction (Mehring et al., 2003). Our fi ndings have important implications of the use of LFP signals for prosthetic devices. Given that our data show that the LFP refl ects activity from an area of probably at least the size of ocular dominance columns in V1 (∼450 μm), certainly larger than fi ne spatial representation of orientation tuning (∼50 μm), the LFP does not seem to be a good choice for decoding parameters which are spatially organized at a smaller scale if other signals with a better signal to noise ratio are available. In other words, the LFP is better suited to be used in the regions of the brain where the spatial organization is at least at order of hundreds of microns. In practical applications this result has to be carefully weighted against other factors like implant lifetime as well as MU activity and single unit isolation quality and stability. Nevertheless, recent advances in chronic multi-tetrode recordings in non-human primates with the capability to record from the same neurons across many days and weeks (Tolias et al., 2007) combined with online single unit isolation and sophisticated machine learning algorithms (Eichhorn et al., 2004;Shpigelmann et al., 2005) may help improve the quality of cortical motor prostheses.

CONCLUSION
While the intricate relationship between the LFP signal, spikes, and synaptic events in single neurons is not yet fully understood, the gamma-band activity as measured with extracellular tetrodes seems to be generated by ensembles of neurons larger than 50-100 μm, as the spatial organization of V1 suggests. It resembles the activity of neurons from an area spanning a few hundred micrometers of cortical tissue. Exploiting the organization of physiological properties in primary visual cortex we have been able to provide evidence for a lower bound on the spatial resolution of the local fi eld potential. These results cast some doubt on the prevalent interpretation of coherence between close-by LFP sites as a sign of local synchrony, but rather suggest that part of these fi ndings may be attributed to the poor spatial resolution of the LFP as a measuring tool. We suggest that more care is needed in the interpretation of fi ndings based on the LFP and argue for an increased effort to the study of well-isolated neurons.