Fractal cycles of sleep: a new aperiodic activity-based definition of sleep cycles

Reviewer #1 (Public Review):

Summary:

In this study, Rosenblum et al introduce a novel and automatic way of calculating sleep cycles from human EEG. Previous results have shown that the slope of the non-oscillatory component of the power spectrum (called the aperiodic or fractal component) changes with the sleep stage. Building on this, the authors present an algorithm that extracts the continuous-time fluctuations in the fractal slope and propose that peaks in this variable can be used to identify sleep cycle limits. Cycles defined in this way are termed "fractal cycles". The main focus of the article is a comparison of fractal and classical, manually defined sleep cycles in numerous datasets.

Strengths:

The manuscript amply illustrates through examples the strong overlap between fractal and classical cycle identification. Accordingly, a high percentage (81%) can be matched one-to-one between methods and sleep cycle duration is well correlated (around R = 0.5). Moreover, the methods track certain global changes in sleep structure in different populations: shorter cycles in children and longer cycles in patients medicated with REM-suppressing anti-depressants. Finally, a major strength of the results is that they show similar agreement between fractal and classical sleep cycle length in 5 different data sets, showing that it is robust to changes in recording settings and methods.

These results suggest that the fractal cycle methodology could provide a valuable new method to study sleep architecture and avoid the time-consuming steps of manual cycle identification. Moreover, it has the potential to be applied to animal studies which rarely deal with sleep cycle structure.

Weaknesses:

The match between fractal and classical cycles is not one-to-one. For example, the fractal method identifies a correlation between age and cycle duration in adults that is not apparent with the classical method. This raises the question as to whether differences are due to one method being more reliable than another or whether they are also identifying different underlying biological differences. It is not clear for example whether the agreement between the two methods is better or worse than between two human scorers, which generally serve as a gold standard to validate novel methods. The authors provide some insight into differences between the methods that could account for differences in results. However, given that the fractal method is automatic it would be important to clearly identify criteria for recordings in which it will produce similar results to the classical method.

Reviewer #2 (Public Review):

Summary:

This study focused on using strictly the slope of the power spectral density (PSD) to perform automated sleep scoring and evaluation of the durations of sleep cycles. The method appears to work well because the slope of the PSD is highest during slow-wave sleep, and lowest during waking and REM sleep. Therefore, when smoothed and analyzed across time, there are cyclical variations in the slope of the PSD, fit using an IRASA (Irregularly resampled auto-spectral analysis) algorithm proposed by Wen & Liu (2016).

Strengths:

The main novelty of the study is that the non-fractal (oscillatory) components of the PSD that are more typically used during sleep scoring can be essentially ignored because the key information is already contained within the fractal (slope) component. The authors show that for the most part, results are fairly consistent between this and conventional sleep scoring, but in some cases show disagreements that may be scientifically interesting.

Weaknesses:

One weakness of the study, from my perspective, was that the IRASA fits to the data (e.g. the PSD, such as in Figure 1B), were not illustrated. One cannot get a sense of whether or not the algorithm is based entirely on the fractal component or whether the oscillatory component of the PSD also influences the slope calculations. This should be better illustrated, but I assume the fits are quite good.

The cycles detected using IRASA are called fractal cycles. I appreciate the use of a simple term for this, but I am also concerned whether it could be potentially misleading? The term suggests there is something fractal about the cycle, whereas it's really just that the fractal component of the PSD is used to detect the cycle. A more appropriate term could be "fractal-detected cycles" or "fractal-based cycle" perhaps?

The study performs various comparisons of the durations of sleep cycles evaluated by the IRASA-based algorithm vs. conventional sleep scoring. One concern I had was that it appears cycles were simply identified by their order (first, second, etc.) but were not otherwise matched. This is problematic because, as evident from examples such as Figure 3B, sometimes one cycle conventionally scored is matched onto two fractal-based cycles. In the case of the Figure 3B example, it would be more appropriate to compare the duration of conventional cycle 5 vs. fractal cycle 7, rather than 5 vs. 5, as it appears is currently being performed.

There are a few statements in the discussion that I felt were either not well-supported. L629: about the "little biological foundation" of categorical definitions, e.g. for REM sleep or wake? I cannot agree with this statement as written. Also about "the gradual nature of typical biological processes". Surely the action potential is not gradual and there are many other examples of all-or-none biological events.

The authors appear to acknowledge a key point, which is that their methods do not discriminate between awake and REM periods. Thus their algorithm essentially detected cycles of slow-wave sleep alternating with wake/REM. Judging by the examples provided this appears to account for both the correspondence between fractal-based and conventional cycles, as well as their disagreements during the early part of the sleep cycle. While this point is acknowledged in the discussion section around L686. I am surprised that the authors then argue against this correspondence on L695. I did not find the "not-a-number" controls to be convincing. No examples were provided of such cycles, and it's hard to understand how positive z-values of the slopes are possible without the presence of some wake unless N1 stages are sufficient to provide a detected cycle (in which case, then the argument still holds except that its alterations between slow-wave sleep and N1 that could be what drives the detection).

To me, it seems important to make clear whether the paper is proposing a different definition of cycles that could be easily detected without considering fractals or spectral slopes, but simply adjusting what one calls the onset/offset of a cycle, or whether there is something fundamentally important about measuring the PSD slope. The paper seems to be suggesting the latter but my sense from the results is that it's rather the former.

Author response:

We thank the reviewers and editors for their review and assessment of our manuscript and comprehensive feedback. The manuscript will be revised to address all the reviewers’ comments. Specifically, to address the comment of Reviewer 1 and the editor regarding the lack of quantitative comparison between the classical and fractal cycle approaches and identification of the source of the discrepancies between classical and fractal cycles, we plan to perform and report the following analyses and comparisons:

(1) Intra-method reliability

a) Classical cycles. An additional scorer will independently define onsets and offsets of all classical sleep cycles for all datasets and mark sleep cycles with skipped REM sleep. Likewise, we will perform automatic sleep cycle detection. We will add a new Supplementary table showing the averaged cycle durations obtained by the two scorers and automatic algorithm as well as the inter-scorer rate agreement and update the Supplemental Excel file with corresponding information for each cycle for each participant for each dataset.

b) Fractal cycles. We will correlate the durations of fractal cycles calculated using the parameters defined in the Main text with those calculated using different parameters, namely, the longer and shorter smoothing window lengths, higher and lower minimum peak prominence. Likewise, we will correlate the durations of fractal cycles calculated using frontal vs other available electrodes.

(2) Origin of method differences

In the current version of our Manuscript, we describe a few possible sources of discrepancies between classical and fractal cycle durations and numbers. Following the suggestion of one of the reviewers, in the revised Manuscript, we will quantify the sources of discrepancies between the two methods in order to identify the “criteria for recordings in which fractal cycles will produce similar results to the classical method”. Specifically, we will calculate the correlation between the difference in classical vs fractal sleep cycle durations on one side, and either the amplitudes of fractal descend/ascend, relative durations of cycles with skipped REM sleep and wake after sleep onset, or peak flatness on the other side.

In addition, we will include a new figure, illustrating the goodness of fit of the data as assessed by the IRASA method. Likewise, we will update Supplementary File 1 (that shows classical and fractal sleep cycles for each participant) with marks that highlight the onsets and offsets of sleep cycles as well as the cycles with skipped REM sleep.