2.1.

Data

The data used in this study were aggregated from a variety of research studies conducted between 2018 and 2021. Measurements were obtained under the Macquarie University Ethics Application References 52020640814625 and 5201500948. In total, 310 measurements are included in this dataset. The studies contained a variety of optode-placement montages, sample rates, experimental designs, tasks, and stimuli. As such, it is not appropriate to compare task-evoked responses across measurements. However, a comparison of systemic oscillations within the signal, which are unrelated to the task-evoked aspect of the data (e.g., Mayer waves), is valid.

Although the dataset of 310 measurements contained a variety of experimental designs, all datasets met a minimum criterion for inclusion in this study. All measurements included a stimulus, in which the repetition rate of the stimulus was never a multiple of 10 s, as this would produce a frequency component indistinguishable from the Mayer wave in the data. Further, all measurements included a randomized interstimulus interval. Although the exact range of interstimulus interval duration varied slightly between experiments, the minimum interval jitter across the dataset was 10 s and the maximum was 30 s. Similarly, the task repetition rate was not a multiple of 10 s in any measurement.

All participants were seated in a sound-attenuating booth in a comfortable chair for the duration of the experiments. NIRS data were recorded using a continuous-wave NIRx NIRScoutX device with avalanche photodiode detectors. Measurements were obtained with between 8 and 16 sources and detectors. Experiments lasted between 15 and 80 min. All data were stored in BIDS data format.¹⁹ Data were processed with MNE-Python,^20,21 MNE-NIRS,¹⁸ and Nilearn.^22,23

2.2.

Quantification of Mayer-Wave Parameters

The FOOOF method of Donoghue et al.¹² was employed to quantify oscillations in the fNIRS signal associated with Mayer waves. This method was designed to extract oscillations in neural signals while accounting for the natural structure of the frequency spectrum of neuroimaging signals. As such, it is well suited for quantifying Mayer waves; the method extracts peaks in the power spectra without the need to predefine analysis parameters, such as the signal center frequency or bandwidth.

To quantify the parameters of Mayer waves, a minimal processing pipeline was applied to convert the raw data to oxyhemoglobin concentration. Specifically, the raw data were first converted to optical density. Channels (both long and short) with a scalp coupling index $<0.7$ were excluded from further analysis.²⁴ The scalp coupling index was computed using a frequency range of 0.5 to 1.2 Hz. Next the data were downsampled to 1.7 Hz. The data were then converted to hemoglobin concentration using the modified Beer–Lambert law with a partial pathlength factor of 0.1.^25–27 Channels with a source–detector distance of less than $1.5$ or greater than $4.5\mathrm{cm}$ were excluded from further analysis. Finally, as the oxyhemoglobin measurement contains a greater contribution from Mayer-wave signals than deoxyhemoglobin,⁸ only the oxyhemoglobin signal was retained for further analysis.

The power spectral-density was then calculated for each channel using the Welch method with a Hamming window comprising 300 samples and 150 samples of overlap, and the spectra averaged across all channels per measurement to generate a single-power spectral-density estimate per recording (in units of ${\mu \mathrm{M}}^2/\mathrm{Hz}$). These spectra were then passed to the FOOOF software. The FOOOF software returns estimates of the aperiodic component and oscillations in the signal; if multiple oscillations are detected (e.g., respiratory rate) then the oscillation closest to 0.1 Hz is retained for further analysis as it is assumed to contain a Mayer-wave component. The output of this analysis is a single estimate of the oscillations present in a recording. Utilizing the software provided by the FOOOF authors is recommended, as it reports the oscillations within the likely Mayer-wave range in terms of their center frequency in Hz, bandwidth in Hz, and log power in arbitrary units.

2.3.

Effect of Short-Channel Correction

We evaluated a subset of 222 files that contained data from short-separation channels to quantify the effect of systemic signal attenuation on the presence of Mayer-wave oscillations in the fNIRS signal. After estimating Mayer-wave parameters when no attenuation was applied to the systemic signal (see Sec. 2.2), we employed the same approach with the additional step of reducing the systemic component of the hemodynamic response through the assessment of activity in short channels being applied after resampling. Many methods have been proposed for attenuating systemic components. This study utilized the method of short-channel regression based on the nearest short channel as described in Sec. 2.1.6 of Scholkmann et al.¹⁶ (and implementation as provided by NIRx).^14,16 As a result, the parameters of Mayer-wave oscillations (center frequency, bandwidth, and power) were estimated with and without short-channel-based correction of systemic signals in the hemodynamic response.

A Bland–Altman analysis²⁸ was used to determine whether short-channel correction affected Mayer waves differentially as a function of their amplitude. The bootstrapping approach of Ho et al.²⁹ was used to compare the magnitude of Mayer-wave oscillations with and without short-channel correction.

2.4.

Single Dataset Example

To demonstrate the practical utility of measuring the parameters of Mayer waves, a single, publicly available dataset of 17 participants was analyzed.¹⁸ Participants were exposed to stimuli in a block design protocol but were not asked to actively respond to any stimulus. Each speech stimulus was 5.25 s in duration, blocks were separated by a random interstimulus interval that was randomly selected from a uniform distribution in the range of 10 to 20 s, a complete protocol description is provided with the source of the openly available dataset by Luke et al.¹⁸ The presence of an evoked response to auditory-speech stimuli was quantified at an individual level to determine whether data from participants with larger Mayer waves benefited from correction of systemic components in their hemodynamic responses. Mayer waves were quantified for the data from each participant as described in Sec. 2.2.

The data were analyzed using a generalized linear model (GLM), as, due to the statistical properties of the noise in fNIRS signals,³⁰ this is suggested to be more appropriate than averaging the data. The data were analyzed as described in Ref. 18. Briefly, the raw data were first converted to optical density and then to hemoglobin concentration using the modified Beer–Lambert Law with a differential pathlength factor of 0.1. They were then downsampled to 0.6 Hz, and a GLM was fitted to all channels using a 3-s boxcar function convolved with a glover model.^18,22,31 A cosine drift was included with components up to 0.01 Hz. The fit was performed with a prewhitening procedure using a first-order auto regressive model. Two analyses were performed, one including the mean of the short channels as a regressor in the GLM, and one without any short-channel regressor. Channels over the left and right superior temporal gyri, comprising typical auditory regions of interest, were then combined into a single region of interest using a weighted average of the GLM estimates.³² If the $p$ value of the regressor component of the speech task in the GLM estimate was $<0.05$ (i.e., a significant HbO response evoked by auditory speech), a response was deemed present. As such, for each participant, a task-locked neural response was quantified as either present or absent for both analyses, with and without short-channel regressions.

3.1.

Quantification of Mayer-Wave Parameters on a Cohort of 310 Measurements

The FOOOF algorithm was applied to a cohort of 310 measurements. An oscillatory component was detected in all but four measurements. The mean center frequency of the oscillations was 0.108 Hz and the median value was 0.097 Hz [see Fig. 2(a)]. This was expected as the analysis approach actively selected the frequency component closest to 0.1 Hz in instances when more than one oscillatory peak was identified in the signal. To confirm that the selected peaks were indeed related to Mayer-wave activity, the model was rerun while retaining oscillations with frequencies closest to typical cutoff frequencies used in frequency-band aggregates of Mayer waves, including 0.05 and 0.15 Hz. With these modified parameters, the median frequency of the resulting oscillatory component was essentially unchanged at 0.105 and 0.109 Hz for the lower and upper cutoff frequencies, respectively, demonstrating that the model was fitting robust oscillatory components in the data related to Mayer-wave activity.

Fig. 2

Quantification of Mayer-wave parameters: (a) center frequency of oscillation components, (b) oscillation bandwidth, and (c) power of oscillation component. Note that the power of Mayer waves is not normally distributed, with some participants having much larger values than the group majority.

The bandwidth of the oscillations was highly non-normally distributed with a median value of 0.035 Hz [Fig. 2(b)], corresponding to a typical Mayer-wave frequency range of $\sim 0.065$ to 0.135 Hz. Similarly, Mayer-wave power was not uniformly distributed across participants [Fig. 2(c)]. Instead, the median log power of oscillations was 0.55 a.u., and the distribution was positively skewed. This corresponds to an oscillatory component in the fNIRS signal of $3.5{\mu \mathrm{M}}^2/\mathrm{Hz}$. Nineteen of 310 measurements (6%) contained Mayer waves that were 2 standard deviations above the median oscillation power, largely consistent with anecdotal reports of a small proportion of participants having particularly large Mayer waves. Unbiased quantification of the parameters of these oscillations while including the aperiodic component in the spectra will assist in the development of algorithms for identifying and attenuating these unwanted signals in hemodynamic responses.

These results demonstrate the added utility of the FOOOF method over a simple band-pass power metric. In addition to extracting oscillation power, the proposed technique also quantifies the oscillation center frequency and bandwidth. Although the average values for each metric are in line with expectations from the previous studies, the variability of values demonstrates that further research is required into the underlying cause of the variation and interaction between each characteristic of the Mayer-wave signals. For example, research using a band-pass power metric has shown that the magnitude of Mayer waves varies across the scalp,⁸ yet as demonstrated by Donoghue et al.,¹² this may be caused by either a true variation in oscillation power or confounding variation in another characteristic such as bandwidth. This study included a wide range of sensor positions and experimental designs to demonstrate that the algorithm works for a variety of data, and also to demonstrate the variability in Mayer-wave characteristics. We hope that this new tool will facilitate research into variation in Mayer-wave oscillations across various factors such as scalp position, participant state, and experimental paradigm.

3.2.

Effect of Short-Channel Correction on Mayer Waves

Next, the degree to which the power of Mayer waves is attenuated following short-channel correction was evaluated, and it was assessed if any characteristic of the uncorrected Mayer-wave oscillations (i.e., greater oscillatory power) was associated with larger power attenuation after correction. Of the 310 recordings in the dataset, 222 contained short-channel data, providing a means by which to assess the effect of short-channel correction on Mayer-wave power. These measurements were reanalyzed to quantify the center frequency, bandwidth, and power of the Mayer waves after short-channel systemic correction was applied to the long-channel data.

Applying short-channel correction did not significantly alter the frequency distribution or bandwidth of Mayer-wave components in the signal [Fig. 3(a)]. A small but significant reduction in the signal power of Mayer waves was apparent when short-channel systemic correction was applied to the entire dataset ($\text{effect}=-0.0459$, 95%CI $[-0.066,-0.027]$, $N=222$, $p<0.001$).

Fig. 3

Effect of short-channel correction on the power of Mayer-wave oscillations. (a) Distribution of frequency component of Mayer waves with and without short-channel correction applied. Inset illustrates an example measurement with and without short-channel correction. Note that the increase in power around 0.1 Hz is reduced when correction is applied. (b) Bland–Altman plot illustrating the difference in Mayer-wave power when short-channel correction is applied as a factor of the oscillation power. (c) Paired comparison illustrating the effect of short-channel correction on oscillation power. Note that short-channel correction does not affect the frequency of the oscillation component but does reduce the power of the oscillation, particularly for measurements containing a large Mayer-wave oscillatory component.

The reduction in Mayer-wave power was more pronounced in measurements with a large systemic component in the uncorrected data. Bland–Altman analysis [Fig. 3(b)] demonstrates that the difference in oscillation power when the correction is applied varies as a function of oscillation power. As such, we analyzed the measurements with the largest Mayer-wave power using a median split to divide the dataset into two groups. The group with larger Mayer waves (107 measurements) showed a reduction of 0.11 in log power when short-channel correction was applied ($\text{effect}=-0.11$, 95%CI $[-0.136,-0.086]$, $N=107$, $p<0.001$), whereas the group with smaller Mayer-wave oscillations showed no consistent change in oscillation power following short-channel correction ($\text{effect}=-0.0018$, 95%CI $[-0.0145,0.021]$, $N=115$, $p=0.841$). On this basis, short-channel correction to reduce Mayer-wave components in hemodynamic signals provides significant benefit when Mayer-wave components are relatively large, supporting the HRF modeling of Yücel et al.⁴ Further, short-channel correction does not systematically alter the oscillation component when applied to measurements with small Mayer waves, indicating that short-channel systemic component correction can be broadly applied to fNIRS measurements without unwanted signal distortion.

3.3.

Effect of Short-Channel Correction on the Amplitude of Evoked Responses

Systemic noise can mask the presence of neural responses in fNIRS measurements. Accounting for data obtained from short channels in the signal processing pipeline may mitigate unwanted systemic components and improve the detection of neural responses. As such, we analyzed the measurements from a publicly available dataset¹⁸ comprising fNIRS data of 17 participants, to determine if measurements with large Mayer waves particularly benefited from short-channel correction.

As for the larger data set (Sec. 3.2), data were divided into two groups using a median split of the oscillation power in Mayer waves. Without short-channel regression, just two of nine measurements with the largest Mayer waves were observed to contain significant evoked responses to auditory-speech stimuli. When short-channel regression was employed, however, this increased to eight of nine measurements, suggesting that short-channel correction does indeed improve the detection of auditory-evoked cortical responses in participants with large Mayer waves. These data were collected with an experimental design with randomized interstimulus interval times to minimize listener expectation and mitigate the effect of Mayer-wave contributions. Even greater benefits from short-channel correction may be observed for data collected without randomized interstimulus intervals.