Article Figures & Data
Figures
- Figure 1.
Schematic comparison between the current and previous methodologies. a, To relate the peristimulus α phase with visual detection, the correlation approach (top panel), during which a stimulus sequence is arbitrarily presented, quantifies the link between behavioral outcomes and offline sorted prestimulus phases [phase(t−1)] instead of peristimulus phases [phase(t)]. This limitation reflects the constraints of window-based/acausal signal processing that typically utilizes the data extended in time. Specifically, the poststimulus phase activity elicited by the stimulus may crossover into the peristimulus window, thus obscuring direct examination of the effect of the α phase around stimulus onset. Alternatively, noninvasive brain stimulation (NIBS; middle panel) aligns the brain phase with the phase of external stimulation so that stimulus presentation can be locked to the desired phase [phase(t)] of the stimulation waveform; however, concerns regarding the efficacy of such phase alignment have been raised. The current approach instead aims to monitor the instantaneous, endogenous phase in real time to guide phase-locked stimulus presentation (PLSP; bottom panel) to provide directional inference. b, To implement PLSP, the core of the algorithms is to resolve the limitations and artifacts resulting from the system and standard acausal signal processing so that phase (Φ) and instantaneous frequency (IF) at the current time point (black vertical bar) can be accurately estimated. Because the current phase actually indicates the near past phase because of a system-specific time lag, when the current phase approaches the proximity of the future desired phase (red vertical bar), a time delay between tcurrent and tdesired is calculated based on the estimated Φcurrent and IFcurrent. A stimulus is then presented immediately after this time delay to phase-lock to the desired phase. To estimate Φcurrent and IFcurrent, the autoregressive (AR; top panel) algorithm extracts the temporal pattern of the past signal (black curve) to construct a forward-estimated segment (orange curve). The fast Fourier transform (FFT; middle panel) projects the past signal into the frequency domain to capture the dominant frequency and then uses this information (blue curve) to perform forward phase estimation. For the current adaptive Kalman filtering (AKF; bottom panel) algorithm, a new estimated phase (green curve) is recursively formed over time, part way between the measured phase derived from the signal (blue curve) and the predicted phase (brown curve) derived from the state transition function (STF). The STF describes how phase states transition between time points (e.g., t−1 to t) and assumes that the instantaneous phase evolves with a constant IF. To improve phase estimation, the AKF algorithm adaptively favors the contribution of the predicted phase whenever the measured IF exceeds the α range because of signal noise.
- Figure 2.
The general pipeline of phase-locked stimulus presentation (PLSP). Incoming data were consecutively read in chunks of 30 samples (30 ms on average) because of system limitations using rtMEG (Sudre et al., 2011). Three α-cycles of the data segment were extracted back from the current time point and zero-phase bandpass filtered (8–12 Hz). Filtered data were then submitted to each algorithm to estimate the instantaneous phase and frequency at the current time point. To correct for the system lag that occurred during real-time implementation because of data, hardware and real-time sampling processing, the phase/time delay between the current and desired phases was continuously updated. When the phase delay equaled to 90° or 180° during simulation and to 180° during the real-time experiment, a marker (synthetic data), trigger pulse (resting-state MEG data), or a stimulus (visual detection experiment) was labeled or sent immediately to compensate for the lag so that a given desired phase was locked. When the current phase fell within the range of the prespecified phase delay, the pipeline was reinitiated because the system lag was not properly compensated.
- Figure 3.
Algorithm performance during simulated phase-locked stimulus presentation (PLSP). a, Synthetic data. The right panels show the circular histograms of the phase distances between the estimated and predetermined desired α phases collapsed across all four phase conditions for the 90° and 180° phase delays. The distance from the origin indicates the number (1000×) of presentations (estimated desired phases) falling within a bin. The left panels display the accuracy (i.e., the absolute phase distances from the desired phases) and precision (i.e., the spread of the absolute phase distances) as a function of the phase delay and the algorithm. Small accuracy or precision values indicate that the phases estimated by the algorithm are close to the desired phases or more concentrated (high certainty). AR: autoregressive; FFT: fast Fourier transform; AKF: adaptive Kalman filtering. b, Same format as in a but using resting-state MEG data from 15 participants. The circular histograms were collapsed across all phase conditions and participants. Individual participants’ accuracies and precisions in absolute phase distance are displayed for each phase condition, in which horizontal lines indicate mean values and error bars represent ± within-subject SEM.
- Figure 4.
The design and behavioral results of real-time visual detection experiment. a, Task design. Between the fixation and the target, a jittered blank screen (mean ± SD across participants) was naturally introduced by the analysis pipeline, reflecting its decision time for forward phase estimation. When the instantaneous phase derived from the predetermined posterior parietal MEG signal (red dot) approached the proximity of the desired phase (i.e., 180° of the phase delay from the future desired phase), the phase-locked target was presented at a given desired phase after accounting for the delay. Half of the trials contained both the target and mask (masked-target), a quarter of the masked-only trials had a blank screen in place of the target, and the remaining quarter of the target-only trials were without the mask. The stimuli were adjusted at the individual luminance threshold and thereby physically identical across trials. b, Detection rates of the phase-locked masked targets as a function of the desired α phases. The red horizontal lines indicate mean values and are connected by the dotted lines. The profiles of the individual participants are depicted on the top, where the detection rates are z score normalized for visual comparison; *p < 0.05.
- Figure 5.
Assessment of the real-time adaptive Kalman filter (AKF) performance of phase-locked stimulus presentation (PLSP). a, Real-time AKF performance of PLSP during the masked-target trials. The left panel shows the time courses of the cosine-similarity version of the intertrial phase coherence (ITCCS) during the masked-target trials from the predetermined sensor. The ITCCS courses are plotted according to the original results and the surrogate control, which were created by computing the mean of surrogate ITCCS values derived from the surrogate time series of the original data for 1000 repetitions. The green horizontal bar highlights the significant period. Shaded regions indicate ± within-subject SEM; **p < 0.01. The middle panels show the circular histograms of the absolute phase distances between the estimated and predetermined desired α phases collapsed across participants for each desired phase. The distance from the origin indicates the number of presentations falling within a bin. The right panels display individual participants’ accuracies and precisions in absolute phase distance as a function of the four phases. Red horizontal lines indicate mean values, and error bars represent ± within-subject SEM. b, Real-time AKF performance of PLSP during the mask-only trials. Same format as in a.
- Figure 6.
The neural dynamics underlying phase-dependent visual detection. a, Time courses of the event-related fields (ERFs) during the masked-target trials from the predetermined parietal sensor. The ERFs are plotted according to the behavioral outcome (hits vs misses) and the desired phase (90° vs 180°). The green horizontal bar highlights the significant period for the interaction effect. Shaded regions indicate ± within-subject SEM; *p < 0.05. b, Same format as in a but using the target-only miss trials and the masked-only hit trials. The green dotted horizontal bar highlights the significant interaction based on the period identified from the masked-target trials. c, Subject-averaged representational dissimilarity matrices of the ERFs based on hits (H)/misses (M) and phases from the masked-target trials (left panel) or from the mask-only and target-only trials (right panel). The matrices were constructed by calculating cosine similarity between the ERFs during the significant interaction period (horizontal green solid or dotted line). Each matrix is separately rank-transformed and scaled into [0,1]. d, Decoding the relevance of the data during the significant interaction period in shaping behavioral outcomes. A logistic regression classifier was separately trained to distinguish hit trials versus miss trials based on single-trial MEG activity recording from the 90° or 180° desired phase. Classifier output on test trials produced higher decoding detection during the 90° relative to 180° phases after repeated stratified cross-validation; *p < 0.05.
- Figure 7.
The generalization of phase-dependent neural modulation. a, Schematic of the analysis flow. The green diagram represents the analyses that were conducted on the predetermined sensor, whereas the black diagrams represent the remaining sensors with similar or dissimilar phase-locked behavior to be examined. b, Scalp topographies of the circular means of the absolute phase distances from the 90° (top panel) and 180° (bottom panel) desired phases at target onset after collapsing across participants. The green solid circles indicate the predetermined posterior parietal sensor (p < 0.05). c, Scalp topographies of the event-related field (ERF) interaction on the hit-miss differences between the 90° and 180° desired phases during the effect period (70–121 ms). The green crosses highlight the sensors exhibiting significant interactions. Among those sensors, the red circles highlight the ones whose single-trial peristimulus phase distributions closely matched that of the predetermined sensor (p < 0.05).
- Figure 8.
A schematic comparison between the previous correlation and current phase-locked stimulus presentation (PLSP) approaches. Notably, although both the PLSP and correlation approaches produce the relationship between phases and behavioral outcomes, the generative processes underlying this relationship are different.
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