A common approach for studying entrainment in tACS-studies is to administer tACS at a fixed frequency within the frequency band of interest for all participants of the study (e.g., 10 Hz for Alpha, and 20 Hz for Beta, as in Lafleur et al., 2021). Although all neural regions respond to all frequencies to some degree, there is evidence to suggest that specific corticothalamic networks have preferred frequencies (see Rosanova et al., 2009; Okazaki et al., 2021). Target regions for stimulation are chosen based on the regions that are a part of the functional neural network that is relevant for the research question. The preferred frequency of that region (i.e., the endogenous frequency) is chosen as the fixed stimulation frequency so that the endogenous frequency can synchronize to the applied frequency. Perceptual stimuli can then be presented at certain phases of an oscillation, and causal conclusions can be drawn based on differences in reported perception at different phases of that oscillation. Studies using this approach show that positive and negative oscillatory phase are generally associated with improved and impaired perception, respectively. For instance, Riecke et al. (2015) applied delta (4-Hz) stimulation while participants heard near-threshold click trains presented at different parts of the delta phase. They found that participants were better able to perceive click trains presented in the positive parts of the delta phase than those presented in the negative parts.

The lack of neural measures (e.g., EEG and MEG) to test the physiological effects of tACS in studies can sometimes limit interpretation of the neural basis of phasic modulation of behavior. In the ideal case, evidence for entrainment would come from studies that analyze behavioral and electrophysiological data during stimulation (which can help assess phase modulation during stimulation), as well as after stimulation (which can help assess the lasting effects of entrainment). Studies that do measure electrophysiological data during human tACS find a huge stimulation artifact which complicates data analysis. The artifact produced by tACS is difficult to filter out because the frequency of stimulation is often chosen to match the frequency of interest. Thus, if the artifact is not completely removed, it is likely that it would leave systematic noise that would also be consistent with evidence for neural entrainment. Although there have been several attempts to remove the stimulation artifact and analyze physiological data during stimulation (e.g., Helfrich et al., 2014a,b; Neuling et al., 2017), there is no consensus on whether any methods remove the stimulation artifact effectively (see Noury et al., 2016; Noury and Siegel, 2018).

Many researchers bypass the issue of stimulation artifact rejection by focusing on online behavioral effects (such as the phase dependent modulations of behavior described above) and/or offline physiological effects (referred to as “aftereffects”). Aftereffects may be, for example, an increase in post- versus pre-stimulation power (e.g., Zaehle et al., 2010; Neuling et al., 2013; Kasten et al., 2016), or an increase in phase coherence between two cortical regions (e.g., Helfrich et al., 2016; Schwab et al., 2019).

In studies that examine tACS aftereffects, there is mixed evidence for the effects of stimulation on specific oscillatory frequencies when stimulating with a fixed frequency. For example, Harada et al. (2020) found that performance on a visuomotor learning task improved after 10-Hz alpha stimulation in comparison with a 20-Hz stimulation and sham conditions. However, they did not find aftereffects for either stimulation condition which complicates the interpretation of their data. Neuling et al. (2012) found an increase in post- versus pre-stimulation alpha power when participants were stimulated with 10-Hz alpha stimulation; whereas Lafleur et al. (2021) did not find any increases in power in the alpha or beta frequency range after stimulating with 10 Hz and 20 Hz, respectively. The authors note some potential reasons for the lack of aftereffects in their study and the varying results in tACS-studies; among these reasons is the match between stimulation frequency and the peak of the individuals’ endogenous frequency. In the following section, we highlight the possible importance of matching the stimulation frequency to the endogenous frequency of the individual in order to achieve entrainment (Pikovsky et al., 2002; Ali et al., 2013).

Pikovsky et al. (2002) suggest that, at low stimulation intensities, external stimulation is more likely to entrain ongoing oscillations if the external frequency matches the frequency of the ongoing oscillation. For example, Negahbani et al. (2019) applied tACS at several frequencies and intensities, including the individual alpha frequency (IAF), while they measured activity in the posterior parietal cortex of awake ferrets. They found that matching the endogenous frequency with the stimulation frequency produced phase-locking of neural spikes, even at low stimulation intensities. In contrast, stimulation frequencies adjacent to the endogenous frequency required greater stimulation intensities to produce similar phase-locking of neural spikes.

In contrast to animal studies, the young field of tACS research still lacks systematic human studies using an extensive range of frequencies and intensities to map out the parameter space. One approach to mapping out the parameter space is to utilize physiologically plausible computational models. For instance, Ali et al. (2013) used a large-scale cortical network model of spiking neurons to investigate the relationship between stimulation frequency and intensity of stimulation. Their model demonstrates that regions of high-synchrony between tACS and endogenous brain rhythms follow an upside-down triangular shape, referred to as the “Arnold tongue” (see Figure 2). If the stimulation intensity is very low, the frequency of the endogenous oscillator (referred to as the eigenfrequency; Veniero et al., 2015) and the applied frequency of the external driving force must be close to each other to achieve entrainment. If the stimulation intensity is higher, the external driving force could entrain the endogenous oscillations despite a mismatch between the endogenous frequency and the stimulation frequency. However, entrainment may not occur with greater mismatches between the endogenous and external frequencies. Therefore, the Arnold tongue suggests that stimulating with the individual’s endogenous frequency would be the optimal for producing entrainment.

In addition to an Arnold tongue centered on the endogenous frequency, Ali et al.’s (2013) model suggests that there are also Arnold tongues centered on the harmonics of the endogenous frequency (e.g., 1:2 or 2:1 as illustrated by the inverted triangles in Figure 2A). Furthermore, the frequency range that is entrained by the stimulation increases with higher intensity stimulation.

Supporting evidence for Ali et al.’s (2013) model also comes from several studies that correlate the size of tACS aftereffects with the match between the stimulation and endogenous frequencies. For instance, Kasten et al. (2019) showed that the match between stimulation frequency in the alpha band and IAF correlates with the size of the aftereffect. Furthermore, a mismatch between stimulation frequency and IAF over the course of the experiment also accounted for the lack of aftereffects in some conditions. Similarly, while Stecher and Herrmann (2018) reported a lack of alpha-power enhancement after stimulating participants with their IAF, when analyzing the IAF from the last observational window they found that the stimulation frequency matched the IAF in only 20 out of 44 participants by the end of the experiment. In a follow-up analysis, they found that a mismatch between the IAF and the stimulation frequency might explain the lack of tACS aftereffects in their study.

In contrast to the studies outlined above, a mismatch between the stimulation frequency and the endogenous frequency during, or at the end of, an experiment does not always account for the lack of effects observed (e.g., Ahn et al., 2019). Furthermore, a few studies have shown an inverse relationship between aftereffects and deviation between stimulation frequency and IAF (e.g., Vossen et al., 2015). However, as several parameters differ between these experiments, it is difficult to ascertain whether a mismatch between the stimulation frequency and the endogenous frequency would account for differences in aftereffects if all other parameters were equal. These mixed results highlight the need for systematic studies that specifically explore the relationship between the stimulation and endogenous frequencies and tACS effects.

In the previous section, we discussed how a mismatch between the endogenous frequency and the stimulation frequency may produce weaker entrainment effects. However, adding complexity to the issue, there is also evidence that the endogenous frequency within the individual shifts over time (Haegens et al., 2014; Benwell et al., 2019). Benwell et al. (2019) demonstrated that endogenous frequency determined at the start of an experiment may not match with the endogenous frequency over the entire course of the experiment. Based on the assumptions of the Arnold tongue (Ali et al., 2013) at low stimulation intensities a match between the stimulation frequency and endogenous frequency produces maximal entrainment effects. However, if the endogenous frequency is measured at the start of an experiment to determine the stimulation frequency and then the endogenous frequency shifts over time, there would be an increasing mismatch between the stimulation frequency and endogenous frequency over the course of the experiment.

In order to address the mismatch between the stimulation frequency determined at the start of the experiment and the endogenous frequency during the course of the experiment, Stecher et al. (2021) used a “closed-loop” stimulation approach. The authors compared aftereffects from a sham condition to stimulation conditions with IAF determined either at the start of the experiment, or measured and updated throughout the experiment (i.e., closed-loop stimulation). During both stimulation conditions, the authors applied 8 s of tACS, followed by 8-s breaks in which they recorded EEG. In the closed-loop condition, data from the breaks were used to calculate the IAF and update the frequency for the next 8 s of stimulation. In order to test for behavioral effects of entrainment during stimulation, participants were required to detect near-threshold light that was presented in four different phases of the stimulation sine wave.

Contrary to Stecher et al.’s (2021) hypothesis, the closed-loop protocol did not produce significantly stronger aftereffects as compared with the fixed IAF stimulation or the sham condition. However, there was a significantly stronger aftereffect for the fixed IAF stimulation condition as compared with sham. Furthermore, the authors did not find modulations of near-threshold light detection in either of the stimulation conditions compared with the sham condition. The authors suggest that this lack of behavioral modulation as a function of phase may be due to inclusion of only four bins, which Zoefel et al. (2019) suggest may be too few to observe phasic modulations given the number of trials included in the experiment. A similar study with a larger number of phase bins, or an analysis of artifact-free data during stimulation, may provide a clearer picture of whether entrainment occurred during either of the stimulation conditions.

Stecher et al. (2021) also discussed the challenges to obtaining an accurate estimate of the IAF from short recordings that are contaminated with artifacts. They suggest that future closed-loop designs may benefit from advanced online EEG artifact rejection methods, as these may allow for a better approximation of the shifting endogenous frequencies. Although their study does not provide compelling evidence for adapting the tACS stimulation frequency throughout the experiment, it highlights specific considerations and avenues for future closed-loop tACS research.

In contrast to the closed-loop approach utilized in Stecher et al. (2021), the closed-loop approach has also been used to trigger the onset of tACS based on the state of the neural system (e.g., Lustenberger et al., 2016; Ketz et al., 2018). For instance, Lustenberger et al. (2016) used the closed-loop approach to detect (in real time) transient rhythmic activity (called sleep spindles) during sleep and motor memory. The sleep spindle consisted of five peaks above the threshold of zero in the 11–16-Hz range. Once the threshold had been met, tACS stimulation was applied for 1.5 s and there was a lag of 5 s before the next threshold measurement was assessed. Using this approach, the authors found a selective enhancement in the sleep spindle activity post stimulation. Furthermore, they found an enhanced motor memory performance post- versus pre-stimulation, and this correlated with elevated spindle activity. Lustenberger et al. also found that the increase in spindle activity post- versus pre-sleep in the sham condition was also correlated with performance on the motor memory task, suggesting that there is a relationship between spindle activity and cognition. Studies such as these demonstrate the utility of a closed-loop approach, not only in tracking shifting endogenous frequencies but also in timing stimulation based on endogenous frequencies.

A similar closed-loop approach has also been implemented in the TMS literature. Here the ongoing EEG is used to trigger TMS at specific phases of the EEG (e.g., Zrenner et al., 2018; also see Zrenner et al., 2016, for a discussion of different conceptual feedback loops in TMS research). TMS and tACS have also been combined to examine phase-dependent modulation of the motor evoked potential (MEP), which is thought to be a measure of corticospinal excitability. For example, Raco et al. (2016) applied 20-Hz stimulation over the primary motor cortex and applied TMS in four different phases of the ongoing tACS (0, 90, 180, and 270). They found phase-dependent modulation of the MEP, suggesting that the neural state during stimulation is important for accounting for variations in MEPs. The results also illustrate that closed-loop tACS and TMS approaches can be promising avenues for investigating neural entrainment effects.

Animal studies of entrainment have shown that low intensity sinusoidal current can synchronize neuronal spiking activity to the stimulated frequency (e.g., Fröhlich and McCormick, 2010; Ozen et al., 2010), but do not produce aftereffects (see Reato et al., 2013, for discussion). Strüber et al. (2015) point out that the studies in animal models did not aim to investigate aftereffects, and suggest that the discrepancy between shorter stimulation durations in animal versus human studies may account for the lack of aftereffects. Consistent with this hypothesis, Strüber et al. did not find any aftereffects in a human EEG study using short (1-s) stimulation trains, consistent with the durations used in studies in animal models. These results converge with data from Vossen et al. (2015) who also did not find aftereffects when they applied stimulation trains of 3 s. In contrast, they did find aftereffect when they applied stimulation trains of 8 s. Taken together, these data suggest that there may be a critical duration of stimulation required to produce aftereffects.

As animal studies illustrate that entrainment is possible with short stimulation durations, it is possible that entrainment might have occurred in both Strüber et al.’s (2015) and Vossen et al.’s (2015) experiments, and that entrainment can occur without aftereffects (and by extension STDP). However, neither study presents direct evidence of entrainment (i.e., online phasic modulation of electrophysiological or behavioral data). Furthermore, Stecher et al. (2021) did not find evidence for phase-dependent modulations of near-threshold visual-stimulus detection (i.e., behavioral evidence for entrainment), despite using similar stimulation duration as (Vossen et al., 2015) (i.e., 8 s stimulation trains). Stecher et al. (2021) suggest that their results may be due to an insufficient number of phase bins utilized in the study (see Zoefel et al., 2019). Assessing online electrophysiological and/or behavioral consequences of short stimulation durations could help bridge the gap between animal studies and human studies that typically use longer stimulation durations (e.g., Neuling et al., 2012; Helfrich et al., 2014a,b). The results of these future studies would help discern whether entrainment is possible without STDP.

In contrast to online effects of tACS, that are thought to be driven by entrainment, offline effects are discussed as if they are driven by both entrainment (e.g., Neuling et al., 2012) and STDP (e.g., Zaehle et al., 2010). This is likely due to the idea that entrainment may not disappate immediately, and thus it may be possible to observe entrainment effects for a brief period after stimulation (Halbleib et al., 2012; Hanslmayr et al., 2014).

Vossen et al. (2015) showed that entrainment may not be required to produce tACS aftereffects. They applied short durations of IAF tACS with short breaks of an equal duration. They ran four conditions: short/phase continuous (i.e., synchronized phase) with 3 s of stimulation and 3 s of break; long/phase continuous with 8 s of stimulation and 8 s of break; long/phase discontinuous (i.e., asynchronized phase) with 8 s of stimulation and 8 s of break, and phase angle changes of 0, 90, 180, or 270° between trains of stimulation; and a sham condition with only one train of stimulation at the start of the experiment.

As entrainment involves synchronization of the endogenous frequency to the stimulated frequency (which involves phase alignment), it is hypothesized that keeping the phase consistent between stimulation trains would facilitate entrainment. In contrast, changing the phase angle between stimulation trains is thought to disrupt entrainment but not STDP because changing the phase angle does not change the stimulation frequency. Vossen et al. (2015) compared pre- versus post-stimulation EEG and found a significant increase in alpha power after the long stimulation train conditions, in comparison with short stimulation trains and sham. The increased aftereffect was observed irrespective of the continuity of phase, suggesting that entrainment is not required for aftereffects.

Vossen et al. (2015) determined the IAF in the first of four sessions and used it as the stimulation frequency in all four sessions. As the individual frequencies were only determined once, Vossen et al. (2015) also examined the difference between the stimulation frequency and the IAF during each session; in most cases, the stimulation frequency was slightly below the IAF. Furthermore, the mismatch between the stimulation frequency and IAF was positively correlated with the magnitude of the aftereffect in the stimulation condition, relative to sham condition. Vossen et al.’s (2015) result suggests that a match between stimulation frequency and IAF (i.e., the endogenous frequency) may not be required to produce aftereffects (cf. Stecher and Herrmann, 2018; Kasten et al., 2019).

In another analysis, Vossen et al. (2015) compared the phase during intervals between stimulation with the phase of the stimulation train (i.e., the phase locking value), and did not find evidence for phase locking during the intervals. Lack of phase locking suggests that the effects of entrainment do not seem to last beyond the stimulation duration (assuming entrainment did occur during stimulation). Vossen et al.’s (2015) finding of aftereffects in the alpha band irrespective of phase continuity in stimulation trains, in conjunction with lack of phase locking during intervals between stimulation, seem to suggest that plasticity (perhaps STDP), and not entrainment, might be sufficient to produce tACS aftereffects.

There are also alternative interpretations of Vossen et al.’s (2015) findings. It is possible that their novel intermittent-stimulation procedure did not provide sufficient time for entrainment to occur. Most tACS studies use stimulation periods in the order of minutes (e.g., Zaehle et al., 2010; Neuling et al., 2012; Helfrich et al., 2014a,b; Kasten et al., 2016). In theory, this would provide many more oscillation cycles for entrainment to occur, which may in turn lead to aftereffects that are driven by both entrainment and STDP. However, this explanation does not undermine the finding that STDP may be sufficient to account for tACS aftereffects at short stimulation durations. A direct comparison of Vossen et al.’s (2015) results with longer continuous tACS would enable the assessment of whether entrainment could explain aftereffects using typical study durations. Furthermore, a systematic investigation of stimulation durations using (Vossen et al.’s 2015) novel paradigm could help track the time course in which phase-synchronous stimulation (and by extension entrainment) does modulate aftereffects compared with asynchronous phase stimulation.

In another line of logic, if tACS aftereffects are not associated with the specific neural oscillation, then stimulation aftereffects should be present for a wide range of frequencies (i.e., irrespective of the stimulated frequency). Kleinert et al. (2017) targeted the fronto-parietal sites of participants with bifocal 5-Hz theta stimulation that was either in-phase or anti-phase between hemispheres. They found no increase in theta power post- versus pre-stimulation. Instead, they found that alpha power decreased in the sham condition, but there was no such decrease in alpha power post- versus pre-theta stimulation. As alpha power seems to be differently modulated across individuals over time (Benwell et al., 2019), it is worth examining whether Kleinert et al.’s effects are replicable across different studies. In particular, future studies can help determine whether frequencies besides those in the alpha band also vary across time, and if they are also modulated when they are not stimulated/a part of the functional network that is stimulated.

Frequency-independent effects have also been observed when Transcranial Random Noise stimulation (tRNS), another form of non-invasive alternating current, has been applied. TRNS involves applying alternating current at a random range of frequencies and intensities (e.g., Terney et al., 2008). Ghin et al. (2021) found that tRNS applied in random frequencies ranging from 100–600 Hz produced aftereffects in the gamma frequency range. Others report that tRNS increases overall excitability, which is assessed via the magnitude of MEPs recorded post-stimulation (e.g., Chaieb et al., 2011). Antal and Herrmann (2016) suggest that tRNS effects may be attributed to modulation of ion channels and/or the noise raising the peaks of sub-threshold neural oscillations above the threshold for firing (mechanism referred to as stochastic resonance), rather than neural entrainment. Therefore, tRNS effects may support the notion STDP is possible without entrainment.

In contrast to stimulation effects that are unrelated to the stimulated frequency which are outlined above, if tACS aftereffects are associated with entrainment effects, they should occur only in a narrow range of frequencies (including harmonics and subharmonics, as described by Ali et al., 2013), and with frequencies that are coupled (i.e., phase synchronized; see Engel et al., 2013, for a review; also see Thut et al., 2011; Veniero et al., 2015). The majority of studies that report aftereffects have outlined frequency-specific offline effects of stimulation (e.g., Zaehle et al., 2010; Neuling et al., 2013; Kasten et al., 2016). However, there is a paucity of research in humans that systematically investigates an extensive range of stimulation frequencies and their consequences. Instead, we rely on animal research and biologically plausible neural models that can inform choices of stimulation frequency (e.g., Ali et al., 2013). Although this is a sound approach, more empirical human research investigating wider ranges of frequencies may provide strong converging evidence for frequency-specific tACS effects.

Evidence for tACS effects on cross-frequency coupling (or phase coherence) comes from studies that apply bifocal tACS over two different cortical regions, and stimulate each region with a frequency that is either in or out of phase with stimulation in the other region. For example, in an EEG study, Helfrich et al. (2014a) administered bifocal tACS targeting the parieto-occipital areas and administered 40-Hz gamma frequency stimulation which was either in-phase between the hemispheres or anti-phase (i.e., shifted by π between the hemispheres). As perception of horizontal motion is thought to be enhanced when there is phase-coupling in the parieto-occipital areas, the participants performed an ambiguous motion task during stimulation.

Helfrich et al. (2014a) used a stimulation artifact removal method and measured phase coherence between the electrodes during and after the task. They found increased coherence in the gamma frequency band for in-phase stimulation compared with anti-phase stimulation during and up to 20 min after the task. Furthermore, the increase in phase coherence was associated with better performance on the ambiguous motion task. Using source reconstruction, the authors also showed that increased gamma coherence was confined to the parieto-occipital areas (i.e., coherence was location specific). In both stimulation conditions, they also found a decrease in alpha power. Although this modulation is of a different frequency than that stimulated, it is thought to be consistent with the idea that alpha and gamma have an inverse relationship (i.e., there is phase-amplitude coupling between the two frequencies; e.g., Osipova et al., 2008; see Canolty and Knight, 2010, for a review of the functional role of cross-frequency coupling). Taken together, these results show that tACS may modulate the phase relationship between two different regions as well as phase coupling of two frequencies (e.g., alpha and gamma) that may be part of the same functional network.

Schwab et al. (2019) showed that there may be an overlap between entrainment and STDP using an alternative approach to analyzing aftereffects. They administered alpha (10-Hz) stimulation bifocally for 13 min and varied the phase relationship of the stimulated frequency between the two hemispheres. The stimulation was either in phase, antiphase, or jittered phase, where the frequency was shifted between 9.5–10.5 Hz across the two hemispheres. They analyzed the coherence of phase across the EEG sensors pre- versus post-stimulation. Pre-stimulation power was similar across all three conditions. In contrast, post stimulation, the authors reported that connectivity at the sensor level was greatest for the in-phase condition, followed by jitter, and then the anti-phase. The authors argue that connectivity differences can be attributed to the stimulation condition. However, alpha coherence decayed in the first 120 ms after stimulation offset. They also did not analyze data during stimulation. In a subsequent paper, Schwab et al. (2021) used two computational modeling methods to assess data from Schwab et al. (2019) and suggested that STDP (as described in Zaehle et al., 2010) may account for the observed effects.

Taken together, the evidence listed in the three sections above suggests that both entrainment and STDP may account for effects observed in tACS studies; however, the time course of these effects is yet to be established. There is also evidence that, at short stimulation durations, entrainment may not be required to produce tACS aftereffects (Vossen et al., 2015). A systematic investigation of the time in which in-phase versus anti-phase stimulation modulate the tACS aftereffect could help unpack the time course in which entrainment contributes to stimulation aftereffects.

In studies with humans, the choice of tACS frequency is often based on the principles of entrainment (see Pikovsky et al., 2002; and modeling by Ali et al., 2013) and stimulation based on the principles of STDP seem to be incidental. For instance, Vossen et al. (2015) intended to examine the consequences of stimulating at the endogenous frequency, as informed by the theory of entrainment, but discovered that the actual frequencies used were under the endogenous frequencies for some participants, presumably because of natural shifts in endogenous frequency (Benwell et al., 2019). Therefore, studies that explicitly investigate the consequences of stimulating frequencies slightly below and above the endogenous frequency could test whether STDP underlies tACS aftereffects.