Interictal activity fluctuations follow rather than precede seizures on multiple time scales in a mouse model of focal cortical dysplasia

Interictal activity fluctuations follow rather than precede seizures on multiple time scales in a mouse model of focal cortical dysplasia Jan Kudlacek a,1,* , Jan Chvojka a , Michaela Kralikova a , Salome Kylarova a , Tejasvi Ravi b , Ondrej Novak a , Jakub Otahal b,d , Martin Balastik c , Premysl Jiruska a,**,1 a Department of Physiology, Second Faculty of Medicine, Charles University, Prague, Czech Republic b Department of Developmental Epileptology, Institute of Physiology of the Czech Academy of Sciences, Prague, Czech Republic c Department of Molecular Neurobiology, Institute of Physiology of the Czech Academy of Sciences, Prague, Czech Republic d Department of Pathophysiology, Second Faculty of Medicine, Charles University, Prague, Czech Republic ARTICLE INFO Keywords: Seizures Clustering Long-term profile Focal cortical dysplasia Interictal spike Circadian rhythm Seizure prediction Seizure forecasting ABSTRACT The unpredictability of seizure occurrence is a major debilitating factor for people with epilepsy. A seizure forecasting system would greatly improve their quality of life. Successful seizure forecasting necessitates a comprehensive understanding of the factors influencing seizure timing at multiple temporal scales. In this study, we investigated multiscale properties of interictal epileptiform discharges (IEDs) and seizure parameters in a highly realistic mouse model of focal cortical dysplasia-related epilepsy. We analyzed the properties’ evolution at four timescales, ranging from epilepsy progression and seizure clusters to circadian and peri-ictal changes. We discovered that the FCD-related epilepsy syndrome was progressive in terms of interictal activity rate and seizure characteristics. Sixty percent of seizures occurred in clusters. During the clusters, the seizure duration, seizure power, and IED rate were increasing. Circadian rhythm influenced seizure occurrence with the peak seizure probability at 4 p.m. under a standard 12/12 light dark cycle with lights-on at 6 a.m. Peri-ictal analysis revealed no significant change in IED rate preceding individual seizures; however, a consistent two-peak pattern of IED elevation was observed following seizures. Specifically, an initial peak in IED rate emerged 5–10 minutes postseizure, returning to baseline within two hours, followed by a secondary peak 4–12 hours later, which again subsided to baseline levels in 24–48 hours. This pattern could be fitted with a sum of three exponentials. Using the three-exponential pattern, we simulated IED rate fluctuations in each animal. The smoothed simulated IED rates showed good agreement with the smoothed real recorded IED rates, suggesting that the cumulative effect of post-ictal IED patterns can account for long-term fluctuations in IED rate. Our results indicate that, in our model of FCD-related epilepsy, consistent IED rate fluctuations follow rather than precede individual seizures. Therefore, fluctuations in IED rate can be viewed as a reflection of cyclic seizure occurrence. This implies that either IED rate fluctuations or accurate seizure records may be equally valuable for seizure risk forecasting. 1. Introduction Epilepsy is a chronic neurological disorder affecting 0.5 to 1 % of population (Beghi, 2020, Ngugi et al., 2010). It is characterized by spontaneous recurrent seizures which can be pharmacologically controlled in less than two thirds of patients (Chen et al., 2018). Importantly, the number of drug-resistant patients has not changed significantly with the introduction of new anti-seizure medications. Other therapies such as surgery, neurostimulation or ketogenic diet are only suitable for a small population of people with drug-resistant epilepsy and the results are often less than optimal (Fattorusso et al., 2021). Therefore, there is a need for novel tools for seizure management, including approaches for seizure prediction or forecasting which could decrease the fear from suddenly occurring seizures (Fisher et al., 2000) and help optimize therapies (Ramgopal et al., 2013). Although sophisticated mathematical analyses of intracranial EEG (iEEG) showed some * Correspondence to: J. Kudlacek, Department of Physiology, Second Faculty of Medicine, Charles University, Plzenska 311, Prague 5, CZ-15006, Czech Republic. ** Correspondence to: P. Jiruska, Department of Physiology, Second Faculty of Medicine, Charles University, Plzenska 311, Prague 5, CZ-15006, Czech Republic. E-mail addresses: [email protected] (J. Kudlacek), [email protected] (P. Jiruska). 1 Premysl Jiruska and Jan Kudlacek should be regarded as joint corresponding authors. The authors are members of Epilepsy Research Centre EpiReC Prague (https://epirec.cz/). Contents lists available at ScienceDirect Neurobiology of Disease journal homepage: www.elsevier.com/locate/ynbdi https://doi.org/10.1016/j.nbd.2025.107102 Received 2 June 2025; Received in revised form 12 September 2025; Accepted 12 September 2025 Neurobiology of Disease 216 (2025) 107102 Available online 13 September 2025 0969-9961/© 2025 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). promise for predicting individual seizures, seizure prediction has not yet been introduced to the clinical practice (Lehnertz and Br¨ ohl, 2023). The seizures are, however, not completely random, i.e. they are not a Poisson process. This fact gives hope for another approach, called seizure forecasting, which aims at informing the patient about their seizure risk in a probabilistic manner rather than predicting individual approaching seizures based on pre-ictal markers (Baud and Rao, 2018; Karoly et al., 2020). The non-Poissonian nature of seizure occurrence is evident on multiple levels. First, the seizure rate may be increasing (Gorter et al., 2001; Raedt et al., 2009; Williams et al., 2009) or decreasing (Behr et al., 2017) over lifetime. Second, seizure rate fluctuates in multiday cycles in most patients (Balish et al., 1991; Bauer and Burr, 2001; Griffiths and Fox, 1938; Sunderam et al., 2007; Tauboll et al., 1991). This has been confirmed using continuous chronic intracranial EEG (iEEG) recordings spanning durations of months to years (Baud et al., 2018; Karoly et al., 2021; Maturana et al., 2020). The fluctuations can lead to the formation of seizure clusters interspersed by periods of low seizure risk or even seizure freedom. Importantly, this slow dynamics of seizure occurrence and clustering observed in patients is replicated in various animal models of epilepsy, including models of temporal lobe epilepsy (TLE) in rats (Bajorat et al., 2011; Dudek and Staley, 2011; Eskikand et al., 2025; Goffin et al., 2007; Grabenstatter et al., 2005; Hawkins and Mellanby, 1987; Kudlacek et al., 2021) and mice (Mazzuferi et al., 2012), neocortical epilepsy induced by tetanus toxin (Chang et al., 2018a) or by perinatal hypoxia (Kadam et al., 2010), and in spontaneously epileptic dogs (Gregg et al., 2020). Fluctuations of seizure rate were also apparent in a murine model of focal cortical dysplasia (Almacellas Barbanoj et al., 2024) but were not investigated in detail. In a model of TLE, seizure duration was also reported to be linked to cycles of seizure rate (Eskikand et al., 2024). Interictal epileptiform discharges (IEDs) are a hallmark of epileptic tissue. IED rate is known to fluctuate in circadian and multidien cycles in both human patients (Leguia et al., 2021; Maturana et al., 2020) and animal models of epilepsy (Baud et al., 2019; Kadam et al., 2010; Levesque et al., 2011). Seizures were shown to occur with the highest probability on the rising phase of the IED rate cycles giving rise to forecasting algorithms based on non-causal estimation of IED rate cycle phase (Proix et al., 2021). The multidien cycle period, however, varies from cycle to cycle (Schroeder et al., 2023) which complicates the causal estimation of the cycle phase. This limitation was recently overcome by estimating the phase of the cycle causally using hippocampal functional connectivity patterns in a cohort of patients with bitemporal epilepsy. This approach enabled pseudo-prospective forecasting of seizure risk for the first time (Khambhati et al., 2024). Similar studies on neocortical epilepsy are, however, missing. Circadian distribution of seizures has been well studied in patients and animal models of epilepsy. Analysis of continuous long-term iEEG recordings from people with intractable epilepsy confirmed that seizures and IEDs follow a circadian patterns with the phases of IED rate and seizure rate circadian fluctuations often aligned (Karoly et al., 2016). Moreover, neocortical seizures tended to peak during the night whereas temporal lobe seizures during the day (Spencer et al., 2016) which is in line with the data from presurgical intracranial EEG monitoring which showed that probability of seizures originating in frontal and parietal cortices peaked between 4 a.m. and 7 a.m. (Durazzo et al., 2008) whereas temporal lobe seizures were most likely to occur in the afternoon. In status epilepticus-based models of TLE, some studies reported no circadian variation of seizure likelihood (Bajorat et al., 2011) and in others, seizures were more common during the light period (Baud et al., 2019; Bertram and Cornett, 1994; Gorter et al., 2001; Hellier and Dudek, 1999; Pitsch et al., 2017; Quigg et al., 1998; Raedt et al., 2009) which corresponded to lower activity phase of the day since mice and rats are nocturnal animals. In the intrahippocampal tetanus toxin model of TLE, no circadian pattern of seizure occurrence was observed (Eskikand et al., 2025) and dogs with spontaneously occurring epilepsy presented subject-specific times of peak seizure occurrence (Gregg et al., 2020). In a model of FCD, seizures were more prevalent during the day (Almacellas Barbanoj et al., 2024). When considering seizure prediction, one of the easiest approaches could be based on detection of changes in IED rate ahead of seizures. Although such a simple strategy has so far never led to successful seizure prediction, patient-specific increases or decreases of IED rate in the preictal period were occasionally reported in patients (Karoly et al., 2016). No such data exist from a murine model of FCD. In this study, we explored the multiscale temporal distribution of seizures and accompanying changes in IED rate to disclose the underlying disease dynamics in a murine model of FCD-related neocortical epilepsy. We identified that seizures induced early (minutes) and delayed (hours) increases in IED rate. The cumulative effect of seizurerelated IED facilitation replicates the long-term IED profile and allows estimation of the future evolution of IED rate. 2. Methods 2.1. Animals We analyzed long-term EEG recordings from 14 C57BL6/N mice (10 males and 4 females) with experimentally induced focal cortical dysplasia (FCD). The mice were housed under standard conditions in a room with controlled temperature (22 ±1 ◦C) and 12/12 h light/dark cycle and had ad libitum access to food and water. All animal experiments were performed under the Animal Care and Animal Protection Law of the Czech Republic, fully compatible with the guidelines of the European Union directive 2010/63/EU. 2.2. FCD induction The FCD lesion was induced by in utero electroporation (Saito and Nakatsuji, 2001; Tabata and Nakajima, 2001). Pregnant mice (day 14.5 ±0.5 post-fertilization) were anesthetized with isoflurane. Uterine horns were exposed by midline laparotomy, and the right lateral ventricle of each embryo was injected with a mixture of plasmids diluted in 2 μ g/ml Fast Green (F7252, Sigma, USA), using pulled and beveled glass capillaries. The plasmid mixture contained two plasmids: 3 μ g/ μ l of pCAG-mTOR-IRES-mAmetrine where the mTOR had the mutation p. Leu2427Pro to induce the FCD (SoVarGen Co., Ltd., Korea; Lim et al., 2015) and 1.5 μ g/ μ l of pCAG-EGFP to visualize the lesion (Fig. 1A-C). After injection, forceps-type electrodes (3 mm, CUY650P3, Nepa Gene) were positioned on the head of each embryo, and electroporation of plasmids was elicited by NEPA21 (Nepa Gene, Japan) electroporator delivering five 35 V, 50 ms pulses, with 950 ms interpulse intervals (Proch´ azkov´ a et al., 2024). 2.3. Electrode implantation and EEG recording Mice were implanted with EEG electrodes at 6–10 weeks of age. Prior to implantation, custom EEG implants were prepared by soldering coated silver wires (127 μ m in diameter, AM Systems, Inc., USA, cat. no. 786000) to prefabricated connectors (TME Electronic Components, Poland, cat. no. DS1065-03-2*6S8BV). Mice were anesthetized with isoflurane, a small area of skin on the head was removed to expose the frontal and parietal bones of the skull, and GFP fluorescence macroscopic imaging was performed to determine the position of the FCD (Fig. 1A). Five holes were drilled through the skull. Four epidural electrodes were implanted bilaterally in the frontal and parietal bones at approximate coordinates from bregma AP: ±1.5 mm, L: ±1.5 mm. One hole was drilled above the cerebellum for grounding/reference electrode. The electrodes together with the connector were attached to the skull using cyanoacrylate glue (Loctite, USA, cat. no. 1363589). Following a five-day recovery period, the animals were individually video-EEG monitored continuously for >2 weeks using custom-made J. Kudlacek et al. Neurobiology of Disease 216 (2025) 107102 2 hardware and software. The signal was amplified directly on the mouse head using a headstage amplifier, filtered between 1 and 500 Hz and digitized at 2 kHz sample rate. 2.4. EEG analysis EEG was analyzed using custom-written scripts in Matlab 2024b computing environment (Mathworks Inc., USA). First, data were downsampled to 250 Hz sample rate. Seizures (Fig. 1D, E) were identified by manual review of the EEG. Interictal epileptiform discharges (IEDs; Fig. 1F) were detected using a published detector (Janca et al., 2014) with the default settings. IEDs from the same or different channels occurring less than 100 ms apart were considered one event. The EEG was contaminated by electromyographic (EMG) artifacts, which were occasionally mistaken for IEDs by the detector. Therefore, the EMGcontaminated epochs were excluded from the analysis of IED rate (see below). Examples of automatic detections are in Supplementary Fig. 1. 2.5. Electromyographic artifact detection The electromyographic (EMG) artifacts were automatically detected by a custom-made detector based on the following algorithm. For the EMG detection, we used the original data sampled at 2 kHz. For each mouse, four 5-minute EEG files were randomly selected (two from the daytime period and two from the nighttime period) and the EMG artifacts were manually labeled. Then, signal features of the EMGcontaminated and clean epochs were computed in 0.5-second bins. The features were signal variance, entropy, sum of amplitude spectrum in four bands (2–10 Hz, 10–50 Hz, 50–200 Hz, 200–800 Hz), entropy of phase spectrum and sum of phase spectrum difference which aimed to make the detector sensitive not only to the frequency content but also to shape of the signal, i.e. random noise (EMG) vs. high-amplitude spike (IED). Multiple classifiers (Coarse Tree, Medium Tree, Boosted Trees and Bagged Trees) were then trained using Matlab’s built-in Classification Learner application or built-in functions. For each mouse, we selected the one that yielded the highest accuracy in the cross-validation Fig. 1. Basic features of the mouse model of FCD. (A) View of the mouse skull during the surgery with the GFP fluorescence-marked FCD lesions in the right frontal cortex and left medial cortex. (B) Coronal slice from the same mouse reveals two areas of dysplastic cortex with GFP-positive cells scattered across the cortex and the white matter. (C) An example of a dysmorphic neuron characterized by large body and abnormal dendritic branching. (D) EEG recording of a cluster of five seizures. (E) Detailed example of a seizure and interictal epileptiform discharges (F). (G) Seizure profile showing times of occurrence and durations of seizures. (H) Corresponding IED rate profile. J. Kudlacek et al. Neurobiology of Disease 216 (2025) 107102 3 procedure. In the whole recording, the signal features were then computed and the classifier applied to automatically label the EMGcontaminated epochs. 2.6. Analysis of trends in seizure characteristics For the seizures, we analyzed their rate of occurrence, duration and mean EEG signal power (see example in Fig. 1G). In order to evaluate a possible trend in the characteristic, we divided the analyzed period into bins. In case of the analysis of the progression over the whole recording period, the bins were 24-hour long with edges at midnight. The first bin was from the first seizure to the first midnight and the last bin was from the last midnight to the last seizure. Thus, the first and last seizure were shorter than the standard 24-hour bins. In case of a signal dropout, the length of the bin is considered to be the total time of the valid signal only. Then, we computed the mean of the characteristic in the given bin. In the analysis of the seizure rate, we took into account the length of the bin. The bin means were then fitted with a straight line using the least squares method (Matlab function fit). For the fitting of characteristics other than seizure rate, the bins were weighted by their length so that the shorter bins had proportionately lower influence on the fit. In the interictal signal, IED rate was analyzed in 1-hour or 1-minute bins, and trends were analyzed similarly. For each bin, we accounted for the actual duration of usable signal, which was often shorter than the bin length due to signal dropouts or contamination from electromyographic (EMG) artifacts. 2.7. Statistical evaluation of trends Population statistics were always computed at the level of subjects, i. e. N =14 for all statistical tests. The statistical evaluation of increasing or decreasing trends in each characteristic was performed by the following procedure. We fitted a straight line to the binned data of each period of interest (whole recording or periods related to seizure clusters or seizures, see Results). The slopes of the lines were extracted. If multiple periods of interest occurred in a subject (e.g. multiple clusters), the slopes within each subject were averaged, thus giving one number per subject. Subject-wise statistics was then calculated using the Wilcoxon signed-rank test to determine whether the slopes were statistically significantly different from zero. Since we analyzed four characteristics, the p-values were subjected to Benjamini-Hochberg false discovery rate correction at the false discovery rate 0.1. The circadian rhythm-related analyses were computed using MATLAB Circular Statistics Toolbox (Berens, 2009). 2.8. IED rate simulation The IED rate after the seizures showed a consistent two-peak shape which could be modelled by a sum of exponentials. At the shorter time scale of two hours, we fitted the after-seizure IED rate by a sum of two exponentials (expression ’A1*exp(k1*x)+A2*exp(k2*x)’ with the independent variable x). At the longer time scale of two days, we used three exponentials (’A1*exp(k1*x)+A2*exp(k2*x)+A3*exp (k3*x)’). The fitting was performed by the least squares method using Matlab function fit. Then, we leveraged the knowledge of the shape of IED rate after seizure to simulate artificial IED rate based solely on the seizure occurrence times. For this purpose, we designed an IIR filter with the impulse response equal to the fitted exponentials. Thus, the impulse response of the filter is h[n] = ∑ N i=1 Aipn i where n is discrete time index, i is index of fitted exponential, N is number of exponentials Ai is amplitude of ith exponential and pi is the ith pole of the filter which is computed from the fitted values of ki and sample period Ts as pi=eTski. The filter transfer function in the z-transform is then H[z] = ∑ N i=1 Ai 1−piz−1 This can be expanded to H[z] = ∑N i=1Ai∏N j=1j∕=i(1−piz−1) ∏N i=1(1−piz−1) By expanding the numerator and denominator we convert the expression to the form of H[z] = ∑N i=0biz−i ∑N i=0aiz−i where bi and ai are the feedforward and feedback coefficients of the filter, respectively. The obtained filter was then applied on the seizure rate evaluated in the same time bins as the IED rate (1-minute). The seizure rate signal contained zeros most of the time with occasional ones and rarely higher values marking the seizure occurrence. The result of the filtration was regarded as the simulated IED rate. Both original and simulated IED rates were smoothed by a 4-hour moving average. The similarity of the two IED rates was then evaluated using Pearson correlation coefficient and Relative error, which is essentially a normalized root mean squared error computed according to the formula Relative error = ∑L n=0(IEDoriginal −IEDsimulated)2 √  ∑L n=0(IEDoriginal)2 √ 3. Results 3.1. Seizure profiles The data are presented as means and medians in form mean ±SD (median ±interquartile range). We analyzed data from 14 mice with FCD-related epilepsy, which developed seizures and interictal activity (Fig. 1). The mice were monitored for 37 ±25 (32 ±44) days. During this period, individual mice experienced 87 ±110 (42 ±54) seizures and the mean seizure frequency was 2.3 ±1.4 (1.9 ±0.7) seizures/day. Mean seizure duration was 51 ±11 (48 ±15) s. Visual inspection of the seizure profiles in a raster plot (Fig. 2) revealed fluctuations of seizure rate and seizure clusters. Since the mean seizure rate differed between the mice and the cluster durations were variable we used a statistical, data-driven definition of a seizure cluster. We defined seizure cluster as a group of at least four seizures separated from other seizures by at least 2⋅ISI cluster max , where ISI cluster max stands for the longest inter-seizure interval within the cluster. Apart from that, the cluster had to be separated >2⋅ISI cluster max from the beginning and end of the recording. The cluster was also removed from analysis if it contained a significant signal dropout or was separated <2⋅ISI cluster max from a significant signal dropout. A signal dropout was considered significant if it was longer than both the IED analysis window (1 hour) and the shortest interseizure interval of a given mouse. This definition allows for the existence of nested clusters. We observed nesting over up to four levels (Fig. 2, inset). We identified 10 ±18 (4 ±6) clusters per mouse. When only non-nested clusters were taken into account it was 7 ±12 (3 ±3) clusters per mouse. In the subsequent analyses, the nested clusters were included unless stated otherwise. The clusters lasted 13 ±11 (10 ±16) hours and contained 7.1 ±3.4 (6.8 ±2.8) seizures. Out of all seizures, 47 ±28 (44 ±48) % occurred within a cluster. The between-cluster period was 7.4 ±12 (3.4 ±2.5) days (only non-nested clusters J. Kudlacek et al. Neurobiology of Disease 216 (2025) 107102 4 considered). Note that during the between-cluster period, there could have occurred non-clustered seizures. 3.2. Life-long progression of the epileptic phenotype First, we evaluated whether the FCD-related epilepsy in our model has a progressive nature. We divided the whole recording of each mouse into 24-hour time bins from midnight to midnight, except for the first bin which was from the first recorded seizure to the first midnight and the last bin which was from the last midnight to the last recorded seizure (Fig. 3A). We calculated seizure rate, mean seizure duration and mean seizure signal power in these bins. IED rate was calculated in 1-hour long bins (Fig. 3B). The trends were evaluated by fitting a line to the bin values and processed according to the Methods. The plots for all individual mice are in Supplementary Fig. 2. The seizure rate showed statistically significant increase or decrease in 4/14 individual animals but the population data do not show any consistent trend (p =0.54, Fig. 3C). The seizure duration was, however increasing in 8/14 animals and also the population data show a significant increase (p =0.033, Fig. 3D). The signal power shows only mild indication of an increase (p =0.094, Fig. 3E). The most prominent progression was found in the IED rate which was increasing in 12/14 individual animals (Supplementary Fig. 2) and in the population data (p =0.0081, Fig. 3F). Thus, the syndrome appeared progressive in terms of seizure duration and interictal activity but not seizure rate. In none of the mice we observed indications of seizure remission. 3.3. Seizure clusters Next, we analyzed the same characteristics on a shorter timescale defined by the naturally occurring clusters of seizures. The seizure characteristics were binned in four equal bins per cluster (Fig. 4A) and the bin values were fitted with a straight line (Fig. 4B). Then, the slopes of the lines were averaged over clusters within each animal, and then, population statistics was computed (Fig. 4C-E). The IED rate in 1-hour bins was fitted not only during the cluster but also in the pre-cluster and post-cluster periods of the same duration as the cluster (Fig. 4FH). Note, that nested clusters were included in this analysis. Similarly to lifelong progression, the data do not show any consistent trend in the seizure rate (p =1, Fig. 4C). Along the seizure clusters, we observed an increase of seizure duration (p =0.021, Fig. 4D), seizure signal power (p =0.027, Fig. 4E), and IED rate (p =0.0034, Fig. 4F). No significant change in IED rate was observed ahead of clusters (p =0.74, Fig. 4G) and an indication of a decrease was observed after the clusters (p =0.08, Fig. 4H). The data for individual mice are in Supplementary Fig. 3. Apart from that, we compared the duration and signal power of the cluster terminating seizures (last seizure of a given cluster) to the other seizures within the respective clusters. The non-terminating seizures had the duration of 52 ±14 (53 ±16) seconds whereas the terminating seizures had the duration of 57 ±17 (58 ±23) (p =0.027, Wilcoxon signed rank test). The seizure signal power of the non-terminating and terminating seizures was 0.039 ±0.017 (0.041 ±0.021) and 0.042 ±0.020 (0.043 ±0.029), respectively, which was not significantly different (p =0.18, Wilcoxon signed rank test). 3.4. Circadian rhythm The next timescale, on which we analyzed the data, was the circadian one. For the analysis of the seizure characteristics, we divided the day into 8 time bins. The seizure data were then binned according to the time of the seizure’s occurrence while ignoring the date (Fig. 5A, B). The IED rate was averaged similarly in 24 bins around the day (Fig. 5E). From the Fig. 2. Seizure profiles. Red vertical lines indicate seizures. Red horizontal line at the bottom of each animal’s row indicates the presence of recording; gaps indicate recording dropouts due to technical failures. Black horizontal lines mark seizure clusters. Note the cluster nesting, sometimes over multiple levels (example in the inset). Female mice are marked by italic font. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) J. Kudlacek et al. Neurobiology of Disease 216 (2025) 107102 5 binned data of each mouse, we calculated the mean resultant vector (Fig. 5A, E), i.e. the vector sum of all bin values while considering the angle of the bin center and bin value as the modulus. Then, from the set of resultant vectors, we calculated the population resultant vector which pointed at at 4 p.m. with the radius r =0.6 (Fig. 5C). We applied the Rayleigh test and the Omnibus test of circular distribution nonuniformity to the angles of the individual resultant vectors. The results showed that most animals had the highest seizure likelihood in the afternoon and early night (p Ray =0.008, Rayleigh test; p Omn =0.11, Omnibus test; Fig. 5C, D). At the individual level, we observed a circadian modulation of seizure occurrence in a subset of mice (p <0.05 in 8/ 14 mice by the Rayleigh test and in 4/14 mice by the Omnibus test, Supplementary Fig. 4). Surprisingly, we did not observe any consistent circadian modulation of the IED rate (Fig. 5F, G), although in 10/14 individual mice, the circadian modulation was statistically significant (Supplementary Fig. 4). We also tested if the seizure duration and signal power are modulated by the circadian rhythm but we did not find any trend (Supplementary Fig. 4). To further explore possible rhythmicity in the cycles of seizure occurrence and IED rate, we performed a power spectrum density analysis (PSD, Supplementary Fig. 5) and continuous wavelet transform (CWT, Supplementary Fig. 6) of the seizure rate signal (number of seizures in 1-hour bins) and IED rate (also in 1-hour bins). For these analyses, we interpolated the missing values during dropouts linearly. In 8/ 14 mice we observed mild peak at the 1-day period in the PSD suggestive of circadian rhythmicity. In the mice with longer recordings we occasionally observed cycles with periods between 2 and 8 days but the cycle never persisted across the whole recording, consistently with the observation of only occasional rhythmic patterns in Supplementary Fig. 2. Clusters of seizures and IED rate increases occurred non-periodically. To analyze the interaction between the seizures and IEDs, we analyzed them using wavelet coherence (Matlab function wcoherence). The results indicate that seizures and IEDs are coupled but not in a periodic fashion since the coupling usually spanned multiple scales and never Fig. 3. Long-term progression of epileptic phenotype. (A) Top: An example characteristic of seizures, the seizure signal power, is shown as the height of the lines. Bottom: The characteristics were averaged in 1-day-long bins from midnight to midnight (bar graph) and the bin values were fitted with a straight line (red solid line). Note that the first and last bins are shorter since the analyzed period was defined by the first and last recorded seizure and these never happened at midnight. (B) The IED rate was analyzed in 1-hour bins (black line) and fitted with a straight line (red line). (C – F) Slopes of the fitted lines of individual animals (red) and median slope (black) with corresponding violin plots. The units of the slopes are the change per day of the quantity indicated to the left (e.g. the change of IED rate (IEDs/hour) per day). The yaxis in the violin plots is the same as in the line plots. The solid line in the violin plot marks the median, and dashed lines mark the bootstrapped 95% confidence interval. P-values of the Wilcoxon signed rank test are shown. The sign in the parentheses indicates if the median trend was positive or negative. Statistically significant p-values after FDR correction are in bold. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 4. Analysis of trends before, during and after seizure clusters, colour-coded by orange, green and blue, respectively. (A) An example of the analysis of a seizure cluster from Mouse 13. Seizure data were analyzed similarly to Fig. 3 but with a different bin duration. In this analysis, each cluster was divided into four equal bins. (B) IED rate was analyzed in 1-hour bins, same as in Fig. 3. In this example there is no change before, an increase during and a decrease after the cluster. The preand post-cluster periods are defined to have the same duration as the cluster. For each mouse, we averaged the slopes from all of its clusters. Thus, for each characteristic, we got one value per mouse. (C-G): Mean slopes from individual mice (colour) and median slopes across subjects (black). The units are the change of the indicated quantity per day. P-values of the Wilcoxon signed rank test are shown. The sign in the parentheses indicates if the median trend was positive or negative. Statistically significant p-values after FDR correction are in bold. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) J. Kudlacek et al. Neurobiology of Disease 216 (2025) 107102 6 extended over more than a few periods. We especially focused on the 4to 5-day period (0.2 to 0.25 cycles/day frequency) since this is the period of the mouse estrous cycle. Although a mild suggestion of these rhythms was present in 2/4 female mice, in 6/10 male mice a similar rhythm was also present, often with an even higher amplitude in both PSD and CWT analyses. Therefore, the observed fluctuations in seizure or IED rate are unlikely to be caused by the estrous cycle. 3.5. Peri-seizure changes in IED rate On the shortest timescale, we analyzed pre-seizure and post-seizure IED rate curves (Fig. 6). Here, the IED rate was analyzed in 1-minute time bins, to capture more detail in the temporal profile of IED rate. Since, it was not obvious how fast the preand post-ictal changes can be expected we analyzed two durations of beforeand after-seizure periods: 2 hours and 2 days. In the case of the 2-hour period before the seizure, we required the separation of the analyzed seizure from the previous one to be at least four hours. Similarly, the after-seizure period was only included if the next seizure occurred at least 4 hours after the analyzed one. A similar safety margin was, however, not applied in the 2-day period analysis since very few mice showed seizure-free periods longer than 2 days. Therefore, in this case we only required the analyzed 2-daylong beforeor after-seizure period to be seizure-free. Most postictal periods displayed an increase in the IED rate in the raw signal (Fig. 6A, B). In the IED rate curve, a transient fast increase in IED rate was observed approximately 10 minutes after the seizure in both individual mice data (Supplementary Fig. 7) and averaged population data (Fig. 6C). No change in the IED rate was observed before the seizure. When the IED rate curves were fitted with straight lines, their slopes were not different from zero before (p =0.3), but clearly negative after the seizure (p =0.0001, Fig. 6D). The 2-hour after-seizure curve could be fitted with a sum of two exponentials (Fig. 6E) both in individual mice (Supplementary Fig. 8) and averaged data (Fig. 6F). The time constants for the rising exponentials were τ 1=5.4±2.2(5.4± 3.5)and for the falling exponentials τ 2=12 ±4(11 ±6.8)minutes. When the IED rate curves were averaged over mice (Fig. 6C, black line) and fitted with the sum of two exponentials (Fig. 6F, black line), the time constants were τ 1=4.9 and τ 2=12.2 minutes (Fig. 6G). Next, we analyzed 2-day periods before and after the seizures which displayed a >2-day seizure-free period before or after them, respectively (Fig. 6H). After the seizure, there was not only the previously mentioned fast transient increase (which appears as a sharp spike right after the seizure in the Fig. 6H and Supplementary Fig. 9) but also a much longer period of slightly increased IED rate 1 to 2 days after the seizure. Before the seizure, we observed a mild decreasing trend which, however, might be identical to the later stage of the after-seizure profile from the previous seizure (Fig. 6I). We fitted the after-seizure data with a sum of three exponentials (increasing, decreasing, increasing) with τ 1= 1.8±2.2(0.96 ±1.5), τ 2=12 ±26 (3.9±6.6), and τ 3=24 ± 27 (14 ±25)hours (Fig. 6K, L and Supplementary Fig. 10). For the fit of the averaged IED curves over mice, it was with τ 1=0.6, τ 2=2.4, and τ 3=22.3 hours (Fig. 6L). The individual mice data can be found in Supplementary Figs. 9 and 10. The mean IED rate in 2-hour before-seizure periods (no seizure-free requirement in this case) was by 36 ±64 (19 ±34) IEDs/hour higher than the mean IED rate outside these periods (p =0.013, Wilcoxon signed-rank test). Since we did not find any pre-seizure trend (see above), we argue that this might be due to the slowly decaying effect of previous seizures within the same seizure cluster. 3.6. Simulation of IED rate In the previous analysis, we identified a characteristic shape of the post-ictal IED rate temporal profile. Since we did not observe any characteristic changes in the IED rate ahead of seizures, we speculated that the long-term changes in the IED rate could be attributed to the time-dependent cumulative effect of the seizure-related increase in IED rate. To test this hypothesis, we simulated a long-term IED profile by causal filtering of the seizure rate data (see Methods and Fig. 7A). We tested two approaches. In the first, subject-specific approach, we simulated the data using a filter derived only from the data of the given mouse, i.e. the green curves in Fig. 6K (green in Fig. 7). In the second approach, we used a filter derived from the averaged data over all mice, i.e. the black curve in Fig. 6K (blue in Fig. 7). We also tested using either the raw filtered seizure rate (Fig. 7B, C, F) or filtered seizure rate with additional smoothing by a causal 4-hour moving average (Fig. 7D, E, G). This gave us four types of simulation. We evaluated the similarity of the simulated IED rate to the original IED rate by two metrics. The first one was Relative error, which was the root mean squared error normalized by the root mean squared value of the original IED rate. The second was Pearson’s correlation coefficient r. The four methods performed significantly differently in terms of both Relative error and Pearson’s r (p <0.001 for both, Kruskal-Wallis test). The smallest Relative error 0.62 ±0.15 (0.63 ±0.13) was observed for the smoothed data obtained with the subject-specific filter. The highest Pearson’s r =0.68 ±0.13 (0.70 ±0.21) was observed for the smoothed data obtained with the population-derived filter. Thus, we conclude, that the smoothing emphasizes the trends which are common to the original and simulated IED rate. The subject-specific filter seems to perform similarly to the population-derived filter. On the smoothed data, the population-derived filter has a slightly higher Relative error but the Pearson’s r is better. Notably, in three mice, the subject-specific filter yielded negative Pearson’s r due to inadequate fitting of the noisy after-seizure IED rate. Simulations of all individual mice are in Fig. 5. Circadian variation of seizure characteristics and IED rate. In each circular graph, midnight is at the bottom, noon at the top and time goes clockwise (H). (A) Example of seizure distribution from Mouse 5. Each red line marks the time of day of a seizure (regardless of date). The dark red arrow shows mean resultant vector (the radius of the circle is one). Below the graph, the length of the mean resultant vector r and the p-values of the Rayleigh and Omnibus test are shown. (B) Normalized circular histogram of seizure rate of Mouse 5. (C) Mean resultant vectors of all mice (dark red) and the population mean resultant vector created from those vectors (black). Radius of the circle is one. Below is the length of the mean resultant vector r and the p-values of the Rayleigh and Omnibus tests. Note that for the tests, only the directions of the mice’s mean resultant vectors were used. (D) Average of normalized circular histograms of all mice. (E) Circadian distribution of IED rate (red) with mean resultant vector (dark red) with its length r indicated below and p-value of Rayleigh test for Mouse 5. (F) Mean resultant vectors of IED rates of all mice and population mean resultant vector with its length r and Rayleigh test p-value below. Note that the mean resultant vectors are very short due to almost uniform IED rate distribution. (G) Mean circadian distribution of IED rate over all mice. (H) Explanatory figure for the time orientation. The lights were switched on at 6 a.m. and off at 6 p.m. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) J. Kudlacek et al. Neurobiology of Disease 216 (2025) 107102 7 Fig. 6. IED rate trends before and after seizure. (A) Seizure with two hours before and two hours after it. Increased IED rate is visible after the seizure. (B) Detail of the seizure from A with three minutes before and after. (C) IED rate before and after a seizure was analyzed in 1-minute bins, averaged across all seizures within each mouse and normalized to the maximum value within the mouse (red lines). Median across the mice is shown by the black line. (D) Straight lines were fitted to twohour segments before and after each seizure. Mean slopes over all seizures of each mouse are shown in yellow (before seizure) and blue (after seizure). The units are the change of IED rate in IEDs/hour per day. Note that after the seizure, negatives of the slopes are plotted at the seizure offset time and zero at the end of the fit because it corresponds visually to the raw data in (C). Correspondingly, the blue violin plot shows negatives of the slopes. The y-axis for the violin plots is the same as for the line plots. (E) Sum of two exponentials was fitted to the after-seizure IED rate. (F) Green curves: Fits for each mouse’s post-seizure IED rate (i.e. fits to the red curves in C). Black curve: Fit to the median post-seizure IED rate over all mice (i.e. to the black curve in C). (G) Violin plots indicating the time constants of the two exponentials for each mouse. The solid green horizontal line indicates the median and the green dashed lines the bootstrapped 95% confidence intervals of the individual mice data. The black horizontal line indicates the values from the fit of the averaged data (black line in F). (H-L) Analyses for the longer fitted segment (two days here) and fitted curve consisting of the sum of three exponentials. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) J. Kudlacek et al. Neurobiology of Disease 216 (2025) 107102 8 Supplementary Figs. 11 and 12. 4. Discussion This study provides novel information about the spontaneous seizure dynamics in a murine model of FCD-related epilepsy and, more importantly, about the nature of long-term and seizure-related dynamics of interictal epileptiform activity. The study demonstrates a two-peak profile of seizure-induced changes in IED activity that can explain long-term fluctuations in IED rate and their mutual relationship with seizures. On the longest timescale, the whole recording of several weeks or months duration, we did not observe consistent increase or decrease in the seizure rate and seizure signal power with time but the seizure duration increased. One can argue that a longer monitoring period could potentially reveal a trend in seizure rate since Williams et al. (2009) reported that the increase in seizure rate in the kainate model of temporal lobe epilepsy (TLE) was not apparent until the second month of recording in some subjects. We recorded multiple subjects for almost two months and approximately half of them showed an increasing trend and the other half a decreasing trend in seizure rate, similarly to the mice with shorter recording. This renders it rather unlikely that having two-month or longer recordings from all the mice would uncover a significant and consistent trend. Rats with pilocarpine-induced TLE showed a long-term decrease in IED rate possibly due to gradual cell loss (Behr et al., 2017). We observed an increase in IED rate over the whole recording period. Thus, the FCD-related epilepsy in our model was progressive in terms of seizure severity (duration) and interictal activity. Future studies should evaluate if the progression is also accompanied by a gradual cognitive decline and changes in behavior. Similarly to the vast majority of longitudinal studies on seizure occurrence in patients (Balish et al., 1991; Bauer and Burr, 2001; Griffiths and Fox, 1938; Sunderam et al., 2007; Tauboll et al., 1991) and animal models of epilepsy (Bajorat et al., 2011; Chang et al., 2018a; Dudek and Staley, 2011; Eskikand et al., 2025; Goffin et al., 2007; Grabenstatter et al., 2005; Gregg et al., 2020; Hawkins and Mellanby, )- ( ro r r eev i taleR ) -( rnos r a e P )- (r or r e e v ita leR )-( r n o sr a e P 968972756 3 2000 0 4000 ruoh /DEI 2000 0 4000 ruo h/DEI 300 0 ruo h / DEI 600 972756 Age (days) 9683 300 0 ruoh/DEI 600 83 83.5 84 84.5 85 85.5 86 1 0 Simulated IED rate Smoothed imulated IED rates Seizures 0.2 0.4 0.6 0.8 Age (days) ru o h/DEI A FG C B D E Subj. All 15 10 0 1 0.5 0 1 0.5 0 -1 0 1 Subj. All 5 Subject-specific impulse response Population-derived impulse response Subject-specific impulse response 4-hour smoothing Population-derived impulse response 4-hour smoothing Fig. 7. Simulation of the long-term profile of IED rate. (A) Example of a seizure cluster from Mouse 13 as an explanation of how each seizure (non-zero element in the seizure rate signal, marked by *), results in the presence of an impulse response (rainbow colors). The impulse responses add up to create a simulated IED rate (black curve). The dashed gray line is the black curve smoothed by 4-hour-long moving average filter. (B) Example of the original (black line) and simulated (green line) IED rate analyzed in 1-minute bins using the subject-specific impulse response. The red vertical lines represent seizures and the red line at the bottom indicates presence of the recording. Note a significant dropout on day 74. (C) Same as B but with the impulse response derived from the averaged IED rate over all mice. (D, E) Same as B, C but with 4-hour-long moving average smoothing of both original and simulated IED rate. (F) Relative error and Pearson’s correlation coefficient between the original IED rate and the simulated one using subject-specific impulse response derived from the mouse’s post-ictal IED rate (green) or impulse response derived from the mean post-ictal IED rate of all mice (blue). Data points from individual mice are overlaid. Solid horizontal line indicates median, dashed lines indicate interquartile range. (G) Same as B but for smoothed versions of both original and simulated IED rate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) J. Kudlacek et al. Neurobiology of Disease 216 (2025) 107102 9