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. Author manuscript; available in PMC: 2022 Sep 1.
Published in final edited form as: Clin Neurophysiol. 2021 Jun 11;132(9):2012–2018. doi: 10.1016/j.clinph.2021.06.001

Measuring the Effects of Sleep on Epileptogenicity with Multifrequency Entropy

Aarti Sathyanarayana 1,2, Rima El Atrache 3, Michele Jackson 3, Aliza S Alter 3, Kenneth D Mandl 1,2, Tobias Loddenkemper 1,3, William J Bosl 1,2,4
PMCID: PMC8384705  NIHMSID: NIHMS1725767  PMID: 34284235

Abstract

Objective.

We demonstrate that multifrequency entropy gives insight into the relationship between epileptogenicity and sleep, and forms the basis for an improved measure of medical assessment of sleep impairment in epilepsy patients.

Methods.

Multifrequency entropy was computed from electroencephalography measurements taken from 31 children with Benign Epilepsy with Centrotemporal Spikes and 31 non-epileptic controls while awake and during sleep. Values were compared in the epileptic zone and away from the epileptic zone in various sleep stages.

Results.

We find that I) in lower frequencies, multifrequency entropy decreases during non-rapid eye movement sleep stages when compared with wakefulness in a general population of pediatric patients, II) patients with Benign Epilepsy with Centrotemporal Spikes had lower multifrequency entropy across stages of sleep and wakefulness, and III) the epileptic regions of the brain exhibit lower multifrequency entropy patterns than the rest of the brain in epilepsy patients.

Conclusions.

Our results show that multifrequency entropy decreases during sleep, particularly sleep stage 2, confirming, in a pediatric population, an association between sleep, lower multifrequency entropy, and increased likelihood of seizure.

Significance.

We observed a correlation between lowered multifrequency entropy and increased epileptogenicity that lays preliminary groundwork for the detection of a digital biomarker for epileptogenicity.

Keywords: epilepsy, entropy, BECTS, sleep

Introduction

Sleep has a crucial impact on quality of life, memory and cognition (Sathyanarayana et al., 2017). As a result, poor sleep may exacerbate many serious health problems, including epilepsy. Of the fifty million epilepsy patients globally, between 7 and 45% have a sleep-related epilepsy, which is defined by 90% of their seizures occurring during sleep (Thomas et al., 2010). In particular, benign childhood epilepsy with centrotemporal spikes (BECTS) occurs in 15% of children with seizures between age one and fifteen years (Panayiotopoulos et al., 2008), and is associated with seizures and high voltage spikes predominantly occurring during non-rapid eye movement sleep (NREM) (Ng and Pavlova, 2013). Although the prognosis is often relatively good, sleep-related epilepsies have been associated with linguistic, cognitive and behavioral impairments (Ay et al., 2009, Clarke et al., 2007, Danielsson and Petermann, 2009, Kavros et al., 2008, Lee et al., 2017, Staden et al., 1998, Weglage et al., 1997).

While several studies have explored a connection between sleep and epileptogenicity -- the propensity to have a seizure -- many of them have relied on spike counts (Bruni et al., 2010, Lambert et al., 2018, Nobili et al., 1999, Perucca et al., 2019), or high frequency oscillations (HFOs)(Frauscher et al., 2017, Klimes et al., 2019). However, it is unknown whether these features define the epileptogenic conditions in the brain, or if they are a reaction to those conditions. While spike counts and HFOs could be a proxy for epileptogenicity, they do not provide insight into the underlying electrodynamics of the brain. There is a critical medical need for independent standard measures to assess sleep impairment, epileptogenicity and the relationship between the two to provide more reliable diagnostic and management tools.

Electroencephalography (EEG) measurements contain information about brain dynamics that can be extracted using methods of nonlinear time series analysis to compute dynamical measures (Lopes da Silva et al., 2003). One measure that has been found to be especially useful for analyzing neurobiological signals is multifrequency entropy (Costa et al., 2005, Courtiol et al., 2016). Lower entropy has been associated with seizures or a propensity to have seizures (Hussain et al., 2018, Sato et al., 2019, Wu et al., 2013). We hypothesize that multifrequency entropy will change during sleep in a direction that enhances the propensity for seizures in patients with epilepsy. Understanding how sleep affects brain dynamics in epileptic patients will form the basis for an improved measure for medical assessment of sleep impairment in epilepsy patients.

Specifically, we hypothesize that I) there will be differences in the frequency distribution of multifrequency entropy across NREM sleep stages in a general population of pediatric patients, II) patients diagnosed with BECTS will have different multifrequency entropy patterns compared to a control population, and III) in patients with focal epilepsy, the epileptic regions of the brain will exhibit different multifrequency entropy patterns than the rest of the brain. If our hypotheses are correct, our study will provide crucial and urgently needed diagnostic and management tools not only regarding BECTS, but also regarding other epilepsies and learning disorders.

Methods

We retrospectively identified a cohort of pediatric patients BECTS. We specifically selected patients with a diagnosis of BECTS because the epileptic region of the brain is known, and it is possible to control for confounding factors such as spiking and generalized seizures. This selection criterion provides a homogeneous cohort with known focal epilepsy and allows us to compare the electrodynamics in parts of the brains with heavy epileptiform activity to areas that either do not exhibit or have only minimal visible interictal epileptiform discharges (IEDs).

Data Collection

We performed retrospective clinical chart review of all patients with BECTS diagnosis codes admitted for EEG monitoring (outpatient or inpatient) at Boston Children’s Hospital (BCH) between April 2009 and March 2019. We included all patients whose EEGs were retrievable and did not have a history of neurosurgery. For the control cohort, we performed retrospective clinical chart review of patients with normal EEGs admitted for EEG monitoring (outpatient or inpatient) between July 2016 and June 2018. We included all patients that had no abnormal EEGs preceding or following the EEG for analysis and had no seizure-related medical conditions or treatment with anti-seizure medications. For both cohorts, we included patients that had EEG recordings taken while awake and asleep.

For each patient, we selected thirty-second EEG intervals when the patient was awake, in sleep stage 2 and in sleep stage 3. A board-certified neurophysiologist reviewed the EEGs of both cohorts to confirm the clinical epilepsy syndrome diagnosis as classified by the International League Against Epilepsy guidelines, and confirm sleep staging. For the awake intervals, we selected portions of the EEG that did not contain spikes. Due to the frequency of nocturnal IEDs, the sleep intervals do contain spikes. Whilst spiking could be an important confounder, BECTS patients have the vast majority of their spikes in the centrotemporal (CT) region of the brain. By comparing the centrotemporal region to the extra-CT regions of the brain, the effect of spiking can be controlled.

All EEGs were collected on 19 channels according to the 10-20 system, and were not filtered. The BCH Institutional Review Board approved this study prior to data acquisition.

Signal Processing

In this study, we use wavelet transform details with db4 basis to derive wavelet details, which are frequency bands defined by powers of two divisions of the base sampling rate. i.e. if the sampling rate for an EEG file is 500Hz, then the resulting wavelet frequency bands are D1: 125-250 Hz, D2: 62.5-125 Hz, D3: 31.3-62.5 Hz, D4: 15.6-31.3 Hz, D5: 7.8-15.6 Hz, D6: 3.9-7.8 Hz, D7: 1.95-3.9Hz.

Using wavelet decomposition (pywavelets: https://pywavelets.readthedocs.io) on each EEG extract, seven frequency bands were reconstructed using the details for each of the 19 channels. These correspond approximately to the commonly used bands, delta, theta, alpha, beta, gamma, and gamma+. Sample entropy was computed on each frequency band using the publicly available nolds package (https://pypi.python.org/pypi/nolds). Multifrequency entropy plots were created for each sensor using these computed values.

Results

We identified thirty-one patients with BECTS (age 3-14 years, 39% females) and thirty-one controls (age 0.5-17 years, 35% females) with awake and sleep stage 2 intervals. This sample is representative of the population of patients with BECTS in terms of both age range (Beaumanoir et al., 1974, Beaussart, 1972, Guerrini and Pellacani, 2012, Holmes, 1993, Larsson and Eeg-Olofsson, 2006), and gender (Beaussart, 1972, Lerman and Kivity, 1975).

Twenty-six of the patients with BECTS underwent brain imaging and were found to be normal for twenty three patients. Three patients had an MRI showing evidence of either a pineal cyst, choroidal fissure cyst or mild hippocampal asymmetry. Nineteen of the controls had an MRI and all were normal. The reason an EEG was completed for patients in the control cohort ranged from other developmental or psychiatric disorders (including autism, ADHD and anxiety) to abnormal body movements (such as staring, jerking, eye-rolling, dizziness, confusion etc.). Ten patients with BECTS and twenty-eight control patients had sleep stage 3 intervals during the EEG recording. The rest of the patients had a short EEG study which did not allow enough time for patients to go into stage 3 sleep. The following sections align with the three key questions this study addresses: I) Does the frequency distribution of multifrequency entropy differ across NREM sleep stages in pediatric patients?, II) Do patients diagnosed with BECTS have different multifrequency entropy patterns than patients in a control cohort?, and III) In patients with epilepsy, do the epileptic regions of the brain exhibit different multifrequency entropy patterns than the rest of the brain? Each of these questions are answered in the sections below, and illustrated in the corresponding figures.

I). Multifrequency Entropy across NREM Sleep

The frequency distribution of multifrequency entropy computed from the EEGs across all channels decreased across NREM sleep stage 2, in pediatric patients. For the lower frequency ranges (~less than 30 Hz, or delta through beta bands), multifrequency entropy of the control cohort decreases during sleep stage 2 (figure 1). Awake versus sleep 2 group comparisons reveal significance levels of p<0.001. The results illustrated for the lower frequencies (~less than 30Hz) are reversed for the higher frequencies (~more than 30Hz). Figure 2 further illustrates this result for a smaller cohort of patients that had EEG recordings during sleep stage 3 as well as stage 2 and awake. On the lower frequencies, despite sleep stage 3 being a deeper NREM sleep, sleep stage 2 has lower sample entropy than sleep stage 3 in controls. Significance levels for each of these individual group comparisons are shown in Table 1.

Figure 1:

Figure 1:

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A multifrequency entropy graph of the sample entropy computed on all channels of the standard 10-20 electroencephalography system for a control population and patients with epilepsy, separated by sleep-awake stage. The 95% confidence intervals for each curve are represented by the shaded boundaries. Entropy is lower for patients with BECTS than controls at all frequencies. In the lower frequency range (~ below 40 Hz), sample entropy is lower when asleep and when awake.

BECTS: benign childhood epilepsy with centrotemporal spikes.

Figure 2:

Figure 2:

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A multifrequency entropy graph of the sample entropy computed on all channels of the standard 10-20 electroencephalography system for a control population and patients with epilepsy, separated by awake, sleep stage 2 and sleep stage 3. The 95% confidence intervals for each curve are represented by the shaded boundaries. In the lower frequencies (~ below 40 Hz), entropy is lower in sleep stage 2 than in sleep stage 3 for both controls and patients diagnosed with a BECTS.

BECTS: benign childhood epilepsy with centrotemporal spikes.

Table 1.

Entropy decreases from awake to sleep II to sleep III stages for all pediatric patients, with or without epilepsy, particularly in the lower frequencies (delta, theta, and alpha).

BECTS: benign childhood epilepsy with centrotemporal spikes.

Sleep
State		 BECTS Controls
Delta (Up to 4 Hz)
Awake Sleep II Sleep III Awake Sleep II Sleep III
Awake 1 < 2.2e-16 < 2.2e-16 1 < 2.2e-16 < 2.2e-16
Sleep 2 - 1 < 2.2e-16 - 1 < 2.2e-16
Sleep 3 - - 1 - - 1
Theta (4-8 Hz)
Awake Sleep II Sleep III Awake Sleep II Sleep III
Awake 1 2.014e-12 0.01843 1 7.5e-6 < 2.2e-16
Sleep 2 - 1 7.0e-5 - 1 < 2.2e-16
Sleep 3 - - 1 - - 1
Alpha (8-15 Hz)
Awake Sleep II Sleep III Awake Sleep II Sleep III
Awake 1 < 2.2e-16 < 2.2e-16 1 7.5e-6 < 2.2e-16
Sleep 2 - 1 < 2.2e-16 - 1 < 2.2e-16
Sleep 3 - - 1 - - 1
Beta (15-31 Hz)
Awake Sleep II Sleep III Awake Sleep II Sleep III
Awake 1 0.05982 0.0357 1 0.05982 0.0357
Sleep 2 - 1 0.3695 - 1 0.3695
Sleep 3 - - 1 - - 1
Gamma (31+ Hz)
Awake Sleep II Sleep III Awake Sleep II Sleep III
Awake 1 1.1e-5 0.007404 1 < 2.2e-16 < 2.2e-16
Sleep 2 - 1 0.7306 - 1 0.2389
Sleep 3 - - 1 - - 1
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II). Multifrequency Entropy across NREM Sleep in Patients Diagnosed with Epilepsy

Patients diagnosed with BECTS showed lower multifrequency entropy in their EEGs than patients in the control cohort while awake or asleep in different frequency bands. While awake, BECTS patients had lower sample entropy in delta (p<0.001) and beta (p<0.001) bands. In sleep stage 2, the differences in sample entropy between BECTS patients and controls were found in delta, beta, and gamma bands. Multifrequency entropy across all channels, at the lower frequency ranges, was highest when awake, decreased during sleep stage 2, and was in between these two states during sleep stage 3 (figures 1 and 3). Sample entropy is consistently lower in the EEGs of epileptic patients than controls, for each of the corresponding awake and sleep stages. Moreover, the differences in multifrequency entropy of BECTS patients and controls are heightened during sleep as compared to wakefulness (figure 1). The lowest entropy occurs in the EEGs of BECTS patients during sleep stage 2. The significance of group comparisons corresponding to Figure 3 values are shown in table 2.

Figure 3:

Figure 3:

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A multifrequency entropy graph of the sample entropy computed on all centrotemporal (CT) versus all non-centrotemporal (non-CT) channels of the standard 10-20 electroencephalography system for a control population and patients with epilepsy, separated by sleep-awake stage and CT versus non-CT region of the brain . The 95% confidence intervals for each curve are represented by the shaded boundaries. Entropy is lower in the CT region than the non-CT region for patients with epilepsy, particularly when asleep. This same difference is not present in control patients implying a correlation between epileptogenicity and a drop in entropy during sleep.

Table 2.

Patients with epilepsy have lower entropy while awake (delta and beta bands) during sleep stage II (all frequencies), and during sleep stage III (beta and gamma).

BECTS: benign childhood epilepsy with centrotemporal spikes.

Frequency Band P-value,
BECTS v. Controls
Delta (Up to 4 Hz)
Awake 3.5e-8
Sleep 2 4.3e-5
Sleep 3 0.3393
Theta (4-8 Hz)
Awake 0.52
Sleep 2 1.8e-3
Sleep 3 0.12
Alpha (8-15 Hz)
Awake 0.7739
Sleep 2 9.2e-3
Sleep 3 0.36
Beta (15-31 Hz)
Awake 8.9e-11
Sleep 2 5.8e-5
Sleep 3 2.6e-13
Gamma (31+ Hz)
Awake 0.109
Sleep 2 < 2.2e-16
Sleep 3 < 2.2e-16
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III). Multifrequency Entropy across NREM Sleep in Irritative Regions of the Brain

Epileptic regions of the brain exhibited lower multifrequency entropy than the rest of the brain during awake and sleep stages in BECTS patients, with differences being greatest during sleep stages 2 and 3 in the beta band. The cohort of patients with epilepsy all have a diagnosis of BECTS, meaning the epileptic portion of their brain is generally in the centrotemporal region. BECTS often has a lateralized focus (Mendizabal et al., 2016), which could affect the significance of our results, as we did not examine individual patients for lateralization. We can observe that the largest variation in sample entropy levels between awake and sleep EEGs occurs in the centrotemporal region of epileptic patients in alpha and beta bands (figure 3). Moreover the multifrequency curve for all channels in the centrotemporal region during sleep stage 2 in epileptic patients shows the lowest sample entropy. In contrast, the corresponding multifrequency curves for the centrotemporal and non-centrotemporal regions in control patients do not show differences. Additionally, in the smaller cohort of patients with sleep stage 3 EEG recordings, the centrotemporal region also has lowered entropy during sleep stage 3 compared with the non-centrotemporal region (Figure 4). Differences between the centrotemporal and non-centrotemporal regions for all frequency bands in both BECTS and control subjects are shown in table 3.

Figure 4:

Figure 4:

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A multifrequency entropy graph of the sample entropy computed on all centrotemporal (CT) versus all non-centrotemporal (non-CT) channels of the standard 10-20 electroencephalography system for a control population and patients with epilepsy, separated by awake, sleep stage 2 and sleep stage 3, and CT versus non-CT regions of the brain. The 95% confidence intervals for each curve are represented by the shaded boundaries. At the lower frequencies (~ below 40 Hz), entropy is lowest in the CT region during sleep stage 2. This further confirms a correlation between epileptogenicity and a drop in entropy during sleep.

Table 3.

Patients with epilepsy have lower entropy levels in the centrotemporal region when compared to the rest of the brain during sleep, in the beta frequency band. This difference does not occur in controls.

BECTS: benign childhood epilepsy with centrotemporal spikes.

Frequency band BECTS Controls
Centrotemporal
vs.
noncentroTemporal		 Centrotemporal
vs.
noncentroTemporal
Delta (Up to 4 Hz)
Awake 0.31 0.17
Sleep 2 0.42 0.11
Sleep 3 0.18 0.35
Theta (4-8 Hz)
Awake 0.081 1.4e-3
Sleep 2 0.41 0.53
Sleep 3 0.22 0.14
Alpha (8-15 Hz)
Awake 0.19 1.4e-3
Sleep 2 0.093 0.53
Sleep 3 0.15 0.14
Beta (15-31 Hz)
Awake 0.059 0.032
Sleep 2 1.8e-4 0.53
Sleep 3 8.1e-3 0.30
Gamma (31+ Hz)
Awake 0.034 0.029
Sleep 2 0.21 0.73
Sleep 3 0.99 0.27
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Discussion

Multifrequency entropy has proven to be a useful tool for analyzing EEG signals to find differences between controls and brain dysfunction in epilepsy (Bosl et al., 2017, Hussain et al., 2018, Lu et al., 2015, Xi and Zhu, 2015, Zavala-Yoe et al., 2016), autism (Bosl et al., 2011, Catarino et al., 2011, Heunis et al., 2018), ADHD (Chenxi et al., 2016, Rezaeezadeh et al., 2020), Alzheimer’s Disease (Gómez and Hornero, 2010), and many other disorders. The coarse-graining procedure used in most multifrequency entropy studies (Costa et al., 2005) can be shown to be equivalent to the approximations that are derived from a Haar wavelet transform, as discussed in (Bosl et al., 2018). Multifrequency entropy showed clear distinctions across sleep stages, across cohorts with and without epilepsy, and across regions of the brain with different epileptogenicity levels. These findings may provide a better understanding of how sleep affects the pediatric brain, how epileptogenicity changes with sleep, and how multifrequency entropy can be used as a metric to measure these changes.

I). Multifrequency Entropy across NREM Sleep

Our results match those in adult cohorts, and extend the literature to a cohort of pediatric patients (Chung et al., 2013, Miskovic et al., 2019). Past research has observed that complexity and entropy decrease within the adult brain during sleep when compared to awake states (Acharya et al., 2005, Bruce et al., 2009, jiayi et al., 2007, Li et al., 2015). We observed the same pattern of entropy decreasing during sleep for a pediatric cohort, but also noted that entropy was lowest in sleep stage 2 as opposed to the deeper sleep stages. These results held true in our data at the lower frequencies, as seen in figure 3. There is literature indicating a trend reversal dependent on the spatiotemporal scale selected, indicating the importance of a multifrequency approach to analyzing signal dynamics (Miskovic et al., 2019). These patterns are observed in the control cohort, a heterogenous patient group, and can thus be used to infer patterns in the general pediatric population.

II). Multifrequency Entropy across NREM Sleep in Patients Diagnosed with Epilepsy

We propose that brains with higher levels of chaotic activity may be able to synchronize only transiently, and thus have a lower chance for the runaway synchronization that results in seizures (Sathyanarayana et al., 2020). We can thus expect lower entropy to be associated with epileptogenicity and seizure occurrence. Since sample entropy is lowered during sleep for control patients as well as patients with BECTS, it is not alone sufficient for epileptic seizures. However, sleep appears to decrease entropy in certain frequency ranges, in the same direction as epilepsy, thus making sleep a more favorable environment for epileptogenesis. Therefore, there may be a correlation between decreased entropy during sleep and higher epileptogenicity.

Furthermore, in the lower frequency range, patients with epilepsy had lower multifrequency entropy across all states of wakefulness and sleep in our data set. This distinction increased during sleep. In patients with epilepsy, 61% of seizures occur during NREM sleep stage 2, versus 14% during deeper sleep stages (Minecan et al., 2002). Similarly, our results showed lowest entropy during sleep stage 2. Since BECTS patients have most of their seizures during NREM sleep (Berroya et al., 2005), this result aligns with the intuition that BECTS patients and controls will see larger differences in dynamical measures, such as entropy, during sleep.

III). Multifrequency Entropy across NREM Sleep in Irritative Regions of the Brain

We observed that the lowest entropy occurs in BECTS patients during sleep stage 2, which aligns with past research that found abnormal sleep structure in BECTS patients, particularly in sleep stage 2 (Bruni et al., 2010). Although it is unclear whether the measured dynamical changes are simply reflecting epileptic spikes, or are measuring foundational changes in neural dynamics that can cause spikes, these results hold for the non-centrotemporal region of the brain as well as the centrotemporal region in our results (Figure 3). Given that the non-centrotemporal region of the brain contains little to no maximal IEDs, and there remains an association between increased epileptogenicity and decreased sample entropy, this decreases the likelihood that the findings are due solely to IEDs. However, as the IEDs can have a neurophysiological field visually detectable in the non-centrotemporal regions, it is still possible that the non-centrotemporal regions could reflect epileptic spikes, though to a lesser extent than centrotemporal regions.

Additionally, the multifrequency curve for the centrotemporal region of the epilepsy patients during sleep had the absolute lowest entropy. This distinction between the centrotemporal and non-centrotemporal regions was not observed in control patients, further indicating that the differences in entropy observed in the centrotemporal region of BECTS patients are related to epileptogenicity, rather than confounding factors.

Although BECTS is generally localized to the centrotemporal region, it is not uniformly distributed, may be lateralized (Bedoin et al., 2006), and may change lateralization over time (Miziara and Manreza, 2010). This is particularly important when considering the potential effects of epileptiform activity on the developing brain. For example, left lateralized BECTS is thought to affect language development in children (Monjauze et al., 2011). Our results concerning lower sample entropy in the focal region might be further refined in future studies with more precise localization information for each case.

Results need to be interpreted in the setting of retrospective data acquisition, including selection and information bias. Our control cohort, though not diagnosed with epilepsy or an epilepsy related condition, consisted of patients who had clinical justification for an EEG. We evaluated the EEGs of sixty-one patients, thirty-one with BECTS, and thirty-one as controls. This limited cohort size may not allow for generalization. Moreover, our study included only BECTS patients as the epilepsy cohort, in order to provide a homogeneous group with known epileptogenic areas that enabled controlling for IEDs. As a result, the findings related directly to BECTS patients may not be generalizable to a more heterogeneous epilepsy population. This study also does not take into consideration the effect of sleep spindles during NREM sleep, which may play a functional role in sleep (Chu et al., 2012, Cox et al., 2017).

Our results extend past research results on sample entropy from adult populations to a pediatric cohort. We found that multifrequency entropy decreases in all subjects when going from awake to sleep, particularly sleep stage 2, but the change is more pronounced in BECTS patients, confirming an association between sleep, lower multiscale entropy, and increased likelihood of seizure in our patient population. Our results are consistent with past literature tying pathological physiological signals to lower complexity (Bosl et al., 2011, Iasemidis, 2003, Sathyanarayana et al., 2020, Zhang et al., 2001). We also observed a correlation between lowered multifrequency entropy and increased epileptogenicity in the general epileptic zone that lays preliminary groundwork for the detection of a digital biomarker for epileptogenicity.

Highlights:

  • Patients with Benign Epilepsy with Centrotemporal Spikes (BECTS) had lower multifrequency entropy (MSE) across all stages of sleep and wakefulness.

  • Epileptic regions of the brain exhibit lower MSE patterns than the rest of the brain in epilepsy patients.

  • MSE decreases during sleep, confirming an association between sleep, lower MSE, and increased likelihood of seizure.

Acknowledgements

We would like to thank Latania Reece, Alfonso del Aguila, Sarah Cantley, Emily Loose and Kristin Ratliff for their assistance in clinical data collection and downloading EEGs.

Funding

AS was supported by T32HD040128 from the NICHD/NIH. TL, REA, and MJ were supported by the Epilepsy Research Fund.

Footnotes

Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Competing Interests

W.J.B. and T.L. are named on a patent submitted and held by the Boston Children’s Hospital Technology Development Office that includes the signal analysis methods discussed in this article. T.L. is part of patent applications to detect and predict clinical outcomes, and to manage, diagnose, and treat neurological conditions, epilepsy, and seizures. The authors declare that they have no other competing financial or non-financial interests.

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