Human Gamma Oscillations during Slow Wave Sleep Figure 4. Percentage of intracranial contacts presenting depth-positive (blue bars) or depth-negative components (red bars) during the IN-phase (left) and ANTI-phase (right) patterns for 15/19 and 7/19 subjects respectively, see the text. This analysis was performed by taken into account all contacts ( ‘‘ALL’’) or only contacts located in the frontal (Fro) and temporal (Tem) cortex. doi:10.1371/journal.pone.0033477.g004 the slow wave cycle (Figure 3D bottom). To further investigate the phase relationship between slow waves and gamma oscillations, we distinguished two different moments of the gamma events: first, the onset time at which the event was first detected (to in Figure 1) and, second, the time at which the event reached its maximal amplitude (tm in Figure 1). In order to quantify whether these events tended to systematically occur at a particular phase of the slow wave, we used a circular statistical test to assess the nonuniformity of the corresponding phase distribution across all the detected slow waves (see Materials and Methods). Quantitative assessment revealed that, from all contacts associated respectively with IN-phase (122 from 15 subjects) and ANTI-phase (21 from 7 subjects) patterns, 44% (54/122) and 52% (11/21) presented statistically significant phase-locking (p,0.01, Rayleigh test for circular uniformity) when considering the event’s onset time, and 52% (64/122) and 52% (11/21) when considering the event’s maximal amplitude time (Figure 5). In accordance with the distributions in time, relative to the central peak of the slow wave, the preferred phases calculated for the onset times and maximal amplitude times respectively, were obtained for the IN-phase and the ANTI-phase patterns at 6.13 radians (,0.5625 sec) and 3.05 radians (,20.015 sec), and at 0.1 radians (,20.5675 sec) and 3.8 radians (,0.125 sec) for the same, respective patterns. Interest- ingly, for the onset time of ANTI-phase patterns, the phases of the slow wave tended to be highly concentrated in a sharp peak, whereas the phases of maximal amplitude time tended to lie in a wider interval. The spatial distribution of the electrode contacts related to each of these two patterns revealed that phase-modulated gamma patterns were strongly expressed in the frontal and temporal lobes (Figure 6). In particular, 39% and 37% of electrodes associated with the IN-phase pattern were localized in the frontal and temporal lobes respectively while, for the ANTI-phase patterns, 29% and 62% of electrodes were associated respectively with the frontal and temporal lobes. This suggests a tendency for the ANTI-phase pattern to be more expressed in temporal regions while the IN-phase pattern was more homogeneously distributed in any of these two lobes (percentages of electrodes in other regions are not presented because the involved contacts were less than 10%, partially due to the fact that most of the contacts were located in frontal and temporal regions, see Table S1). We further examined if the sites expressing IN-phase or ANTI- phase patterns were related to pathological areas. We observed that most of the contacts associated with both modulation patterns were neither located in ictal nor inter-ictal regions. More precisely, from all contacts associated with IN-phase patterns, 84% and 80% were not located respectively in ictal or inter-ictal zones; For ANTI-phase patterns, 90% and 71% of contacts were not correspondingly associated with ictal or inter-ictal zones (Tables S2 and S3). Short-range intracortical coherence of gamma oscillations during SWS The synchronization properties of gamma events occurring at different intracranial contacts during slow waves were evaluated. We first estimated the co-detection probability, i.e. the probability of detecting a gamma event in one contact at a specific time, given that an event has been also detected in another contact, for the same time and for the same frequency band (see Materials and Methods). The distribution of this probability revealed an exponential-like decrement (Figure 7A) which was best fitted to a gamma distribution (4.7961025 mean squared error; shape and scale parameters: k = 0.88 and h = 23.26). This observation implied that the probability to find a co-activation between two arbitrary channels was very low despite the fact that gamma oscillations emerged in a large number of investigated individual channels. This obtained tendency was further confirmed by the relation between the co-detection probability and the distance between contacts, calculated via their Talairach coordinates in the 3D space (n = 11 subjects, Figure 7B). We found that the co-detection probability of gamma oscillations fell off quickly with distance, suggesting that gamma co-activations can only be frequently observed over short-distances, therefore within a single cortical area or between adjacent cortical areas. The slope of the decrement was estimated to be around 20.41 mm per probability percentage, meaning, for example, that the probability for a given PLoS ONE | www.plosone.org 6 April 2012 | Volume 7 | Issue 4 | e33477