Analysis of the Three-dimensional Superradiance Problem and Some Generalizations

We study the integral equation related to the three and higher dimensional superradiance problem. Collective radiation phenomena has attracted the attention of many physicists and chemists since the pioneering work of R. H. Dicke in 1954. We first consider the three-dimensional superradiance problem and find a differential operator that commutes with the integral operator related to the problem. We find all the eigenfunctions of the differential operator and obtain a complete set of eigensolutions for the three-dimensional superradiance problem. Generalization of the three-dimensional superradiance integral equation is provided. A commuting differential operator is found for this generalized problem. For the three dimensional superradiance problem, an alternative set of complete eigenfunctions is also provided. The kernel for the superradiance problem when restricted to one-dimension is the same as appeared in the works of Slepian, Landau and Pollak. The uniqueness of the differential operator commuting with that kernel is indicated. Finally, a concentration problem for the signals which are bandlimited in disjoint frequency-intervals is considered. The problem is to determine which bandlimited signals lose the smallest fraction of their energy when restricted in a given time interval. A numerical algorithm for solution and convergence theorems are given. Orthogonality properties of analytically extended eigenfunctions over L2(−∞,∞) are also proved. Numerical computations are carried out in support of the theory

Detection of anomalous high-frequency events in human intracranial EEG.

ObjectiveHigh-frequency oscillations (HFOs) are a promising biomarker for the epileptogenic zone. However, no physiological definition of an HFO has been established, so detection relies on the empirical definition of an HFO derived from visual observation. This can bias estimates of HFO features such as amplitude and duration, thereby hindering their utility as biomarkers. Therefore, we set out to develop an algorithm that detects high-frequency events in the intracranial EEG that are morphologically distinct from background without requiring assumptions about event amplitude or shape.MethodWe propose the anomaly detection algorithm (ADA), which uses unsupervised machine learning to identify segments of data that are distinct from the background. We apply ADA and a standard HFO detector using a root mean square amplitude threshold to intracranial EEG from 11 patients undergoing evaluation for epilepsy surgery. The rate, amplitude, and duration of the detected events and the percent overlap between the two detectors are compared.ResultIn the seizure onset zone (SOZ), ADA detected a subset of conventional HFOs. In non-SOZ channels, ADA detected at least twice as many events as the standard approach, including some conventional HFOs; however, ADA also identified many low and intermediate amplitude events missed by the standard amplitude-based method. The rate of ADA events was similar across all channels; however, the amplitude of ADA events was significantly higher in SOZ channels (P < .0045), and the amplitude measurement was more stable over time than the HFO rate, as indicated by a lower coefficient of variation (P < .0125).SignificanceADA does not require human supervision, parameter optimization, or prior assumptions about event shape, amplitude, or duration. Our results suggest that the algorithm's estimate of event amplitude may differentiate SOZ and non-SOZ channels. Further studies will examine the utility of HFO amplitude as a biomarker for epilepsy surgical outcome

Beyond rates: time-varying dynamics of high frequency oscillations as a biomarker of the seizure onset zone

Objective. High frequency oscillations (HFOs) recorded by intracranial electrodes have generated excitement for their potential to help localize epileptic tissue for surgical resection. However, the number of HFOs per minute (i.e. the HFO 'rate') is not stable over the duration of intracranial recordings; for example, the rate of HFOs increases during periods of slow-wave sleep. Moreover, HFOs that are predictive of epileptic tissue may occur in oscillatory patterns due to phase coupling with lower frequencies. Therefore, we sought to further characterize between-seizure (i.e. 'interictal') HFO dynamics both within and outside the seizure onset zone (SOZ).Approach. Using long-term intracranial EEG (mean duration 10.3 h) from 16 patients, we automatically detected HFOs using a new algorithm. We then fit a hierarchical negative binomial model to the HFO counts. To account for differences in HFO dynamics and rates between sleep and wakefulness, we also fit a mixture model to the same data that included the ability to switch between two discrete brain states that were automatically determined during the fitting process. The ability to predict the SOZ by model parameters describing HFO dynamics (i.e. clumping coefficients and coefficients of variation) was assessed using receiver operating characteristic curves.Main results. Parameters that described HFO dynamics were predictive of SOZ. In fact, these parameters were found to be more consistently predictive than HFO rate. Using concurrent scalp EEG in two patients, we show that the model-found brain states corresponded to (1) non-REM sleep and (2) awake and rapid eye movement sleep. However the brain state most likely corresponding to slow-wave sleep in the second model improved SOZ prediction compared to the first model for only some patients.Significance. This work suggests that delineation of SOZ with interictal data can be improved by the inclusion of time-varying HFO dynamics

A new method to determine the electrical transfer function of the human thorax

Traditional analyses have assumed that cardiac electrical activity is reflected on the surface ECG without distortion as the signal passes through the body tissues. This study aims to explore the frequency dependence of thoracic attenuation of surface-recorded intracardiac electrical activity. Twenty patients (14 men, 55 +/- 15 yr of age) undergoing electrophysiological study were enrolled. Rectangular unipolar stimuli were applied from a catheter positioned in the right ventricular apical area and another in the posteroseptal area without contact with the myocardium. An orthogonal Frank-lead surface ECG and a unipolar intracardiac electrogram near the pacing site were recorded. Frequency domain characteristics of the signal-averaged pacing impulses were analyzed. Linear regression analysis showed significant frequency-dependent attenuation in the magnitude transfer functions (R(2) = 0.84-0.89, P < 0.0001) and good linear fit for the phase transfer characteristics (R(2) = 0.98-1.0, P < 0.0001). Age, physical dimension, and respiratory characteristics had significant effects on the magnitude and phase characteristics of the transfer functions. Application of models of the low- and high-slope transfer functions to signal-averaged ECGs from 33 subjects showed differences in the attenuation of P and T waves relative to the QRS

Responsive Neurostimulation System (RNS) in setting of cranioplasty and history of multiple craniotomies

Introduction: Stereoelectroencephalography (SEEG) and subdural grids (SDG) are both effective options for localizing the ictal onset zone in patients with frequent seizures. The choice of intracranial monitoring technique utilized depends upon several factors, including the patient's clinical presentation and history. This article addresses a rare instance in which SEEG was not an option due to patient's morphology. Case report A 36-year-old man with history of medically intractable epilepsy and multiple craniotomies complicated by infection and subsequent cranioplasty was presented for possible surgical evaluation. Initially, SEEG was attempted but ultimately terminated because of difficulty related to prior cranioplasty and scarring to the brain. Eventually, a subdural grid system was placed to establish the patient's ictal onset zones after which RNS implantation was performed. Discussion: The SDG placement was successful and localized the patient's ictal onset to the hand-motor region of the left hemisphere. RNS was then implanted and postoperatively the patient had a significant decrease in his seizure burden. Conclusion: The case illustrates a possible limitation of SEEG placement, particularly in patients with a history of cranioplasty and multiple prior craniotomies. We also describe the first placement of an RNS generator and system in the setting of prior cranioplasty

Robot-assisted placement of depth electrodes along the long Axis of the amygdalohippocampal complex

AbstractBackgroundClassically, transoccipital hippocampal depth electrode implantation requires a stereotactic headframe and arc and the patient to be placed in a seated or prone position, which can be cumbersome to position and uncomfortable for the surgeon. Robotic intracranial devices are increasingly being utilized for stereotactic procedures such as stereolectroencephalography (SEEG) but commonly require patients be placed in head-neutral position to perform facial registration.ObjectiveHere we describe a novel robotic implantation technique where a stereotactic intracranial robot is used to place bilateral hippocampal depth electrodes in the lateral position.MethodsFour patients underwent SEEG depth electrode placement, which included placement of bilateral hippocampal depth electrodes. Each patient was positioned in the lateral position and registered to the robot with laser facial registration. Trajectories were planned with the robotic navigation software, which then identified the appropriate entry points and trajectories needed to reach the targets. After electrode implantation, target localization was confirmed using computed tomography (CT).ResultsElectrodes targeting the amygdalohippocampal complex were accurate and there were no complications in this group. An average of seven electrodes were placed per patient. Ictal onset was localized for each patient. All patients subsequently underwent temporal lobectomy and 75% have been seizure free since surgery.ConclusionsWe have developed the Robot-Assisted Lateral Transoccipital Approach (RALTA), which is an advantageous technique for placing bilateral amygdalohippocampal depth electrodes using robotic guidance. Benefits of this technique include fewer electrodes required per patient and ease of positioning compared with seated or prone positioning

Theta mediated dynamics of human hippocampal-neocortical learning systems in memory formation and retrieval.

Episodic memory arises as a function of dynamic interactions between the hippocampus and the neocortex, yet the mechanisms have remained elusive. Here, using human intracranial recordings during a mnemonic discrimination task, we report that 4-5 Hz (theta) power is differentially recruited during discrimination vs. overgeneralization, and its phase supports hippocampal-neocortical when memories are being formed and correctly retrieved. Interactions were largely bidirectional, with small but significant net directional biases; a hippocampus-to-neocortex bias during acquisition of new information that was subsequently correctly discriminated, and a neocortex-to-hippocampus bias during accurate discrimination of new stimuli from similar previously learned stimuli. The 4-5 Hz rhythm may facilitate the initial stages of information acquisition by neocortex during learning and the recall of stored information from cortex during retrieval. Future work should further probe these dynamics across different types of tasks and stimuli and computational models may need to be expanded accordingly to accommodate these findings