Mathematical models of patterns of seizures. Their use in the evaluation of drugs

The Winner by a Nose: Intranasal Midazolam

Safety and Efficacy of Midazolam Nasal Spray in the Outpatient Treatment of Patients With Seizure Clusters—A Randomized, Double-Blind, Placebo-Controlled Trial.

Detyniecki K, Van Ess PJ, Sequeira DJ, Wheless JW, Meng TC, Pullmnaan WE. Epilepsia. 2019. doi:10.1111/epi.15159. Epub ahead of print.

Objective:

To evaluate the safety and efficacy of a novel formulation of midazolam administered as a single-dose nasal spray (MDZ-NS) in the outpatient treatment of patients experiencing seizure clusters (SCs).

Methods:

This was a phase III, randomized, double-blind, placebo-controlled trial (ClinicalTrials.gov NCT01390220) with patients aged ≥12 years on a stable regimen of antiepileptic drugs. Following an in-clinic test dose phase (TDP), patients entered an outpatient comparative phase (CP) and were randomized (2:1) to receive double-blind MDZ-NS 5 mg or placebo nasal spray, administered by caregivers when they experienced an SC. The primary efficacy end point was treatment success (seizure termination within 10 minutes and no recurrence 10 minutes to 6 hours after trial drug administration). Secondary efficacy end points were proportion of patients with seizure recurrence 10 minutes to 4 hours and time to next seizure >10 minutes after double-blind drug administration. Safety was monitored throughout.

Results:

Of 292 patients administered a test dose, 262 patients were randomized and 201 received double-blind treatment for an SC (n = 134 MDZ-NS, n = 67 placebo, modified intent-to-treat population). A significantly greater proportion of MDZ-NS than placebo-treated patients achieved treatment success (53.7% vs 34.4%; P = .0109). Significantly, fewer MDZ-NS- than placebo-treated patients experienced seizure recurrence (38.1% vs 59.7%; P = .0043). Time-to-next seizure analysis showed early separation (within 30 minutes) between MDZ-NS and placebo that was maintained throughout the 24-hour observation period (21% difference at 24 hours; P = .0124). Sixteen (5.5%) patients discontinued because of a treatment-emergent adverse event (TEAE) during the TDP and none during the CP. During the CP, 27.6% and 22.4% of patients in the MDZ-NS and placebo groups, respectively, experienced ≥1 TEAE.

Significance:

The MDZ-NS was superior to placebo in providing rapid, sustained seizure control when administered to patients experiencing an SC in the outpatient setting and was associated with a favorable safety profile.

Characteristics of large patient-reported outcomes: Where can one million seizures get us?

Objective

To analyze data from Seizure Tracker, a large electronic seizure diary, including comparison of seizure characteristics among different etiologies, temporal patterns in seizure fluctuations, and specific triggers.

Methods

Zero‐inflated negative binomial mixed‐effects models were used to evaluate temporal patterns of seizure events (during the day or week), as well as group differences in monthly seizure frequency between children and adults and between etiologies. The association of long seizures with seizure triggers was evaluated using a mixed‐effects logistic model with subject as the random effect. Incidence rate ratios (IRRs) and odds ratios were reported for analyses involving zero‐inflated negative binomial and logistic mixed‐effects models, respectively.

Results

A total of 1,037,909 seizures were logged by 10,186 subjects (56.7% children) from December 2007 to January 2016. Children had more frequent seizures than adults did (median monthly seizure frequency 3.5 vs. 2.7, IRR 1.26; p < 0.001). Seizures demonstrated a circadian pattern (higher frequency between 07:00 a.m. and 10:00 a.m. and lower overnight), and seizures were reported differentially across the week (seizure rates higher Monday through Friday than Saturday or Sunday). Longer seizures (>5 or >30 min) had a higher proportion of the following triggers when compared with shorter seizures: “Overtired or irregular sleep,” “Bright or flashing lights,” and “Emotional stress” (p < 0.004).

Significance

This study explored a large cohort of patients with self‐reported seizures; strengths and limitations of large seizure diary databases are discussed. The findings in this study are consistent with those of prior work in smaller validated cohorts, suggesting that patient‐recorded databases are a valuable resource for epilepsy research, capable of both replication of results and generation of novel hypotheses.

Predicting seizure by modeling synaptic plasticity based on EEG signals - a case study of inherited epilepsy

This paper explores the internal dynamical mechanisms of epileptic seizures through quantitative modeling based on full brain electroencephalogram (EEG) signals. Our goal is to provide seizure prediction and facilitate treatment for epileptic patients. Motivated by an earlier mathematical model with incorporated synaptic plasticity, we studied the nonlinear dynamics of inherited seizures through a differential equation model. First, driven by a set of clinical inherited electroencephalogram data recorded from a patient with diagnosed Glucose Transporter Deficiency, we developed a dynamic seizure model on a system of ordinary differential equations. The model was reduced in complexity after considering and removing redundancy of each EEG channel. Then we verified that the proposed model produces qualitatively relevant behavior which matches the basic experimental observations of inherited seizure, including synchronization index and frequency. Meanwhile, the rationality of the connectivity structure hypothesis in the modeling process was verified. Further, through varying the threshold condition and excitation strength of synaptic plasticity, we elucidated the effect of synaptic plasticity to our seizure model. Results suggest that synaptic plasticity has great effect on the duration of seizure activities, which support the plausibility of therapeutic interventions for seizure control.

Human focal seizures are characterized by populations of fixed duration and interval

OBJECTIVE

We report on a quantitative analysis of data from a study that acquired continuous long-term ambulatory human electroencephalography (EEG) data over extended periods. The objectives were to examine the seizure duration and interseizure interval (ISI), their relationship to each other, and the effect of these features on the clinical manifestation of events.

METHODS

Chronic ambulatory intracranial EEG data acquired for the purpose of seizure prediction were analyzed and annotated. A detection algorithm identified potential seizure activity, which was manually confirmed. Events were classified as clinically corroborated, electroencephalographically identical but not clinically corroborated, or subclinical. K-means cluster analysis supplemented by finite mixture modeling was used to locate groupings of seizure duration and ISI.

RESULTS

Quantitative analyses confirmed well-resolved groups of seizure duration and ISIs, which were either mono-modal or multimodal, and highly subject specific. Subjects with a single population of seizures were linked to improved seizure prediction outcomes. There was a complex relationship between clinically manifest seizures, seizure duration, and interval.

SIGNIFICANCE

These data represent the first opportunity to reliably investigate the statistics of seizure occurrence in a realistic, long-term setting. The presence of distinct duration groups implies that the evolution of seizures follows a predetermined course. Patterns of seizure activity showed considerable variation between individuals, but were highly predictable within individuals. This finding indicates seizure dynamics are characterized by subject-specific time scales; therefore, temporal distributions of seizures should also be interpreted on an individual level. Identification of duration and interval subgroups may provide a new avenue for improving seizure prediction.

The dynamics of the epileptic brain reveal long-memory processes

The pattern of epileptic seizures is often considered unpredictable and the interval between events without correlation. A number of studies have examined the possibility that seizure activity respects a power-law relationship, both in terms of event magnitude and inter-event intervals. Such relationships are found in a variety of natural and man-made systems, such as earthquakes or Internet traffic, and describe the relationship between the magnitude of an event and the number of events. We postulated that human inter-seizure intervals would follow a power-law relationship, and furthermore that evidence for the existence of a long-memory process could be established in this relationship. We performed a post hoc analysis, studying eight patients who had long-term (up to 2 years) ambulatory intracranial EEG data recorded as part of the assessment of a novel seizure prediction device. We demonstrated that a power-law relationship could be established in these patients (β = - 1.5). In five out of the six subjects whose data were sufficiently stationary for analysis, we found evidence of long memory between epileptic events. This memory spans time scales from 30 min to 40 days. The estimated Hurst exponents range from 0.51 to 0.77 ± 0.01. This finding may provide evidence of phase-transitions underlying the dynamics of epilepsy.

Proposing a two-level stochastic model for epileptic seizure genesis

By assuming the brain as a multi-stable system, different scenarios have been introduced for transition from normal to epileptic state. But, the path through which this transition occurs is under debate. In this paper a stochastic model for seizure genesis is presented that is consistent with all scenarios: a two-level spontaneous seizure generation model is proposed in which, in its first level the behavior of physiological parameters is modeled with a stochastic process. The focus is on some physiological parameters that are essential in simulating different activities of ElectroEncephaloGram (EEG), i.e., excitatory and inhibitory synaptic gains of neuronal populations. There are many depth-EEG models in which excitatory and inhibitory synaptic gains are the adjustable parameters. Using one of these models at the second level, our proposed seizure generator is complete. The suggested stochastic model of first level is a hidden Markov process whose transition matrices are obtained through analyzing the real parameter sequences of a seizure onset area. These real parameter sequences are estimated from real depth-EEG signals via applying a parameter identification algorithm. In this paper both short-term and long-term validations of the proposed model are done. The long-term synthetic depth-EEG signals simulated by this model can be taken as a suitable tool for comparing different seizure prediction algorithms.

Computational modeling of epilepsy for an experimental neurologist

Computational modeling can be a powerful tool for an experimentalist, providing a rigorous mathematical model of the system you are studying. This can be valuable in testing your hypotheses and developing experimental protocols prior to experimenting. This paper reviews models of seizures and epilepsy at different scales, including cellular, network, cortical region, and brain scales by looking at how they have been used in conjunction with experimental data. At each scale, models with different levels of abstraction, the extraction of physiological detail, are presented. Varying levels of detail are necessary in different situations. Physiologically realistic models are valuable surrogates for experimental systems because, unlike in an experiment, every parameter can be changed and every variable can be observed. Abstract models are useful in determining essential parameters of a system, allowing the experimentalist to extract principles that explain the relationship between mechanisms and the behavior of the system. Modeling is becoming easier with the emergence of platforms dedicated to neuronal modeling and databases of models that can be downloaded. Modeling will never be a replacement for animal and clinical experiments, but it should be a starting point in designing experiments and understanding their results.

Predicting seizures: a behavioral approach

This article reviews the epilepsy cycle, distinguishing the interictal, preictal, ictal, and postictal phases. Evidence suggesting that the preictal phase can sometimes be identified based on neurophysiologic signals, premonitory features, the presence of trigger factors, or self-report is also reviewed. Diary studies have shown that seizures are not randomly distributed in time and that a subgroup of persons with epilepsy can predict an impending seizure. Paper diary data and preliminary analysis of electronic diary data suggest that seizure prediction is feasible. Whereas all of this evidence sets the stage for seizure prediction and preemptive therapy, several questions remain unanswered. First, what proportion of persons with epilepsy can predict their seizures? Second, within and among individuals, how accurate is prediction? Third, can prediction be improved through education about group level or individual predictors? And finally, in a group that can make robust predictions what are the most effective interventions for reducing seizure probability at times of high risk? The answers to these questions could reduce the burden of epilepsy by making seizures predictable and setting the stage for preemptive therapy. This work could improve the understanding of epilepsy by providing a context for studying the transitions from the interictal to preictal and ictal states. More prospective studies are needed; challenges certainly exist, but as the studies discussed here demonstrate, the field is rich with promise for improving the lives of patients with epilepsy.

Computer modelling of epilepsy

Epilepsy is a complex set of disorders that can involve many areas of the cortex, as well as underlying deep-brain systems. The myriad manifestations of seizures, which can be as varied as déjà vu and olfactory hallucination, can therefore give researchers insights into regional functions and relations. Epilepsy is also complex genetically and pathophysiologically: it involves microscopic (on the scale of ion channels and synaptic proteins), macroscopic (on the scale of brain trauma and rewiring) and intermediate changes in a complex interplay of causality. It has long been recognized that computer modelling will be required to disentangle causality, to better understand seizure spread and to understand and eventually predict treatment efficacy. Over the past few years, substantial progress has been made in modelling epilepsy at levels ranging from the molecular to the socioeconomic. We review these efforts and connect them to the medical goals of understanding and treating the disorder.

Epileptic seizures are temporally interdependent under certain conditions

PURPOSE

The possibility that seizures may be intercorrelated has not been sufficiently investigated. A handful of studies, the majority based on patient seizure diaries, provide disparate results: some claim that seizures are serially correlated and others that they are random events. This study investigates the effect that a seizure may have on the time of occurrence and severity of subsequent ones in subjects undergoing invasive surgical evaluation.

METHODS

The Savit-Green statistic, a measure of time series lag dependency, was applied to seizure sequences derived from the ECoGs of 26 epilepsy surgery candidates. Seizure onset times, intensities and durations were obtained using a validated seizure detection algorithm, and from these, inter-seizure intervals (ISI) and severities were computed and their lag dependencies were compared to suitably randomized and amplitude-scaled linear surrogate sets.

RESULTS

The null hypothesis (seizures are uncorrelated) was rejected (p<0.05) for ISI in 12/26 subjects and for seizure severity in 13/26. The temporal correlations spanned up to three preceding seizures and were nonlinear in 7/12 subjects for ISI and in 8/13 for severity. An important finding is that dependencies may be related to the frequency of seizures in the sample.

CONCLUSIONS

This study demonstrates that under certain conditions, there are linear and nonlinear seizure dependencies of low order and at small time scales (minutes to hours), for ISI and seizure severity. This observation has important implications for studies of seizure predictability, which de facto treat seizures as independent occurrences. Given the study subjects' conditions, it is not clear if the dependencies reflect innate brain dynamics, drug withdrawal, local trauma or a combination of these.

Dose–response population analysis of levetiracetam add-on treatment in refractory epileptic patients with partial onset seizures

In this post hoc analysis, individual seizure counts from four double-blind trials of adjunctive treatment with levetiracetam were analyzed by non-linear mixed-effects modeling (NONMEM). First, a model was fitted to the individual count data assuming a Poisson distribution, in order to classify the patients as either improving or deteriorating from baseline. In the second stage, the dose-response relationship in improving patients was determined by fitting the data to an E(max) model including a placebo effect. The percentage of improvers was 59% on placebo and 73%, 74%, 77% and 73% on levetiracetam 1, 2, 3 and 4g/day, respectively. The ED(50) of 1408mg/day was close to the current WHO Defined Daily Dose of levetiracetam (1500mg). The maximum recommended dose of 3000mg/day was predicted to reduce seizures by >or=90% in 10% of improving patients. Age, gender, body weight, race, and number of concomitant antiepileptic drugs neither affected the percentage of responders nor the extent of change in seizure frequency from baseline.

A stochastic framework for evaluating seizure prediction algorithms using hidden Markov models

Responsive, implantable stimulation devices to treat epilepsy are now in clinical trials. New evidence suggests that these devices may be more effective when they deliver therapy before seizure onset. Despite years of effort, prospective seizure prediction, which could improve device performance, remains elusive. In large part, this is explained by lack of agreement on a statistical framework for modeling seizure generation and a method for validating algorithm performance. We present a novel stochastic framework based on a three-state hidden Markov model (HMM) (representing interictal, preictal, and seizure states) with the feature that periods of increased seizure probability can transition back to the interictal state. This notion reflects clinical experience and may enhance interpretation of published seizure prediction studies. Our model accommodates clipped EEG segments and formalizes intuitive notions regarding statistical validation. We derive equations for type I and type II errors as a function of the number of seizures, duration of interictal data, and prediction horizon length and we demonstrate the model's utility with a novel seizure detection algorithm that appeared to predicted seizure onset. We propose this framework as a vital tool for designing and validating prediction algorithms and for facilitating collaborative research in this area.

Seizure clustering

Seizure clusters, also known as repetitive or serial seizures, occur commonly in epilepsy. Clustering implies that the occurrence of one seizure may influence the probability of a subsequent seizure; thus, the investigation of the clustering phenomenon yields insights into both specific mechanisms of seizure clustering and more general concepts of seizure occurrence. Seizure clustering has been defined clinically as a number of seizures per unit time and, statistically, as a deviation from a random distribution, or interseizure interval dependence. This review explores the pathophysiology, epidemiology, and clinical implications of clustering, as well as other periodic patterns of seizure occurrence. Risk factors for experiencing clusters and potential precipitants of clustering are also addressed.

[Eletroencephalographic ambulatory monitoring in refractory epilepsies in childhood]

The objective of our study was, by means of continuous prolonged ambulatory electroencephalographic monitoring, to analyze the temporal distribution of paroxysmal discharges during sleep and awake in children and adolescents with refractory epilepsies. Twenty-one patients in the 4-to-17 year age bracket with refractory epilepsies, with 52.3% (n=11) male and 47.6% (n=10) female from the Discipline of Neurology of the Universidade Federal de São Paulo (Federal University of São Paulo). Cerebral Holter was carried out with Bioware EEG-2008 of prolonged ambulatory electroencephalographic monitoring equipment. We observed greater frequency of isolated and grouped epileptic discharges in day and in night sleep in relation to awake; day and night sleep led to activation of epileptic discharges, both isolated and grouped. The cerebral Holter was more effective in detecting epileptiform discharges than the routine EEG in 33.33% of the patients. The cerebral Holter proved a useful and precise method in detecting epileptic discharges, as an aid in the assessment of the fluctuations in frequency of paroxysmal activity in children with refractory epilepsies, both in relation to activities in daily life, and to the relation to the biological cycle of sleep and awake.

Time dependencies in the occurrences of epileptic seizures

A new method of analysis, developed within the framework of nonlinear dynamics, is applied to patient recorded time series of the occurrence of epileptic seizures. These data exhibit broad band spectra and generally have no obvious structure. The goal is to detect hidden internal dependencies in the data without making any restrictive assumptions, such as linearity, about the structure of the underlying system. The basis of our approach is a conditional probabilistic analysis in a phase space reconstructed from the original data. The data, recorded from patients with intractable epilepsy over a period of 1-3 years, consist of the times of occurrences of hundreds of partial complex seizures. Although the epileptic events appear to occur independently, we show that the epileptic process is not consistent with the rules of a homogeneous Poisson process or generally with a random (IID) process. More specifically, our analysis reveals dependencies of the occurrence of seizures on the occurrence of preceding seizures. These dependencies can be detected in the interseizure interval data sets as well as in the rate of seizures per time period. We modeled patient's inaccuracy in recording seizure events by the addition of uniform white noise and found that the detected dependencies are persistent after addition of noise with standard deviation as great as 1/3 of the standard deviation of the original data set. A linear autoregressive analysis fails to capture these dependencies or produces spurious ones in most of the cases.

Clinical audit and neurology

Medical audit has been defined as "a systematic critical analysis of the quality of medical care, including the procedures used for diagnosis and treatment, the use of resources, and the resulting outcome for the patient". In Britain, recent reforms of the Health Service increase the need for neurologists to undertake audit. The basic principles of audit in relation to the management of common conditions such as headache and epilepsy are described. Audit must consider not only efficiency but also effectiveness, but the difficulty of developing valid outcome measures should not be underestimated, especially in chronic disabling conditions.

Seizure frequency in intractable partial epilepsy: a statistical analysis

We examined the seizure records of 13 patients (nine men and four women, ages 27-50 years) with intractable partial epilepsy, maintained with steady anti-epileptic drug dosages. Patients recorded daily seizure frequency on calendars. Periods of outpatient observation ranged from 99 to 1,710 days and the number of observed seizures ranged from 18 to over 400, with daily seizure rates of 0.1-4.3 per day. We used the quasi-likelihood regression model to examine the following four departures of the daily seizure counts from a Poisson (random) model: (1) linear increasing or decreasing time trends in expected seizure rates; (2) clustering, where the expected seizure rate on a given day depends on the number of seizures observed on the immediate prior days; (3) monthly cyclicity; and (4) increased variability (overdispersion). Linear time trends were seen in six patients (four increasing and two decreasing), clustering was seen in 10 patients, and a near-monthly cycle appeared in four patients (two of nine men and two of four women). A significant amount of extra variation (overdispersion) relative to a Poisson distribution was observed in all but one of the 13 patients. Departures from a Poisson (random) model appear more common in this population of patients with medically intractable epilepsy than is commonly recognized, and have clinical importance as well as implications for the design of clinical studies.

Temporal distribution of seizures in epilepsy

A major problem in epileptology is why a seizure occurs at a particular moment in time. An initial step in solving this problem is a detailed analysis of the temporal distribution of seizures. Using methods and theories of stochastic processes, seizure patterns in a group of epileptic outpatients were examined for stationarity, randomness, dependency and periodicity in a prospective study. Sixteen of the 21 seizure diaries included in the study showed stationarity; 2 were non-stationary and 3 inconclusive. Eleven of the 16 stationary diaries were non-Poisson (P less than 0.005), indicating that in the majority of patients seizures did not occur randomly. The most frequently encountered phenomenon was seizure clustering. Clustering was considered when the diaries fulfilled all three criteria: (1) a positive R-test (P less than 0.001); (2) deviation from the fitted Poisson distribution towards clustering; and (3) the feature of an autoregressive process in the autocorrelogram plot. Dependency between seizure events was demonstrated in 8 of the 16 stationary diaries, computing first order transition probabilities. A detailed analysis of seizure occurrence is a major step towards a better understanding of the mechanisms underlying seizure precipitation. This is exemplified by our finding of a relation between seizure frequency and the menstrual cycle.

Experimental studies and controlled clinical testing of valproate and vigabatrin

Gamma-aminobutyric acid (GABA) is the most important inhibitory transmitter, quantitatively, in the CNS. Evidence exists that decreased GABAergic neurotransmission may play a role in some forms of epilepsy. Consequently, manipulating the GABA system may be a therapeutic possibility in the treatment of this disease. Inhibition of the major GABA degrading enzyme, GABA-transaminase (GABA-T), seems to be the most promising approach. Currently, 2 antiepileptic drugs, valproate (VPA) and vigabatrin, gamma-vinyl GABA (GVG), are available, which are supposed to inhibit the degradation of GABA. Both drugs cause an increase in the total concentration of GABA in the brain, but to a different extent. VPA produces a moderate elevation, which seems to be the result of a marked increase in the transmitter-related GABA pool, while the pronounced elevation in GABA concentration observed during treatment with GVG seems to be caused mainly by an increase in the non-transmitter-related (glial) GABA pool. In order to investigate this apparently differential influence of VPA and GVG on the GABA system, a number of studies were undertaken in selectively cultured astrocytes and neurons from mice. For both drugs neuronal GABA-T proved far more sensitive with regard to inhibition than glial GABA-T. In order to obtain a more direct measure of a potential GABAergic mechanism of action of VPA and GVG, synaptic release of endogenous GABA was determined after culturing neurons in the presence of clinically relevant concentrations of the drugs. GVG caused a significant increase in GABA release, even at concentrations as low as 25 microM. For VPA only the highest of the investigated concentrations (300 microM) augmented GABA release. It is concluded that the antiepileptic effect of GVG seems to be caused by a direct GABAergic mechanism of action. For VPA an influence on the GABA system may play a role in the antiepileptic effect of the drug. However, the lack of definite data on human brain levels of VPA after chronic treatment, combined with evidence that VPA exhibits a number of other effects that may be relevant for its antiepileptic properties, makes the interpretation of a GABAergic mechanism of action difficult. Controlled clinical trials have been increasingly applied within all areas of medicine. In 1982 a survey of the literature identified 29 studies of antiepileptic drugs, where the design involved randomization, the double-blind principle and a statistical analysis of the results.(ABSTRACT TRUNCATED AT 400 WORDS)

Timing of seizure recurrence in adult epileptic patients: a statistical analysis

Seizure diaries were maintained prospectively in 24 epileptic patients (19 with partial complex, three with partial simple, and three with primary generalized seizures) who were selected consecutively, had stable seizure patterns, were reliable historians, and were known to be compliant with medications. Diaries were maintained for an average of 237 days (range, 61-365), and an average of 18 seizures were recorded per patient (range, 5-76). Seizure patterns were analyzed by using the methods appropriate for a time series of events (point process). Two patients had a decreasing trend in seizure frequency. For 12 patients, seizure occurrence was indistinguishable from that of a Poisson process. The remaining 10 patients had an exponential distribution of seizure intervals, but did not fit other criteria for a Poisson process; 3 of these showed evidence for seizure clustering; none showed evidence for a seizure cycle. It is concluded that the pattern of seizure occurrence in most epileptic people is random, but in approximately 50%, it is not occurring according to a Poisson process. These observations indicate that seizure cycling and/or clustering are not common in epileptic patients, but do not exclude the possibility that seizures have been precipitated by some randomly occurring event, such as sleep deprivation or increased stress.

High-dose phenytoin in the treatment of refractory epilepsy

Refractory, long-standing, high-frequency epilepsy was successfully managed with high-dose phenytoin treatment. Side effects were observed in only three patients and were easily corrected. Most of the patients had partial seizures, but many also had a myoclonic component. Emphasis was placed on monotherapy whenever possible. Results, interpretation of serum levels, and toxic reactions to phenytoin are discussed.