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An unusual alternating reflection method on conics is presented to evaluate inverse trigonometric and hyperbolic functions.

Orthoptic curves for the conics are well known. It is the Monge's circle for ellipse and hyperbola, and for parabola it is its directrix. These conics are level sets of quadratic functions in the plane. We consider level sets of quadratic functions in higher dimension, known as quadric hypersurfaces. For these hypersurfaces we present and study their orthoptic sets, which extend the idea of orthoptic curves for conics.

Epileptic spikes are the traditional interictal electroencephalographic (EEG) biomarker for epilepsy. Given their low specificity for identifying the epileptogenic zone (EZ), they are given only moderate attention in presurgical evaluation. This study aims to demonstrate that it is possible to identify specific spike features in intracranial EEG that optimally define the EZ and predict surgical outcome.We analyzed spike features on stereo-EEG segments from 83 operated patients from 2 epilepsy centers (37 Engel IA) in wakefulness, non-rapid eye movement sleep, and rapid eye movement sleep. After automated spike detection, we investigated 135 spike features based on rate, morphology, propagation, and energy to determine the best feature or feature combination to discriminate the EZ in seizure-free and non-seizure-free patients by applying 4-fold cross-validation.The rate of spikes with preceding gamma activity in wakefulness performed better for surgical outcome classification (4-fold area under receiver operating characteristics curve [AUC] = 0.755 ± 0.07) than the seizure onset zone, the current gold standard (AUC = 0.563 ± 0.05, p = 0.015) and the ripple rate, an emerging seizure-independent biomarker (AUC = 0.537 ± 0.07, p = 0.006). Channels with a spike-gamma rate exceeding 1.9/min had an 80% probability of being in the EZ. Combining features did not improve the results.Resection of brain regions with high spike-gamma rates in wakefulness is associated with a high probability of achieving seizure freedom. This rate could be applied to determine the minimal number of spiking channels requiring resection. In addition to quantitative analysis, this feature is easily accessible to visual analysis, which could aid clinicians during presurgical evaluation. ANN NEUROL 2022.

Objective To determine if properties of epileptic networks could be delineated using interictal spike propagation seen on stereo‐electroencephalography (SEEG) and if these properties could predict surgical outcome in patients with drug‐resistant epilepsy. Methods We studied the SEEG of 45 consecutive drug‐resistant epilepsy patients who underwent subsequent epilepsy surgery: 18 patients with good post‐surgical outcome (Engel I) and 27 with poor outcome (Engel II–IV). Epileptic networks were derived from interictal spike propagation; these networks described the generation and propagation of interictal epileptic activity. We compared the regions in which spikes were frequent and the regions responsible for generating spikes to the area of resection and post‐surgical outcome. We developed a measure termed source spike concordance, which integrates information about both spike rate and region of spike generation. Results Inclusion in the resection of regions with high spike rate is associated with good post‐surgical outcome (sensitivity = 0.82, specificity = 0.73). Inclusion in the resection of the regions responsible for generating interictal epileptic activity independently of rate is also associated with good post‐surgical outcome (sensitivity = 0.88, specificity = 0.82). Finally, when integrating the spike rate and the generators, we find that the source spike concordance measure has strong predictability (sensitivity = 0.91, specificity = 0.94). Interpretations Epileptic networks derived from interictal spikes can determine the generators of epileptic activity. Inclusion of the most active generators in the resection is strongly associated with good post‐surgical outcome. These epileptic networks may aid clinicians in determining the area of resection during pre‐surgical evaluation.

Objective Gain insight and improve our interpretation of measurements from intracerebral electrodes. Determine if interpretation of intracerebral EEG is dependent on electrode characteristics. Methods We use intracerebral EEG measurements differing only in the recording electrodes (Dixi or homemade electrodes), and numerical simulations to determine the spatial sensitivity of intracerebral electrodes and its dependence on several parameters. Results There is a difference in the high frequency (>20 Hz) power depending on the electrode type, which cannot be explained by the different contact sizes or distance between contacts. Simulations show that the width of the gap between electrode and brain and the extent of the generators have an effect on sensitivity, while other parameters are less important. Conclusions The sensitivity of intracerebral electrodes is not affected in an important way by the dimensions of the contacts, but depends on the extent of generators. The unusual insertion technique of homemade electrodes resulting in a large gap between functional brain and electrodes, explains the observed signal difference. Significance Numerical simulation is a useful tool in the choice or design of intracerebral electrodes, and increases our understanding of their measurements. The interpretation of intracerebral EEG is not affected by differences between typical commercially available electrodes.

We present a rare patient clinically suspected to have mixed idiopathic generalized and focal epilepsy, which was supported by BOLD pattern based on EEG-fMRI. A 37-year-old female with three types of refractory seizures starting at age six - tonic with breathing difficulties and confusion, generalized tonic-clonic, and focal with brief impairment of awareness and versive head movement, initially thought to represent atypical absences - was evaluated by EEG-fMRI. She was also shown to have three types of interictal epileptic discharges: generalized spike or polyspikes and slow waves, and left fronto-temporal and right fronto-temporal discharges. We assessed BOLD activation and deactivation for each type. For generalized patterns, the BOLD activation and deactivation were typical of that seen in primary generalized epilepsy. Whereas maximum activation for left fronto-temporal EEG patterns was observed in the left superior frontal gyrus and posterior superior temporal gyrus, maximum activation for right fronto-temporal patterns was bilateral in the right posterior middle temporal gyrus and left posterior middle temporal gyrus. The EEG-fMRI results suggested that the patient had both refractory idiopathic generalized and focal epilepsy, and not a generalized epilepsy originating from a focus.

OBJECTIVE Disturbed sleep is common in epilepsy. The direct influence of nocturnal epileptic activity on sleep fragmentation remains poorly understood. Stereo-electroencephalography paired with polysomnography is the ideal tool to study this relationship. We investigated whether sleep-related epileptic activity is associated with sleep disruption. METHODS We visually marked sleep stages, arousals, seizures, and epileptic bursts in 36 patients with focal drug-resistant epilepsy who underwent combined stereo-electroencephalography/polysomnography during presurgical evaluation. Epileptic spikes were detected automatically. Spike and burst indices (n/sec/channel) were computed across four 3-second time windows (baseline sleep, pre-arousal, arousal, and post-arousal). Sleep stage and anatomic localization were tested as modulating factors. We assessed the intra-arousal dynamics of spikes and their relationship with the slow wave component of non-rapid eye-movement sleep (NR) arousals. RESULTS The vast majority of sleep-related seizures (82.4%; 76.5% asymptomatic) were followed by awakenings or arousals. The epileptic burst index increased significantly before arousals as compared to baseline and postarousal, irrespective of sleep stage or brain area. A similar pre-arousal increase was observed for the spike index in NR stage 2 and rapid eye-movement sleep. In addition, the spike index increased during the arousal itself in neocortical channels, and was strongly correlated with the slow wave component of NR arousals (r = 0.99, p

ObjectiveTo examine whether fast ripples (FRs) are an accurate marker of the epileptogenic zone, we analyzed overnight stereo-EEG recordings from 43 patients and hypothesized that FR resection ratio, maximal FR rate, and FR distribution predict postsurgical seizure outcome.MethodsWe detected FRs automatically from an overnight recording edited for artifacts and visually from a 5-minute period of slow-wave sleep. We examined primarily the accuracy of removing ≥50% of total FR events or of channels with FRs to predict postsurgical seizure outcome (Engel class I = good, classes II–IV = poor) according to the whole-night and 5-minute analysis approaches. Secondarily, we examined the association of low overall FR rates or absence or incomplete resection of 1 dominant FR area with poor outcome.ResultsThe accuracy of outcome prediction was highest (81%, 95% confidence interval [CI] 67%–92%) with the use of the FR event resection ratio and whole-night recording (vs 72%, 95% CI 56%–85%, for the visual 5-minute approach). Absence of channels with FR rates >6/min (p = 0.001) and absence or incomplete resection of 1 dominant FR area (p < 0.001) were associated with poor outcome.ConclusionsFRs are accurate in predicting epilepsy surgery outcome at the individual level when overnight recordings are used. Absence of channels with high FR rates or absence of 1 dominant FR area is a poor prognostic factor that may reflect suboptimal spatial sampling of the epileptogenic zone or multifocality, rather than an inherently low sensitivity of FRs.Classification of evidenceThis study provides Class II evidence that FRs are accurate in predicting epilepsy surgery outcome.

The integration of high-frequency oscillations (HFOs; ripples [80-250 Hz], fast ripples [250-500 Hz]) in epilepsy evaluation is hampered by physiological HFOs, which cannot be reliably differentiated from pathological HFOs. We evaluated whether defining abnormal HFO rates by statistical comparison to region-specific physiological HFO rates observed in the healthy brain improves identification of the epileptic focus and surgical outcome prediction.We detected HFOs in 151 consecutive patients who underwent stereo-electroencephalography and subsequent resective epilepsy surgery at two tertiary epilepsy centers. We compared how HFOs identified the resection cavity and predicted seizure-free outcome using two thresholds from the literature (HFO rate1/min; 50% of the total number of a patient's HFOs) and three thresholds based on normative rates from the Montreal Neurological Institute Open iEEG Atlas (https://mni-open-ieegatlas.mcgill.ca/): global Atlas threshold, regional Atlas threshold, and regional + 10% threshold after regional Atlas correction.Using ripples, the regional + 10% threshold performed best for focus identification (77.3% accuracy, 27% sensitivity, 97.1% specificity, 80.6% positive predictive value [PPV], 78.2% negative predictive value [NPV]) and outcome prediction (69.5% accuracy, 58.6% sensitivity, 76.3% specificity, 60.7% PPV, 74.7% NPV). This was an improvement for focus identification (+1.1% accuracy, +17.0% PPV; p .001) and outcome prediction (+12.0% sensitivity, +1.0% PPV; p = .05) compared to the 50% threshold. The improvement was particularly marked for foci in cortex, where physiological ripples are frequent (outcome: +35.3% sensitivity, +5.3% PPV; p = .014). In these cases, the regional + 10% threshold outperformed fast ripple rate1/min (+3.6% accuracy, +26.5% sensitivity, +21.6% PPV; p .001) and seizure onset zone (+13.5% accuracy, +29.4% sensitivity, +17.0% PPV; p .05-.01) for outcome prediction. Normalization did not improve the performance of fast ripples.Defining abnormal HFO rates by statistical comparison to rates in healthy tissue overcomes an important weakness in the clinical use of ripples. It improves focus identification and outcome prediction compared to standard HFO measures, increasing their clinical applicability.

Objective Developmental epileptic encephalopathies (DEEs) are genetically heterogeneous severe childhood-onset epilepsies with developmental delay or cognitive deficits. In this study, we explored the pathogenic mechanisms of DEE-associated de novo mutations in the CACNA1A gene. Methods We studied the functional impact of four de novo DEE-associated CACNA1A mutations, including the previously described p.A713T variant and three novel variants (p.V1396M, p.G230V, and p.I1357S). Mutant cDNAs were expressed in HEK293 cells, and whole-cell voltage-clamp recordings were conducted to test the impacts on CaV 2.1 channel function. Channel localization and structure were assessed with immunofluorescence microscopy and three-dimensional (3D) modeling. Results We find that the G230V and I1357S mutations result in loss-of-function effects with reduced whole-cell current densities and decreased channel expression at the cell membrane. By contrast, the A713T and V1396M variants resulted in gain-of-function effects with increased whole-cell currents and facilitated current activation (hyperpolarized shift). The A713T variant also resulted in slower current decay. 3D modeling predicts conformational changes favoring channel opening for A713T and V1396M. Significance Our findings suggest that both gain-of-function and loss-of-function CACNA1A mutations are associated with similarly severe DEEs and that functional validation is required to clarify the underlying molecular mechanisms and to guide therapies.

In this paper, we introduce a nonlinear model which can be used as a regression model for modeling phenomena requiring a two-phase growth curves. The proposed model is defined as a continuo...

Objective A vast network involving the nodules and overlying cortices is believed to be responsible for the epileptogenicity in gray matter heterotopia with multiple nodules, which often associated with difficult‐to‐treat epilepsy. We sought to determine if functional magnetic resonance imaging (fMRI) could detect internodular functional connectivity (FC), and if this connectivity reflects an actual synchronized neuronal activity and partakes in epileptogenicity. Methods We studied 16 epilepsy patients with multiple heterotopic nodules; eight underwent subsequent intracerebral EEG. We examined the internodular FC using fMRI and its correspondence with internodular synchrony of intracerebral interictal activity. We then compared the spreading speed of ictal activity between connected and unconnected nodules; and the FC among possible combinations of nodule pairs in terms of their involvement at seizure onset. Results Seventy nodules were studied: 83% have significant connection to at least one other nodule. Among the 49 pairs studied with intracerebral EEG, (1) synchronized interictal activity is more prevalent in fMRI‐connected pairs (P

Objective We hypothesized that the number of interictal epileptic discharges (IEDs) during scan and their spatial extent are contributing factors in obtaining appropriate activations that reveal the seizure onset zone (SOZ) in EEG-fMRI. Methods 157 IED types, each corresponding to one EEG scalp distribution, in 64 consecutive EEG-fMRI studies from 64 patients with refractory localization-related epilepsy were reviewed. To determine reliable activation, we used the threshold corresponding to corrected whole-brain topological false discovery rate (FDR). The location with maximum activation was compared to the presumed SOZ as defined by a comprehensive evaluation for each patient. Results The number of IEDs was significantly higher in the types with t-value above FDR than with t-value below FDR. The presumed SOZ could be delineated in 30 of the 64 patients. Among these patients, the types of IED concordant with the SOZ had significantly larger extent on scalp EEG than the IED types discordant with the SOZ. Conclusions The number of IEDs is important factor in obtaining reliable activations in EEG-fMRI. IEDs with larger spatial extent are more likely to reveal, on maximum BOLD, accurate location of the SOZ. Significance Widespread discharges are more likely to yield a reliable activation for SOZ in EEG-fMRI.

OBJECTIVE To investigate whether high-frequency oscillations (HFOs) show spatiotemporal propagation and assess the relevance of the earliest oscillations in relation to the seizure onset zone (SOZ) and postsurgical outcome. METHODS We retrospectively investigated the intracerebral electroencephalography (EEG) of patients who became seizure free after subsequent surgery. We marked HFOs during 1 hour of recordings. We calculated the time delay between pairs of channels as the median delay between their HFOs and constructed a time line of the delay of each channel with respect to the earliest channel (first source channel). A network was defined when a temporal order could be established among the channels based on the existence of statistically significant delays. RESULTS Fifteen patients with good surgical outcome were included. We found ripple networks in all patients, and fast ripple networks in 9. For ripples, first source channels were found in a higher proportion in the SOZ than the rest of the network channels (15 of 27 [56%] versus 93 of 262 [35%]; p = 0.04). For both ripples and fast ripples, first source channels were resected more often that the rest of the network channels (ripples: 13 of 27 [48%] versus 65 of 262 [25%]; p = 0.01; fast ripples: 8 of 9 [89%] versus 17 of 40 [43%]; p = 0.002); channels with the highest rates of ripples and fast ripples were resected in a similar proportion. INTERPRETATION These results demonstrate that interictal HFOs are organized in networks and indicate a possible need for the resection of first source channels. However, resecting them is not superior to resecting channels with highest rates of HFOs. Ann Neurol 2019;85:485-494.

A simple standard problem in physics is the study of elastic collisions between elements of an ideal system, which consists of two point masses and a wall. Based on energy and momentum conservation laws, solving the problem consists in finding the intersection of a straight line with a conic. Relationships between the solutions are easily obtained if we consider the right (fundamental) basis to express the solutions. The geometric interpretation follows easily: moving from one point to another on a conic using directions given by this basis. With simple changes in variables, reflections and rotations appear clearly. Similarities with other phenomena such as Heron’s reflection principle in optics and Kepler’s second law of planetary motion are pointed out.

OBJECTIVE In an attempt to improve postsurgical seizure outcomes for poorly defined cases (PDCs) of pediatric focal epilepsy (i.e., those that are not visible or well defined on 3T MRI), the authors modified their presurgical evaluation strategy. Instead of relying on concordance between video-electroencephalography and 3T MRI and using functional imaging and intracranial recording in select cases, the authors systematically used a multimodal, 3-tiered investigation protocol that also involved new collaborations between their hospital, the Montreal Children’s Hospital, and the Montreal Neurological Institute. In this study, the authors examined how their new strategy has impacted postsurgical outcomes. They hypothesized that it would improve postsurgical seizure outcomes, with the added benefit of identifying a subset of tests contributing the most. METHODS Chart review was performed for children with PDCs who underwent resection following the new strategy (i.e., new protocol [NP]), and for the same number who underwent treatment previously (i.e., preprotocol [PP]); ≥ 1-year follow-up was required for inclusion. Well-defined, multifocal, and diffuse hemispheric cases were excluded. Preoperative demographics and clinical characteristics, resection volumes, and pathology, as well as seizure outcomes (Engel class Ia vs > Ia) at 1 year postsurgery and last follow-up were reviewed. RESULTS Twenty-two consecutive NP patients were compared with 22 PP patients. There was no difference between the two groups for resection volumes, pathology, or preoperative characteristics, except that the NP group underwent more presurgical evaluation tests (p < 0.001). At 1 year postsurgery, 20 of 22 NP patients and 10 of 22 PP patients were seizure free (OR 11.81, 95% CI 2.00–69.68; p = 0.006). Magnetoencephalography and PET/MRI were associated with improved postsurgical seizure outcomes, but both were highly correlated with the protocol group (i.e., independent test effects could not be demonstrated). CONCLUSIONS A new presurgical evaluation strategy for children with PDCs of focal epilepsy led to improved postsurgical seizure freedom. No individual presurgical evaluation test was independently associated with improved outcome, suggesting that it may be the combined systematic protocol and new interinstitutional collaborations that makes the difference rather than any individual test.

Through Taylor’s expansions and a thorough analysis of the necessary and sufficient conditions that will entail for fixed point and Newton’s iterative methods to be of higher order convergence in Banach space, we are able to present a unified way to make these methods faster. Numerical examples illustrate the theoretical results.

Background and ObjectivesTo assess the utility of EEG-fMRI for epilepsy surgery, we evaluated surgical outcome in relation to the resection of the most significant EEG-fMRI response.MethodsPatients with postoperative neuroimaging and follow-up of at least 1 year were included. In EEG-fMRI responses, we defined as primary the cluster with the highest absolute t value located in the cortex and evaluated 3 levels of confidence for the results. The threshold for low confidence was t ≥ 3.1 (p < 0.005); the one for medium confidence corresponded to correction for multiple comparisons with a false discovery rate of 0.05; and a result reached high confidence when the primary cluster was much more significant than the next highest cluster. Concordance with the resection was determined by comparison to postoperative neuroimaging.ResultsWe evaluated 106 epilepsy surgeries in 84 patients. An increasing association between concordance and surgical outcome with higher levels of confidence was demonstrated. If the peak response was not resected, the surgical outcome was likely to be poor: for the high confidence level, no patient had a good outcome; for the medium and low levels, only 18% and 28% had a good outcome. The positive predictive value remained low for all confidence levels, indicating that removing the maximum cluster did not ensure seizure freedom.DiscussionResection of the primary EEG-fMRI cluster, especially in high confidence cases, is necessary to obtain a good outcome but not sufficient.Classification of EvidenceThis study provides Class II evidence that failure to resect the primary EEG-fMRI cluster is associated with poorer epilepsy surgery outcomes.

Epilepsy associated with periventricular nodular heterotopia (PNH), a developmental malformation, is frequently drug-resistant and requires focal therapeutic intervention. Invasive EEG study is usually necessary to delineate the epileptogenic zone, but constructing an accurate hypothesis to define an appropriate electrode implantation scheme and the treatment is challenging. This article reviews recent studies that help understanding the epileptogenicity and potential therapeutic options in PNH. New noninvasive diagnostic and intracerebral EEG analytic tools demonstrated that cortical hyperexcitability and aberrant connectivity (between nodules and cortices and among nodules) are likely mechanisms causing epilepsy in most patients. The deeply seated PNH, if epileptogenic, are ideal target for stereotactic ablative techniques, which offer concomitant ablation of multiple regions with relatively satisfactory seizure outcome. Advance in diagnostic and analytic tools have enhanced our understanding of the complex epileptogenicity in PNH. Development in stereotactic ablative techniques now offers promising therapeutic options for these patients.

Background: Epilepsy surgery failure is not uncommon, with several explanations having been proposed. In this series, we detail cases of epilepsy surgery failure subsequently attributed to insular involvement. Methods: We retrospectively identified patients investigated at the epilepsy monitoring units of two Canadian tertiary care centers (2004–2020). Included patients were adults who had undergone epilepsy surgeries with recurrence of seizures post-operatively and who were subsequently determined to have an insular epileptogenic focus. Clinical, electrophysiological, neuroimaging, and surgical data were synthesized. Results: We present 14 patients who demonstrated insular epileptic activity post-surgery-failure as detected by intracranial EEG, MEG, or seizure improvement after insular resection. Seven patients had manifestations evoking possible insular involvement prior to their first surgery. Most patients (8/14) had initial surgeries targeting the temporal lobe. Seizure recurrence ranged from the immediate post-operative period to one year. The main modality used to determine insular involvement was MEG (8/14). Nine patients underwent re-operations that included insular resection; seven achieved a favorable post-operative outcome (Engel I or II). Conclusions: Our series suggests that lowering the threshold for suspecting insular epilepsy may be necessary to improve epilepsy surgery outcomes. Detecting insular epilepsy post-surgery-failure may allow for re-operations which may lead to good outcomes.

IMPORTANCE: Stereoelectroencephalography (SEEG) has become the criterion standard in case of inconclusive noninvasive presurgical epilepsy workup. However, up to 40% of patients are subsequently not offered surgery because the seizure-onset zone is less focal than expected or cannot be identified. OBJECTIVE: To predict focality of the seizure-onset zone in SEEG, the 5-point 5-SENSE score was developed and validated. DESIGN, SETTING, AND PARTICIPANTS: This was a monocentric cohort study for score development followed by multicenter validation with patient selection intervals between February 2002 to October 2018 and May 2002 to December 2019. The minimum follow-up period was 1 year. Patients with drug-resistant epilepsy undergoing SEEG at the Montreal Neurological Institute were analyzed to identify a focal seizure-onset zone. Selection criteria were 2 or more seizures in electroencephalography and availability of complete neuropsychological and neuroimaging data sets. For validation, patients from 9 epilepsy centers meeting these criteria were included. Analysis took place between May and July 2021. MAIN OUTCOMES AND MEASURES: Based on SEEG, patients were grouped as focal and nonfocal seizure-onset zone. Demographic, clinical, electroencephalography, neuroimaging, and neuropsychology data were analyzed, and a multiple logistic regression model for developing a score to predict SEEG focality was created and validated in an independent sample. RESULTS: A total of 128 patients (57 women [44.5%]; median [range] age, 31 [13-58] years) were analyzed for score development and 207 patients (97 women [46.9%]; median [range] age, 32 [16-70] years) were analyzed for validation. The score comprised the following 5 predictive variables: focal lesion on structural magnetic resonance imaging, absence of bilateral independent spikes in scalp electroencephalography, localizing neuropsychological deficit, strongly localizing semiology, and regional ictal scalp electroencephalography onset. The 5-SENSE score had an optimal mean (SD) probability cutoff for identifying a focal seizure-onset zone of 37.6 (3.5). Area under the curve, specificity, and sensitivity were 0.83, 76.3% (95% CI, 66.7-85.8), and 83.3% (95% CI, 72.30-94.1), respectively. Validation showed 76.0% (95% CI, 67.5-84.0) specificity and 52.3% (95% CI, 43.0-61.5) sensitivity. CONCLUSIONS AND RELEVANCE: High specificity in score development and validation confirms that the 5-SENSE score predicts patients where SEEG is unlikely to identify a focal seizure-onset zone. It is a simple and useful tool for assisting clinicians to reduce unnecessary invasive diagnostic burden on patients and overutilization of limited health care resources.

Objective High-frequency oscillations (HFOs) are a promising biomarker for the epileptogenic zone. It has not been possible, however, to differentiate physiological from pathological HFOs, and baseline rates of HFO occurrence vary substantially across brain regions. This project establishes region-specific normative values for physiological HFOs and high-frequency activity (HFA). Methods Intracerebral stereo-encephalographic recordings with channels displaying normal physiological activity from nonlesional tissue were selected from 2 tertiary epilepsy centers. Twenty-minute sections from N2/N3 sleep were selected for automatic detection of ripples (80-250Hz), fast ripples (>250Hz), and HFA defined as long-lasting activity > 80Hz. Normative values are provided for 17 brain regions. Results A total of 1,171 bipolar channels with normal physiological activity from 71 patients were analyzed. The highest rates of ripples were recorded in the occipital cortex, medial and basal temporal region, transverse temporal gyrus and planum temporale, pre- and postcentral gyri, and medial parietal lobe. The mean rate of fast ripples was very low (0.038/min). Only 5% of channels had a rate > 0.2/min HFA was observed in the medial occipital lobe, pre- and postcentral gyri, transverse temporal gyri and planum temporale, and lateral occipital lobe. Interpretation This multicenter atlas is the first to provide region-specific normative values for physiological HFO rates and HFA in common stereotactic space; rates above these can now be considered pathological. Physiological ripples are frequent in eloquent cortex. In contrast, physiological fast ripples are very rare, making fast ripples a good candidate for defining the epileptogenic zone. Ann Neurol 2018;84:374-385.

Objectives There are different neurophysiological markers of the Epileptogenic Zone (EZ), but their sensitivity and specificity for the EZ is not known in Focal Cortical Dysplasia (FCD) patients. Methods We studied patients with FCD who underwent stereoelectroencephalography (SEEG) and surgery. We marked in the SEEG: (a) typical and atypical interictal epileptiform patterns, (b) ictal onset patterns, and (c) rates of ripples (80–250 Hz) and fast ripples (FRs) (>250 Hz). High frequency oscillations were marked automatically during one hour of deep sleep. Surgical outcome was defined as good (Engel I) or poor (Engel II–IV). We computed the sensitivity and, as a measure of specificity, the false positive rate to identify the EZ, and compared them across the different neurophysiological markers. Results We studied 21 patients, 19 with FCD II. Ictal and typical interictal pattern were the markers with highest sensitivity, while the atypical interictal pattern had the lowest. We found no significant difference in specificity among markers. However, there is a tendency that FRs had the lowest false positive rate. Conclusion The typical interictal pattern has the highest sensitivity. The clinical use of FRs is limited by their low sensitivity. Significance We suggest to analyze the typical interictal pattern first. FRs should be analyzed in a second step. If, for instance, a focus with FRs and no typical interictal pattern is found, this area could be considered for resection.

We show that Halley’s basic sequence, resulting from accelerating the order of convergence of Newton’s method, is the most efficient way of doing so in terms of usage of certain derivatives. This fact could explain why this process of accelerating the convergence of Newton’s method is so frequently rediscovered. Then we present an algorithmic way of recognizing Halley’s family and we apply this algorithm to examples of rediscoveries.

In contrast to scalp EEG, our knowledge of the normal physiological intracranial EEG activity is scarce. This multicentre study provides an atlas of normal intracranial EEG of the human brain during wakefulness. Here we present the results of power spectra analysis during wakefulness. Intracranial electrodes are placed in or on the brain of epilepsy patients when candidates for surgical treatment and non-invasive approaches failed to sufficiently localize the epileptic focus. Electrode contacts are usually in cortical regions showing epileptic activity, but some are placed in normal regions, at distance from the epileptogenic zone or lesion. Intracranial EEG channels defined using strict criteria as very likely to be in healthy brain regions were selected from three tertiary epilepsy centres. All contacts were localized in a common stereotactic space allowing the accumulation and superposition of results from many subjects. Sixty-second artefact-free sections during wakefulness were selected. Power spectra were calculated for 38 brain regions, and compared to a set of channels with no spectral peaks in order to identify significant peaks in the different regions. A total of 1785 channels with normal brain activity from 106 patients were identified. There were on average 2.7 channels per cm 3 of cortical grey matter. The number of contacts per brain region averaged 47 (range 6-178). We found significant differences in the spectral density distributions across the different brain lobes, with beta activity in the frontal lobe (20-24 Hz), a clear alpha peak in the occipital lobe (9.25-10.25 Hz), intermediate alpha (8.25-9.25 Hz) and beta (17-20 Hz) frequencies in the parietal lobe, and lower alpha (7.75-8.25 Hz) and delta (0.75-2.25 Hz) peaks in the temporal lobe. Some cortical regions showed a specific electrophysiological signature: peaks present in > 60% of channels were found in the precentral gyrus (lateral: peak frequency range, 20-24 Hz; mesial: 24-30 Hz), opercular part of the inferior frontal gyrus (20-24 Hz), cuneus (7.75-8.75 Hz), and hippocampus (0.75-1.25 Hz). Eight per cent of all analysed channels had more than one spectral peak; these channels were mostly recording from sensory and motor regions. Alpha activity was not present throughout the occipital lobe, and some cortical regions showed peaks in delta activity during wakefulness. This is the first atlas of normal intracranial EEG activity; it includes dense coverage of all cortical regions in a common stereotactic space, enabling direct comparisons of EEG across subjects. This atlas provides a normative baseline against which clinical EEGs and experimental results can be compared. It is provided as an open web resource (https://mni-open-ieegatlas.research.mcgill.ca).

Simultaneous scalp EEG/functional MRI measures non-invasively haemodynamic responses to interictal epileptic discharges, which are related to the epileptogenic zone. High frequency oscillations are also an excellent indicator of this zone, but are primarily recorded from intracerebral EEG. We studied the spatial overlap of these two important markers in patients with drug-resistant epilepsy to assess if their combination could help better define the extent of the epileptogenic zone. We included patients who underwent EEG-functional MRI and later intracerebral EEG. Based on intracerebral EEG findings, we separated patients with unifocal seizures from patients with multifocal or unknown onset seizures. Haemodynamic t-maps were coregistered with the intracerebral electrode positions. Each EEG channel was classified as pertaining to one of the following categories: primary haemodynamic cluster (maximum t-value), secondary cluster (t-value > 90% of the primary cluster) or outside the primary and secondary clusters. We marked high frequency oscillations (ripples: 80–250 Hz; fast ripples: 250–500 Hz) during 1 h of slow wave sleep, and compared their rates in each haemodynamic category. After classifying channels as high- or low-rate, the proportion of high-rate channels within the primary or primary plus secondary clusters was compared to the proportion expected by chance. Twenty-five patients, 11 with unifocal and 14 with multifocal/unknown seizure onsets, were studied. We found a significantly higher median high frequency oscillation rate in the primary cluster compared to secondary cluster and outside these two clusters for the unifocal group (P < 0.0001), but not for the multifocal/unknown group. For the unifocal group, the number of high-rate channels within the primary or primary plus secondary clusters was significantly higher than expected by chance. This held only for the high-ripple-rate channels in the multifocal/unknown group. At the patient level, most patients (18/25, or 72%) had at least one high-rate channel within a primary cluster. In patients with unifocal epilepsy, the maximum haemodynamic response (primary cluster) related to scalp interictal discharges overlaps with the tissue generating high frequency oscillations at high rates. If intracranial EEG is warranted, this response should be explored. As a tentative clinical use of the combination of these techniques we propose that higher high frequency oscillation rates inside than outside the maximum response indicates that the patient has indeed a focal epileptogenic zone demarcated by this response, whereas similar rates inside and outside may indicate a widespread epileptogenic zone or an epileptogenic zone not covered by the implantation.

Fusion of electroencephalography (EEG) and magnetoencephalography (MEG) data using maximum entropy on the mean method (MEM-fusion) takes advantage of the complementarities between EEG and MEG to improve localization accuracy. Simulation studies demonstrated MEM-fusion to be robust especially in noisy conditions such as single spike source localizations (SSSL). Our objective was to assess the reliability of SSSL using MEM-fusion on clinical data. We proposed to cluster SSSL results to find the most reliable and consistent source map from the reconstructed sources, the so-called consensus map. Thirty-four types of interictal epileptic discharges (IEDs) were analyzed from 26 patients with well-defined epileptogenic focus. SSSLs were performed on EEG, MEG, and fusion data and consensus maps were estimated using hierarchical clustering. Qualitative (spike-to-spike reproducibility rate, SSR) and quantitative (localization error and spatial dispersion) assessments were performed using the epileptogenic focus as clinical reference. Fusion SSSL provided significantly better results than EEG or MEG alone. Fusion found at least one cluster concordant with the clinical reference in all cases. This concordant cluster was always the one involving the highest number of spikes. Fusion yielded highest reproducibility (SSR EEG = 55%, MEG = 71%, fusion = 90%) and lowest localization error. Also, using only few channels from either modality (21EEG + 272MEG or 54EEG + 25MEG) was sufficient to reach accurate fusion. MEM-fusion with consensus map approach provides an objective way of finding the most reliable and concordant generators of IEDs. We, therefore, suggest the pertinence of SSSL using MEM-fusion as a valuable clinical tool for presurgical evaluation of epilepsy.

Objective We aimed to (1) assess the concordance between various polymicrogyria (PMG) types and the associated epileptogenic zone (EZ), as defined by stereoelectroencephalography (SEEG), and (2) determine the postsurgical seizure outcome in PMG-related drug-resistant epilepsy. Methods We retrospectively analyzed 58 cases: 49 had SEEG and 39 corticectomy or hemispherotomy. Results Mean age at SEEG or surgery was 28.3 years (range, 2-50). PMG was bilateral in 9 (16%) patients and unilateral in 49, including 17 (29%) unilobar, 12 (21%) multilobar, 15 (26%) perisylvian, and only 5 (9%) hemispheric. Twenty-eight (48%) patients additionally had schizencephaly, heterotopia, or focal cortical dysplasia. The SEEG-determined EZ was fully concordant with the PMG in only 8 (16%) cases, partially concordant in 74%, and discordant in 10%. The EZ included remote cortical areas in 21 (43%) cases and was primarily localized in those in 5 (10%), all related to the mesial temporal structures. All but 1 PMG patient with corticectomy or hemispherotomy had a unilateral PMG. At last follow-up (mean, 4.6 years; range, 1-16), 28 (72%) patients remained seizure free. Shorter epilepsy duration to surgery was an independent predictor of seizure freedom. Interpretation PMG-related drug-resistant epilepsy warrants a comprehensive presurgical evaluation, including SEEG investigations in most cases, given that the EZ may only partially overlap with the PMG or include solely remote cortical areas. Seizure freedom is feasible in a large proportion of patients. PMG extent should not deter from exploring the possibility of epilepsy surgery. Our data support the early consideration of epilepsy surgery in this patient group. Ann Neurol 2017;82:781-794.

Objective Source localization of interictal epileptic discharges (IEDs) is clinically useful in the presurgical workup of epilepsy patients. It is usually obtained by equivalent current dipole (ECD) which localizes a point source and is the only inverse solution approved by clinical guidelines. In contrast, magnetic source imaging using distributed methods (dMSI) provides maps of the location and the extent of the generators, but its yield has not been clinically validated. We systematically compared ECD versus dMSI performed using coherent Maximum Entropy on the Mean (cMEM), a method sensitive to the spatial extent of the generators. Methods 340 source localizations of IEDs derived from 49 focal epilepsy patients with foci well-defined through intracranial EEG, MRI lesions, and surgery were analyzed. The comparison was based on the assessment of the sublobar concordance with the focus and of the distance between the source and the focus. Results dMSI sublobar concordance was significantly higher than ECD (81% vs 69%, P

SummaryObjective To increase the diagnostic power of scalp electroencephalography (EEG) by investigating whether lesion type and location influence the morphology of interictal epileptic discharges (IEDs) and the likelihood that IEDs and high-frequency oscillations (HFOs) are present. Methods We studied EEG activity in epilepsy patients with lesional epilepsy. Lesions were classified by type and by location (region and depth). We marked a maximum of 50 IEDs during deep non–rapid eye movement sleep. IEDs were identified as spikes or sharp waves with or without slow waves, or bursts of spikes or sharp waves with or without slow waves. We analyzed HFOs in the studies showing at least 50 IEDs. Results In 192 scalp EEG studies, the differences in the percentage of studies showing IEDs in each depth-related group were not statistically significant, whereas HFOs (55 studies) predominated in patients exhibiting superficial lesions (p

Objective: Structural and functional imaging studies in focal epilepsy often reveal distributed regions of abnormality. These are interpreted as representing the existence of epileptic networks but the presence of actual neuronal interactions between these regions has not been demonstrated. We sought to determine if the distributed hemodynamic responses often seen in fMRI studies of scalp interictal epileptic discharges (IEDs) actually correspond to synchronized neuronal activities when examining the intracerebral EEG (iEEG) at distant nodes of the network. Methods: We studied 28 patients who underwent first EEG-fMRI and then iEEG, and had significant hemodynamic responses in the gray matter. We co-registered the hemodynamic responses to the iEEG electrode contacts positions and analyzed synchrony, measured by correlation, between IEDs recorded by iEEG in regions with and without hemodynamic responses. Results: The synchrony of intracerebral IED activity between pairs of regions showing a hemodynamic response was higher compared to that between pairs of regions without (p

Since the middle of the 19th century, both neurologists and psychiatrists have linked psychosis and epilepsy. Clozapine, the most effective antipsychotic drug, alters electroencephalographic activity and carries a significant risk of causing seizures. Unfortunately, this risk limits the drug's potential use in treating pharmacoresistant psychosis in patients with epilepsy. We present a unique case in which we used clozapine successfully as a last resort treatment for chronic interictal psychosis in a 43-year-old woman with severe pharmacoresistant epilepsy and recurrent status epilepticus. Her psychotic symptoms improved markedly without an increase in the frequency of seizures despite gradual titration of the clozapine dose up to 300 mg daily. Her response demonstrates that, properly monitored, clozapine can be an effective treatment for psychosis even in patients with daily seizures.

SummaryObjective Intracranial electroencephalography (EEG), performed presurgically in patients with drug-resistant and difficult-to-localize focal epilepsy, samples only a small fraction of brain tissue and thus requires strong hypotheses regarding the possible localization of the epileptogenic zone. EEG/fMRI (functional magnetic resonance imaging), a noninvasive tool resulting in hemodynamic responses, could contribute to the generation of these hypotheses. This study assessed how these responses, despite their interictal origin, predict the seizure-onset zone (SOZ). Methods We retrospectively studied 37 consecutive patients who underwent stereo-EEG (SEEG) and EEG/fMRI that resulted in significant hemodynamic responses. Hemodynamic response maps were co-registered to postimplantation anatomic imaging, allowing inspection of these responses in relation to SEEG electrode's location. The area containing the most significant t-value (primary cluster) explored with an electrode was assessed for concordance with SEEG-defined SOZ. Discriminant analysis was performed to distinguish the primary clusters having a high probability of localizing the SOZ. Results Thirty-one patients had at least one study with primary cluster explored with an electrode, and 24 (77%) had at least one study with primary cluster concordant with the SOZ. Each patient could have multiple types of interictal discharge and therefore multiple studies. Among 59 studies from the 37 patients, 44 had a primary cluster explored with an electrode and 30 (68%) were concordant with the SOZ. Discriminant analysis showed that the SOZ is predictable with high confidence (>90%) if the primary cluster is highly significant and if the next significant cluster is much less significant or absent. Significance The most significant hemodynamic response to interictal discharges delineates the subset of the irritative zone that generates seizures in a high proportion of patients with difficult-to-localize focal epilepsy. EEG/fMRI generates responses that are valuable targets for electrode implantation and may reduce the need for implantation in patients in whom the most significant response satisfies the condition of our discriminant analysis.

Sleep spindles and K-complexes (KCs) are a hallmark of N2 sleep. While the functional significance of spindles is comparatively well investigated, there is still ongoing debate about the role of the KC: it is unclear whether it is a cortical response to an arousing stimulus (either external or internal) or whether it has sleep-promoting properties. Invasive intracranial EEG recordings from individuals with drug-resistant epilepsy offer a unique opportunity to study in-situ human brain physiology. To better understand the function of the KC, we aimed to (i) investigate the intracranial correlates of spontaneous scalp KCs, and (ii) compare the intracranial activity of scalp KCs associated or not with arousals. Whole-night recordings from adults with drug-resistant focal epilepsy who underwent combined intracranial-scalp EEG for pre-surgical evaluation at the Montreal Neurological Institute between 2010 and 2018 were selected. KCs were visually marked in the scalp and categorized according to the presence of microarousals: (i) Pre-microarousal KCs; (ii) KCs during an ongoing microarousal; and (iii) KCs without microarousal. Power in different spectral bands was computed to compare physiological intracranial EEG activity at the time of scalp KCs relative to the background, as well as to compare microarousal subcategories. A total of 1198 scalp KCs selected from 40 subjects were analyzed, resulting in 32,504 intracranial KC segments across 992 channels. Forty-seven percent of KCs were without microarousal, 30% were pre-microarousal, and 23% occurred during microarousals. All scalp KCs were accompanied by widespread cortical increases in delta band power (0.3–4 ​Hz) relative to the background: the highest percentages were observed in the parietal (60–65%) and frontal cortices (52–58%). Compared to KCs without microarousal, pre-microarousal KCs were accompanied by increases (66%) in beta band power (16–30 ​Hz) in the motor cortex, which was present before the peak of the KC. In addition, spatial distribution of spectral power changes following each KC without microarousal revealed that certain brain regions were associated with increases in delta power (25–62%) or decreases in alpha/beta power (11–24%), suggesting a sleep-promoting pattern, whereas others were accompanied by increases of higher frequencies (12–27%), suggesting an arousal-related pattern. This study shows that KCs can be generated across widespread cortical areas. Interestingly, the motor cortex shows awake-like EEG activity before the onset of KCs followed by microarousals. Our findings also highlight region-specific sleep- or arousal-promoting responses following KCs, suggesting a dual role for the human KC.

PURPOSE In comatose patients, distinguishing between nonconvulsive status epilepticus and diffuse structural or metabolic encephalopathies is often challenging. Both conditions can generate periodic discharges on EEG with similar morphology and periodicity. We investigated the occurrence of high-frequency oscillations-potential biomarkers of epileptogenesis-on scalp EEG of comatose patients with periodic discharges in the EEG. METHODS Fifteen patients were included. Patients were divided into three groups, according to underlying etiology: Group 1, seizure related; group 2, structural; group 3, nonstructural. EEG recordings were compared with respect to the presence and rates of gamma (30-80 Hz) and ripples (80-250 Hz). RESULTS Patients were 23 to 106 years old (median, 68 years); 60% were female. 206 channels were eligible for analysis (median, 15 channels/patient). Overall, 43% of channels showed gamma, and 24% had ripples. Group 2 showed the highest proportion of channels with gamma (47%), followed by group 1 (38%) and group 3 (36%). Mean gamma rates were higher in group 2 (4.65 gamma/min/channel) than in group 1 (1.52) and group 3 (1.44) (P < 0.001). Group 2 showed the highest proportion of channels with ripples (29.2%), followed by group 1 (15%) and group 3 (24.2%). Mean ripple rates were higher in group 2 (5.09 ripple/min/channel) than in group 1 (0.96) and group 3 (0.83) (P < 0.001). CONCLUSIONS Fast oscillations, including high-frequency oscillations, can be detected in scalp EEG of patients with altered consciousness. High rates of fast activity may suggest an underlying structural brain lesion. Future studies are needed to determine whether fast oscillations in the setting of acute/subacute brain lesions are a biomarker of subsequent development of human epilepsy.

Objective Regional variations in oscillatory activity during human sleep remain unknown. Using the unique ability of intracranial electroencephalography to study in situ brain physiology, this study assesses regional variations of electroencephalographic sleep activity and creates the first atlas of human sleep using recordings from the first sleep cycle. Methods Intracerebral electroencephalographic recordings with channels displaying physiological activity from nonlesional tissue were selected from 91 patients of 3 tertiary epilepsy centers. Sections during non-rapid eye movement sleep (stages N2 and N3) and rapid eye movement sleep (stage R) were selected from the first sleep cycle for oscillatory and nonoscillatory signal analysis. Results of 1,468 channels were grouped into 38 regions covering all cortical areas. Results We found regional differences in the distribution of sleep transients and spectral content during all sleep stages. There was a caudorostral gradient, with more slow frequencies and fewer spindles in temporoparieto-occipital than in frontal cortex. Moreover, deep-seated structures showed spectral peaks differing from the baseline electroencephalogram. The regions with >60% of channels presenting significant rhythmic activity were either mesial or temporal basal structures that contribute minimally to the scalp electroencephalogram. Finally, during deeper sleep stages, electroencephalographic analysis revealed a more homogeneous spatial distribution, with increased coupling between high and low frequencies. Interpretation This study provides a better understanding of the regional variability of sleep, and establishes a baseline for human sleep in all cortical regions during the first sleep cycle. Furthermore, the open-access atlas will be a unique resource for research (https://mni-open-ieegatlas. Research mcgill.ca). ANN NEUROL 2020;87:289-301.

Interictal epileptiform anomalies such as epileptiform discharges or high-frequency oscillations show marked variations across the sleep-wake cycle. This study investigates which state of vigilance is the best to localize the epileptogenic zone (EZ) in interictal intracranial electroencephalography (EEG).Thirty patients with drug-resistant epilepsy undergoing stereo-EEG (SEEG)/sleep recording and subsequent open surgery were included; 13 patients (43.3%) had good surgical outcome (Engel class I). Sleep was scored following standard criteria. Multiple features based on the interictal EEG (interictal epileptiform discharges, high-frequency oscillations, univariate and bivariate features) were used to train a support vector machine (SVM) model to classify SEEG contacts placed in the EZ. The performance of the algorithm was evaluated by the mean area under the receiver-operating characteristic (ROC) curves (AUCs) and positive predictive values (PPVs) across 10-minute sections of wake, non-rapid eye movement sleep (NREM) stages N2 and N3, REM sleep, and their combination.Highest AUCs were achieved in NREM sleep stages N2 and N3 compared to wakefulness and REM (P .01). There was no improvement when using a combination of all four states (P .05); the best performing features in the combined state were selected from NREM sleep. There were differences between good (Engel I) and poor (Engel II-IV) outcomes in PPV (P .05) and AUC (P .01) across all states. The SVM multifeature approach outperformed spikes and high-frequency oscillations (P .01) and resulted in results similar to those of the seizure-onset zone (SOZ; P .05).Sleep improves the localization of the EZ with best identification obtained in NREM sleep stages N2 and N3. Results based on the multifeature classification in 10 minutes of NREM sleep were not different from the results achieved by the SOZ based on 12.7 days of seizure monitoring. This finding might ultimately result in a more time-efficient intracranial presurgical investigation of focal epilepsy.