3.3 Power
3.3.1 Power: Local Field Potentials
LFP power spectra were normalized prior to level-based statistical analyses through mul-tiplication of power with the square of frequency values to account for the approximately
1{f2 decay of spectral power (Miller et al., 2009; Siegel et al., 2009).1 Note, however, that the qualitative findings described in this section are not artifacts of the normalization procedure per se which is performed at this point for illustration purposes only. We obtained the same qualitative results when computing purely raw spectra.
Grand average raw, normalized power spectra of monopolar LFPs as shown in panel a of Figure 3.3 display three prominent features. First, power increases considerably between rest and running, with absolute values being largely comparable between struc-tures during both behavioral states. Second, all spectra exhibit two localized peaks, one of them situated in lower and the other one situated in higher frequency ranges. Third, both low- and high-frequency peaks shift from below to around 8 and 64 Hz, respectively, between resting and running states.
We explicitly quantified the change in spectral power between behavioral conditions by computing the relative power taking resting as a baseline for running activities. For each trial, we divided the power values at each frequency of the level-average running spectrum by the corresponding values of the resting spectrum. We then performed statistical tests of the null hypothesis of no difference between resting and running power separately for the data in each frequency bin by comparing the respective values pooled across all electrodes against those of alternative distributions obtained through random assignment of epoch labels (Section 2.7.4). Panel b of Figure 3.3 shows the grand average relative power spectra of cortical and striatal monopolar LFPs. A strong increase of power is obvious across almost the entire spectrum in both structures which is largest in terms of magnitude and variability in lower regions where also distinct peaks below and above 8 Hz can be observed. The increase of raw power is smaller in intermediate regions reaching its lowest values around the resting high peak-frequency. After that, power increases again and reaches a plateau beyond the running high peak-frequency (cf. panel a of Figure 3.3). These changes of spectral power are statistically significant in both structures and across the whole frequency range investigated (paired, two-sided Wilcoxon sign-rank tests, pă0.01;n“24 and n“30 cortical and striatal electrodes, respectively).
Panel c of Figure 3.3 depicts the grand average power spectra computed from bipolar derivations of cortical and striatal LFPs (Section 2.6.2.2). As in the case of monopolar
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Figure 3.3: Grand average raw LFP power. (a) Monopolar LFPs: raw, normalized power. (b) Monopolar LFPs: relative, normalized power. (c) Bipolar LFPs: raw, nor-malized power. (d) Bipolar LFPs: relative, nornor-malized power. Results are given as mean˘sem. Black dashed lines in panels b and d indicate no change. Colored bottom lines denote significance.
LFPs, bipolar spectra all exhibit a bimodal distribution of power between lower and higher frequency ranges. Second, power mostly increases between resting and running states and most prominently so at lower frequencies. Third, a small, positive shift of low peak frequencies can be observed in both cortex and striatum between behavioral states. However, absolute power values in both structures are smaller in the bipolar as compared to the monopolar spectra, and power changes between rest and running are also markedly reduced. In addition, power is more broadly distributed in the high frequency range. As a result, either no or far less prominent high-frequency peaks are present in bipolar spectra as compared to monopolar ones, with no obvious shifts of peak frequencies between resting and running states. Also, in most of the spectra from single subjects peak frequencies were found to be different from their monopolar counterparts and they were more diverse in terms of exact location, overall shape, and magnitude of
shift. We note here, however, that we did indeed also observe high-frequency peaks and associated shifts in some within-subject average power spectra from both structures.
Panel d of Figure 3.3 depicts the grand average relative power spectra of bipolar LFPs.
Overall, they exhibit similar qualitative characteristics as their monopolar counterparts.
Note, however, the smaller absolute values of bipolar as compared to monopolar relative LFP power in both structures and the larger variability in mid-frequency regions of striatal spectra. Still, power changes in both low and high peak-frequency ranges as defined based on monopolar raw spectra were found to be statistically significant in the bipolar case as well (paired, two-sided Wilcoxon sign-rank tests, p ă 0.01; n “12 and n“22cortical and striatal bipolar electrodes, respectively).
3.3.1.2 Percentage LFP power
In view of the marked, spectrum-wide increase of raw power between rest and running we aimed to determine the relative contributions of power components from different fre-quency ranges to the total amount of power in the whole spectrum during both behavioral states. To this end, we divided each individual power value of the frequency-normalized spectra of each level by the sum of all values of the respective spectrum. This is a common approach in spectral analysis of neuronal signals and yields a representation of power in each frequency bin expressed as percentage of total power in the whole spectrum.
Figure 3.4 depicts the grand averages of percentage power of monopolar (panel a) and bipolar (panel c) cortical and striatal LFPs. Some of the major findings described in the previous section (3.3.1.1) are present here as well, including a bimodal distribution of fractions of power between upper and lower parts of the spectra as well as a shift of peak frequencies between rest and running in both low and high frequency ranges. Remarkably, percentage power values in the different parts of the spectra are practically equal between the two structures during rest. Note, however, that the fraction of high-frequency power during running is larger in striatum as compared to cortex.
Changes of percentage power between behavioral states are again quantified explicitly in relative power spectra shown in panels b (monopolar LFPs) and d (bipolar LFPs) of Figure 3.3.1.2. Fractions of monopolar power increase between rest and running almost exclusively in the lowest frequency range between 4 and 16 Hz while they are diminished from above that point up to about 64 Hz and largely unaltered from there up to the end of the spectra, as is also confirmed by the results of corresponding statistical tests (paired, two-sided Wilcoxon sign-rank tests, p ă 0.01; n“ 24 and n“ 30 cortical and striatal electrodes, respectively). In contrast, percentage bipolar power values change in a statistically significant fashion only in terms of a decrease between 16 and 32 Hz in
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Figure 3.4: Grand average percentage LFP power. (a) Monopolar LFPs: raw, percent-age normalized power. (b) Monopolar LFPs: relative, percentpercent-age normalized power. (c) Bipolar LFPs: raw, percentage normalized power. (d) Bipolar LFPs: relative, percentage normalized power. Results are given as mean˘sem. Black dashed lines in panels b and d indicate no change. Colored bottom lines denote significance.
both cortex and striatum (paired, two-sided Wilcoxon sign-rank tests, pă0.01;n“12 and n“22 cortical and striatal bipolar electrodes, respectively).
We obtained valid monopolar LFP data from both structures and both behavioral states in 7 out of 10 animals initially implanted and valid data from the striatum of another subject. Grand average results presented here and above (Section 3.3.1.1) were highly consistent across animals. In the case of raw LFP power, with the exception of 2 cortical and 3 striatal within-subject averages all spectra unambiguously exhibited all three of the above described characteristics. In the others, low-frequency peaks and their shifts were variable or hardly present at all. In contrast, high-frequency peaks were much more robust and could be observed in all cortical and all striatal spectra during rest as well as in all striatal and all but one cortical spectrum during running, which holds also true for their shifts. In the case of percentage power spectra, within- or between-trial
fluctuations of power are more readily leveled out through normalization, rendering some qualitative findings even more distinct in certain subjects.
3.3.2 Power: Multi-Unit Activities (MUA)