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Smell-induced gamma oscillations in human olfactory cortex are required for accurate perception of odor identity

['Qiaohan Yang', 'Department Of Neurology', 'Feinberg School Of Medicine', 'Northwestern University', 'Chicago', 'Illinois', 'United States Of America', 'Guangyu Zhou', 'Torben Noto', 'Jessica W. Templer']

Date: 2022-01 

Studies of neuronal oscillations have contributed substantial insight into the mechanisms of visual, auditory, and somatosensory perception. However, progress in such research in the human olfactory system has lagged behind. As a result, the electrophysiological properties of the human olfactory system are poorly understood, and, in particular, whether stimulus-driven high-frequency oscillations play a role in odor processing is unknown. Here, we used direct intracranial recordings from human piriform cortex during an odor identification task to show that 3 key oscillatory rhythms are an integral part of the human olfactory cortical response to smell: Odor induces theta, beta, and gamma rhythms in human piriform cortex. We further show that these rhythms have distinct relationships with perceptual behavior. Odor-elicited gamma oscillations occur only during trials in which the odor is accurately perceived, and features of gamma oscillations predict odor identification accuracy, suggesting that they are critical for odor identity perception in humans. We also found that the amplitude of high-frequency oscillations is organized by the phase of low-frequency signals shortly following sniff onset, only when odor is present. Our findings reinforce previous work on theta oscillations, suggest that gamma oscillations in human piriform cortex are important for perception of odor identity, and constitute a robust identification of the characteristic electrophysiological response to smell in the human brain. Future work will determine whether the distinct oscillations we identified reflect distinct perceptual features of odor stimuli.

Our results show that odors elicit a stereotyped oscillatory response in human piriform cortex that is consistent in timing and frequency composition across participants: Immediately following odor onset, early theta increases are quickly followed by gamma and beta increases. The phase of early low-frequency responses drives the amplitude of high-frequency rhythms only when odor is present. Finally, the distinct oscillatory rhythms we identified were differentially related to behavioral performance, suggesting that these rhythms could potentially give rise to noninterfering representations of different features of odor stimuli [ 81 , 82 ], though future work is needed to test this hypothesis.

In this study, we used stereotactic intracranial electroencephalography (iEEG) to test 3 main hypotheses about neural responses in human piriform cortex during an olfactory identification task. First, based on the fundamental role of gamma oscillations in human sensory perception and the established rhythms in the rodent olfactory system, we hypothesized that odors would induce theta, beta, and gamma oscillations in human piriform cortex. Second, based on the fact that olfactory oscillations are modulated by sniffing [ 39 , 58 , 62 , 63 , 77 – 79 ], which is inextricably linked to odor onset times, we hypothesized that the timing of responses relative to sniff onset would vary across the different frequency bands. Third, based on established links between gamma/beta oscillations and sensory coding [ 24 , 25 , 27 , 28 , 30 , 40 , 43 , 64 ], and the fact that activity in rodent piriform cortex can be used to decode odor identity [ 80 – 82 ], we hypothesized that human piriform beta and gamma oscillations would emerge only during trials where odors were accurately identified and that features of their oscillatory rhythms would predict odor identification accuracy.

In the olfactory system, odor-driven increases in beta and gamma oscillations have not been consistently identified in direct recordings from human piriform (olfactory) cortex, which has been found to exhibit low-frequency oscillations in response to odor [ 57 ]. However, in mammals and insects, the cellular and network processes underlying gamma oscillations in the olfactory bulb and cortex have been studied extensively [ 19 , 32 , 42 , 58 – 63 ], and more recent work has begun to provide insight on their functional role as well [ 24 , 25 , 28 , 29 , 32 , 33 , 39 , 64 ], suggesting involvement in the organization of sensory information to enable fine odor discrimination and identification [ 33 , 65 – 69 ]. In addition to gamma oscillations, beta and theta oscillations have been extensively studied in the mammalian olfactory system and are involved in olfactory learning and respiratory tracking, respectively [ 18 , 25 , 28 , 30 , 32 , 40 , 41 , 43 , 64 , 65 , 70 , 71 ]. Thus, theta, beta, and gamma oscillations constitute 3 key rhythms that have functional significance for olfactory processing in mammals [ 9 ]. However, against this background of extensive animal work, the electrophysiological underpinnings of the human olfactory system are vastly understudied. Only a few intracranial studies have directly measured odor-induced oscillations in the human brain: in the amygdala [ 72 – 76 ] and piriform cortex [ 57 ]. Human piriform recordings suggest an important role for low-frequency (<8 Hz) oscillations in olfactory processing [ 57 ]; theta oscillations were consistently found in piriform cortex within 200 ms of sniff onset during an odor detection task, and their features could be used to decode odor identity. However, the full spectral characteristics of early and later emerging odor responses in human olfactory cortex remain unknown. Furthermore, the functional role of high-frequency oscillations in human piriform cortex is virtually unexplored.

Gamma oscillations, which comprise the synchronized rhythmic patterns of spiking and synaptic inhibition, have been established as an important mechanism in sensory cortical processing in the mammalian brain [ 44 , 45 ]. In the visual cortex, gamma oscillations are locally generated and reflect low-level stimulus attributes [ 46 ], including grating size, contrast, spatial structure, and color [ 47 – 50 ], and are thought to support visual perception by synchronizing the processing and transfer of information within and across areas of visual cortex [ 51 – 53 ]. Similarly, in the auditory cortex, locally generated gamma oscillations may provide a mechanism to integrate neurons according to the similarity of their receptive fields [ 54 ] and are involved in pitch perception and sound discrimination [ 55 , 56 ].

Oscillations are ubiquitous across mammalian brain networks [ 1 – 11 ], and studies on their spectrotemporal dynamics have contributed important insight into the mechanisms underlying visual, auditory, and somatosensory perception [ 11 – 16 ]. Some of the earliest recordings of brain oscillations occurred in the olfactory system of hedgehogs [ 17 ], leading to decades of highly productive animal research on oscillations in the mammalian olfactory system with significant work in rabbit and cat piriform [ 18 – 22 ] and more recently mainly focusing on the rodent olfactory bulb [ 6 , 9 , 23 – 43 ]. However, 80 years later, we still lack understanding of the spectral and temporal dynamics of these oscillations in olfactory processing in the human brain, particularly in higher frequency ranges including beta and gamma.

Results

To examine odor-driven oscillations in human olfactory cortex, we recorded local field potentials (LFPs) from 7 participants who took part in an odor identification task. Each participant’s clinical electrode coverage included piriform cortex (Fig 1A). The olfactory task was performed during clinical recording of ongoing electrophysiological activity, at sampling rates ranging between 500 to 2,000 Hz, using a 256-channel clinical EEG acquisition system (Nihon Kohden). Each trial began with an auditory cue signaling that odor would be presented and providing the potential identity of the odor (rose or mint). After a jittered delay (3 to 7 s), odor was presented to the participant, while sniff onset was precisely measured via a pressure sensor at the nose (Salter Labs). On each trial, participants identified the odor by indicating whether or not it matched the identity prompt (Fig 1B). To isolate effects driven by odor from those driven by inhalation, which also impacts oscillations in human piriform cortex [78,83–85], we analyzed and directly compared LFPs during inhalations that contained odor and those that did not, resulting in 2 experimental conditions: odor and no-odor (Fig 1B, areas shaded in pink and blue).

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TIFF original image Download: Fig 1. Electrode contact locations and experimental design. (A) The location of the piriform cortex electrode contact (red dot) is shown on each participant’s (P1–P7) brain image. L, left hemisphere. (B) Schematic illustration of the olfactory task, showing odor and no-odor conditions drawn on an illustrative breathing signal (black line). The light blue area indicates experimental trials (starting from cue delivery to the end of the breathing cycle in which odor was delivered), and the pink area indicates between trials. The black boxes indicate the analysis time windows for odor and no-odor trials. The darker blue area indicates odor delivery. https://doi.org/10.1371/journal.pbio.3001509.g001

The time course of olfactory cortical oscillations varies across frequency bands The spectrograms in Fig 2 showed apparent variable time courses of oscillations relative to sniff onset across frequency bands (Fig 2A and 2B). Theta appeared to emerge and dissipate soonest, with beta and gamma emerging later and persisting longer. To quantify these differences, we conducted a series of analyses to characterize the timing of responses across frequency bands. These included a percent change analysis to examine oscillatory increases over time, a bootstrapping analysis to minimize potential impact of noisy trials, a cluster-based analysis to quantify the exact timing and magnitude of continuously significant increases in oscillatory amplitude, and a circular distribution analysis to examine oscillatory peaks over respiratory phase. In our first analysis, we calculated the percent change in amplitude for each frequency band at each time point, for each condition (Fig 3A). This allowed us to determine the timing of the emergence of significant differences between odor and no-odor conditions (two-tailed paired t test; P < 0.05, FDR corrected). This analysis showed distinct temporal dynamics of odor responses for each frequency (Fig 3A, black lines above each panel). Theta oscillations were the earliest to emerge and dissipate, beginning 126 ms prior to sniff onset and ending 516 ms after sniff onset. Gamma oscillations emerged next, 116 ms after sniff onset, intermittently persisted through exhalation, and dissipated 3,678 ms after sniff onset. Beta oscillations emerged last, 144 ms after sniff onset, and persisted longest, ending 3,786 ms after sniff onset. PPT PowerPoint slide

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TIFF original image Download: Fig 3. Odor-induced theta, beta, and gamma oscillations have different time courses relative to sniff onset. (A) Percent-amplitude-change time series for odor (blue line) and no-odor (red line) conditions for each frequency band. Shaded areas indicate 1 standard error from the mean across all trials. Thick black lines above indicate statistically significant differences between conditions (FDR corrected P < 0.05, paired t test). (B) Bootstrap colormap of z-normalized amplitude for each frequency band, with results from each repetition stacked along the y-axis. Vertical stripes of consistent color indicate consistent amplitudes across subsampled sets of trials. (C) Colored shaded areas represent clusters of statistical significance of the trial-by-trial baseline-corrected amplitude time series, for each frequency band (cluster correction test P < 0.05, corrected). Upper boundaries of the shaded areas represent the t statistic from the one-sample t test of baseline-corrected amplitude at each time point against 0. Scales for t statistics are shown to the left of each cluster. Overlaid darker dots indicate the average timing of the bootstrapped distribution of peak amplitude occurrence for each frequency band, for each participant. Each dot represents data from 1 participant. Dots from the same participant are connected by black lines. On the right, cluster masses in relation to the permuted null distribution for each frequency band are shown, with actual values represented by the vertical red line. (D) Respiratory phase angle distributions corresponding to bootstrapped peak amplitudes for each frequency band. Scale of the polar histogram represents pdf of the distribution. Darker lines overlaid on the distribution indicate the mean vector of the phase distribution. Angle and radius represent averaged phase angle and PLV value respectively. The source data for panels (A–D) are available in S2 Data. FDR, false discovery rate; PLV, phase locking value. https://doi.org/10.1371/journal.pbio.3001509.g003 In a second analysis, designed to minimize the contribution of noisy trials and to statistically evaluate the time courses, we tested whether differences in temporal dynamics of responses across frequency bands were stable across resampled sets of trials. We conducted a bootstrapping analysis to create separate profiles of the timing of emergence of responses for each frequency band. We created a z-normalized time series of resampled mean values for each frequency band, represented as a colormap (Fig 3B; y-axis is each bootstrap repetition). We found stable time courses across repetitions, indicated by stripes of increased amplitude at particular times for each frequency band. To quantify the timing of amplitude increases, we performed a cluster-based statistical analysis; for each frequency band, we generated a t-statistic at each time point for all z-normalized odor trials, and then conducted a permutation-based analysis to correct for cluster size. We found clusters that corresponded well with the spectrograms shown in Fig 2, with the percent change analysis and with the bootstrap analysis (Fig 3C). We found 1 significant cluster for the theta band extending 266 ms presniff to 810 ms postsniff (permutation test; P < 0.0001), one for the beta band extending from 238 ms to 3,524 ms postsniff(P < 0.0001), and 4 separate clusters for the gamma band (326 ms to 452 ms postsniff, P = 0.0346; 764 ms to 892 ms postsniff, P = 0.0145; 1,374 ms to 1,642 ms postsniff, P < 0.0001; 1,902 ms to 2,016 ms postsniff, P = 0.0451). We subsequently conducted the same bootstrapping analysis at the single-participant level and plotted the average time point of each participant’s bootstrapped peak distribution on top of the significant clusters in Fig 3C (see overlayed dots, each representing the peak value for a single participant, with lines connecting each participant’s values across frequencies). Although single-participant data were more variable, beta and gamma peaks occurred later than theta peaks for almost all participants. These results suggest that the unique time courses of odor responses across frequencies were unlikely to be caused by noise, spikes, and other artifacts. In a third analysis, designed to account for individual respiratory differences in the time domain, we examined the circular distributions of oscillatory peaks over the respiratory phase. On each repetition of a bootstrapping analysis, the peak amplitude and corresponding phase angle were calculated from the average LFP and respiratory time series. We found that theta peaks narrowly aggregated at early stages of inhale (mean phase angle = −0.67 rad, phase locking value (PLV) = 0.99, Rayleigh’s z = 998.05, P < 0.0001) (Fig 3D, left), consistent with previous findings in humans [57]. By contrast, beta peaks consistently aggregated at the exhale trough (mean phase angle = 2.98 rad, PLV = 0.80, Rayleigh’s z = 647.78, P < 0.0001) (Fig 3D, middle). Gamma peaks were more broadly distributed, with most centered around inhale peak or the transition between inhale and exhale (mean phase angle = 0.57 rad, PLV = 0.63, Rayleigh’s z = 401.69, P < 0.0001) (Fig 3D, right). Combined, these findings suggest that following presentation of odor, theta oscillations increase earlier than beta and gamma oscillations and that while theta and gamma oscillations are maximal during inhalation, beta oscillations peak during exhale.

Gamma and beta oscillations are required for accurate odor identification Piriform cortex has been postulated to be a major driver of gamma oscillations in the brains of rodents [18,92] and cats [19–22,93]. Furthermore, numerous rodent studies suggest that beta and gamma oscillations relate to odor learning and discrimination, through both local odor coding [25,27,32,33,64,94] and recruitment of larger-scale networks [27–29,40,43,64]. We therefore hypothesized that beta and gamma oscillations in human piriform cortex would correlate more strongly with task performance than theta. We conducted 3 separate analyses to explore the relationship between odor-driven LFP oscillations and odor identification accuracy. These included a time-frequency analysis to look for gross differences between correct and incorrect trials, a correlation analysis to look for a relationship between accuracy and oscillations across trials, and a machine learning analysis to determine whether amplitudes of different frequency responses could predict accuracy. First, in a combined time-frequency analysis, we computed odor-onset aligned spectrograms during correct and incorrect trials separately, in order to look for differences across frequency bands. We found that during trials in which the participant correctly identified the odor, there were statistically significant increases in theta, beta, and gamma band amplitudes (Fig 4A, left panel; P < 0.05, FDR corrected). By contrast, during trials in which the participant failed to identify the odor, statistically significant increases were found only in the theta band, with no such increases in the beta or gamma bands (Fig 4A, right panel; P < 0.05, FDR corrected; Fig 4B, upper panels and lower left panel show the distribution of single-trial theta, beta, and gamma values for correct and incorrect trials). Since most participants performed above chance on the task, there were a larger number of correct trials than incorrect trials (252 versus 71). To account for this difference, we conducted sampling analysis with 200 repetitions in which correct and incorrect trials were resampled with replacement to include the same number of trials on each repetition, and we computed the distribution of the differences in amplitude (correct–incorrect) within each frequency band (Fig 4B, lower left panel). We found statistically significantly larger responses during correct trials compared to incorrect trials for beta and gamma bands only, with no significant differences in the theta band. (One-sample t test against 0 for the difference between correct and incorrect trials: theta: T 199 = 1.21, P = 0.2247; beta: T 199 = 35.55, P < 0.0001; gamma: T 199 = 42.61, P < 0.0001. Paired sample t tests for differences between frequency bands: theta versus beta: T 199 = −41.02, P < 0.0001; beta versus gamma: T 199 = 17.36, P < 0.0001; gamma versus theta: T 199 = 37.10, P < 0.0001.). This combined resampling analysis was designed to account for differences in numbers of correct and incorrect trials, which had the advantages of ensuring a balanced comparison across conditions and a robust number of incorrect trials. However, the contribution of individual participants to the observed effects was unclear. To account for this, we quantified theta, beta, and gamma responses for correct and incorrect trials separately, in each participant. Since some participants had no, or just a few, incorrect trials, we limited this analysis to include participants with more than 3 trials of each condition (resulting N = 5). Though numbers of incorrect trials were relatively low for some participants, results of this analysis confirmed the combined findings: Responses in all 3 frequencies were significantly above zero for correct trials (theta: T 4 = 4.12, P = 0.014; beta: T 4 = 2.87, P = 0.045; gamma: T 4 = 4.71, P = 0.0092), whereas only responses in theta band were significantly above zero for incorrect trials (theta:T 4 = 7.28, P = 0.0019; beta: T 4 = 1.77, P = 0.15; gamma:T 4 = 1.41, P = 0.23) (Fig 4B, lower right panels). These findings were also apparent in individual participant spectrograms (S4B Fig). PPT PowerPoint slide

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TIFF original image Download: Fig 4. Beta and gamma oscillations predict odor identification accuracy. (A) Z-normalized spectrograms for correct (left) and incorrect (right) trials separately. Averaged respiratory signals are overlayed on each spectrogram (red lines). Dashed lines represent sniff onset. Black contours indicate statistical significance of permutation test against precue baseline (P < 0.05, FDR corrected). (B) Amplitudes within each frequency band, for correct and incorrect trials separately. The upper panels show the distribution of z score amplitude values for each trial for the theta, beta, and gamma bands, for correct (blue) and incorrect (red) trials. The lower left panel shows box plots for the bootstrapped distributions of the difference between correct and incorrect trials. Boxes represent the 25th to 75th percentile of each distribution, the central marker indicates median, and whiskers extend to the extremes of the data excluding outliers. Colored dots represent raw difference values for each distribution. The lower right panels show individual participant’s mean response amplitudes in the theta, beta, and gamma bands, for correct and incorrect trials separately. Each dot represents data from a single participant, bars indicate the mean across participants, and error bars are standard error across participants. Stars indicate statistical significance (paired, two-tailed t tests). See Fig 2B for the color code of single participant dots. (C) Bar plots of bootstrapped Pearson’s correlation coefficients computed between oscillatory amplitudes and task accuracy for each frequency band, over the inhale and exhale time periods separately. Error bars indicate 95% confidence interval of the mean. Dashed line indicates FDR threshold for significant r value. Dots represent single correlation coefficient calculated from each bootstrap. (D) Scatter plots show bootstrapped percent change relative to baseline for correct and incorrect trials, during inhale and exhale time periods for each frequency band. Each dot is the average result from 1 bootstrap repetition. (E) ROC curves of linear binary SVM classifier applied to each of the scatter plots in panel C. Black dots represent optimized classifier; AUC is indicated for each ROC curve. The source data for panels (A–E) are available in S3 Data. AUC, area under the curve; FDR, false discovery rate; ROC, receiver operating characteristic; SVM, support vector machine. https://doi.org/10.1371/journal.pbio.3001509.g004 Second, we looked for a relationship between task performance and responses in each frequency band on a trial-by-trial basis. To account for differences within frequency bands over time, we conducted this analysis during the inhale and exhale periods separately. Trials were resampled to generate a distribution of correlation coefficients representing the relationship between response amplitudes and behavioral accuracy for each frequency band across the resampled trial sets. Significant correlations between accuracy and amplitude were evident in the beta and gamma bands during both inhale and exhale (50 bootstraps, t test against 0, FDR-corrected threshold for significant correlation coefficient; beta during inhale: T 49 = 31.25, P < 0.0001; beta during exhale: T 49 = 17.64, P < 0.0001; gamma during inhale: T 49 = 23.70, P < 0.0001; gamma during exhale: T 49 = 28.25, P < 0.0001.), but no such correlation was found in the theta band (theta during inhale: T 49 = −2.04, P = 0.97; theta during exhale: T 49 = −12.90, P = 1). In line with this, a direct statistical comparison across frequency bands showed that correlations were significantly stronger between behavioral accuracy and amplitude for beta and gamma bands compared to theta band during both inhale and exhale time periods (Fig 4C) (two-way repeated measures ANOVA: main effect of time window: F 1, 49 = 111.08, P < 0.0001; main effect of frequency band: F 2, 98 = 547.98, P < 0.0001. Paired sample t test across frequency bands during inhale for theta versus beta: T 49 = −29.37, P < 0.0001; for beta versus gamma: T 49 = 3.11, P = 0.0031; for gamma versus theta: T 49 = 24.95, P < 0.0001; paired sample t test across frequency bands during exhale for theta versus beta: T 49 = −26.51, P < 0.0001; for beta versus gamma: T 49 = −11.13, P < 0.0001; for gamma versus theta: T 49 = 33.95, P <0.0001); also see S4A Fig. Finally, we used machine learning to perform a classification analysis on inhale and exhale amplitudes for each frequency band, to determine whether these features could predict task accuracy. To this end, we applied a binary linear support vector machine (SVM) classifier to the bootstrapped data, plotted the receiver operative characteristic (ROC) curves, and calculated the area under the curve (AUC), which was used together with optimized classifier accuracy as the predictor of data separability. We found that beta and gamma amplitudes were highly successful at separating the trials by accuracy, while theta amplitudes were less so (Fig 4D). Specifically, gamma accuracy was maximal at 91.5%, beta accuracy was also high at 91%, whereas theta accuracy was lower at 66.5%. This same procedure was applied to shuffled data, which resulted in chance performance (accuracy = 52%), validating our methods. These findings correspond well with the results from the 2 previous analyses and, taken together, suggest that beta and gamma band amplitudes are more strongly correlated with task performance than theta amplitudes.

Odor-elicited high-frequency oscillations are not driven by attention Because the odor condition occurred during experimental trials and the no-odor condition occurred between experimental trials, responses during the odor condition could potentially have been impacted by attentional states that were not present during the no-odor condition. Previous human and animal work suggests that olfactory cortical responses are modulated by attention [95,96], particularly in lower frequency LFPs [97,98]. To control for potential effects of attention on our findings, we analyzed odorless sniffs taken in attended states during experimental trials. Each trial began with a cue, followed by a delay (3 to 7 s) prior to presentation of odor. Therefore, during many trials, sniffs of clean air occurred between the cue and odor (Fig 5A). These sniffs occurred during attended states, but did not contain odor, thus providing a means to isolate the effects of attention from the effects of odor. Because a sniff did not always occur between the cue and the odor, the number of trials in the attended odorless condition was lower than the odor condition. Therefore, we resampled odor trials to match the number across conditions. We computed spectrograms aligned to attended odorless sniffs and compared them to those aligned to odor sniffs (Fig 5B, left and middle). We found that attended odorless sniffs induced oscillations in low frequencies (below 8 Hz) only (P < 0.05, FDR corrected) and found no stable higher frequency oscillations (>8 Hz). We then computed the z-normalized difference across conditions (Fig 5B, right) and found significant differences between attended odor trials and attended no-odor trials in the theta, beta, and gamma bands, such that oscillations in all three frequency bands were increased when odor was present, even after removing the effects of attention (Fig 5B, right; P < 0.05, FDR corrected). Since theta oscillations were still detected in the attended no-odor condition, these findings suggest that the increases in beta and gamma bands were independent of attention, whereas theta band increases reflected, at least to some degree, attentional states. PPT PowerPoint slide

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TIFF original image Download: Fig 5. High-frequency odor-elicited oscillations are not driven by attention. (A) Schematic illustration of attended and unattended conditions. Attended no-odor trials were defined as breaths taken during experimental trials, between the cue and the odor. No odor was present, but the participant was in an attended state. Blue area indicates the time of experimental trials, and pink areas indicates the time between trials. Black boxes indicate the analysis time windows for the different conditions. (B) Z-normalized spectrograms of attended odor and attended no-odor trials, and the difference between the two. Average respiratory signals are overlayed for each condition (red lines). Dashed line represents inhalation onset. Black contours indicate statistical significance (permutation tests as described elsewhere, P < 0.05, FDR corrected). The source data for panel (B) are available in S4 Data. FDR, false discovery rate. https://doi.org/10.1371/journal.pbio.3001509.g005

Low-frequency phase modulates high-frequency amplitude during inhale when odor is present Previous work suggests that odor-induced theta oscillations predict odor identities, even during a detection task that does not require participants to identify odors [57]. Here, we found that theta rhythms in our data appeared to have a relationship with beta responses, which appeared to oscillate at around 5 Hz during inhale. Specifically, the overall magnitude of beta oscillations increased and decreased rhythmically with a frequency in the theta range, particularly in the first 1.5 to 2 s of the response (Fig 6A, gray box). Based on this observation, we hypothesized that theta oscillations might organize later-emerging higher frequency oscillations through phase modulation. To estimate modulation of higher frequency amplitude by theta phase, we calculated the modulation index (MI) [99] using theta phase as the modulating signal and a range of high frequencies (13 to 150 Hz) as the amplitude signals, for both odor and no-odor conditions (Fig 6B). We found that in the 1-s time window following sniff onset, theta phase significantly modulated beta and gamma oscillations during the odor condition (P < 0.05, FDR corrected for MI in all frequency bands; peak MI at 16.16 Hz, mean z score across all frequencies = 7.52) but not during the no-odor condition (mean z score across all frequencies = 2.02). PPT PowerPoint slide

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TIFF original image Download: Fig 6. Theta phase modulates higher frequency amplitudes during inhale, when odor is present. (A) Apparent rhythmic beta amplitude modulations at the theta frequency. With effects of attention subtracted out, the average Z score of the amplitude of the odor responses over time is displayed for beta (green) and theta (blue) frequency bands. The overall magnitude of beta oscillations increased and decreased rhythmically with a frequency in the theta range, particularly in the first 1.5 to 2 s of the response (gray box). (B) Phase-amplitude coupling between theta phase and higher frequency amplitudes. Z-normalized MI of theta phase and higher frequency amplitudes (13 to 150 Hz), during 0–1 s postsniff for all trials in the odor and no-odor conditions. Dashed line indicates FDR threshold for significant MI (P < 0.05, FDR corrected). The source data for panels (A) and (B) are available in S4 Data. FDR, false discovery rate; MI, modulation index. https://doi.org/10.1371/journal.pbio.3001509.g006 Our phase-amplitude coupling analyses was performed during a window in which a sensory-evoked potential could have occurred, and, therefore, the derived phase-amplitude coupling could have been driven by the evoked potential having a steep slope. To control for this possibility, we conducted a permutation analysis [100] in which we shuffled the trial-by-trial relationship between theta phase and higher frequency amplitude to test whether the modulation effect was due to the exact trial-by-trial relationship or rather induced by a steep slope during each trial. We normalized the observed MI to the trial order–shuffled null distribution and still found significant effects for the odor condition but not the no-odor condition (S5 Fig). This finding suggests that higher frequency oscillations were modulated by theta phase during the early period of sniffing, when theta amplitudes were significantly increased.

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