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

Theta-phase dependent neuronal coding during sequence learning in human single neurons

This work was supported by grants from the French Agence Nationale de la Recherche (ANR-12-JSH2-0004-01 and ANR AI-REPS–18-CE37-0007-01), the Fyssen foundation, and the Université Paul Sabatier, Toulouse, France (BQR, 2009 and Appel à Projets de Recherche Labellisés, 2013), to L.R., the European Research Council (ERC Consolidator Grant P-Cycles number 614244), the French Agence Nationale de la Recherche (ANR OSCI-DEEP ANR-19-NEUC-0004), and an ANITI (Artificial and Natural Intelligence Toulouse Institute) Research Chair (ANR-19-PI3A-0004) to R.V., the Studienstiftung des Deutschen Volkes (German Academic Scholarship Foundation) to B.Z., the European Union (ERC Grant Agreement n. 339490 “Cortic_al_gorithms” and grant agreements 720270 and 785907 “Human Brain Project SGA1 and SGA2’) and the Friends Foundation of the Netherlands Institute for Neuroscience to P.R.R.The ability to maintain a sequence of items in memory is a fundamental cognitive function. In the rodent hippocampus, the representation of sequentially organized spatial locations is reflected by the phase of action potentials relative to the theta oscillation (phase precession). We investigated whether the timing of neuronal activity relative to the theta brain oscillation also reflects sequence order in the medial temporal lobe of humans. We used a task in which human participants learned a fixed sequence of pictures and recorded single neuron and local field potential activity with implanted electrodes. We report that spikes for three consecutive items in the sequence (the preferred stimulus for each cell, as well as the stimuli immediately preceding and following it) were phase-locked at distinct phases of the theta oscillation. Consistent with phase precession, spikes were fired at progressively earlier phases as the sequence advanced. These findings generalize previous findings in the rodent hippocampus to the human temporal lobe and suggest that encoding stimulus information at distinct oscillatory phases may play a role in maintaining sequential order in memory.Publisher PDFPeer reviewe

Human Synapses Show a Wide Temporal Window for Spike-Timing-Dependent Plasticity

Throughout our lifetime, activity-dependent changes in neuronal connection strength enable the brain to refine neural circuits and learn based on experience. Synapses can bi-directionally alter strength and the magnitude and sign depend on the millisecond timing of presynaptic and postsynaptic action potential firing. Recent findings on laboratory animals have shown that neurons can show a variety of temporal windows for spike-timing-dependent plasticity (STDP). It is unknown what synaptic learning rules exist in human synapses and whether similar temporal windows for STDP at synapses hold true for the human brain. Here, we directly tested in human slices cut from hippocampal tissue removed for surgical treatment of deeper brain structures in drug-resistant epilepsy patients, whether adult human synapses can change strength in response to millisecond timing of pre- and postsynaptic firing. We find that adult human hippocampal synapses can alter synapse strength in response to timed pre- and postsynaptic activity. In contrast to rodent hippocampal synapses, the sign of plasticity does not sharply switch around 0-ms timing. Instead, both positive timing intervals, in which presynaptic firing preceded the postsynaptic action potential, and negative timing intervals, in which postsynaptic firing preceded presynaptic activity down to −80 ms, increase synapse strength (tLTP). Negative timing intervals between −80 to −130 ms induce a lasting reduction of synapse strength (tLTD). Thus, similar to rodent synapses, adult human synapses can show spike-timing-dependent changes in strength. The timing rules of STDP in human hippocampus, however, seem to differ from rodent hippocampus, and suggest a less strict interpretation of Hebb's predictions

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

Topographical Organization of Mu and Beta Band Activity Associated with Hand and Foot Movements in Patients with Perirolandic Lesions

To study the topographical organization of mu and beta band event-related desynchronization (ERD) associated with voluntary hand and foot movements, we used magnetoencephalographic (MEG) recordings from 19 patients with perirolandic lesions. Synthetic aperture magnetometry (SAM) was used to detect and localize changes in the mu (7 - 11 Hz) and beta (13 - 30 Hz) frequency bands associated with repetitive movements of the hand and foot and overlaid on individual coregistered magnetic resonance (MR) images. Hand movements showed homotopic and contralateral ERD at the sensorimotor (S/M) cortex in the majority of cases for mu and to a lesser extent for beta rhythms. Foot movements showed an increased heterotopic distribution with bilateral and ipsilateral ERD compared to hand movements. No systematic topographical segregation between mu and beta ERD could be observed. In patients with perirolandic lesions, the mu and beta band spatial characteristics associated with hand movements retain the expected functional-anatomical boundaries to a large extent. Foot movements have altered patterns of mu and beta band ERD, which may give more insight into the differential functional role of oscillatory activity in different voluntary movements

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

The role of epidemic spreading in seizure dynamics and epilepsy surgery

AbstractEpilepsy surgery is the treatment of choice for drug-resistant epilepsy patients, but only leads to seizure freedom for roughly two in three patients. To address this problem, we designed a patient-specific epilepsy surgery model combining large-scale magnetoencephalography (MEG) brain networks with an epidemic spreading model. This simple model was enough to reproduce the stereo-tactical electroencephalography (SEEG) seizure propagation patterns of all patients (N = 15), when considering the resection areas (RA) as the epidemic seed. Moreover, the goodness of fit of the model predicted surgical outcome. Once adapted for each patient, the model can generate alternative hypothesis of the seizure onset zone and test different resection strategies in silico. Overall, our findings indicate that spreading models based on patient-specific MEG connectivity can be used to predict surgical outcomes, with better fit results and greater reduction on seizure propagation linked to higher likelihood of seizure freedom after surgery. Finally, we introduced a population model that can be individualized by considering only the patient-specific MEG network, and showed that it not only conserves but improves the group classification. Thus, it may pave the way to generalize this framework to patients without SEEG recordings, reduce the risk of overfitting and improve the stability of the analyses

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

Word Processing differences between dyslexic and control children

BACKGROUND: The aim of this study was to investigate brain responses triggered by different wordclasses in dyslexic and control children. The majority of dyslexic children have difficulties to phonologically assemble a word from sublexical parts following grapheme-to-phoneme correspondences. Therefore, we hypothesised that dyslexic children should mainly differ from controls processing low frequent words that are unfamiliar to the reader. METHODS: We presented different wordclasses (high and low frequent words, pseudowords) in a rapid serial visual word (RSVP) design and performed wavelet analysis on the evoked activity. RESULTS: Dyslexic children had lower evoked power amplitudes and a higher spectral frequency for low frequent words compared to control children. No group differences were found for high frequent words and pseudowords. Control children had higher evoked power amplitudes and a lower spectral frequency for low frequent words compared to high frequent words and pseudowords. This pattern was not present in the dyslexic group. CONCLUSION: Dyslexic children differed from control children only in their brain responses to low frequent words while showing no modulated brain activity in response to the three word types. This might support the hypothesis that dyslexic children are selectively impaired reading words that require sublexical processing. However, the lacking differences between word types raise the question if dyslexic children were able to process the words presented in rapid serial fashion in an adequate way. Therefore the present results should only be interpreted as evidence for a specific sublexical processing deficit with caution

High Bandwidth Synaptic Communication and Frequency Tracking in Human Neocortex

Neuronal firing, synaptic transmission, and its plasticity form the building blocks for processing and storage of information in the brain. It is unknown whether adult human synapses are more efficient in transferring information between neurons than rodent synapses. To test this, we recorded from connected pairs of pyramidal neurons in acute brain slices of adult human and mouse temporal cortex and probed the dynamical properties of use-dependent plasticity. We found that human synaptic connections were purely depressing and that they recovered three to four times more swiftly from depression than synapses in rodent neocortex. Thereby, during realistic spike trains, the temporal resolution of synaptic information exchange in human synapses substantially surpasses that in mice. Using information theory, we calculate that information transfer between human pyramidal neurons exceeds that of mouse pyramidal neurons by four to nine times, well into the beta and gamma frequency range. In addition, we found that human principal cells tracked fine temporal features, conveyed in received synaptic inputs, at a wider bandwidth than for rodents. Action potential firing probability was reliably phase-locked to input transients up to 1,000 cycles/s because of a steep onset of action potentials in human pyramidal neurons during spike trains, unlike in rodent neurons. Our data show that, in contrast to the widely held views of limited information transfer in rodent depressing synapses, fast recovering synapses of human neurons can actually transfer substantial amounts of information during spike trains. In addition, human pyramidal neurons are equipped to encode high synaptic information content. Thus, adult human cortical microcircuits relay information at a wider bandwidth than rodent microcircuits