EEG data (16 electrodes, Cumulus Neuroscience dry-sensor 16 electrode headset) were recorded during a resting state and a mismatch negativity task under saline or ketamine injection (Fig. 1A). A pipeline based on multivariate information theory was applied to investigate whether saline could be discriminated against ketamine under both rest and task. The complete set of possible combinations between electrodes at all orders of interactions (from 2 to 16) was assessed (Fig. 1B-C). The EEG used here has been presented previously on reference40, where a detailed description can be found.
Figure 1. Overview of experimental design and data analysis. A. Subjects participated in a double-blind crossover design using portable EEG, capturing both resting states and task-based recordings (namely, a gamified oddball paradigm inducing a typical mismatch negativity). In randomized sessions, participants received both ketamine and saline infusions. B. Analysis of high-order interactions (HOI) entailed measurements of total correlation (TC) and dual total correlation (DTC), O-information and S-information (see Methods). C. Feature selection across the two designs (rest and task) was employed to pinpoint the primary differences between the ketamine and saline conditions.
2.1 Participants
Study participants (N = 30 males, 25.57 +/- 3.74y) were carefully selected to ensure a consistent and controlled environment for the research. To qualify, individuals had to be males aged between 18 and 55. Women were excluded to avoid undetected pregnancy risk and to reduce sample variability. Participants’ health was critically assessed through a physical examination, medical history, vital signs, a 12-lead Electrocardiogram (ECG), and clinical laboratory tests. Participants were excluded if they had a current or past history of psychiatric disorders as per the ICD-10, especially those with a history of drug or alcohol dependence/abuse in the last 6 months. Furthermore, any serious unstable illnesses, including but not limited to hepatic, renal, respiratory, cardiovascular, endocrine, and neurological disorders, led to exclusion. This also encompassed subjects with unresolved seizure causes, conditions that likely alter brain morphology or physiology such as uncontrolled hypertension or diabetes, significant acute illnesses a week before the drug administration, notable history of drug or food allergies, and the use of specific medications including antidepressants, anti-psychotics, anxiolytics, and others. Additionally, color-blind individuals were also not considered for this study. Each participant's commitment to the study's guidelines and restrictions was crucial, and they had to demonstrate their understanding and willingness to participate. This study was approved by the Institutional Review Board of the Otto-von-Guericke University Magdeburg, Germany, and informed consent was obtained from all participants (Approbation code number: 123/18).
2.2 Study Design
The study was a saline-controlled, double-blind, randomized, crossover study with healthy participants in their homes, designed to investigate the acute and delayed effects of ketamine on EEG and behavioral measures. Participants were invited to the laboratory to complete repeated measurements: at enrollment, on the days of infusion of ketamine or saline administration (randomized across two visits), and on the days after infusion (Fig. 1). The two infusion days occurred four weeks apart following the same study protocol. All EEG recordings were performed with the portable dry EEG system developed by Cumulus Neuroscience (www.cumulusneuro.com).
2.3 Ketamine infusion
During the infusion, participants were seated in a comfortable chair, and their legs were elevated on a footrest. Overall mobility was restricted as a cannula was placed in each arm; one for the delivery of ketamine or saline and the other to draw blood samples. Participants were administered a single IV infusion (of a total volume of 50 ml) of 0.5 mg/kg of racemic ketamine hydrochloride over 40 mins or IV saline solution (0.9%) over 40 mins. During the infusions, the tablet was mounted on a tablet holder and operated by the researchers as participants could not bend their arms at that time.
2.4 EEG recordings
EEG data was collected using the wireless 16-channel dry sensor EEG system developed by Cumulus Neuroscience (Cumulus, www.cumulusneuro.com), suitable for use in various supervised and unsupervised settings 34. The analog front-end is based on the ADS1299 chip-set from Texas Instruments, incorporating a high input impedance of 1GΩ, a configurable driven bias function for common-mode rejection, built-in impedance checking, and configurable gain and sampling rates. The left mastoid is used for reference and the right mastoid for driven-bias, with single-use, snap-on electrodes attached to wires extending from the headset. An onboard processor and Bluetooth module transmit 250Hz EEG data to another device (an Android tablet in this case), transferring it to a cloud server for storage and processing. Flexible Ag/AgCl coated polymer sensors of a comb-design (ANT-Neuro/eemagine GmbH) are used to achieve a stable and dermatologically safe contact to the scalp through the hair. The electronics and sensors are mounted on a flexible neoprene net for comfort and ease of montage. Incorporating natural landmarks in the headset form factor and the stretchable structure enable consistent placement by non-experts in line with the 10–20 sensor system.
2.5 Resting-state session
Eyes-closed resting state EEG recordings were collected during the first 20 mins after either saline or ketamine infusion. Participants were instructed to rest with closed eyes and remain still during the recording. For the resting state, the first 10 minutes post-injection were not considered in the analysis to discard transients associated with injection, yielding 10 minutes of stable post-injection resting state performed at home.
2.6 Passive-listening auditory oddball paradigm
During the last 15 minutes of each infusion, we used an app-based version of the passive auditory oddball task developed by Cumulus – Sonic Scenes – eliciting the Mismatch Negativity (MMN) of infrequent ‘deviant’ stimuli in a train of ‘standard’ stimuli. The task was performed passively – the subject merely needed to remain still while listening to repetitive auditory stimuli. The participant was prompted to put on headphones and adjust the volume until he could clearly hear some sample tones. When ready, the participant asked to press play on a silent movie, which lasted 15 mins. Tones played throughout while the participant watched the film. Eight short films were used in an arbitrary cycled order, each consisting of silent clip montages compiled from stock footage. There were no narratives or subtitles. Each movie session incorporated 1000 ‘standard’ tones (100ms; 1000Hz) and 200 pitch deviants (100ms; 1200Hz).
2.7 Subjective scores of dissociative states
We assessed the Clinician-Administered Dissociative States Scale (CADSS), which measures dissociative states 41, and the 5D-ABZ, which assesses self-reported altered states of consciousness 42. CADSS has 3 subscales ("Amnesia", "Derealization", "Depersonalization"), while 5D-ASC entails five dimensions ("Oceanic Boundlessness", "Dread of Ego Dissolution (DED)", "Visionary Restructuralization", “Auditory Alterations”, “Vigilance Reduction“). Both questionnaires were administered in the laboratory 1h before and 1.5hr after the infusion. The scores' difference between before and after infusion were used to rate the subjective changes for both saline and ketamine infusion. All questionnaires used validated German-language versions, except for the CADSS questionnaire translated by the research team as no validated translation was available when the study was conducted.
2.8 EEG data preprocessing
Using Cumulus’ proprietary algorithms, EEG data were pre-processed to correct the integrity of timing information and eye-movement artifacts. For the oddball paradigm, baseline-adjusted EEG data were band-filtered between 0.25–40 Hz and analyzed in 30-s epochs. Corrective procedures are applied for epochs with missing and anomalous data, including eye and movement artifacts. To preserve the same number of channels (16) during the whole analysis, time points from all channels were removed if at least one channel had a flat signal in those points, which was required to explore all the possible high-order interactions. One subject was removed from further resting state analysis because there was < 1s of valid data in the ketamine condition. No differences in the number of selected points were found after the artifact removal (Supplementary Tables 1 and 2) across conditions (ketamine/saline) and recordings (rest/task). Resting-state data were bandpass filtered in the canonical EEG frequency bands: δ: 0.5-4 Hz, θ: 4–8 Hz, α: 8–12 Hz, β: 12–30 Hz, γ: 30–40 Hz). Given that our goal was not to compute ERPs, we pooled all the valid trials (with at least 125ms valid signal) corresponding to the deviant and standard tones separately to perform the analysis. In the following analysis, the 5 bands plus broadband (0.5–40 Hz) data was used for the resting state, while for the tasks only broadband data were used to focus only on the evoked rather than the induced response. EEG data obtained appeared reliable as the standard effects on ketamine vs. saline solution were noticeable in the EEG spectrum (across the alpha peak and typical frequency/power decay, see Figure S1).
2.9 Pairwise and high-order interactions
To assess the hypothesis of ketamine-induced specific effects of redundancy in brain dynamics, different measures of entropy characterizing different properties of brain dynamics were computed. We used tools from multivariate information theory i) to quantify the nonlinear statistical dependencies between all the possible combinations between electrodes and ii) to distinguish the nature of these dependencies in terms of collective constraints (total correlation, TC), shared randomness (dual total correlation, DTC), synergy (O-info < 0), redundancy (O-info > 0), and overarching correlations (S-info) (see reference 35 for a detailed explanation of these measures).
Consider a system of n random variables denoted by Xn = (X1, … ,Xn). The TC, DTC, O-information (O), and S-information (S) are generalizations of the mutual information (MI) 35, which can be respectively expressed as:
$$TC\left({X}^{n}\right) = {\sum }_{i=1}^{n}H\left({X}_{i }\right) -H({X}_{1}, . . . ,{X}_{n})$$
1
$$DTC\left({X}^{n}\right) = H({X}_{1}, . . . ,{X}_{n}) -{\sum }_{i=1}^{n}H\left({X}_{i }\right|{{ X}^{n}}_{-i} )$$
2
$$O\left({X}^{n}\right) =TC\left({X}^{n}\right)-DTC\left({X}^{n}\right)$$
3
$$S\left({X}^{n}\right) = TC({X}^{n}+DTC({X}^{n})$$
4
where \(H({X}_{1}, . . . ,{X}_{n})\)is the joint Shannon’s entropy of the n variables, \(H\left({X}_{i }\right)\) the entropy of the i-th region and \(H\left({X}_{i }\right|{{ X}^{n}}_{-i} )\) is the entropy of the i-th region conditioned by the activity of the whole system without it - which is known as “residual entropy,” and is denoted as \({R}_{i }\). Above, X− in represents the vector of all variables except Xi, i.e., (X1, …, Xi−1, Xi+1, …, Xn). Estimations were performed using the Gaussian copula approximation 25,43. As for n = 2 TC = DTC = mutual information, only the TC was computed for each possible pair of electrodes. For the high-order interactions (from 3 to 16) all metrics were computed for each possible combination of electrodes at each order of interaction (Fig. 1B and C).
Broadband (0.5–40 Hz) and filtered EEG signals (δ: 0.5-4 Hz, θ: 4–8 Hz, α: 8–12 Hz, β: 12–30 Hz, γ: 30–40 Hz) were analyzed considering all the possible combinations of electrodes at each order of interaction, here denoted by k (120 interactions for k = 2, 560 for k = 3, 1.820 for k = 4, 4.368 for k = 5, 8.008 for k = 6, 11.440 for k = 7, 12.870 for k = 8, 11.440 for k = 9, 8.008 for k = 10, 4.368 for k = 11, 1.820 for k = 12, 560 for k = 13, 120 for k = 14, 16 for k = 15 and 1 for k = 16). An n-plet represents a particular combination of n electrodes, and the effect of ketamine on it was assessed via the effect sizes.
2.10 Effect sizes
To characterize the size of the effect associated with each measurement, we used Cohen’s \(d\) effect size for paired samples 44:
\(d = \frac{{\mu }_{ket }-{ \mu }_{sal} }{s}\) (5),
where \({ \mu }_{ket }\)and\({ \mu }_{sal }\) are the average measure of the ketamine and saline condition, respectively, and \(s\) is the standard deviation of the difference of means (i.e \({\mu }_{ket }-{ \mu }_{sal}\)). This metric measures a standardized mean difference between paired samples, and its sign indicates the direction of the effect, i.e. if d > 0 means that ketamine increases the measure.
2.11 Statistical analyses
For the selected features, a non-parametric Wilcoxon sign rank test for paired samples with the False Discovery Rate (FDR) correction for multiple comparisons was performed. As in previous work on HIOs 22–26, the statistical correction was not directly assessed for each HOI given the non-selective data approach, including all interactions 45. Conversely, we used Cohen's D to report the effect size of HOI 22,24,25 as p-values can be artificially inflated. To compute the association between HOI and subjective scores, the change (ketamine - saline) in HOI was (Pearson) correlated with the change in subjective scores, yielding one R2 per n-plet and subjective score. We evaluated the significance of associations by a permutation test followed by post-hoc FDR correction for multiple comparisons. First, we generated a null distribution of R2 values by randomly permuting the correspondence between HOI and subjective scores 1000 times. Only correlations values above the 99.9-th percentile of their respective null distribution were submitted to FDR correction (p < 0.005).