Rhythmic light stimulation with a constant frequency elicits steady-state visual evoked potentials (SSVEPS) measurable with electroencephalography (EEG) over the occipital cortex (Silberstein, 1995; Notbohm et al., 2016). Frequency-modulated (FM)-SSVEPs have been introduced as a novel stimulation method for brain-computer interfaces (Dreyer and Herrmann, 2015) which uses a sinusoidal carrier modulated by a second frequency as stimulation signals to evoked SSVEP responses at the difference between carrier and modulation frequency. Traditionally used SSVEPs can be evoked in a wide range of frequencies (Herrmann, 2001) and different stimulation parameters have been investigated in depth (Ng et al., 2012; Kuś et al., 2013; Norcia et al., 2015) along with detailed investigations into brain-computer interface (BCI) applications (Vialatte et al., 2010) as well as their potential user base (Allison et al., 2010). In contrast, detailed comparisons for different stimulation parameters that are required for FM-SSVEP stimulation are missing. In prior research, FM-SSVEPs have been shown in a variety of frequencies with simultaneously flickering light sources (Dreyer et al., 2017) as well as in different attention and perceptibility conditions (Lingelbach et al., 2021a). Other FM-SSVEP stimulation parameters have not been investigated in detail, especially the modulation index. Dreyer and Herrmann (2015) used a modulation index of 0.5 whereas more recent studies used a modulation index of 2.0 (Dreyer et al., 2017; Lingelbach et al., 2021b). The intuitive reasoning behind this increase was that it elevates the signal power in the targeted frequency in the stimulation signal and should therefore equally increase the measured FM-SSVEP power in EEG electrodes over occipital cortex. While this sounds straight-forward, an empirical investigation of this effect is so far missing.

Additionally, an argument against the use of SSVEPs in general is how rhythmic light stimulation affects the potential users. Constant attention to flickering light sources results in user discomfort (Ortner et al., 2011) and increased fatigue levels (Cao et al., 2014). Such effects can be reduced with high frequency stimulation paradigms (Sakurada et al., 2015) but high frequency stimulation can in turn reduce BCI performance (Volosyak et al., 2011). Other methods like amplitude modulated signals (Chang et al., 2014) or specific low frequency signals (Jiang et al., 2022) have been reported to increase user experience as well. In addition, we have previously shown that FM stimulation signals with a high carrier frequency are less perceptible (Dreyer and Herrmann, 2015) and more comfortable (Dreyer et al., 2017) than traditionally used stimulation signals. Similar to the FM-SSVEP power mentioned above, the effect of the modulation index on such subjective user experience factors has to the best of our knowledge not been empirically investigated.

In the current study, our goal was to investigate the effect of changing the modulation index on FM-SSVEP power to guide parameter decisions in future research. We tested four different modulation conditions in three different frequencies. Our results reveal that increasing the signal power in the target frequency through the modulation index does in fact lead to increased FM-SSVEP power in the EEG. In addition, we found a tradeoff between increased modulation index and user-comfort during the stimulation.

We were able to reliably evoked FM-SSVEPS in all three target frequencies with all four modulation indices (see Figure 2A) as well as in their first harmonics. The respective amplitudes and SNRs increased with increasing modulation index. Individual subject data can be found in the Supplementary Materials Data Sheet 1. The SNRs in increasing modulation index order and averaged over frequencies were 4.25, 5.41, 7.08, and 10.6. For individual frequencies, the minimal SNR was 3.0 and the maximum SNR was 13.77. This means we were able to evoke statistically significant FM-SSVEPs at all frequency x modulation index combinations, as based on the SNR estimation approach we used (Meigen and Bach, 1999), SNR significance thresholds are 2.82 (p = 0.05) / 4.55 (p = 0.01). Analysis of variance with a single within-subject factor design with repeated measure revealed significant main effects of the modulation index levels on FM-SSVEP SNR [F(3,39) = 10.73, p < 0.0001] as well as amplitude [F(3,39) = 18.68, p < 0.0001]. Post-hoc pairwise t-tests with false-discovery rate (FDR) adjusted p-values revealed that amplitudes in all combinations significantly (p < 0.01) differed from each other except for the difference between 0.5 and 0.78. All statistical comparisons can be found in the Supplementary Material Tables 1, 2. Additionally, we used a simple linear regression to fit the relationship between our modulation index values and the SSVEP amplitudes combined over frequencies (see Figure 2B) and found a significant relationship [R² = 0.204, F(1,166) = 42.44, p < 0.0001].

These findings empirically confirm the intuitive notion that increased power in the targeted frequency in a frequency-modulated stimulation signal results in increased FM-SSVEP responses.

Our goal in the current study was to assess the effect of different values for the modulation index on the FM-SSVEP response as well as the user experience during stimulation. We used four different values for the modulation index with increasing values leading to elevated sideband power in the target SSVEP frequencies. Our results reveal that these increases translate to stronger FM-SSVEP responses. These stronger responses go along with a rise in the perceived flicker intensity as well as a decrease in comfort during the stimulation.

We provide the missing empirical evidence for this intuitive notion that has already guided the choice of the modulation index in prior literature (Dreyer et al., 2017). Regarding the FM-SSVEP response, it seems plausible to suggest the use of a modulation index which leads to a relatively large amplitude in the first FM sideband especially for BCI applications where a high performance is wanted. It has to be noted, however, that sideband amplitudes in FM signals do not constantly increase with increasing modulation indices, but actually decrease above a certain modulation index threshold (≈ 2), as the power gets distributed to additional sidebands. Exact sideband amplitudes can be calculated using Bessel functions.

Overall, we found visible FM-SSVEP peaks with all modulation indices in all tested frequencies (23, 26, 29 Hz) with significant SNRs (Meigen and Bach, 1999) even though the FM-SSVEP amplitudes were rather small. Prior research has shown that FM-SSVEPs can be reliably classified even at relatively small amplitudes (Dreyer et al., 2017). It has to be taken into account that our stimulus LED only covered a small part of the visual field. For actual BCI implementations, larger stimuli of at least 2° visual angle have been suggested (Ng et al., 2012). Additionally, we also found peaks at the first harmonics of the target frequencies which could be useful for classification approaches (Müller-Putz et al., 2005).

Our results also show that increasing FM-SSVEP power via the modulation index comes with the tradeoff of increased flicker perceptibility and decreased comfort. Depending on the goal of the implementation and the target population, such factors have to be considered. It is quite intriguing to see that the least intrusive stimulation signal (modulation index = 0.25) already results in significant FM-SSVEPs. When user comfort is the highest priority, tweaking other stimulation parameters, stimulation size for example, might be preferable. Whether an increase in FM-SSVEP power via larger stimuli would lead to a similar tradeoff with user experience or not remains to be tested in future research, however.

The current manuscript complements a growing body of research on FM-SSVEPs for which we now have evidence that:

Together, these findings provide a foundation for future FM-SSVEP implementations into BCI applications as well as neurophysiological research approaches.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving human participants were reviewed and approved by Research Ethics Committee, University of Oldenburg, Germany. The patients/participants provided their written informed consent to participate in this study.

AD: study design, manuscript preparation, and data analysis. BH: manuscript preparation, data acquisition, and analysis. CH: study design, manuscript preparation, and study supervision. All authors read and approved the final manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.