Novel Cyclic Homogeneous Oscillation Detection Method for High Accuracy and Specific Characterization of Neural Dynamics

Reviewer #1 (Public Review):

Summary: The study introduces and validates the Cyclic Homogeneous Oscillation (CHO) detection method to precisely determine the duration, location, and fundamental frequency of non-sinusoidal neural oscillations. Traditional spectral analysis methods face challenges in distinguishing the fundamental frequency of non-sinusoidal oscillations from their harmonics, leading to potential inaccuracies. The authors implement an underexplored approach, using the auto-correlation structure to identify the characteristic frequency of an oscillation. By combining this strategy with existing time-frequency tools to identify when oscillations occur, the authors strive to solve outstanding challenges involving spurious harmonic peaks detected in time-frequency representations. Empirical tests using electrocorticographic (ECoG) and electroencephalographic (EEG) signals further support the efficacy of CHO in detecting neural oscillations.

Strengths:

1. The paper puts an important emphasis on the 'identity' question of oscillatory identification. The field primarily identifies oscillations through frequency, space (brain region), and time (length, and relative to task or rest). However, more tools that claim to further characterize oscillations by their defining/identifying traits are needed, in addition to data-driven studies about what the identifiable traits of neural oscillations are beyond frequency, location, and time. Such tools are useful for potentially distinguishing between circuit mechanistic generators underlying signals that may not otherwise be distinguished. This paper states this problem well and puts forth a new type of objective for neural signal processing methods.

2. The paper uses synthetic data and multimodal recordings at multiple scales to validate the tool, suggesting CHO's robustness and applicability in various real-data scenarios. The figures illustratively demonstrate how CHO works on such synthetic and real examples, depicting in both time and frequency domains. The synthetic data are well-designed, and capable of producing transient oscillatory bursts with non-sinusoidal characteristics within 1/f noise. Using both non-invasive and invasive signals exposes CHO to conditions which may differ in extent and quality of the harmonic signal structure. An interesting followup question is whether the utility demonstrated here holds for MEG signals, as well as source-reconstructed signals from non-invasive recordings.

3. This study is accompanied by open-source code and data for use by the community.

Weaknesses:

1. Due to the proliferation of neural signal processing techniques that have been designed to tackle issues such as harmonic activity, transient and event-like oscillations, and non-sinusoidal waveforms, it is naturally difficult for every introduction of a new tool to include exhaustive comparisons of all others. Here, some additional comparisons may be considered for the sake of context, a selection of which follows, biased by the previous exposure of this reviewer. One emerging approach that may be considered is known as state-space models with oscillatory and autoregressive components (Matsuda 2017, Beck 2022). State-space models such as autoregressive models have long been used to estimate the auto-correlation structure of a signal. State-space oscillators have recently been applied to transient oscillations such as sleep spindles (He 2023). Therefore, state-space oscillators extended with auto-regressive components may be able to perform the functions of the present tool through different means by circumventing the need to identify them in time-frequency. Another tool that should be mentioned is called PAPTO (Brady 2022). Although PAPTO does not address harmonics, it detects oscillatory events in the presence of 1/f background activity. Lastly, empirical mode decomposition (EMD) approaches have been studied in the context of neural harmonics and non-sinusoidal activity (Quinn 2021, Fabus 2022). EMD has an intrinsic relationship with extrema finding, in contrast with the present technique. In summary, the existence of methods such as PAPTO shows that researchers are converging on similar approaches to tackle similar problems. The existence of time-domain approaches such as state-space oscillators and EMD indicates that the field of time-series analysis may yield even more approaches that are conceptually distinct and may theoretically circumvent the methodology of this tool.

2. The criteria that the authors use for neural oscillations embody some operating assumptions underlying their characteristics, perhaps informed by immediate use cases intended by the authors (e.g., hippocampal bursts). The extent to which these assumptions hold in all circumstances should be investigated. For instance, the notion of consistent auto-correlation breaks down in scenarios where instantaneous frequency fluctuates significantly at the scale of a few cycles. Imagine an alpha-beta complex without harmonics (Jones 2009). If oscillations change phase position within a timeframe of a few cycles, it would be difficult for a single peak in the auto-correlation structure to elucidate the complex time-varying peak frequency in a dynamic fashion. Likewise, it is unclear whether bounding boxes with a pre-specified overlap can capture complexes that maneuver across peak frequencies.

3. Related to the last item, this method appears to lack implementation of statistical inferential techniques for estimating and interpreting auto-correlation and spectral structure. In standard practice, auto-correlation functions and spectral measures can be subjected to statistical inference to establish confidence intervals, often helping to determine the significance of the estimates. Doing so would be useful for expressing the likelihood that an oscillation and its harmonic has the same auto-correlation structure and fundamental frequency, or more robustly identifying harmonic peaks in the presence of spectral noise. Here, the authors appear to use auto-correlation and time-frequency decomposition more as a deterministic tool rather than an inferential one. Overall, an inferential approach would help differentiate between true effects and those that might spuriously occur due to the nature of the data. Ultimately, a more statistically principled approach might estimate harmonic structure in the presence of noise in a unified manner transmitted throughout the methodological steps.

4. As with any signal processing method, hyperparameters and their ability to be tuned by the user need to be clearly acknowledged, as they impact the robustness and reproducibility of the method. Here, some of the hyperparameters appear to be: a) number of cycles around which to construct bounding boxes and b) overlap percentage of bounding boxes for grouping. Any others should be highlighted by the authors and clearly explained during the course of tool dissemination to the community, ideally in tutorial format through the Github repository.

5. Most of the validation demonstrations in this paper depict the detection capabilities of CHO. For example, the authors demonstrate how to use this tool to reduce false detection of oscillations made up of harmonic activity and show in simulated examples how CHO performs compared to other methods in detection specificity, sensitivity, and accuracy. However, the detection problem is not the same as the 'identity' problem that the paper originally introduced CHO to solve. That is, detecting a non-sinusoidal oscillation well does not help define or characterize its non-sinusoidal 'fingerprint'. An example problem to set up this question is: if there are multiple oscillations at the same base frequency in a dataset, how can their differing harmonic structure be used to distinguish them from each other? To address this at a minimum, Figure 4 (or a followup to it) should simulate signals at similar levels of detectability with different 'identities' (i.e. different levels and/or manifestations of harmonic structure), and evaluate CHO's potential ability to distinguish or cluster them from each other. Then, does a real-world dataset or neuroscientific problem exist in which a similar sort of exercise can be conducted and validated in some way? If the "what" question is to be sufficiently addressed by this tool, then this type of task should be within the scope of its capabilities, and validation within this scenario should be demonstrated in the paper. This is the most fundamental limitation at the paper's current state.

References:

Beck AM, He M, Gutierrez R, Purdon PL. An iterative search algorithm to identify oscillatory dynamics in neurophysiological time series. bioRxiv. 2022. p. 2022.10.30.514422. doi:10.1101/2022.10.30.514422

Brady B, Bardouille T. Periodic/Aperiodic parameterization of transient oscillations (PAPTO)-Implications for healthy ageing. Neuroimage. 2022;251: 118974.

Fabus MS, Woolrich MW, Warnaby CW, Quinn AJ. Understanding Harmonic Structures Through Instantaneous Frequency. IEEE Open J Signal Process. 2022;3: 320-334.

Jones SR, Pritchett DL, Sikora MA, Stufflebeam SM, Hämäläinen M, Moore CI. Quantitative analysis and biophysically realistic neural modeling of the MEG mu rhythm: rhythmogenesis and modulation of sensory-evoked responses. J Neurophysiol. 2009;102: 3554-3572.

He M, Das P, Hotan G, Purdon PL. Switching state-space modeling of neural signal dynamics. PLoS Comput Biol. 2023;19: e1011395.

Matsuda T, Komaki F. Time Series Decomposition into Oscillation Components and Phase Estimation. Neural Comput. 2017;29: 332-367.

Quinn AJ, Lopes-Dos-Santos V, Huang N, Liang W-K, Juan C-H, Yeh J-R, et al. Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics. J Neurophysiol. 2021;126: 1190-1208.

Reviewer #2 (Public Review):

Summary: A new toolbox is presented that builds on previous toolboxes to distinguish between real and spurious oscillatory activity, which can be induced by non-sinusoidal waveshapes. Whilst there are many toolboxes that help to distinguish between 1/f noise and oscillations, not many tools are available that help to distinguish true oscillatory activity from spurious oscillatory activity induced in harmonics of the fundamental frequency by non-sinusoidal waveshapes. The authors present a new algorithm which is based on autocorrelation to separate real from spurious oscillatory activity. The algorithm is extensively validated using synthetic (simulated) data, and various empirical datasets from EEG, intracranial EEG in various locations and domains (i.e. auditory cortex, hippocampus, etc.).

Strengths: Distinguishing real from spurious oscillatory activity due to non-sinusoidal waveshapes is an issue that has plagued the field for quite a long time. The presented toolbox addresses this fundamental problem which will be of great use for the community. The paper is written in a very accessible and clear way so that readers less familiar with the intricacies of Fourier transform and signal processing will also be able to follow it. A particular strength is the broad validation of the toolbox, using synthetic, scalp EEG, EcoG, and stereotactic EEG in various locations and paradigms.

Weaknesses: At many parts in the results section critical statistical comparisons are missing (e.g. FOOOF vs CHO). Another weakness concerns the methods part which only superficially describes the algorithm. Finally, a weakness is that the algorithm seems to be quite conservative in identifying oscillatory activity which may render it only useful for analysing very strong oscillatory signals (i.e. alpha), but less suitable for weaker oscillatory signals (i.e. gamma).