3.1. Quantifying pathological gamma oscillations
We quantified the amplitude, frequency, duration, and phase of 4800 manually marked PGOs in the iEEG recordings of all six patients using the training dataset and produced histograms (). From each of the four histograms, we calculated measures of central tendency: amplitude (mean: 10.300 ± 0.187 mV, median: 8.779 mV), frequency (mean: 48.5832 ± 0.7375 Hz, median: 41.861 Hz), duration (mean: 435.073 ± 9.028 ms, median: 361.396 ms), and normalized phase (mean: −0.010 ± 0.020, median: 0.029). Overall, the PGOs were very low-amplitude, low-frequency, brief events in the iEEG.
Fig. 3 The results of the mapping algorithm for four selected interictal records from two patients. In these examples, mapping was executed with a threshold of 2.0 for the normalized rate of PGOs, but the threshold was varied from 0 to 6 for each interictal (more ...)
3.2. Detecting pathological gamma oscillations
We tabulated () the performance and threshold of a conventionally tuned detector and a robustly tuned detector, using the ROC curve and hypothesis-testing, for each patient (). The two thresholds differed in each case, resulting in different performances. The latter approach returned thresholds for higher selectivity than sensitivity in detection, and the former approach returned thresholds with either higher or lower selectivity than sensitivity.
Table A1 We performed both a standard ROC and a probabilistic ROC (pROC) analyses (‘see Appendix’) to compute patient-specific thresholds for the detecting PGOs.
Fig. A1 The hypothesis-tests with an ROC curve computed patient-specific thresholds for robustly detecting PGOs. For each point (threshold of the detector) of the ROC curve (top, blue points), the mean ± SD p-value (bottom, error-bars) was computed. The (more ...)
3.3. Mapping pathological gamma oscillations
We analyzed the spatial distribution of the mapped PGOs relative to the seizure onset zone, the seizure spread, and areas where no seizure occurred using each the average rate and the average median energy of detected interictal PGOs. illustrated the results of the mapping algorithm for the second and sixth interictal records from Patient C (Fig. 3A1–B2) and Patient F (Fig. 3C1–D2). and summarized the results for all patients. We did not execute an omnibus test for Patient F because whose data presented only two categories (i.e., SOZ, SS). But a Wilcoxon sign-rank test showed no statistically difference between the SOZ and the SS for both the average rate (SOZ: mean = 5.85 ± 1.52/min, median = 4.29/min; SS: mean = 7.22 ± 1.35/min, median = 6.39/min; pF = 0.236) and the average energy (SOZ: mean = 222.42 ± 28.84 μV2, median = 175.22 μV2; SS: mean = 228.82 ± 19.63 μV2, median = 223.58 μV2; pF = 0.074). The omnibus tests found a statistically significant difference in average rate between at least one pair of categories for 3 of the 6 remaining cases (3/5 patients) (pA = 0.025, pB = 0.074, pC1 = 0.034, pC2 = 0.223, pD = 0.039, pE = 0.368) and a statistically significant difference in average median energy between at least one pair of categories for 2 of the 6 remaining cases (2/5 patients) (pA = 0.018, pB = 0.015, pC1 = 0.223, pC2 = 0.846, pD = 0. 472, pE = 0.236).
Fig. 5 We compared the normalized PGO-rate (dark blue box-plots) and normalized median PGO-energy (light blue box-plots) across the SOZ, SS, and NS for each patient, including statistical outliers (black dot and label per specific iEEG electrode). (For interpretation (more ...)
Fig. 6 We computed the percentage of mapped electrodes by clinical label (i.e., SOZ, SS, NS). Each mapped electrode exceeded a threshold (value for normalized PGO-rate; higher value means higher rate) (x-axis) and was counted to compute the percentage (y-axis). (more ...)
Post-hoc tests suggested higher average rates in the SOZ vs. NS for patients A, D, and E but statistical significance for only Patient A (pA = 0.023, pB = 0.225, pC1 = 0.050, pC2 = 0.249, pD = 0.068, pE = 0.059). Post-hoc tests found no difference in average rate between the SOZ and the SS for any of the patients (pA = 0.753, pB = 0.075, pC1 = 0.050, pC2 = 0.401, pD = 0. 144, pE = 0.173). The average rates for the SS and the NS did not statistically differ for all patients except patients A and B (pA = 0.016, pB = 0.043, pC1 = 0.674, pC2 = 0.116, pD = 0. 068, pE = 0.374).
Post-hoc tests for only Patient A demonstrated a statistical difference in average median energy between the categories with the most energy in the SOZ, lesser energy in the SS, and the least energy in NS (SOZ: mean = 941.77 ± 160.22 μV2, median = 1027.58 μV2; SS: mean = 764.40 ± 87.83 μV2, median = 795.61 μV2; NS: mean = 517.09 ± 43.97 μV2, median = 448.08 μV2; SOZ vs. NS: pF = 0.039; SS vs. NS: pF = 0.016; SOZ vs. SS: pA = 0.064). For Patient B, more energy was distributed in the SOZ than the NS (SOZ: mean = 473.82 ± 156.73 μV2, median = 291.66 μV2; NS: mean = 233.14 ± 68.57 μV2, median = 169.45 μV2; pB = 0.043) but no clear differences in the other pairings (SS vs. NS: pF = 0.080; SOZ vs. SS: pA = 0.345). Except for SOZ vs. NS in Patient C1 (SOZ: mean = 194.61 ± 28.18 μV2, median = 179.47 μV2; NS: mean = 272.40 ± 48.56 μV2, median = 245.04 μV2; pC1 = 0.017), post-hoc tests (n = 13, p > 0.093) for Patients B–E did not demonstrate statistical significance.
Overall, we noticed an inconsistent relationship between the areas of ictal onset and the measure average median energy but a somewhat consistent relationship between the areas of ictal on-set and the measure average rate.
3.4. Mining pathological gamma oscillations
We analyzed the spatial distribution of the mined PGOs relative to the seizure onset zone, the seizure spread, and areas where no seizure occurred using each the average rate and the median energy measures, but discussed results for the former measure since the results of the mapping algorithm with the median energy of detected interictal PGOs did not produce many statistically significant results. illustrated the results of the mining algorithm for the second and sixth interictal records from Patient C (Fig. 4A1–B2) and Patient F (). summarized the results for all patients. We noticed that mined PGOs mainly localized in electrodes with seizure spread or no seizures (), excluding the iEEG from Patient D, which demonstrated clustered electrodes in mainly either the SOZ or SS, and Patient E, which presented an even distribution of mined PGOs in SOZ, SS, and NS for lower FIM supports (values < 0.50) and mined PGOs in either SOZ or SS for higher FIM supports. For patients other than D and E, varying the FIM support did not considerably change the corresponding findings.
Fig. 4 The results of the mining algorithm for four selected interictal records from two patients. Mining was executed with a support of 0.10—one cluster of electrodes per 6 min—in this example but the support was varied from 0.10 to 0.90 for (more ...)
Fig. 7 We computed the percentage of mined electrodes by clinical label (i.e., SOZ, SS, NS). Each mined electrode exceeded a threshold (value for consistency in connection between a group of electrodes with high normalized PGO-rates; higher value means more (more ...)
The omnibus test found a statistically significant difference in counted mined electrodes between at least one pair of categories for all patients at certain FIM supports (pA < 0.026: 0.10 < λ < 0.90, pB < 0.022: 0.10 < λ < 0.40, pC1 < 0.021: 0.10 < λ < 0.50, pC2 < 0.013: 0.10 < λ < 0.20, pD < 0.032: 0.10 < λ < 0.30, pE > 0.206: 0.10 < λ < 0.80, pF < 0.001: 0.10 < λ < 0.90). Post-hoc tests suggested higher counts in the SS vs. SOZ for patients A, B, C1, C2, and F (pA < 0.013: 0.10 < λ < 0.90, pB < 0.007: 0.20 < λ < 0.30, pC1 < 0.007: 0.30 < λ < 0.50, pC2 < 0.003: 0.10 < λ < 0.20, pD > 0.317: 0.10 < λ < 0.30, pE > 0.194: 0.10 < λ < 0.80, pF < 0.001: 0.10 < λ < 0.90), higher counts in the NS than SOZ for patients all patients except D (lower counts in NS vs. SOZ) and both E and F (no difference) (pA < 0.007: 0.10 < λ < 0.90, pB < 0.020: 0.20 < λ < 0.30, pC1 < 0.007: 0.30 < λ < 0.50, pC2 < 0.020: 0.10 < λ < 0.20, pD < 0.035: 0.20 < λ < 0.30, pE > 0.257: 0.10 < λ < 0.80, pF < 0.257: 0.10 < λ < 0.90), and typically no difference in counts between SS and NS except for patents A (more counts in NS than SS) and both D and F (more counts in SS than NS) (pA < 0.002: 0.10 < λ < 0.50, pB > 0.102: 0.20 < λ < 0.30, pC1 < 0.274: 0.10 < λ < 0.50, pC2 < 0.182: 0.10 < λ < 0.20, pD < 0.035: 0.10 < λ < 0.50, pE > 0.077: 0.10 < λ < 0.80, pF < 0.001: 0.10 < λ < 0.90). Overall, we determined that mined PGOs cluster in all areas of the brain but mostly in the SS and/or NS compared to the SOZ.