Closed-loop Neurostimulation: Targeting human theta oscillations during REM sleep

Closed-loop Neurostimulation: Targeting human

theta oscillations during REM sleep

Bachelor thesis Jasmijn de Mari

Student number: 11692103

Daily Supervisor: João Nascimento Patriota Assessor: dr. Lucia Talamini

Examiner: dr. Joost van Kordelaar

Abstract

Objectives: Theta oscillations, a prominent feature of REM sleep, are increasingly studied for

their relation with emotional memory consolidation. However, discrepancy exists regarding frequency range of theta in humans. Closed-loop neurostimulation is a method which allows for specific targeting of a specific oscillation phase by making real-time phase predictions in an ongoing EEG signal. Where CLNS has been employed in the context of slow oscillations, this study assessed whether this is additionally possible for REM theta cycles (4-8Hz).

Methods: Offline simulations were run using a previously developed phase targeting algorithm

by Cox, Korjoukov, Boer & Talamini (2014b). This algorithm makes phase predictions by fitting an input EEG signal to a sine wave between a set frequency range (4-8Hz). Various algorithm parameters and thresholds can be implemented which restrict the algorithm of making predictions. The effect of implementing different combinations of the parameters and thresholds on the mean target phase, the standard deviation and the stimulation frequency were assessed when the algorithm was instructed to target the 0 phase of theta cycles.

Results: Results show that using approximately two theta cycles (32ms) to make a prediction,

requiring the fit correlation between the sinusoidal model and the EEG signal to be minimally 0.85 and the signal to have a minimal amplitude of 15V within the 32ms time frame, resulted in accurate 0 phase targeting of theta cycles. Using two theta cycles (32ms) to make a prediction showed improved results over using one theta cycle (16ms).

Conclusion: This study showed that using a developed phase targeting algorithm previously

employed in the context of slow waves, additionally allows for accurate 0 phase targeting of REM theta cycles. If the suggested algorithm settings also allow for accurate targeting of processing happening at 4-8Hz during real-time recordings, this may provide useful insights on the fundamental role of human theta oscillations.

Keywords

Theta oscillations, Theta cycles, REM sleep, targeted memory reactivation (TMR), closed-loop neurostimulation (CLNS), phase prediction, phase targeting, 0 phase, electro-encephalogram (EEG), emotional memory

Introduction

Sleep impacting the consolidation of memory is a repeatedly observed phenomenon dating back to over more than a century (Ebbinghaus, 1885; Heine, 1914; Jenkins & Dallenbach, 1924). Over this century a lot of advances in sleep and memory research have been made. It has originally been suggested that sleep plays a passive role in memory consolidation by providing a timeframe in which interfering stimuli are absent (Jenkins & Dallenbach, 1924). Currently, a more active role for sleep in memory consolidation is considered. This theory states that reactivation of previously learned memories during sleep is what leads to optimized consolidation (Buzsaki, 1989; for a comprehensive review see Rasch & Born, 2013).

A dampened receptiveness to external stimuli is preserved when a person is asleep (Kote, Etienne & Campbell, 2001; Kakigi et al., 2003). Presenting sensory stimuli in this time frame can therefore influence the information processing taking place. Both auditory and olfactory cues have shown to lead to reactivation of associated memories and potentially result in a strengthened form of that memory (Rudoy, Voss, Westerberg, & Paller, 2009; Rasch, Buchel, Gais, & Born, 2007; Cousins, El-Deredy, Parkes, Hennies, & Lewis, 2014). It is believed that this strengthened memory representation results from this targeted memory reactivation (TMR) influencing the repeated replay of memories during sleep, thereby tapping into the normal consolidation mechanisms (for a comprehensive review see Lewis & Bendor, 2019). Memory reactivations during sleep are observed in the form of hippocampal sharp wave-ripples and corticothalamic sleep spindles (Cox, Driel, Boer, & Talamini, 2014a). A spatiotemporal coordination and nesting of these ripples and spindles with a slower dynamic, the slow oscillation, has been observed (Cox et al., 2014a). Slow oscillations (<2Hz) are predominantly present during periods of non-rapid eye movement (NREM) sleep (Rodenbeck et al., 2006).

Thus far, studies on TMR have mostly been concerned with NREM sleep and neutral memories. This field of research in humans has explored the role of slow oscillations during NREM sleep extensively with a specific focus on the enhancement of paired-associative learning (Ngo, Martinetz, Born & Mölle, 2013; Talamini, 2017; van Poppel & Talamini, 2019). However, the role of REM sleep in memory consolidation and the effect of TMR on emotional memory is much less clear. REM sleep is a stage characterized by similar brain activation as during

wakefulness, the occurrence of rapid eye movements and muscle atonia (Peever & Fuller, 2017). It has been suggested that where NREM sleep is the stage in which memory reactivations occur, REM sleep might be involved in the stabilization of that memory (Rasch & Born, 2013). Furthermore, studies suggest an involvement of REM sleep specifically in emotional memory consolidation. An increasing body of work is implicating this link (Rasch & Born, 2013; Talamini, Bringmann, Boer, & Hofman, 2013; Hutchison & Rathore, 2015; Nishida, Pearsall, Buckner and Walker, 2008; Groch, Wilhelm, Diekelmann & Born, 2013; Walker, 2009). These papers suggest that emotional memories are strengthened particularly when sleep contains high amounts or periods of REM sleep (Rasch & Born, 2013; Talamini, Bringmann, Boer, & Hofman, 2013; Nishida, Pearsall, Buckner and Walker, 2008; Groch, Wilhelm, Diekelmann & Born, 2013). It is believed that REM sleep selectively strengthens emotional memories and modulates the emotional response (Walker, 2009; Hutchison & Rathore, 2015). However, inconsistencies still exist (Cellini, Torre, Stegagno, & Sarlo, 2016; Lehmann, Schreiner, Seifritz, & Rasch, 2016). Cellini et al. (2016) found an improvement of emotional memory across sleep, however this was independent of whether sleep contained REM. Lehmann et al (2016) found that cueing during sleep only improved emotional memory when the cues were presented during periods of NREM sleep. The fact that studies link emotional memory with macrostructural features of REM sleep, such as the amount or periods, could potentially explain these inconsistencies (Sopp, Michael, Weeß, & Mecklinger, 2017).

A microstructural feature of REM sleep, now increasingly studied for its involvement in emotional memory consolidation, are theta oscillations. Theta oscillations are observed at different stages during a person’s sleep-wake cycle. These oscillations are present during wakefulness and become especially prominent at the transition point from wake to sleep stage N1 (Rodenbeck et al., 2006). During sleep, theta activity additionally appears in the background electroencephalogram (EEG) during N2, however theta is the prominent activity during REM sleep (Rodenbeck et al., 2006). It is believed that presence of these oscillations during REM sleep allow for offline communication between disparate brain regions initially involved in the encoding of an emotional memory and thereby help strengthen specific aspects of an emotional memory representation (Vertes, 2005; Goldstein, & Walker, 2014).

Even though theta oscillations have regularly been reported as an important event, its frequency range is reported differently across papers in human literature. In rodent literature theta oscillations are more extensively studied and more consensus exists regarding its frequency range. In rodents, a 4-10Hz frequency range is used to describe theta oscillations and they are known for their modulation of neuronal activity in the hippocampus, amygdala and cortical structures (Siapas, Lubenov, & Wilson, 2005). Another main characteristic of rodent theta oscillations are their distinct phase-locking with gamma waves (Belluscio, Mizuseki, Schmidt, Kempter & Buzsáki, 2012). Sometimes a 4-8Hz frequency range is used to describe rodent theta (Jacobs, 2014), but generally the reported range is consistent.

The fact that theta synchrony exists across the amygdala and hippocampus has led to the belief that these oscillations may be involved in emotional memory (Pape, Narayanan, Smid, Stork, & Seidenbecher, 2005). Both the amygdala and hippocampus are known for their involvement in memory formation of fear and other emotions (Pape et al., 2005). Causal evidence linking REM theta to emotional memory comes from an optogenetic study in rodents where the attenuation of theta activity resulted in impaired fear conditioned contextual memory (Boyce, Glasgow, Williams and Adamantidis, 2016). However, one difficulty with investigating the link between theta and emotional memory specifically, is that in rodent experiments no non-emotional memory control exists (Hutchison & Rathore, 2015). As a result, distinguishing between emotional memory and other memory forms is only directly possible in human studies.

Human studies on theta have however led to controversial results. The foremost problem in human theta literature is the lacking consensus regarding its frequency range. It appears that the vast majority of scalp EEG studies describe theta in a similar frequency range to that of rodents, namely 4-7Hz. Intracranial studies are however suggesting a slower oscillation between 1 and 4Hz as the human analogous of rodent theta oscillations (Jacobs, 2014). The suggestion for this lower frequency range comes from the observed similar functional properties to rodent theta (Jacobs, 2014).

Several correlational studies using non-invasive EEG have investigated the link between REM theta oscillations and emotional memory and found an association between them (Nishida

et al., 2008; Sopp et al., 2017; Kim et al., 2019; Bottary et al., 2020). These studies describe theta in a 4-7Hz frequency range. In all these reports, increased REM theta activity was correlated with an improvement in emotional memory consolidation. The choice for the 4-7Hz frequency range is however rarely elaborated upon. Nishida et al. (2008) do mention that the chosen frequency range is in accordance with International Federation of Clinical Neurophysiology digital standards (Nuwer et al., 1998). However, in the other studies this frequency range is based purely upon earlier studies or an explanation for their choice is lacking (Sopp et al., 2017, Bottary et al., 2020; Kim et al., 2019). Furthermore, although these studies correlate emotional memory processing with REM sleep theta activity (4-7Hz), their methods vary.

Nishida et al. (2008) had participants learn neutral and negative picture stimuli after which they were allowed to take a nap. In their study right prefrontal theta activity was correlated with recognition memory for negative stimuli. Sopp et al. (2017) made use of a split night paradigm which considers the fact that the first half of the night contains primarily SWS and the second half of the night contains primarily REM sleep. Participants were instructed to learn both the item and source of neutral and negative images. They found that frontal theta lateralization correlated with post-sleep emotional source memory. Kim et al. (2019) and Bottary et al. (2020) both had participants sleep an entire night, however, Kim et al. (2019) tested the association between stress, REM theta power and the memory for negative neutral and positive images. They found that only in stressed participants, REM theta power significantly predicted positive emotional memory. Bottary et al. (2020) made use of a fear extinction paradigm to create an emotional memory. In this study increased REM theta power in healthy participants resulted in greater extinction memory. Lastly, studies also exist which challenge this notion. For example, a large-scale study by Ackermann, Hartmann, Papassotiropoulos, de Quervain, & Rasch (2015) failed to find an association between REM theta activity and emotional pictorial memory. This study however unexpectedly did not find any correlations between sleep and pictorial memory which is in contrast with large amount of previous findings. This could possibly be explained by the participants incidentally encoding memories and not being informed about a post-sleep recall session (Ackermann et al., 2015). However, the researchers do mention that other studies finding significant results could also be due to overestimated effects in small sample sizes.

Intracranial studies investigating theta oscillations readily suggest a slower frequency range as the human analogous of rodent theta. In a study by Cantero et al. (2003) the 4-7Hz frequency range was observed intracranially in the hippocampus of epileptic patients during REM sleep, however phase coherence with the neocortex and with gamma oscillations (30-50Hz) was lacking. This paper has readily led other researchers to believe that the 4-7Hz frequency band is not the analogous of rodent theta. Already prior to this study, Bódisz et al. (2001) suggested an alternative frequency range. Their intracranial study showed a significant correlation between relative hippocampal power in a 1.5-3Hz frequency band and REM sleep specifically. In a follow up study by Clemens et al. (2009) the phase coupling during REM sleep between gamma (11 consecutive frequency band between 20 and 240Hz) and this proposed frequency band was assessed. Statistical analysis revealed the presence of phase coupling. Fell et al. (2003) assessed the phase synchrony between the hippocampus and the entorhinal cortex in a 1-3Hz frequency range during wake. Increased phase synchrony was observed as result of successful encoding. In a study by Lega et al. (2012) a lower-frequency oscillation at ~3Hz was additionally found within the hippocampus during wake which demonstrated increased power during a memory task, was correlated with gamma power and predicted episodic memory formation. They suggest that evidence for 4-8Hz power changes in the human hippocampus comes from non-invasive studies only (Lega et al., 2012). A possible explanation for this slower version of theta in humans suggested by these researchers is that the larger brain size requires slower oscillations to travel larger distances between brain areas (Moroni et al., 2007; for a comprehensive review see Jacobs, 2014).

Although the evidence for a slower theta frequency does seem evident, these studies focus mostly on intracranial measurements in the hippocampus. Intracranial neocortical studies have reported theta in a 4-8Hz frequency range (Jacobs, Kahana, Ekstrom & Fried, 2007; Canolty et al., 2006; Zhang, Watrous, Patel, & Jacobs, 2018; Cox, Rüber, Staresina & Fell, 2020). Canolty et al. (2006) found phase locking between theta (4-8Hz) in the human neocortex and high gamma power (80-150Hz). Rodent studies have led to the hypothesis that the hippocampus communicates with the neocortex through phase-locking in the theta range (Siapas et al., 2005). If human hippocampal theta were to oscillate in the proposed 1-4Hz range a possibility could be that in humans this oscillatory communication occurs via a different pathway such as cross-frequency phase coupling

(Jacobs, 2014). However, up to now no evidence for this has been found (Rings, Cox, Rüber, Lehnertz, & Fell, 2019). Additionally, in a recent study by Cox et al. (2020) synchronization was found between both hippocampal and neocortical REM theta activity in a 4-8Hz frequency range.

It appears that the suggested theta frequency range is dependent on different employed techniques across reports. Due to the correlation found between 4-7Hz oscillations and emotional memory, the fact that a 4-8Hz frequency range is frequently reported as neocortical theta and due to the recent finding by Cox et al. (2020), this study uses a 4-8Hz oscillation range to describe theta oscillations. High-density (HD) EEG data is used and since EEG most readily measures neocortical oscillations, a 4-8Hz frequency range is representative of theta oscillations, according to aforementioned studies (Jacobs et al., 2007; Canolty et al., 2006; Zhang et al., 2018; Cox et al., 2020). The idea that a 1-4Hz oscillation is the analogous of rodent hippocampal theta in humans is however not omitted.

Closed-loop neurostimulation (CLNS) is a method that allows for specific targeting of specific phases of an oscillation happening during sleep by predicting the phase of an oscillation in real-time (Cox, Korjoukov, Boer & Talamini, 2014b). This allows for very specific interaction with sleep-related memory processing. CLNS have been employed in the context of slow oscillations and it has been found that memories can be enhanced or suppressed through interaction with a phase in which memories are reactivated (Talamini, 2017). The growing field of research on CLNS of slow oscillations has led to a lot of promising results (for example: Ngo et al., 2013; Cox et al, 2014b; Van Poppel, 2016; Ngo, Seibold, Boche, Mölle, & Born, 2019). However, up to now CLNS has predominantly been used for the targeting of slow oscillations during human NREM sleep.

This study aims to resolve whether REM human theta oscillations can be employed and targeted accurately in the context of CLNS using a previous developed algorithm by Cox et al. (2014b). Based on the promising results found for CLNS of slow oscillations, it is believed that effective targeting of human theta oscillations during REM sleep can additionally be achieved. Theta is however a faster event than slow oscillations and therefore more prone to suffer from the inherent delays of internal processing of the algorithm during CLNS.

Having a CLNS system which targets theta oscillations during REM sleep could help uncover the fundamental role of these oscillations. This may therefore contribute to enlighten unresolved questions in this field regarding theta’s frequency range and its relation to emotional memory. This could lead to many advances in the neurobiological field. Additionally, a recent study by Sopp, Brueckner, Schäfer, Lass-Hennemann & Michael (2019) found that REM theta activity (4-7Hz) predicts lower re-experiencing PTSD symptoms after traumatic film exposure in healthy participants. Having a method which can directly interact with REM theta activity might therefore lead to a future treatment for PTSD patients.

Materials and Methods EEG test data

Unfiltered high-density EEG data from seven control participants from an earlier study (van Poppel & Talamini, 2019) was collected as test data for this experiment. Ten minutes of consecutive REM sleep data across the first half the night was selected for each participant for the Fz electrode. Although consensus regarding which electrode captures the highest relative theta power is lacking, the regular mention of frontal theta activity having an association with emotional memory consolidation (Nishida et al., 2008; Sopp et al., 2017) led to the decision of using the EEG signal recorded by the Fz electrode. The EEG signals for all participants were evaluated and noisy files were omitted.

The algorithm

The algorithm used is derived from a study by Cox et al. (2014b). This algorithm allows for the making of real-time brainwave phase predictions whilst receiving direct input from an EEG recording software (online), or predictions can be made for existing EEG signal data as if it were being recorded real-time (offline). The algorithm runs in the eventIDE software (http://okazolab.com) and uses a Fast Fourier Transform (FFT) of a to be set number of previous samples. A sine, between a set frequency range, is then fitted to the signal. The algorithm uses this temporal prediction to present an auditory cue in the desired phase (see figure 1). In this experiment the 0 phase of an upgoing theta oscillation (4-8Hz) is targeted.

Figure 1. The associated amount of degrees for the up and down-state of a sine wave (“Harmonics and Harmonic Frequency”, 2018)

The algorithm allows for alterations of different parameters and thresholds to influence the phase prediction. The parameters and thresholds of interest for this investigation are the fitting segment, the model correlation threshold, the residual error threshold, the amplitude threshold and the power threshold. Below a description is provided of each parameter and threshold. More extensive details on the algorithm can be found in the papers by Cox et al. (2014b) and van Poppel (2016). See appendix: table 1 for an overview of the fixed algorithm parameters implemented during simulations.

Fitting segment: The percentage of the analysis window (2048 samples= 4 seconds) that is used

to make a prediction (see figure 2a).

Amplitude threshold: The minimal amplitude (in µV) that the signal should exceed within the

fitting segment. If the threshold is not exceeded no phase prediction is made (see figure 2a).

Power threshold: The power within the desired frequency range that needs to be exceeded before

phase prediction is allowed. The value of the power threshold lies between 0 and 1 and is equivalent to a factor of the total power that a specific frequency band needs to exceed (see figure 2b).

Model correlation threshold: Determines the minimal fit required between the sine wave and the

signal before a stimulation can be made. The value for this threshold lies between 0 and 1 where 1 represents a perfect fit. This fit is calculated using a least squares approach (see figure 2c).

Residual error threshold: The minimal threshold for the normalized residual error. This value

also lies between 0 and 1 and refers to the factor of allowed difference between the observed value and the estimated value for each point in time. A value close to zero means that only a minimal difference is allowed before a prediction is made (see figure 2d).

a.

c.

d.

Figure 2a-d. Graphs showing a single phase prediction made by the algorithm in EventIDE (2a,c,d) and the relative power of different frequencies at a single point in time during a simulation (2b). Figure 2a figuratively represents the fitting segment and the amplitude threshold. Figure 2b figuratively represents the power threshold. Figure 2c shows the difference between a high model correlation threshold (left) and a low model correlation threshold (right). Figure 2d show the difference between a low residual error threshold (left) and a high residual error threshold (right).

Optimizing 0 phase targeting in the context of REM theta oscillations

The aim of this study was to optimize 0 phase targeting of REM theta oscillations using the phase targeting algorithm (Cox et al., 2014b). The gold standard was to achieve a minimal frequency of stimulation of five stimuli per sleep epoch (30 seconds), as close to zero degrees of mean phase and ideally not more than 30-40 degrees of standard deviation (sd). It is believed that these standards are necessary for having a proper CLNS protocol. The reason for this being that this stimulation frequency is necessary to allow for proper stimulation across all epochs. The desired mean phase and sd result in accurate and precise targeting of the phase of interest. These

standards have previously been used for slow oscillation CLNS experiments at the University of Amsterdam Sleep and Memory lab.

Simulations were run to investigate and test the effects of the parameters and thresholds of interest on the prediction count, the mean target phase and sd when targeting theta cycles for the individual participant files. Finally, the individual predictions for each simulation were visually inspected.

Statistics

The offline performance of the algorithm was assessed using Matlab version 2016a. An adaptation of the accuracy check Matlab script from the University of Amsterdam Sleep and Memory lab made by van Poppel (2016) was employed. Although eventIDE itself provides values for the mean phase of stimulation, the sd and the prediction count, the Matlab script allows for more accurate and precise outcomes. A reason for this is that where eventIDE reports the amount of predictions made and bases the target mean phase and sd on this, the accuracy script focuses specifically on the number of stimulations. The prediction count and stimulation frequency vary since not every prediction is translated into a stimulation by eventIDE. After each simulation, a file is written with information on the signal, on the model created over it and on each performed stimulation. This file is then loaded into Matlab and filtered with a Butterworth filter order of 1 for a frequency range between 4 and 8Hz. To obtain the analytical signal phase, a Hilbert transform is then applied and the signal phase shift as a result of this is corrected for by adding π/2. Finally, a rose plot is constructed representing the values for the mean phase of stimulation, the sd and the frequency of stimulation. This analysis is done for all simulations performed. The simulations which led to a high enough prediction count across all participants and the lowest sd achieved were then further assessed.

To evaluate whether a non-uniform distribution of phase prediction was achieved, a Rayleigh’s test (circ_rtest command from the circular circStat toolbox, Matlab (Berens, 2009)) was performed. The significance level for this test was set to alpha is 0.05. A custom made Matlab script was used to further assess each prediction individually. This allowed for the performance of visual inspection and functioned as a way to gain insights on possible patterns.

Results

The parameters and thresholds which proved effective

Simulations were run using the EEG signal files recorded by the Fz electrode. Different combinations and values of the parameters and thresholds of interest were evaluated. The initial focus was on decreasing the sd as much as possible whilst still acquiring a minimal stimulation frequency of five stimulations per sleep epoch. The fitting segment, model correlation threshold and amplitude threshold were selected as the parameter and thresholds which proved effective improving the 0 phase targeting of theta cycles. The physiological reasons for the selection of these parameters are that 1. The fitting segment allows for the selection of the amount of cycles used to make a prediction. This is therefore a reflection of how periodic the signal needs to be before a prediction is made 2. The model correlation selects how well the signal needs to fit to the sine wave before a prediction can be made thereby decreasing the chance that a phase other than the desired phase is targeted. A model correlation threshold close to 1 optimizes the fit between the sinusoidal model and the EEG signal and is therefore favored. 3. The amplitude threshold can result in targeting of clearer signal thereby increasing the chance of targeting correct oscillatory events.

Selecting the most effective fitting segment, model correlation and amplitude threshold

In first instance it appeared that a fitting segment equivalent to approximately one theta cycle (16ms) in combination with a restrictive model correlation threshold and amplitude threshold which still allowed for a sufficient stimulation frequency across the participants, led to the lowest sd. The rose plots however revealed that the mean target phase deviated from the desired 0 phase.

As a result, a larger fitting segment equivalent to approximately two theta cycles (32ms) was tested. This requires more periodicity from the signal before a prediction is made, thereby making the phase prediction more restrictive. Different model correlation thresholds and amplitude thresholds were tested in combination with this fitting segment. A model correlation threshold of 0.85 and an amplitude threshold of 15µV were decided upon. These thresholds values were selected as they provided a good balance between a sufficient number of stimulations and minimalization of the phase error.

To allow for a direct comparison between the two fitting segments, a similar number of stimulations had to be reached for both. Therefore, for the one cycle (16ms) fitting segment simulations, the model correlation threshold was set to 0.93 and the amplitude threshold was kept at 15µV. This led to the most comparable stimulation counts across the individual participants. Figure 4a and b show the rose plots for the simulations using a single participant file for a one theta cycle fitting segment (16ms) and a two theta cycles fitting segment (32ms), respectively. The rose plots for the remaining six participants can be found in the appendix: figure 1 and 2.

For the one cycle fitting segment (16ms), a model correlation threshold of 0.93 and an amplitude threshold of 15µV, a mean target phase of -34.9153.85degrees was achieved for the single participant shown in figure 4a. The simulations using the same algorithm settings for the other participants followed a similar fashion (See appendix: figure 1). Across the seven participants the average mean target phase and sd was -41.3654.76degrees. The stimulation frequency was sufficient across all seven participants. For all participants, a non-uniform distribution of phase predictions was achieved (p<0.001). The exact p-values are listed at the top of the rose plots (See figure 4a and appendix: figure 1).

For the two theta cycles fitting segment (32ms), a model correlation threshold of 0.85 and an amplitude threshold of 15µV, a mean phase of -6.4555.91degrees was achieved for the single participant shown in figure 4b. The simulations using the same algorithm settings for the other participants followed a similar fashion (See appendix: figure 2). Across the seven participants the average mean target phase and sd was -1.4456.72degrees. The stimulation frequency was sufficient across all seven participants. For all participants, a non-uniform distribution of phase predictions was achieved (p<0.001). The exact p-values are listed at the top of the rose plots (See figure 4b and appendix: figure 2).

Figure 4a&b. Rose plots showing the distribution of phase predictions made by the eventIDE algorithm for single simulations. Each rose plot consists of 18 bins, each showing the amount of stimulations for that specific

interval of degrees. Above each rose plot, the mean target phase (mean), the median target phase (median), the standard deviation (SD), the number of stimulations (Number) and the Rayleigh’s test p-value (pvalue) are shown.

Figure 4a shows the rose plot for a single participant simulation with a fitting segment equivalent to one theta

cycle (16ms), a model correlation threshold of 0.93 and an amplitude threshold of 15µV. For this simulation the mean target phase was -34.9153.85degrees. A non-uniform distribution of phase predictions was achieved

p<0.01. Figure 4b shows the rose plot of a simulation using the same participant file with a two theta cycles

fitting segment (32ms) in place, together with a model correlation threshold of 0.85 and an amplitude threshold of 15µV. For this simulation the mean target phase was -6.4555.91degrees. A non-uniform distribution of phase

predictions was achieved, p<0.01.

Post hoc visual inspection of the individual predictions

Visual inspection of the individual predictions revealed that being time constrained to just one theta cycle (16ms) increased the chances of not targeting a subsequent theta cycle, but rather, background noise. Figure 3a shows an example of a false positive prediction. For this prediction, a phase error of 8.43degrees was measured even though it is clear that a theta cycle was not captured. The phase error represents the difference in degrees between the sinusoidal model and the filtered signal at the point of stimulation. Figure 3b shows an example of a good prediction made using the one theta cycle fitting segment (16ms) in place.

It appeared that implementing the two theta cycles (32ms) decreased the chances of not targeting a subsequent theta cycle. Figure 3c shows an example of a good prediction made using the 32ms fitting segment. However, it is important to note that false positive predictions are still being made (see figure 3d for an example).

a.

(

b c. ( V) ( V)

d

Figure 3 a-d. Figure 3a displays a false positive prediction made by the eventIDE algorithm with a one theta

cycle (16ms) fitting segment is in place. Figure 3b displays a good prediction made by the eventIDE algorithm with a one theta cycle (16ms) fitting segment in place. Figure 3c displays a good prediction made by the eventIDE algorithm with a two theta cycles (32ms) fitting segment in place. Figure 3d displays a false positive prediction made by the eventIDE algorithm when a two theta cycles (32ms) fitting segment is in place. The green line shows the sine wave to which the signal is fitted. The yellow line represents the EEG signal. The dashed blue line was obtained post hoc and shows the EEG signal filtered between 4 and 8Hz. The vertical blue line shows the point at which a stimulus would be presented. At the top of each figure the phase error is reported.

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Discussion

Our findings show that human REM theta oscillations can be employed and targeted in the context of CLNS using the algorithm developed by Cox et al. (2014b). Most important is the finding that implementing a two theta cycles (32ms) fitting segment in combination with a model correlation threshold of 0.85 and an amplitude threshold of 15µV resulted in accurate REM theta targeting. These settings allowed for a good balance between sufficient stimulations and a minimalized phase error. The decision was made to run simulations using EEG signal measured by the Fz electrode. This was decided upon due to the regular mention of frontal theta activity having an association with emotional memory consolidation (Nishida et al., 2008; Sopp et al., 2017). The fact that oscillatory events in the theta range were being captured further justified this decision.

This work started off with the premise that to properly execute auditory CLNS a minimal frequency of five stimulations per sleep epoch, an as close zero degrees mean phase and ideally not more than 30-40 degrees of sd is required. Across the seven participants, the best settings led to an average mean target phase and sd of -1.4456.72degrees. For the smaller 16ms fitting segment, the average sd across participants was slightly lower, however the target mean phase was much further off from the targeted 0 phase (-41.3654.76degrees). The improvement in theta phase targeting through increasing of the fitting segment length from 16 to 32ms was therefore affirmed by the improvement in the target mean phase. Post hoc visual inspection additionally revealed a reduction of the presence of false positive predictions with the 32ms fitting segment in place. Quantification of the amount of false positives would however be needed to affirm this.

Using a CLNS approach to target slow oscillations (<2Hz) offline, has resulted in accurate phase targeting with sd’s below 30degrees (For example: van Poppel, 2016; Santostasi et al., 2016). Whilst such low sd was not achieved for theta targeting, we are dealing with two different phenomena, meaning that differences in phase targeting are expected. Various factors could contribute to differences in phase targeting of slow oscillations and theta cycles. Here mentioned are some of such factors. The difference in the theta and slow oscillation frequency range may influence phase targeting. The fact that theta cycles are faster than slow oscillations means that they are more prone to suffer from the inherent delays of internal processing by the algorithm. As

a result, higher phase errors can be expected. Additionally, slow oscillations are known for having a minimal amplitude of 75µV (Rodenbeck et al., 2006). For theta, the amplitude range is undefined (Carskadon & Rechtschaffen, 2005). Slow oscillations are therefore a clearer event. For the best achieved algorithm settings the amplitude threshold was implemented since in certain cases an EEG signal can become more regular with a higher amplitude. Whether this is true for theta oscillations is however not clear. Another potential difference arises from the fact that we are targeting an oscillatory event during REM sleep instead of NREM sleep. Several features are present specifically during REM sleep which may influence the phase targeting. For example, alpha bursts are an electrophysiological feature specific to REM sleep (Cantero & Atienza, 2000). These bursts of alpha activity (8-13Hz) usually last about three seconds and occur throughout REM periods (Rodenbeck et al., 2006). The presence of these alpha bursts in the EEG signal could potentially influence the phase targeting.

During simulations, a clear trade-off between the stimulation frequency and sd was observed. The threshold values of the optimal algorithm settings allowed for a good balance between a sufficient stimulation frequency and minimalized phase error. Further increasing specific parameters and thresholds can indeed result in lower sd, however the stimulation frequency no longer suffices. We do however believe that the achieved average mean target phase of -1.4456.72degrees will allow for proper phase targeting of theta cycles. The stimulations are centered around the 0 phase and even with this deviation in place the stimulations are predominantly presented during the up-phase of a theta cycle.

An important point of consideration is the lacking consensus regarding theta’s frequency range. Whilst the decision was made to target the oscillations at 4-8Hz as was strongly believed that these are the representative of human neocortical theta oscillations (Jacobs et al., 2007; Canolty et al., 2006; Zhang, Watrous, Patel, & Jacobs, 2018; Cox, Rüber, Staresina & Fell, 2020), theta’s frequency range is not fixed across reports. For this reason, the algorithm may thus be targeting the oscillatory activity at 4-8Hz whilst this may not necessarily be the analogous to the theta oscillations described in rodents.

This study contains a degree of novelty by being the first to target theta oscillations through offline CLNS. Future studies may benefit from further analytical analysis on the made predictions as means of reassuring assumptions regarding the achievement of proper theta phase targeting. This may additionally bring suggestions for further development of the algorithm to improve the phase targeting of theta cycles specifically. Specific patterns in the EEG signal and their relation to phase error or the quantification of the amount of true positive predictions could for example bring new insights into the effectiveness of the phase targeting algorithm. However, since we do believe that algorithm settings have been reached which allow for accurate targeting of REM theta cycles, the next step would be to assess the effectiveness of the algorithm during real-life recordings (online). Online assessment will provide essential information regarding if further improvements in the CLNS of theta cycles are necessary.

Our results have shown that human theta cycles can be targeted offline through use of the phase prediction algorithm by Cox et al., 2014b. The exact range of REM theta oscillations are however still a hot topic of debate. If the algorithm proves effective for the phase targeting of 4-8Hz cycles during real-life recordings, this may allow for assessment of the processing happening at this frequency range. This could lead to important insights regarding the interaction between emotional memory consolidation and 4-8Hz oscillations.

Acknowledgements

I would like to thank the University of Amsterdam Sleep and Cognition lab for providing me with all the tools necessary for execution of this project. In particular, I would like to thank João Patriota for his excellent guidance and supervision throughout the entire project. I would also like to thank Ilia Korjoukov for all his insights regarding the phase prediction algorithm. Finally, I would like to thank Lucia Talamini for her insights on the project and the rest of members of the sleep and cognition lab for further sparking my interest in sleep and memory research.

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Appendix

Parameter Definition Value

Frequency range The range of interest 4-8Hz

Central frequency Central frequency of the

Buttersworth bandpass filter. This was set as the average of the

minimum and maximum frequency.

6Hz

Analysis window size The size of the moving window in which the signal analysis occurs

2048samples

Fitting method Method for fitting the signal Non-linear sine fitting

Frequency step Denotes the resolution of the frequency range

0.1Hz

Min prediction interval The minimal time interval between two predictions

125ms

Min crunch time The minimum period of future time in which a prediction of the target phase can be made. The min crunch time should be greater than the hardware lag and the analysis time.

24ms

Max crunch time The maximum period of future time in which a prediction of the target phase can be made. The difference between the min and max crunch time should be the time it takes for the algorithm to make one

computing step.

34ms

Lag duration The hardware induced time lag in

signal recording

0ms

Vertical synchronization Defines whether the onset of a visual event is synchronized with the start of the monitors refresh pass.

False

Table 1. Table showing the fixed parameters for offline simulations for the phase targeting of theta cycles. The parameters are shown with the according definition and values.

______________________________________________________________________________

Figure 1. The remainder rose plots showing the distribution of phase predictions made by the eventIDE algorithm for single simulations using a one theta cycle fitting segment (16ms), a model correlation threshold of 0.93 and an amplitude threshold of 15µV. Each rose plot consists of 18 bins, each showing the amount of stimulations for that specific interval of degrees. Above each rose plot, the mean target phase (mean), the median target phase (median), the standard deviation (SD), the number of predictions (Number) and the Rayleigh’s test p-value (pvalue) are shown.

The average target mean phase and standard deviation across participants was -41.3654.76degrees. A non-uniform distribution of phase predictions was achieved across all participants, p<0.01.

______________________________________________________________________________

Figure 2. The remainder rose plots showing the distribution of phase predictions made by the eventIDE algorithm for single simulations using a two theta cycles fitting segment (32ms), a model correlation threshold of 0.85 and an amplitude threshold of 15µV.. Each rose plot consists of 18 bins, each showing the amount of stimulations for that specific interval of degrees. Above each rose plot, the mean target phase (mean), the median target phase (median), the standard deviation (SD), the number of predictions (Number) and the Rayleigh’s test p-value (pvalue) are shown.

The average target mean phase and standard deviation across participants was-1.4456.72degrees. A non-uniform distribution of phase predictions was achieved across all participants, p<0.01.

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