Abstract
Field potentials (FPs) reflect neuronal activities in the brain, and often exhibit traveling peaks across recording sites. While traveling FPs are interpreted as propagation of neuronal activity, not all studies directly reveal such propagating patterns of neuronal activation. Neuronal activity is associated with transmembrane currents that form dipoles and produce negative and positive fields. Thereby, FP components reverse polarity between those fields and have minimal amplitudes at the center of dipoles. Although their amplitudes could be smaller, FPs are never flat even around these reversals. What occurs around the reversal has not been addressed explicitly, although those are rationally in the middle of active neurons. We show that sensory FPs around the reversal appeared with peaks traveling across cortical laminae in macaque sensory cortices. Interestingly, analyses of current source density did not depict traveling patterns but lamina-delimited current sinks and sources. We simulated FPs produced by volume conduction of a simplified 2 dipoles' model mimicking sensory cortical laminar current source density components. While FPs generated by single dipoles followed the temporal patterns of the dipole moments without traveling peaks, FPs generated by concurrently active dipole moments appeared with traveling components in the vicinity of dipoles by superimposition of individually non-traveling FPs generated by single dipoles. These results indicate that not all traveling FP are generated by traveling neuronal activity, and that recording positions need to be taken into account to describe FP peak components around active neuronal populations.
SIGNIFICANCE STATEMENT Field potentials (FPs) generated by neuronal activity in the brain occur with fields of opposite polarity. Likewise, in the cerebral cortices, they have mirror-imaged waveforms in upper and lower layers. We show that FPs appear like traveling across the cortical layers. Interestingly, the traveling FPs occur without traveling components of current source density, which represents transmembrane currents associated with neuronal activity. These seemingly odd findings are explained using current source density models of multiple dipoles. Concurrently active, non-traveling dipoles produce FPs as mixtures of FPs produced by individual dipoles, and result in traveling FP waveforms as the mixing ratio depends on the distances from those dipoles. The results suggest that not all traveling FP components are associated with propagating neuronal activity.
Introduction
Neuroelectric signals, such as EEG, electrocorticography (ECoG), and field potentials (FPs), and their decomposed components, such as peaks and frequency bands at multiple locations, often exhibit organized patterns (Freeman and Barrie, 2000; Sirota et al., 2008; Maier et al., 2010; Bastos et al., 2018; Rogers et al., 2019). Those patterns may contain information useful for decoding (Ince et al., 2010). One such pattern is spatially gradual progression of signal components, peaks or oscillations, that change systematically with positions and appear as traveling waves (Massimini et al., 2004; Takahashi et al., 2011; Sato et al., 2012). Since FPs reflect neuronal populations' activity, those waves are considered to reflect propagation of neuronal activity (Lubenov and Siapas, 2009; Muller et al., 2018). However, not all studies that addressed traveling patterns revealed the presence of neuronal activities that also propagate along with the wave (e.g., Rubino et al., 2006; Zhang and Jacob, 2015; Townsend et al., 2017).
FPs in the brain are generated by neuronal transmembrane electrical currents composed of active currents that drive the membrane potential and passive return currents (Buzsáki et al., 2012; Einevoll et al., 2013). In extracellular space, those currents appear as sink and source components of current source density (CSD). Those CSD components of a neuronal population approximate dipoles because of the spatially organized architecture of neurons and synapses, such as layer-specific termination of afferents (Einevoll et al., 2013; Mitzdorf, 1985). Therefore, as it is also apparent at scalp as well (Joyce and Rossion, 2005), FPs surrounding each neuronal population have fields of opposite signs. Sources of scalp signals are also approximated by equivalent dipoles or distributed sources (i.e., single layer of distributed dipoles) in the brain (He et al., 2018).
Since electrical potential is neutral at the center of a dipole, one might conjecture that the FP waveform at a dipole's center is flat. On the contrary, FPs in a living brain never cease fluctuations. For example, laminar recordings often exhibit signals that fluctuate differently between upper and lower cortical layers (Lakatos et al., 2005; Maier et al., 2010). However, FPs are never flat at any laminar positions. In event-related FPs, baselines are flattened by averaging out non–event-related activities. Even in these latter instances, laminar FPs to events remain nonflat after averaging, even at the regions of the polarity reversal (Fishman and Steinschneider, 2010; Lipton et al., 2010; Welle and Contreras, 2016; Kajikawa et al., 2017; Francis et al., 2018). No single study explicitly described the waveforms of FP in such transition zones and addressed how they relate to neuronal activity.
In our current study examining macaque auditory and visual cortices, sensory FP components changed their peak latencies gradually across cortical laminae spanning a polarity reversal. The pattern was compatible with neither FPs generated by a single dipole nor far-field, since peak latency of FP components does not change in both cases. Gradual changes of peak latency rendered those components an appearance of traveling across cortical laminae (i.e., negative peak started ascending from deep to upper layers). CSD analyses were performed to describe underlying neuronal activity. Multiple laminar CSD components had peak latencies different from those of FP components and occurred without spatial translation, which led to these CSD components not appearing as traveling waves. However, forward derivation of FP from such CSD reproduced smoothly traveling components. These results suggested that traveling patterns of FP were produced by volume conduction of non-traveling neuronal activity. Volume conduction of 2 dipoles' models demonstrated that temporal overlaps of dipole moments with different peak latencies resulted in traveling FP components between those dipoles where gradual polarity reversal took place. Complications related to the characterizations of FP components (peak latency and phase of frequency band activity) are discussed.
Materials and Methods
Animals
Data from auditory and visual cortices were collected from 6 (2 male, 4 female) macaque monkeys (Macaca mulatta) and 2 female monkeys, respectively. Auditory cortex data from 5 of the animals and visual cortex data were used also in previous studies (Kajikawa and Schroeder, 2011, 2015; Zoefel et al., 2017; Barczak et al., 2019). All animals were accustomed to experimenters' handling. Four animals were also trained to perform behavioral tasks (Kajikawa et al., 2017; Barczak et al., 2019; Orczyk et al., 2021). Animals were implanted with headposts and one or two recording chambers using aseptic surgery techniques. Chambers were positioned to target the primary auditory cortex (A1) that lies in the lower bank of the lateral sulcus, or foveal regions of primary visual cortex (V1) in the occipital cortex, and to allow for electrodes to penetrate those cortices perpendicularly. All experimental procedures were approved by the Institutional Animal Care and Use Committee of Nathan Kline Institute.
Recordings
All recordings were done in awake monkeys, sitting in a custom-fitted chair (Crist) while either listening to sounds or looking at a computer monitor. Electrical signals, referenced against an electrode in the recording chamber, were recorded using 23 channels linear array micro-electrodes (0.3-0.5 mΩ at 1.0 kHz) with 100 µm spacing and amplified (×10 at pre-amplifier, followed by ×500), and saved using custom software (LabVIEW, National Instruments). Signals from all channels were split into field potentials (FP, 0.1-500 Hz) and multiunit activity (MUA, 0.5-5 kHz, further bandpass filtering 500-3000 Hz and rectifying). Both FP and MUA were sampled at 2 kHz. CSD was calculated as an approximated second-order spatial derivative of FP (Mitzdorf, 1985), using FP signals recorded from three adjacent electrode contacts. The resultant CSD consists of 21 channels.
As electrodes were advanced through a grid hole placed in the recording chamber, sensory stimuli (broadband noise sounds for auditory cortex and diffuse flashes of light for visual cortex) were delivered. Since sensory cortical FP have polarity inversions of all peak components within responsive sensory cortices, electrodes were positioned included inversions of all those components.
Stimuli
After electrodes were placed in the target cortices, the following test stimuli were delivered: Auditory stimuli consisted of 14 pure tones (356 Hz to 32 kHz, 0.5 octave intervals) at 60 dB SPL (duration: 100 ms, SOA: 625 ms) delivered in random order bilaterally through two individually calibrated free field speakers placed 4 inches away from both ears, using TDT System 3 controlled by a custom-written program (MATLAB, The MathWorks). Visual stimuli consisted of red strobe flashes of diffuse light generated by a Grass PS33 Plus Photic Stimulator (Grass-Telefactor) and illuminated onto a light diffuser ∼86 cm in front of the animal. Red light was produced by adding a filter onto the diffuser. Flashes occurred 2 times per second and were 10 ms in duration.
Analyses
All analyses were done in MATLAB. Spatiotemporal profiles of sensory responses were derived by averaging. For auditory data, responses were averaged separately for 14 tones, and the best frequency (BF) tone was defined as the tone that evoked the largest mean MUA amplitude 10-100 ms from the sound onset in granular layers (Kajikawa and Schroeder, 2011). For visual data, responses to red flashes were averaged. Mean FP responses at all channels were low pass filtered (2 poles Butterworth, 256 Hz for auditory, 200 Hz for visual), and baseline-subtracted. The baseline was defined as the mean prestimulus amplitude (−50 to 0 ms from the onset of stimuli). The FP response at the most superficial channel (channel 1) was used to identify temporal peaks. In auditory FP, the first positive peak (P1) was identified as the largest positive peak in a time window ranging from 10 to 50 ms. A negative peak following P1 that occurred withing a time window ranging from 20 to 70 ms was identified as N1. In visual FP, P1 was not apparent. Thus, only N1 was identified within the time window ranging from 15 to 95 ms. Once peak components were identified, the latency (from stimulus onset) and the magnitude of the peaks were estimated.
At channels 2-23, negative peak components were identified as the negative peak whose latency was closest to the negative peak latency at one channel above recursively. Positive peak components in auditory FP were identified in the same manner. However, positive components before the first negative peak generally diminished with depth, while other positive components after the negative peak grew larger at deeper channels (see Fig. 1). Thus, positive peak components were identified at later timings at deeper channels, characterized by either the disappearance of early positive components or that the later positive peak components became larger than earlier ones.
Peak components in CSD responses were identified differently because there were often no apparent peak components corresponding to those of FP responses or occurring at latencies similar to FP components (see Fig. 2). Since CSD inherently has a lower signal-to-noise ratio, CSD at all channels were low pass filtered at 64 Hz to eliminate peaks of small noise extensively. Large spectrotemporal components in those CSD responses are <64 Hz (Kajikawa and Schroeder, 2015); thus, the influence of this filtering on major peaks of the waveforms is small. In the resultant signals, all positive and negative peaks within a wider time window (0-150 ms) were identified. Peaks that had the same polarity as the negative and positive peak components of FP at the same channels with peak latencies closest to the FP components were identified regardless of their magnitudes. The procedure to identify CSD peak components described here was to find the CSD peaks whose latencies were close to those of FP peak components if such CSD peaks existed at every channel.
Volume-conducted auditory FP
The volume conductor model was applied to CSD as described in detail previously (Kajikawa and Schroeder, 2015). CSD responses were bandpass filtered between 1.5 and 256 Hz (2 poles, Butterworth filter). The spatiotemporal profile of CSD from 0 to 150 ms after the onset of stimuli was used to derive the volume-conducted FP (vcFP) using the following expression:
Indices k and j denote channels of FP and CSD, respectively. Variables dk and dj are the depth of FP and CSD channels. It may be noted that the expression is a form of a spatial convolution lowpass filter operated at every moment. The multiplication factor A reflects tissue resistivity, which was assumed to be uniform (Mitzdorf and Singer, 1980), and thereby does not contribute to the spatiotemporal profile of vcFP.
The parameter h is the sole parameter that may influence the spatiotemporal profile of vcFP for a given CSD profile. It represents the distance of horizontal displacement of the CSD sinks/sources from the array electrode under an assumption that all CSD components were parallel to and equidistant from the array (Kajikawa and Schroeder, 2015). Such distance could be variable across recording sites. The value was determined to maximize the similarity score, as follows:
Model CSD of 2 dipoles
To test the effect of temporal overlap and magnitude differences of CSD components on the temporal patterns of vcFP, model CSD consisting of 2 dipoles were used. To simplify calculations, dipole moments were aligned along linearly arranged 23 positions mimicking the channel configuration of electrodes used in recordings, and poles were placed at 9th and 10th channels for one dipole and 14th and 15th channels for the other conventionally. vcFP along the orientations of dipoles was calculated. Color plots of laminar profiles in Figures 4 and 5 were added with additional 5 channels above and below the 23 channels. Those dipoles had activation dynamics defined as follows:
While the onset of the fast dipole was fixed at 0 ms, the onset of slow dipole, t0, was modified systematically to alter the periods of temporal overlaps in activity between the 2 dipoles of equal amplitudes (Aearly = Alate; see Fig. 4). Separately, a fixed t0 value was used while systematically modifying the ratio of Aearly and Alate to alter the relative magnitudes of those dipoles (see Fig. 5). In both cases, the 2 dipoles had the same distance between poles. Those dipoles were displaced radially from each other, similarly to distinct sink/source pairs appearing along linear array electrodes. The distance between the centers of dipoles was 4 times the distance between poles to zoom in on the changes that occur in vcFP between dipoles. Once CSD was modeled, the same expression applied to physiological CSD data (Eq. 1) with a horizontal displacement factor of 4 times the pole distance to derive vcFP.
Statistics
Mean and CIs (95% by bootstrap 1000 resampling) of peak latency were derived at each depth. Spearman's rank correlation coefficient was estimated, and the significance of the correlation was determined by the permutation test. Unless noted, mean and SD are reported.
Results
FP components traveling across auditory cortical lamina
The laminar profile of FP to BF tones at an exemplar auditory cortex site is shown in Figure 1A. Superficial FP at channel 1 (top) had P1 and N1 components whose peak latencies were 26 and 49 ms, respectively. FP at channel 23 (bottom) had peak components of opposite signs with latencies close to those of the superficial P1 and N1 components at 26.5 and 53.5 ms. Thus, waveforms of FPs at channel 1 and channel 23 had peak components of opposite polarities at nearly same timing, and the reversal of polarity occurred in between. However, it occurred gradually with concomitant changes in peak latencies and did not suggest the presence of flat FP at any depth. The gradual changes were incompatible with mere fluctuation of a single dipole or superimposition of far-fields, since both cases would result in FP components of spatially constant peak latencies.
Laminar profiles of auditory FP responses. A, FP responses to 100 ms BF tone at an exemplar penetration site in primary auditory cortex. Top to bottom traces represent superficial to deep channels (1-23). Magenta and cyan dots label positive and negative peak components, respectively, that occurred during sounds at all channels. Vertical dotted line indicates the timing of P1 latency at channel 1. B, Laminar distributions of the peak latency of positive (magenta) and negative (cyan) FP components. Gray line (axis on top) indicates the laminar distribution of current sink peaks in granular layer plotted against the aligned depth. C, Laminar distributions of the normalized peak amplitude of positive (magenta) and negative (cyan) FP components. B, C, Mean (n = 95) and 95% simultaneous confidence bands are plotted against depth.
Negative peaks, labeled with cyan dots in Figure 1A, started in several deep recording channels at once with peak latencies nearly the same as that of P1 at channel 1 (Fig. 1A, vertical dotted line). Then, the negative peaks started moving upward from those deep channels until their latencies matched to that of superficial N1 at channel 1 in upper recording channels. Thus, the negative peaks appear as if they have traveled across middle channels of several hundred micrometers as a single unidirectional wave. Since negativity of FP is often associated with neuronal depolarization, this traveling may be interpreted as the excitation starting in deep layers propagated to upper layers. Positive peaks, labeled with magenta dots in Figure 1A, also changed peak latencies, preceding slightly that of superficial P1 toward middle channels, while their amplitudes diminished concurrently. At deep channels, distinct positive peaks later than negative peaks became larger.
The latency and amplitude of peak components were tracked in the same manner in responses from 106 penetration sites. Across those sites, the peak latency of superficial P1 and N1 components was 25.8 ms (SD: 4.0 ms) and 49.9 ms (SD: 7.6 ms), respectively. The negative and positive peaks at channel 23 mirrored the pattern of superficial P1 and N1 components with latencies of. 25.2 ms (SD: 3.2 ms) and 51.2 ms (SD: 6.1 ms), respectively. Peak latencies of those four components (P1 and N1 at channel 1, and negative and positive peaks at channel 23) differed significantly (one-way ANOVA, F(3,420) = 723, p = 1.4 × 10−164), while they did not differ within pairs of channel 1 and channel 23 peaks of opposite polarities (Tukey's HSD, p > 0.05). However, a small precedence of negative peaks at channel 23 from P1 at channel 1, −0.55 ms (CI: [−1.02 −0.095]), and a small delay of positive peak at channel 23 from N1 at channel 1, 1.29 ms (CI: [0.091 1.01]), were present. Negative peaks first appeared in deep channels as the counter peak of P1 at all sites. In majority of sites (n = 95), the negative peaks traveled upward gradually without interruptions. In 11 sites, FPs around the reversal were dominated by slow positive peaks with no appearance of negative peaks and were excluded from further analyses.
At each site, the depth where the temporal order of the positive and negative peak components changed was identified as the depth of polarity change and used to align the depths between different penetration sites. Figure 1B plots the peak latency against the aligned depth, depicting that gradual traveling of the negative peak latency occurred systematically. Traveling velocity at the depth where peak latency changed most, in the middle of polarity reversal, had a skewed distribution with a median 0.0087 m/s and a quartile ranging from 0.0061 to 0.0154 m/s. Figure 1C plots the peak amplitude against the aligned depth, revealing that both positive and negative peak components became smaller around the reversal. However, negative peaks did not abolish completely during their translations but kept traveling.
The gray line in Figure 1B shows the positions of the strongest current sink in granular layers plotted against the aligned depth. Consistent with the polarity reversal of P1 and N1 in supragranular layers (Kajikawa and Schroeder, 2011), granular layer sinks located below the depth of reversal by 682.8 mm (SD: 227.3 mm). The large variability of the granular sink location is because of variable laminar patterns of polarity reversals and CSD profiles across sites.
No CSD components traveling across auditory cortical lamina
Negative FP components of auditory cortical FP traveled for short distances across cortical laminae. Far-fields are unlikely to be the primary contributor to these components since peak latency did not change spatially. The general idea of traveling waves, as alluded to by their name, may suggest that those traveling FP components reflected traveling neuronal activity (Muller et al., 2018). Since the distributions of such neuronal activity associated with transmembrane currents move along the FP components, there could be dipoles that move across channels as well. This possibility was addressed with CSD.
The laminar CSD profile, derived from FPs depicted in Figure 1A, is shown in Figure 2A. Waveforms were variable across depths, and the peak latency greatly fluctuated across channels. Both positive and negative CSD components were identified as the peaks closest to those of FP components of the same polarity at the same channels (see Materials and Methods). As they were identified without respect to amplitude, some CSD components were barely recognizable, indicating no discernable local neuronal activity. Importantly, even large CSD peak components did not align their peak latencies with those of FP components; thus, temporal correspondence between FP and CSD components was not always apparent, except for a few distinctly large CSD components.
Laminar profiles of auditory CSD responses. A, CSD responses to 100 ms BF tone at the same site as Figure 1A. Top to bottom traces represent superficial to deep channels (2-22). Magenta and cyan dots label positive and negative peak components, respectively. B, Laminar distribution of the peak latency of positive (magenta) and negative (cyan) CSD components (mean and 95% simultaneous confidence bands) is plotted against depth. C, D, Plot of median (n = 95) rate of change of the peak latency per a channel step (100 mm) against relative depth for the positive peaks (C) and negative peaks (D).
Peak latencies of CSD derived from FP in the dataset used for Figure 1B are summarized in Figure 2B. Negative peak components had weak precession with depth and positive peak components had sudden delaying shift, similarly to FP components. However, changes along depth were mostly jagged, unlike the smooth shifts observed in FP. To compare the smoothness of the shift of peak latency between FP and CSD, the spatial derivative of peak latency was approximated by estimating the difference between neighboring channels. The laminar profile of the modulus of the derivative is shown in Figure 2C, D for positive and negative peak components, respectively. The values were unsigned to eliminate cancellation of derivatives by the opposite directions of change between sites. The derivatives of FP peak latency were close to zero, except for a large change at the polarity reversal. Large values for CSD, which were larger than those of FP even at polarity change, were consistent with jagged patterns. Unlike what was seen with FP, CSD peak components did not gradually change across channels. Laminar CSD profiles showed no evidence of traveling neuronal activity.
Emergence of cross-laminar traveling components by volume conduction
Previous studies have shown that waveforms and laminar patterns of FP differ from those of CSD depending on the position relative to the distribution of CSD because of volume conduction (Kajikawa and Schroeder, 2015; Hindriks et al., 2016). Thus, while CSD did not have traveling components, such as FP, such CSDs could still produce traveling components in FP through volume conduction in a manner dependent on the local positions. To test the possibility, we applied volume conductor model (Eq. 1) to CSD profiles, calculated the vcFP, and addressed the peak latencies of vcFP components.
Figure 3A shows a laminar profile of vcFP derived from the CSD shown in Figure 2A. Some features of vcFP differed from FP shown in Figure 1A. At the depth of polarity change, there was a noticeably large positive peak that appeared earlier than the superficial P1 (Fig. 3A, asterisk). However, despite having a smaller amplitude, a later positive peak was identified as the peak corresponding to the FP-positive peak at the same depth because of its timing (see Materials and Methods). Also, vcFP at several deep channels had negative peak components at earlier latencies than those of FP in Figure 1A. Regardless of these differences, the general profile of vcFP across channels was close to what was observed with FP profiles. Importantly, vcFP reproduced the gradual change of polarity reversal with a traveling pattern of negative peak components around the middle channels like FP. Peak latencies of vcFP were calculated for 95 sites (n = 95) and summarized in Figure 3B. Both the positive and negative components of vcFP changed their latencies gradually like those of FP. Plots of similarity score indicated that waveforms of vcFP were more like FP than CSD in general (Fig. 3C). These results suggested that volume conduction of CSD resulted in the emergence of traveling FP components.
Laminar profile of vcFP. A, vcFP of CSD responses shown in Figure 2A. Magenta and cyan dots represent positive and negative peak components, respectively, that occurred during sounds at all channels. Vertical dotted line indicates the P1 latency of original FP at channel 1 (same as that in Fig. 1). B, Mean peak latency of positive (magenta) and negative (cyan) components of vcFP. C, Plot of mean scores of the similarity of temporal patterns between FP and CSD (gray) and vcFP (black) against relative depth. Dotted lines indicate 95% simultaneous confidence bands.
Volume conduction of 2 dipoles: timing differences
Auditory cortical CSD profiles had multiple pairs of sinks and sources or dipoles. Although those dipoles did not move apparently, they produced the traveling FP components through volume conduction. Since a single dipole alone cannot produce traveling FP components without moving itself, we considered the presence of multiple dipoles as a necessary condition to produce the traveling components. We addressed how the components could happen in vcFP by simulating volume conduction of CSD models of 2 dipoles (Fig. 4). Those dipoles are displaced radially from each other and have opposite directions of dipole moment, mimicking dipoles of different cortical layers (Chrobak and Buzsaki, 1998; Staba et al., 2004). Their latency and amplitude relationships were systematically varied to address the conditions for emergence of traveling components in vcFP.
The effect of the relative peak timing of two dipole moments on vcFP. A, Left, Spatiotemporal profiles of CSD consisting of 2 dipoles at different depths and of same peak amplitudes. The onset of one dipole moment activation is delayed from another by 25 ms. Middle, Temporal patterns of vcFP derived from CSD in left column. Colors represent different depths. Insets (top of rows), Waveforms of two dipole moments (black represents early dipole; gray represents delayed dipole). Right, Spatiotemporal profiles of vcFP. White line indicates negative peak latency. Horizontal arrowheads indicate the positions of the polarity reversal of vcFP generated by individual dipoles. Left and right columns, Horizontal dotted lines indicate the positions of the centers of dipoles, and vertical dotted lines indicate the peak latencies of dipole moments. B–D, The onset delay of late dipole activation was gradually shortened from B to D (10 ms in B, 5 ms in C, and 0 ms in D). Other formats are the same as in A. C, D, Right column, Horizontal arrows indicate the delays of vcFP-negative peak components from the peak latency of late dipole moments. D, Right, Vertical arrowheads indicate temporal deviation between early dipole's peak latency and vcFP-negative peak latency at deep positions. Color scalebars for left and right columns, and legend for middle column are at bottom.
Figure 4 shows laminar patterns of modeled CSDs consisting of 2 dipoles (left column) and vcFP generated by the modeled CSDs (right), and the waveforms of dipole moments and vcFP (middle). In Figure 4A, a large delay was placed between the onsets of increases in the dipole moments, and only a single dipole was active at any moment. vcFP generated by the dipoles had polarity changes at the centers of momentarily active dipoles (Fig. 4A, right, arrowheads), where vcFP was flat. Peak components of vcFP had the same peak latencies as the dipole moments regardless of position (Fig. 4A, middle). Negative peak components appeared first with peak latencies same as the peak latency of early dipole moment simultaneously at depths below the midpoint between dipoles, then reappeared with peak latencies same as the late dipole moment at all depth above the 2 dipoles' midpoint. Thus, there were no traveling peak components around the region of polarity changes.
From Figure 4A–D, temporal overlap between activities of the dipoles was increased gradually by reducing the delay of the late dipole's activation. In Figure 4B, C, the onsets of late dipole activation were later than the peak of early dipole's activation. Consequently, the negative vcFP component at the peak latency of the early dipole (Fig. 4B,C, right) remained the same as that in Figure 4A (right) and remained invariant with depth. However, as the activation of the late dipole moment started earlier, the negative peak latencies at depths between the 2 dipoles' centers were shifted earlier and appeared as if the negative peak component started traveling from the middle depth at intermittent latencies. The amount of the shifts depended on the extent of temporal overlap between the 2 dipoles' activation. Concomitantly, since the early dipole's moment had not returned to zero by the time of the late dipole moment's peak, negative peak components of vcFP, which reflect the late dipole's peak, were delayed. The magnitude of the delay from the dipole's peak latency depended on the temporal overlap as well (Fig. 4C,D, right, horizontal arrows). In Figure 4D, the late dipole's activation started before the peak latency of the early dipole moment, resulting in the shift of early vcFP components as well (Fig. 4D, right, arrowheads). These results of 2 dipoles models indicated that two spatially stable dipoles that were concurrently active with different peak latencies were sufficient to produce traveling vcFP components between the dipoles' positions. Additionally, resulting vcFP components showed peak latencies that were different from those of the original dipoles.
Volume conduction of 2 dipoles: magnitude differences
It is rational to consider that the magnitudes of dipole moments would be unequal between neuronal populations while they are spatially segregated and concurrently active like what is found across cortical layers during sensory responses (Lakatos et al., 2007; Kajikawa and Schroeder, 2015). We addressed the effect of the differences in the magnitudes of two dipole moments, adopting the dipoles with temporal overlaps that produced apparent traveling vcFP component in Figure 4D.
Figure 5 shows laminar profiles and waveforms of the CSD models with altered relative magnitudes and vcFP generated by those dipoles in same formats as Figure 4. In Figure 5A, D, an amplitude of one dipole's moment was exceedingly larger than the other. Peak components of vcFP were apparent at the timing of the larger dipole moments' peak latency with polarity changes at the center of the dipole. Although not readily apparent, there were also small vcFP components (Fig. 5, right column, black lines), whose peak latencies were off from peak latencies of smaller dipole moments with traveling peak patterns.
The effect of the relative magnitudes of two dipole activities on vcFP. Two dipoles have the same spatiotemporal patterns as that in Figure 4D, with altered ratio of the amplitudes of early dipole moment to late dipole moment. Ratios are 8 (A), 2 (B), 0.5 (C), and 0.125 (D). Formats of left, middle, and right columns are the same as those in Figure 4. In right column, additional black lines indicate positive peak latency.
In Figure 5B, C, an amplitude of one dipole was twice that of the other. In those cases, traveling negative peak components are apparent with biases of peak depths and latencies toward the centers of dipoles of larger moments. Also, above and below the depths of dipoles, vcFP components have spatially constant peak latencies that are slightly off from those of the dipole moments. These CSD models of 2 dipoles demonstrated that, when multiple dipoles of comparable magnitudes and different peak latencies are concurrently active, traveling FP components appear in the surrounding area of those dipoles and the waveforms of FP differ from those of dipole moments. In addition, such differences in waveforms remain constant over the space of far-fields.
In these models, we used dipoles to exemplify the paired current sinks and sources that appear at different layers in cerebral cortical CSD (Mitzdorf, 1985). At the biological level, these dipoles would be formed by net transmembrane currents of neurons. The modeled dipoles may be tentatively considered to reflect Layer 2/3 pyramidal cells and Layer 4 granular cells, respectively: two of sink/source pairs often observed in supragranular, granular, and infragranular layers (Lakatos et al., 2007; Maier et al., 2011). The temporal peaks of dipole moments would reflect the peak neuronal activity of those cells. However, neurons that are active during sensory responses are presumably composed of various neuron types with different temporal patterns (de Kock et al., 2007), with variable distances from the electrode recording positions. These factors are further complicated by variations in stimulus features, such as stimulus intensity and other characteristics that are represented topographically in the cerebral cortex. Thus, the dipoles in the model should be considered as a very simplified representation of complex populational activities across cortical layers in sensory cortices.
Consequences of multiple dipoles in field potentials
In auditory responses, the peak latency of superficial P1 correlated with that of supragranular CSD source (r2 = 0.35, p = 6.115 × 10−11; Fig. 6A), suggesting that the dipole formed in the supragranular layer was the major generator of both the superficial P1 and the counter negative FP component in deep channels. If a supragranular dipole was the sole generator of P1, the peak latencies of the supragranular CSD source and the P1 would be identical. However, the peak latency of the P1 significantly preceded that of the peak of the supragranular CSD source by 2.4 ms (CI: [1.5, 3.4]) (Wilcoxon's signed rank, Z = 4.888, p = 1.0145 × 10−06). The small but significantly earlier P1 was akin to the pattern described for the 2 dipoles model in Figures 4D and 5, in which the speeding shift of the vcFP component generated by the upper dipole was attributable to the concurrent presence of the lower dipole activity that was peaking later. In other words, P1 preceding the supragranular source is presumably caused by the presence of non-supragranular dipoles that were already active before the timing of P1 peak latency (i.e., granular layer responses).
Consequences of volume conduction with multiple dipoles. A, Plot of supragranular source peak latency against P1 peak latency (n = 95). B, Plot of traveling velocity of negative peaks against the velocity assumed for single dipoles generating both P1 and N1 (n = 95). B, Axes are scaled logarithmically.
Alternatively, if the supragranular dipole was a solely active dipole generating P1 and N1 during auditory responses, peak components would appear traveling around the dipole center for a short distance (i.e., 100 µm) between neighboring channels of an electrode array. The mean velocity of such traveling would be slow by taking the whole time interval between the peak latencies of P1 and N1. However, gradual changes in Figure 1 suggest that the actual traveling of FP components, even at its slowest, was faster than that predicted for supragranular dipole alone. Figure 6B shows the slowest traveling velocity of the negative peaks in each site plotted against the velocity while traveling 100 µm if only a single dipole generating both P1 and N1 was assumed. There are a few sites where the traveling velocity is slower than expected for single dipole's P1-N1 (i.e., data points below diagonal line). In those cases, spatiotemporal profiles contained negative peaks that were later than the superficial N1 at depths between the polarity reversal and channel 1. In a majority of sites, the traveling velocity, 0.0172 m/s (CI: [0.012, 0.0237]), was faster than the velocity expected by P1-N1 time difference of a single dipole, 0.0044 m/s (CI: 0.0042, 0.0045) (Wilcoxon's signed rank, Z = 8.372, p = 5.6626 × 10−17). Together, these results suggest that the cross-laminar traveling of FP components is because of the interplay of at least 1 other dipole in addition to ones in the supragranular layers.
Influences of laminar depth on peak latency of FP components
Because of cross-laminar traveling of FP components, FP waveforms change systematically depending on the laminar position. Thus, biases of recording positions between datasets of FP can introduce systematic differences in waveforms of FP between the datasets. For example, studies that record FP concurrently from electrodes recording single units generally selected recording sites based on the quality of isolation of spike signals (e.g., Hernández et al., 2008; Tsunada et al., 2011; Khamechian et al., 2019). Those criteria could leave possibilities that laminar positions were biased across recording sites, animals, and studies. It may be noted that, even in those studies, recordings during search of spikes could be still useful to find the depths of polarity changes of event-related FP.
In the present study, single-unit spikes were not resolvable from MUA. However, sensory cortical responses of sorted spikes and MUA correlate highly with each other (Kayser et al., 2007). It is rational to assume that the probability of isolating spikes would be high at sites where large MUA responses occur. Thus, we selected one channel from across the linear array electrodes at each penetration site based on the maximum MUA response magnitude and examined the relation of FP peak latency with the channel positions relative to the polarity changes.
In Figure 7A, B, the peak latencies of negative FP and CSD components at channels displaying maximum MUA responses are plotted against the laminar distances of those channels from the depth of polarity reversal of FP. Most of those channels were deeper than the polarity reversal, which was consistent with laminar biases of MUA responses toward layers below supragranular layers (Csercsa et al., 2010; Kajikawa et al., 2017; Leszczyński et al., 2020). Peak latency of negative FP component correlated significantly with the distance (rs2 = −0.3006, p = 0.0016; Fig. 7A). Thus, peak components of FP recorded concurrently with neuronal spikes were affected by the relative laminar position of the recording sites. In contrast, peak latency of negative CSD component did not correlate with the distance (rs2 = −0.0094, p = 0.4632; Fig. 7B), which was consistent with the absence of traveling components in CSD. The laminar position was an independent factor that influenced the peak latencies of FP components and waveforms of FP recorded concurrently with neuronal spikes. In other words, the variability in the waveform of FP could arise partly because of the variability in the recording positions.
Dependence of the peak latency on the depth relative to polarity reversal. A, Peak latency of negative FP component at the depth of maximum MUA responses is plotted against the vertical distance of the depth from the polarity reversal of FP. B, Peak latency of negative CSD component at same depths, derived as in Figure 2B, is plotted against the vertical distance as in A. A, B, Straight lines indicate linear regression (n = 95).
Cross-laminar traveling of FP components in visual cortex
Since the physical properties of cortical tissue lead to volume conduction, the traveling patterns of FP components should also occur in brain regions other than the auditory cortex. We examined laminar change in peak latency of visual FP in the occipital cortex (Barczak et al., 2019). Figure 8A shows the laminar profile of FP to red strobe flashes at an exemplar site in V1 during free viewing. At the superficial channel 1, P1 was not apparent. Typical visual responses during fixation have a sequence of N1-P1 (Schroeder et al., 1991; Shah et al., 2004), with a P1 reversal occurring in layer 2/3 and an N1 reversal at layers below (Schroeder et al., 1991). The absence of a strong P1 could be because of the behavioral conditions during recordings: since animals were trained to perform tasks under free viewing (Barczak et al., 2019), they were not fixating on a fixation point. Flashes were delivered under a passive condition where eye position and attentional state were not controlled for, and both the timing and position of fixation could occur randomly relative to the flashes.
Laminar profile of occipital visual FP to red flashes. A, FP responses to red flashes at an exemplar penetration site in primary visual cortex. Top to bottom traces represent FP recorded at superficial to deep channels (1-23). Black dots label N1 for channel 1 and negative components whose peak latencies were closest to the peak latencies of negative components at channels one above. B, Mean and 95% confidence bands of peak latency of negative components of FP responses to red flashes are plotted against depth relative to the depth of inversions (n = 78). Gray line (axis on top) indicates the distribution of current sink peaks in granular layer.
In Figure 8A, waveforms looked similarly to one another within the top and bottom halves of channels. While the pattern was inverted between those portions, there were no flat FP along the array of channels. Instead, gradual changes or the traveling of negative components in the middle channels (11-15) were observed. Since the initial positive component in superficial depths was obscured in these responses, only the superficial negative component was tracked recursively to deeper channels (Fig. 8A, black dots). The negative peak latency became earlier gradually with depth, suggesting that negative components started deep and traveled upward like what was seen with auditory cortical FP shown in Figure 1.
The mean peak latency of negative component at the most superficial channel was 59.4 ms (SD: 7.6 ms, n = 78). Recording depths were aligned between sites at the depth at which FP reverses polarity at superficial N1 peak latency. Figure 8B plots the peak latency against depth after alignment, showing that the gradual change of the negative peak occurred across sites. The positions of current sinks in the granular layer (gray line) were around the polarity reversal of the negative peak. The appearance of dual peaks suggests 2 current sinks in differentiated layers of layer 4 in macaque V1 (Mitzdorf and Singer, 1979). Thus, cross-laminar traveling FP components occur generally in different cortical areas, and the laminar range of the traveling depends on the laminar positions of source activities.
While cross-laminar traveling FP components were addressed in auditory and visual cortices, multiple dipoles with different laminar patterns are presumably present in other cortical areas as well. Similarly, afferents that differ in laminar targets (e.g., feedforward and feedback) presumably produce different laminar dipoles within a cortical area. Our results suggest that, if a single laminar dipole moment is large, FP across cortical layers would similarly follow the temporal pattern of those larger dipole moments. Traveling FP components may emerge when concurrent activation of dipoles with similar magnitudes and different dynamic patterns occurs regardless of afferent types and cortical areas, and the traveling patterns and peak latencies associated with the waves would depend on the dynamics of those dipoles.
Discussion
We addressed how waveforms of sensory FP change across sensory cortical lamina. Peak latencies shifted gradually over laminar ranges of several hundreds of micrometers, where the reversal of polarity also occurred. Because of gradual peak latency changes, FP components appeared like traveling waves. However, no CSD components were found traveling. To explain the discrepancy between FP and CSD, we modeled CSD of 2 separate dipoles to address the conditions of spatiotemporal patterns that result in spatially gradual changes of FP peaks. When only 1 dipole is active, the laminar-dependent profile of peak latencies was uniform, the same as the peak latency of the momentarily active dipole. When dipoles with similar magnitudes and different temporal patterns were concurrently active, gradual changes in the peak timing of FP appeared as a consequence of superimposing FPs generated by individual dipoles. Consequently, FP components had peak latencies that not only differed from those of CSD components, but also changed in an orderly fashion depending on laminar position. That resulted in the appearance of traveling FP components. These properties are not specific to the auditory cortex but appear to be properties of cortical tissue in general given that similar patterns were observed in visual cortex.
Traveling activity or electrical conduction?
Gradual changes in peak latency appear consistently in laminar recordings of both ongoing and evoked activity (Fishman and Steinschneider, 2010; Lipton et al., 2010; Welle and Contreras, 2016; Kajikawa et al., 2017; Francis et al., 2018), although its explicit description in literature is scarce. Since they appear as traveling waves across electrode contacts, such patterns of laminar FP may be considered as cross-laminar propagation of neuronal activity (Sakata and Harris, 2009; Muller et al., 2018). Propagating activity has been studied in several ways using indicators of local activity, such as voltage-sensitive dyes (Huang et al., 2010; Sato et al., 2012), neuronal spikes (Sakata and Harris, 2009; Patel et al., 2012; Beckers et al., 2014; Hernández-Pérez et al., 2020), and pharmacological interruption (Frostig et al., 2008; Wester and Contreras, 2012). In the case of low-frequency neuroelectric signals, such as FP, traveling wave patterns appear in spatially configured multichannel recordings within the brain (Rubino et al., 2006; Lubenov and Siapas, 2009; Patel et al., 2012; Zhang and Jacob, 2015; Townsend et al., 2017), on epidural ECoG (Zhang et al., 2018), and scalp EEG recordings (Massimini et al., 2004; Fellinger et al., 2012; Patten et al., 2012; Lozano-Soldevilla and VanRullen, 2019). The presence of waves is generally examined by graded phase patterns over space, similarly to the analysis of gradual laminar change in peak latency in the present study.
Cross-laminar traveling waves in FP have been shown at high sampling rates for dendritic spike propagation (Bereshpolova et al., 2007; Somogyvári et al., 2012). In those studies, propagating patterns appeared as brief dendritic spikes in FP that were also apparent in CSD. However, electrical events during sensory responses were much slower than dendritic spikes. While some studies found the cross-laminar propagation of CSD components during cortical sensory responses (Jellema et al., 2004), CSD profiles of sensory response in most studies had laminar sinks/sources that remained within laminae without crossing over (Lakatos et al., 2007; Fishman and Steinschneider, 2010; Szymanski et al., 2011; Godlove et al., 2014; van Kerkoerle et al., 2014; Dougherty et al., 2017; Senzai et al., 2019; Zempeltzi et al., 2020).
FP and CSD are alike in that both are considered to reflect neuronal transmembrane currents. However, FP and CSD are biophysically different quantities (Buzsáki et al., 2012; Einevoll et al., 2013), and their signals have different waveforms in general (Kajikawa and Schroeder, 2015; Hindriks et al., 2016). Like the waveforms of scalp ERP, FP may not reflect a single neuronal ensemble's activity directly, but rather reflects a summation of the ensemble's different activities that have different waveforms (Luck, 2005). Thus, FP peaks may occur at very different timing from the neuronal activities that contribute to those peaks.
Further, FP often consist of both local and far-field components. Unlike local FP components, far-field components occur with no corresponding local CSD components (Kajikawa and Schroeder, 2011; Kajikawa et al., 2017), and do not change peak latency and oscillatory phase over space (Carmichael et al., 2017; Lalla et al., 2017; Parabucki and Lampl, 2017), consistent with negligible effect of tissue permittivity. Spread of far-field components occurs automatically and does not reflect propagating neuronal activity. However, when far-fields are generated by a propagating neuronal activity in a closed cortical region, they may appear as traveling waves in neuroelectric signals at remote sites.
While we showed FP waves that traveled in cross laminar direction within cortical columns, traveling waves in a majority of studies have been shown to travel across columns. It is notable that the velocities of macroscopic traveling waves reported for scalp EEG recordings were usually >1 m/s, and faster than mesoscopic waves reported in some cortical regions, which seem to travel at velocities of <1 m/s (Muller et al., 2018). Hindriks et al. (2014) demonstrated that fast traveling waves at the scalp could be because of volume conduction of relatively slower propagating activity in a limited region of cerebral cortex. It is equivalent to the motion velocity of an object projected onto a screen, which depends on the distance between projector and screen and is faster than the motion on the filmed pictures. Our results added another possibility of traveling waves by the same volume conduction but from different causes, which was also pointed out by Lozano-Soldevilla and VanRullen (2019).
It is also possible that same mechanisms produce waves observed at mesoscopic levels as long as recorded signals are volume-conducted like ECoG. Since those signals are recorded outside of cortical tissue, they cannot track the dipole positions directly and instead require additional experimental techniques to identify current sources. Recently, Halgren et al. (2019) combined ECoG and depth electrodes and showed α traveling wave and oscillatory current sources, therefore revealing that not all traveling waves are generated by discrete dipoles. However, when separate cortical columns or regions are concurrently and strongly active (Huang et al., 2000; Slovin et al., 2002; Reimer et al., 2011), FP and ECoG between those regions may appear to be traveling across cortical columns as well.
What can peak latency tell?
Amplitude and latency have been characterized for peak components of event-related FPs (Eggermont et al., 2011; Sundberg et al., 2012; Pan and Dudman, 2015; Nanda et al., 2019), and compared between sites, cortical areas, subjects, and/or species (Freiwald and Tsao, 2010; Riehle et al., 2013; Brunet et al., 2015; Kim et al., 2015; Land et al., 2018; Li et al., 2019). While laminar position is not considered as an independent variable in most studies, cytoarchitectonically different regions of the cerebral cortex differ in thickness and details of laminar patterns between areas (Wagstyl et al., 2018) and species (De Sousa et al., 2010; Balaram and Kaas, 2014). Also, the criteria for selecting recording sites may differ between studies depending on the target signals.
Our findings show that laminar position systematically affects peak components of FP around the reversal of FP polarity, although peak latency remains relatively constant at sites outside of the region of polarity reversal. This dependence complicates the comparison of FP peaks from different recording sites and subjects, requiring that laminar positions be aligned between different recordings. It may be noted that this issue is obsolete for comparisons of peak latency or phase of FP between stimulus or other parameters within each site (Sundberg et al., 2012; Aasebø et al., 2017; Bruyns-Haylett et al., 2017). However, those position-related factors could contribute to differences in peak latency of FP between subjects within a single study (e.g., Hoffman et al., 2008; Esghaei et al., 2017) or between studies. For example, when measured in the cortical area above IT, face responses in macaque inferior temporal cortex (IT) generate P1, N1, and P2 components whose latencies are 80, 100-120, and 180-200 ms, respectively (Hoffman et al., 2008; Turesson et al., 2012; Kajikawa et al., 2017). Within IT, however, the polarity of visual FP reverses (Anderson et al., 2008), and the negative and positive peaks switch their order of appearance across the depths of polarity reversal (Kajikawa et al., 2017). Different studies, unsurprisingly, report different latencies for these components. For example, the negative peak latencies of face-evoked FP within IT have also been reported as occurring within the 130-145 ms post-stimulus time window (Nielsen et al., 2006; Freiwald and Tsao, 2010). The present study suggests that those intracortical peak latencies may not correspond directly to any specific local maxima in cortical activity, but rather are a consequence of the superposition of multiple neuronal ensembles. The latencies are influenced not only by neuronal activity itself, but also the spatial distance (both horizontal and vertical) between active neuronal ensembles and the recording electrode.
Footnotes
The authors declare no competing financial interests.
This study was supported by National Institutes of Health Grants F32DC015391 to J.J.O., R01DC015780 to Y.K., and R01DC012947 to A.B.; and Marie Curie International Outgoing Fellowship within the 7th European Community Framework Program (FP7-PEOPLE-2012-IOF and PIOF-GA-2012–331251) to J.C.-F.
- Correspondence should be addressed to Yoshinao Kajikawa at ykajikawa{at}nki.rfmh.org
