Localized energy for wave equations with degenerate trapping

Localized energy estimates have become a fundamental tool when studying wave equations in the presence of asymptotically at background geometry. Trapped rays necessitate a loss when compared to the estimate on Minkowski space. A loss of regularity is a common way to incorporate such. When trapping is sufficiently weak, a logarithmic loss of regularity suffices. Here, by studying a warped product manifold introduced by Christianson and Wunsch, we encounter the first explicit example of a situation where an estimate with an algebraic loss of regularity exists and this loss is sharp. Due to the global-in-time nature of the estimate for the wave equation, the situation is more complicated than for the Schr\"{o}dinger equation. An initial estimate with sub-optimal loss is first obtained, where extra care is required due to the low frequency contributions. An improved estimate is then established using energy functionals that are inspired by WKB analysis. Finally, it is shown that the loss cannot be improved by any power by saturating the estimate with a quasimode.Comment: 18 page

Localization of the Epileptogenic Zone Using Interictal MEG and Machine Learning in a Large Cohort of Drug-Resistant Epilepsy Patients

Objective: Epilepsy surgery results in seizure freedom in the majority of drug-resistant patients. To improve surgery outcome we studied whether MEG metrics combined with machine learning can improve localization of the epileptogenic zone, thereby enhancing the chance of seizure freedom.Methods: Presurgical interictal MEG recordings of 94 patients (64 seizure-free >1y post-surgery) were analyzed to extract four metrics in source space: delta power, low-to-high-frequency power ratio, functional connectivity (phase lag index), and minimum spanning tree betweenness centrality. At the group level, we estimated the overlap of the resection area with the five highest values for each metric and determined whether this overlap differed between surgery outcomes. At the individual level, those metrics were used in machine learning classifiers (linear support vector machine (SVM) and random forest) to distinguish between resection and non-resection areas and between surgery outcome groups.Results: The highest values, for all metrics, overlapped with the resection area in more than half of the patients, but the overlap did not differ between surgery outcome groups. The classifiers distinguished the resection areas from non-resection areas with 59.94% accuracy (95% confidence interval: 59.67–60.22%) for SVM and 60.34% (59.98–60.71%) for random forest, but could not differentiate seizure-free from not seizure-free patients [43.77% accuracy (42.08–45.45%) for SVM and 49.03% (47.25–50.82%) for random forest].Significance: All four metrics localized the resection area but did not distinguish between surgery outcome groups, demonstrating that metrics derived from interictal MEG correspond to expert consensus based on several presurgical evaluation modalities, but do not yet localize the epileptogenic zone. Metrics should be improved such that they correspond to the resection area in seizure-free patients but not in patients with persistent seizures. It is important to test such localization strategies at an individual level, for example by using machine learning or individualized models, since surgery is individually tailored

The Lesioned Brain: Still a Small-World?

The intra-arterial amobarbital procedure (IAP or Wada test) is used to determine language lateralization and contralateral memory functioning in patients eligible for neurosurgery because of pharmaco-resistant epilepsy. During unilateral sedation, functioning of the contralateral hemisphere is assessed by means of neuropsychological tests. We use the IAP as a reversible model for the effect of lesions on brain network topology. Three artifact-free epochs (4096 samples) were selected from each electroencephalogram record before and after amobarbital injection. Functional connectivity was assessed by means of the synchronization likelihood. The resulting functional connectivity matrices were constructed for all six epochs per patient in four frequency bands, and weighted network analysis was performed. The clustering coefficient, average path length, small-world index, and edge weight correlation were calculated. Recordings of 33 patients were available. Network topology changed significantly after amobarbital injection: clustering decreased in all frequency bands, while path length decreased in the theta and lower alpha band, indicating a shift toward a more random network topology. Likewise, the edge weight correlation decreased after injection of amobarbital in the theta and beta bands. Network characteristics after injection of amobarbital were correlated with memory score: higher theta band small-world index and increased upper alpha path length were related to better memory score. The whole-brain network topology in patients eligible for epilepsy surgery becomes more random and less optimally organized after selective sedation of one hemisphere, as has been reported in studies with brain tumor patients. Furthermore, memory functioning after injection seems related to network topology, indicating that functional performance is related to topological network properties of the brain

Long-Term Effects of Temporal Lobe Epilepsy on Local Neural Networks: A Graph Theoretical Analysis of Corticography Recordings

Purpose: Pharmaco-resistant temporal lobe epilepsy (TLE) is often treated with surgical intervention at some point. As epilepsy surgery is considered a last resort by most physicians, a long history of epileptic seizures prior to surgery is not uncommon. Little is known about the effects of ongoing TLE on neural functioning. A better understanding of these effects might influence the moment of surgical intervention. Functional connectivity (interaction between spatially distributed brain areas) and network structure (integration and segregation of information processing) are thought to be essential for optimal brain functioning. We report on the impact of TLE duration on temporal lobe functional connectivity and network characteristics. Methods: Functional connectivity of the temporal lobe at the time of surgery was assessed by means of interictal electrocorticography (ECoG) recordings of 27 TLE patients by using the phase lag index (PLI). Graphs (abstract network representations) were reconstructed from the PLI matrix and characterized by the clustering coefficient C (local clustering), the path length L (overall network interconnectedness), and the ‘‘small world index’ ’ S (network configuration). Results: Functional connectivity (average PLI), clustering coefficients, and the small world index were negatively correlated with TLE duration in the broad frequency band (0.5–48 Hz). Discussion: Temporal lobe functional connectivity is lower in patients with longer TLE history, and longer TLE duration i

MEG Network Differences between Low- and High-Grade Glioma Related to Epilepsy and Cognition

OBJECTIVE: To reveal possible differences in whole brain topology of epileptic glioma patients, being low-grade glioma (LGG) and high-grade glioma (HGG) patients. We studied functional networks in these patients and compared them to those in epilepsy patients with non-glial lesions (NGL) and healthy controls. Finally, we related network characteristics to seizure frequency and cognitive performance within patient groups. METHODS: We constructed functional networks from pre-surgical resting-state magnetoencephalography (MEG) recordings of 13 LGG patients, 12 HGG patients, 10 NGL patients, and 36 healthy controls. Normalized clustering coefficient and average shortest path length as well as modular structure and network synchronizability were computed for each group. Cognitive performance was assessed in a subset of 11 LGG and 10 HGG patients. RESULTS: LGG patients showed decreased network synchronizability and decreased global integration compared to healthy controls in the theta frequency range (4-8 Hz), similar to NGL patients. HGG patients' networks did not significantly differ from those in controls. Network characteristics correlated with clinical presentation regarding seizure frequency in LGG patients, and with poorer cognitive performance in both LGG and HGG glioma patients. CONCLUSION: Lesion histology partly determines differences in functional networks in glioma patients suffering from epilepsy. We suggest that differences between LGG and HGG patients' networks are explained by differences in plasticity, guided by the particular lesional growth pattern. Interestingly, decreased synchronizability and decreased global integration in the theta band seem to make LGG and NGL patients more prone to the occurrence of seizures and cognitive decline

The paroxysmal dyskinesias

The paroxysmal dyskinesias are a challenging group of movement disorders characterised by painless dystonic and/or choreiform movements. Lack of familiarity with their features and a normal neurological examination between attacks frequently cause diagnostic delays, or even the diagnosis of a non-organic disorder. They are classified by their mode of triggering, and also by the duration and frequency of attacks, effectiveness of medication, and any associated syndromes. Four subtypes are recognised: paroxysmal kinesigenic dyskinesia induced by sudden movement; paroxysmal non-kinesigenic dyskinesia precipitated by for instance alcohol or caffeine; paroxysmal exercise-induced dyskinesia triggered by longer lasting activity; and paroxysmal hypnogenic dyskinesia occurring during sleep. Here we will summarise the characteristics of the subtypes, discuss the differential diagnosis, genetic aspects and pathophysiology, and give practical advice on the diagnostic work-up and treatmen

The use of single bipolar scalp derivation for the detection of ictal events during long-term EEG monitoring

Aim. Epilepsy is difficult to diagnose using routine EEG recordings of short duration in patients who have low seizure frequency. Long-term EEG may be useful but is impractical in an out-of-hospital setting. We investigated whether single-channel scalp EEG placed behind the earlobe is suitable for seizure identification during prolonged EEG monitoring. Methods. Scalp EEG samples were selected from subjects over 15 years of age, and comprised two segments of either background followed by seizure or background followed by background. Bipolar EEG derivations in three directions (F8-T8, C4-T8 and T8-P8) were evaluated for the presence of a seizure by two experienced reviewers. For each EEG segment containing a seizure, one pair of electrodes was oriented towards the suspected region of seizure onset, while two pairs of electrodes were oriented elsewhere. Results. The EEG data contained five frontally localized seizures, five parietal, five temporal, two occipital, and four primary or secondary generalized seizures. The sensitivity and specificity for recognition of seizures was 86% and 95% for Reviewer 1, and 79% and 99% for Reviewer 2, respectively. When identifying a seizure with the lead orientation towards the region of seizure onset, both reviewers identified 20 out of 21 seizures (95%). When the lead was not oriented towards the region of seizure onset, the reviewers identified 34 and 30 out of 42 ictal records correctly, respectively. Conclusions. These results suggest that it is possible to identify epileptic seizures by bipolar EEG derivation using only two scalp electrodes. Lead orientation towards the suspected region of seizure onset is important for optimal detection sensitivity