High expectations on phase locking: Better quantifying the concentration of circular data.

The degree to which unimodal circular data are concentrated around the mean direction can be quantified using the mean resultant length, a measure known under many alternative names, such as the phase locking value or the Kuramoto order parameter. For maximal concentration, achieved when all of the data take the same value, the mean resultant length attains its upper bound of one. However, for a random sample drawn from the circular uniform distribution, the expected value of the mean resultant length achieves its lower bound of zero only as the sample size tends to infinity. Moreover, as the expected value of the mean resultant length depends on the sample size, bias is induced when comparing the mean resultant lengths of samples of different sizes. In order to ameliorate this problem, here, we introduce a re-normalized version of the mean resultant length. Regardless of the sample size, the re-normalized measure has an expected value that is essentially zero for a random sample from the circular uniform distribution, takes intermediate values for partially concentrated unimodal data, and attains its upper bound of one for maximal concentration. The re-normalized measure retains the simplicity of the original mean resultant length and is, therefore, easy to implement and compute. We illustrate the relevance and effectiveness of the proposed re-normalized measure for mathematical models and electroencephalographic recordings of an epileptic seizure.

Seizure forecasting: Where do we stand?

A lot of mileage has been made recently on the long and winding road toward seizure forecasting. Here we briefly review some selected milestones passed along the way, which were discussed at the International Conference for Technology and Analysis of Seizures-ICTALS 2022-convened at the University of Bern, Switzerland. Major impetus was gained recently from wearable and implantable devices that record not only electroencephalography, but also data on motor behavior, acoustic signals, and various signals of the autonomic nervous system. This multimodal monitoring can be performed for ultralong timescales covering months or years. Accordingly, features and metrics extracted from these data now assess seizure dynamics with a greater degree of completeness. Most prominently, this has allowed the confirmation of the long-suspected cyclical nature of interictal epileptiform activity, seizure risk, and seizures. The timescales cover daily, multi-day, and yearly cycles. Progress has also been fueled by approaches originating from the interdisciplinary field of network science. Considering epilepsy as a large-scale network disorder yielded novel perspectives on the pre-ictal dynamics of the evolving epileptic brain. In addition to discrete predictions that a seizure will take place in a specified prediction horizon, the community broadened the scope to probabilistic forecasts of a seizure risk evolving continuously in time. This shift of gears triggered the incorporation of additional metrics to quantify the performance of forecasting algorithms, which should be compared to the chance performance of constrained stochastic null models. An imminent task of utmost importance is to find optimal ways to communicate the output of seizure-forecasting algorithms to patients, caretakers, and clinicians, so that they can have socioeconomic impact and improve patients' well-being.

Learning to generalize seizure forecasts.

OBJECTIVE: Epilepsy is characterized by spontaneous seizures that recur at unexpected times. Nonetheless, using years-long electroencephalographic (EEG) recordings, we previously found that patient-reported seizures consistently occur when interictal epileptiform activity (IEA) cyclically builds up over days. This multidien (multiday) interictal-ictal relationship, which is shared across patients, may bear phasic information for forecasting seizures, even if individual patterns of seizure timing are unknown. To test this rigorously in a large retrospective dataset, we pretrained algorithms on data recorded from a group of patients, and forecasted seizures in other, previously unseen patients. METHODS: We used retrospective long-term data from participants (N = 159) in the RNS System clinical trials, including intracranial EEG recordings (icEEG), and from two participants in the UNEEG Medical clinical trial of a subscalp EEG system (sqEEG). Based on IEA detections, we extracted instantaneous multidien phases and trained generalized linear models (GLMs) and recurrent neural networks (RNNs) to forecast the probability of seizure occurrence at a 24-h horizon. RESULTS: With GLMs and RNNs, seizures could be forecasted above chance in 79% and 81% of previously unseen subjects with a median discrimination of area under the curve (AUC) = .70 and .69 and median Brier skill score (BSS) = .07 and .08. In direct comparison, individualized models had similar median performance (AUC = .67, BSS = .08), but for fewer subjects (60%). Moreover, calibration of pretrained models could be maintained to accommodate different seizure rates across subjects. SIGNIFICANCE: Our findings suggest that seizure forecasting based on multidien cycles of IEA can generalize across patients, and may drastically reduce the amount of data needed to issue forecasts for individuals who recently started collecting chronic EEG data. In addition, we show that this generalization is independent of the method used to record seizures (patient-reported vs. electrographic) or IEA (icEEG vs. sqEEG).

Measuring synchrony in bio-medical timeseries.

Paroxysms are sudden, unpredictable, short-lived events that abound in physiological processes and pathological disorders, from cellular functions (e.g., hormone secretion and neuronal firing) to life-threatening attacks (e.g., cardiac arrhythmia, epileptic seizures, and diabetic ketoacidosis). With the increasing use of personal chronic monitoring (e.g., electrocardiography, electroencephalography, and glucose monitors), the discovery of cycles in health and disease, and the emerging possibility of forecasting paroxysms, the need for suitable methods to evaluate synchrony-or phase-clustering-between events and related underlying physiological fluctuations is pressing. Here, based on examples in epilepsy, where seizures occur preferentially in certain brain states, we characterize different methods that evaluate synchrony in a controlled timeseries simulation framework. First, we compare two methods for extracting the phase of event occurrence and deriving the phase-locking value, a measure of synchrony: (M1) fitting cycles of fixed period-length vs (M2) deriving continuous cycles from a biomarker. In our simulations, M2 provides stronger evidence for cycles. Second, by systematically testing the sensitivity of both methods to non-stationarity in the underlying cycle, we show that M2 is more robust. Third, we characterize errors in circular statistics applied to timeseries with different degrees of temporal clustering and tested with different strategies: Rayleigh test, Poisson simulations, and surrogate timeseries. Using epilepsy data from 21 human subjects, we show the superiority of testing against surrogate time-series to minimize false positives and false negatives, especially when used in combination with M1. In conclusion, we show that only time frequency analysis of continuous recordings of a related bio-marker reveals the full extent of cyclical behavior in events. Identifying and forecasting cycles in biomedical timeseries will benefit from recordings using emerging wearable and implantable devices, so long as conclusions are based on conservative statistical testing.

Seizure Cycles in Focal Epilepsy.

Importance: Focal epilepsy is characterized by the cyclical recurrence of seizures, but, to our knowledge, the prevalence and patterns of seizure cycles are unknown. Objective: To establish the prevalence, strength, and temporal patterns of seizure cycles over timescales of hours to years. Design, Setting, and Participants: This retrospective cohort study analyzed data from continuous intracranial electroencephalography (cEEG) and seizure diaries collected between January 19, 2004, and May 18, 2018, with durations up to 10 years. A total of 222 adults with medically refractory focal epilepsy were selected from 256 total participants in a clinical trial of an implanted responsive neurostimulation device. Selection was based on availability of cEEG and/or self-reports of disabling seizures. Exposures: Antiseizure medications and responsive neurostimulation, based on clinical indications. Main Outcomes and Measures: Measures involved (1) self-reported daily seizure counts, (2) cEEG-based hourly counts of electrographic seizures, and (3) detections of interictal epileptiform activity (IEA), which fluctuates in daily (circadian) and multiday (multidien) cycles. Outcomes involved descriptive characteristics of cycles of IEA and seizures: (1) prevalence, defined as the percentage of patients with a given type of seizure cycle; (2) strength, defined as the degree of consistency with which seizures occur at certain phases of an underlying cycle, measured as the phase-locking value (PLV); and (3) seizure chronotypes, defined as patterns in seizure timing evident at the group level. Results: Of the 222 participants, 112 (50%) were male, and the median age was 35 years (range, 18-66 years). The prevalence of circannual (approximately 1 year) seizure cycles was 12% (24 of 194), the prevalence of multidien (approximately weekly to approximately monthly) seizure cycles was 60% (112 of 186), and the prevalence of circadian (approximately 24 hours) seizure cycles was 89% (76 of 85). Strengths of circadian (mean [SD] PLV, 0.34 [0.18]) and multidien (mean [SD] PLV, 0.34 [0.17]) seizure cycles were comparable, whereas circannual seizure cycles were weaker (mean [SD] PLV, 0.17 [0.10]). Across individuals, circadian seizure cycles showed 5 peaks: morning, mid-afternoon, evening, early night, and late night. Multidien cycles of IEA showed peak periodicities centered around 7, 15, 20, and 30 days. Independent of multidien period length, self-reported and electrographic seizures consistently occurred during the days-long rising phase of multidien cycles of IEA. Conclusions and Relevance: Findings in this large cohort establish the high prevalence of plural seizure cycles and help explain the natural variability in seizure timing. The results have the potential to inform the scheduling of diagnostic studies, the delivery of time-varying therapies, and the design of clinical trials in epilepsy.

Forecasting seizure risk in adults with focal epilepsy: a development and validation study.

BACKGROUND: People with epilepsy are burdened with the apparent unpredictability of seizures. In the past decade, converging evidence from studies using chronic EEG (cEEG) revealed that epileptic brain activity shows robust cycles, operating over hours (circadian) and days (multidien). We hypothesised that these cycles can be leveraged to estimate future seizure probability, and we tested the feasibility of forecasting seizures days in advance. METHODS: We did a feasibility study in distinct development and validation cohorts, involving retrospective analysis of cEEG data recorded with an implanted device in adults (age ≥18 years) with drug-resistant focal epilepsy followed at 35 centres across the USA between Jan 19, 2004, and May 18, 2018. Patients were required to have had 20 or more electrographic seizures (development cohort) or self-reported seizures (validation cohort). In all patients, the device recorded interictal epileptiform activity (IEA; ≥6 months of continuous hourly data), the fluctuations in which helped estimate varying seizure risk. Point process statistical models trained on initial portions of each patient's cEEG data (both cohorts) generated forecasts of seizure probability that were tested on subsequent unseen seizure data and evaluated against surrogate time-series. The primary outcome was the percentage of patients with forecasts showing improvement over chance (IoC). FINDINGS: We screened 72 and 256 patients, and included 18 and 157 patients in the development and validation cohorts, respectively. Models incorporating information about multidien IEA cycles alone generated daily seizure forecasts for the next calendar day with IoC in 15 (83%) patients in the development cohort and 103 (66%) patients in the validation cohort. The forecasting horizon could be extended up to 3 days while maintaining IoC in two (11%) of 18 patients and 61 (39%) of 157 patients. Forecasts with a shorter horizon of 1 h, possible only for electrographic seizures in the development cohort, showed IoC in all 18 (100%) patients. INTERPRETATION: This study shows that seizure probability can be forecasted days in advance by leveraging multidien IEA cycles recorded with an implanted device. This study will serve as a basis for prospective clinical trials to establish how people with epilepsy might benefit from seizure forecasting over long horizons. FUNDING: None. VIDEO ABSTRACT.

Reconstructing dynamical networks via feature ranking.

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the structure of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the properties and dynamics of the scrutinized network. Here, we use the insights from machine learning to design a new method of network reconstruction that essentially makes no such assumptions. Specifically, we interpret the available trajectories (data) as "features" and use two independent feature ranking approaches-Random Forest and RReliefF-to rank the importance of each node for predicting the value of each other node, which yields the reconstructed adjacency matrix. We show that our method is fairly robust to coupling strength, system size, trajectory length, and noise. We also find that the reconstruction quality strongly depends on the dynamical regime.

Inferring directed networks using a rank-based connectivity measure.

Inferring the topology of a network using the knowledge of the signals of each of the interacting units is key to understanding real-world systems. One way to address this problem is using data-driven methods like cross-correlation or mutual information. However, these measures lack the ability to distinguish the direction of coupling. Here, we use a rank-based nonlinear interdependence measure originally developed for pairs of signals. This measure not only allows one to measure the strength but also the direction of the coupling. Our results for a system of coupled Lorenz dynamics show that we are able to consistently infer the underlying network for a subrange of the coupling strength and link density. Furthermore, we report that the addition of dynamical noise can benefit the reconstruction. Finally, we show an application to multichannel electroencephalographic recordings from an epilepsy patient.