Spatial Coherence Profiles of Ictal High-Frequency Oscillations Correspond to Those of Interictal Low-Frequency Oscillations in the ECoG of Epileptic Patients.

GOAL: We have previously demonstrated that the coherence of high-frequency oscillations (HFOs; 80-300 Hz) increased during extratemporal lobe seizures in a consistent and spatially focused electrode cluster. In this study, we have investigated the relationship between cohered HFO intracranial EEG (iEEG) activity with that of slower low-frequency oscillations (LFOs; <80 Hz). METHODS: We applied wavelet phase coherence analysis to the iEEGs of patients with intractable extratemporal lobe epilepsy (ETLE). RESULTS: It was observed that areas on the implanted patient subdural grids, which exhibited strong ictal HFO coherence were similar to tissue regions displaying strong interictal LFO coherence in the 5-12 Hz frequency range, relative to all other electrodes. A positive surgical outcome was correlated with having the clinically marked seizure onset zone(s) in close proximity to HFO/LFO coherence highlighted regions of interest (ROIs). CONCLUSION: Recent studies have suggested that LFOs (in the 8-12 Hz frequency range) play an important role in controlling cortical excitability, by exerting an inhibitory effect on cortical processing, and that the presence of strong theta activity (4-8 Hz) in awake adults is suggestive of abnormal and/or pathological activity. We speculate that the overlapping spatial regions exhibiting increased coherence in both ictal HFOs and interictal LFOs identified local abnormalities that underlie epileptogenic networks. SIGNIFICANCE: Whereas it is worthwhile to note that the small patient group ( n = 7) studied here, somewhat limits the clinical significance of our study, the results presented here suggest targeting HFO activity in the 80-300 Hz frequency range and/or interictal LFO activity in the 5-12 Hz frequency range, when defining seizure-related ROIs in the iEEGs of patients with ETLE.

Mapping the coherence of ictal high frequency oscillations in human extratemporal lobe epilepsy.

OBJECTIVE: High frequency oscillations (HFOs) have recently been recorded in epilepsy patients and proposed as possible novel biomarkers of epileptogenicity. Investigation of additional HFO characteristics that correlate with the clinical manifestation of seizures may yield additional insights for delineating epileptogenic regions. To that end, this study examined the spatiotemporal coherence patterns of HFOs (80-400 Hz) so as to characterize the strength of HFO interactions in the epileptic brain. We hypothesized that regions of strong HFO coherence identified epileptogenic networks believed to possess a pathologic locking nature in relation to regular brain activity. METHODS: We applied wavelet phase coherence analysis to the intracranial EEG (iEEG)s of patients (n = 5) undergoing presurgical evaluation of drug-resistant extratemporal lobe epilepsy (ETLE). We have also computed HFO intensity (related to the square-root of the power), to study the relationship between HFO amplitude and coherence. RESULTS: Strong HFO (80-270 Hz) coherence was observed in a consistent and spatially focused channel cluster during seizures in four of five patients. Furthermore, cortical regions possessing strong ictal HFO coherence coincided with regions exhibiting high ictal HFO intensity, relative to all other channels. SIGNIFICANCE: Because HFOs have been shown to localize to the epileptogenic zone, and we have demonstrated a correlation between ictal HFO intensity and coherence, we propose that ictal HFO coherence can act as an epilepsy biomarker. Moreover, the seizures studied here showed strong spatial correlation of ictal HFO coherence and intensity in the 80-270 Hz frequency range, suggesting that this band may be targeted when defining seizure-related regions of interest for characterizing ETLE.

Gamma (30-80Hz) bicoherence distinguishes seizures in the human epileptic brain.

We have applied wavelet bicoherence (BIC) analysis to human iEEG data to characterize non-linear frequency interactions in the human epileptic brain. Bicoherence changes were most prominent in the gamma (30-80 Hz) frequency band, and allowed for the differentiation between seizure and non-seizure states in all patients studied (n=3). While gamma band BIC values increased during seizure activity, this trend was only observed in a select number of electrode(s) located on the implanted patient subdural grids. Several studies have suggested that fast frequencies may play a role in the process of seizure genesis. While the small patient numbers limit the significance of our study, our results highlight the bicoherence of the gamma frequency band (30-80 Hz) as an ictal identifier, and suggest an active role of this fast frequency during seizures.

Synchrony of high frequency oscillations in the human epileptic brain.

We have applied wavelet phase coherence (WPC) to human iEEG data to characterize the spatial and temporal interactions of high frequency oscillations (HFOs; >80 Hz). Quantitative analyses were performed on iEEG segments from four patients with extratemporal lobe epilepsy. Interelectrode synchrony was measured using WPC before, during and after seizure activity. The WPC profiles of HFOs were able to elucidate the seizure from non-seizure state in all four patients and for all seizures studied (n=10). HFO synchrony was consistently transient and of weak to moderate strength during non-seizure activity, while weak to very strong coherence, of prolonged duration, was observed during seizures. Several studies have suggested that HFOs may have a significant role in the process of epileptogenesis and seizure genesis. As epileptic seizures result from disturbances in the regular electrical activity present in given areas of the brain, studying the interactions between fast brain waves, recorded simultaneously and from many different brain regions, may provide more information of which brain areas are interacting during ictal and interictal activity.

Wavelet-based Gaussian-mixture hidden Markov model for the detection of multistage seizure dynamics: a proof-of-concept study.

BACKGROUND: Epilepsy is a common neurological disorder characterized by recurrent electrophysiological activities, known as seizures. Without the appropriate detection strategies, these seizure episodes can dramatically affect the quality of life for those afflicted. The rationale of this study is to develop an unsupervised algorithm for the detection of seizure states so that it may be implemented along with potential intervention strategies. METHODS: Hidden Markov model (HMM) was developed to interpret the state transitions of the in vitro rat hippocampal slice local field potentials (LFPs) during seizure episodes. It can be used to estimate the probability of state transitions and the corresponding characteristics of each state. Wavelet features were clustered and used to differentiate the electrophysiological characteristics at each corresponding HMM states. Using unsupervised training method, the HMM and the clustering parameters were obtained simultaneously. The HMM states were then assigned to the electrophysiological data using expert guided technique. Minimum redundancy maximum relevance (mRMR) analysis and Akaike Information Criterion (AICc) were applied to reduce the effect of over-fitting. The sensitivity, specificity and optimality index of chronic seizure detection were compared for various HMM topologies. The ability of distinguishing early and late tonic firing patterns prior to chronic seizures were also evaluated. RESULTS: Significant improvement in state detection performance was achieved when additional wavelet coefficient rates of change information were used as features. The final HMM topology obtained using mRMR and AICc was able to detect non-ictal (interictal), early and late tonic firing, chronic seizures and postictal activities. A mean sensitivity of 95.7%, mean specificity of 98.9% and optimality index of 0.995 in the detection of chronic seizures was achieved. The detection of early and late tonic firing was validated with experimental intracellular electrical recordings of seizures. CONCLUSIONS: The HMM implementation of a seizure dynamics detector is an improvement over existing approaches using visual detection and complexity measures. The subjectivity involved in partitioning the observed data prior to training can be eliminated. It can also decipher the probabilities of seizure state transitions using the magnitude and rate of change wavelet information of the LFPs.

Transmembrane potential generated by a magnetically induced transverse electric field in a cylindrical axonal model.

During the electrical stimulation of a uniform, long, and straight nerve axon, the electric field oriented parallel to the axon has been widely accepted as the major field component that activates the axon. Recent experimental evidence has shown that the electric field oriented transverse to the axon is also sufficient to activate the axon, by inducing a transmembrane potential within the axon. The transverse field can be generated by a time-varying magnetic field via electromagnetic induction. The aim of this study was to investigate the factors that influence the transmembrane potential induced by a transverse field during magnetic stimulation. Using an unmyelinated axon model, we have provided an analytic expression for the transmembrane potential under spatially uniform, time-varying magnetic stimulation. Polarization of the axon was dependent on the properties of the magnetic field (i.e., orientation to the axon, magnitude, and frequency). Polarization of the axon was also dependent on its own geometrical (i.e., radius of the axon and thickness of the membrane) and electrical properties (i.e., conductivities and dielectric permittivities). Therefore, this article provides evidence that aside from optimal coil design, tissue properties may also play an important role in determining the efficacy of axonal activation under magnetic stimulation. The mathematical basis of this conclusion was discussed. The analytic solution can potentially be used to modify the activation function in current cable equations describing magnetic stimulation.

Frequency interactions in human epileptic brain.

We have used two algorithms, wavelet phase coherence (WPC) and modulation index (MI) analysis to study frequency interactions in the human epileptic brain. Quantitative analyses were performed on intracranial electroencephalographic (iEEG) segments from three patients with neocortical epilepsy. Interelectrode coherence was measured using WPC and intraelectrode frequency interactions were analyzed using MI. WPC was performed on electrode pairings and the temporal evolution of phase couplings in the following frequency ranges: 1-4 Hz, 4-8 Hz, 8-13 Hz, 13-30 Hz and 30-100 Hz was studied. WPC was strongest in the 1-4 Hz frequency range during both seizure and non-seizure activities; however, WPC values varied minimally between electrode pairings. The 13-30 Hz band showed the lowest WPC values during seizure activity. MI analysis yielded two prominent patterns of frequency-specific activity, during seizure and non-seizure activities, which were present across all patients.

Transmembrane potential induced on the internal organelle by a time-varying magnetic field: a model study.

BACKGROUND: When a cell is exposed to a time-varying magnetic field, this leads to an induced voltage on the cytoplasmic membrane, as well as on the membranes of the internal organelles, such as mitochondria. These potential changes in the organelles could have a significant impact on their functionality. However, a quantitative analysis on the magnetically-induced membrane potential on the internal organelles has not been performed. METHODS: Using a two-shell model, we provided the first analytical solution for the transmembrane potential in the organelle membrane induced by a time-varying magnetic field. We then analyzed factors that impact on the polarization of the organelle, including the frequency of the magnetic field, the presence of the outer cytoplasmic membrane, and electrical and geometrical parameters of the cytoplasmic membrane and the organelle membrane. RESULTS: The amount of polarization in the organelle was less than its counterpart in the cytoplasmic membrane. This was largely due to the presence of the cell membrane, which "shielded" the internal organelle from excessive polarization by the field. Organelle polarization was largely dependent on the frequency of the magnetic field, and its polarization was not significant under the low frequency band used for transcranial magnetic stimulation (TMS). Both the properties of the cytoplasmic and the organelle membranes affect the polarization of the internal organelle in a frequency-dependent manner. CONCLUSIONS: The work provided a theoretical framework and insights into factors affecting mitochondrial function under time-varying magnetic stimulation, and provided evidence that TMS does not affect normal mitochondrial functionality by altering its membrane potential.

Transformation of neuronal modes associated with low-Mg2+/high-K+ conditions in an in vitro model of epilepsy.

Nonparametric system modeling constitutes a robust method for the analysis of physiological systems as it can be used to identify nonlinear dynamic input-output relationships and facilitate their description. First- and second-order kernels of hippocampal CA3 pyramidal neurons in an in vitro slice preparation were computed using the Volterra-Wiener approach to investigate system changes associated with epileptogenic low-magnesium/high-potassium (low-Mg(2+)/high-K(+)) conditions. The principal dynamic modes (PDMs) of neurons were calculated from the first- and second-order kernel estimates in order to characterize changes in neural coding functionality. From our analysis, an increase in nonlinear properties was observed in kernels under low-Mg(2+)/high-K(+). Furthermore, the PDMs revealed that the sampled hippocampal CA3 neurons were primarily of integrating character and that the contribution of a differentiating mode component was enhanced under low-Mg(2+)/high-K(+).

A wavelet packet-based algorithm for the extraction of neural rhythms.

Neural rhythms are associated with different brain functions and pathological conditions. These rhythms are often clinically relevant for purposes of diagnosis or treatment, though their complex, time-varying features make them difficult to isolate. The wavelet packet transform has proven itself to be versatile and effective with respect to resolving signal features in both time and frequency. We propose a signal analysis technique, called neural rhythm extraction (NRE) that incorporates wavelet packet analysis along with a threshold-based scheme for separating rhythmic neural features from non-rhythmic ones. We applied NRE to rat in vitro intracellular recordings and human scalp electroencephalogram (EEG) signals, and were able to isolate and classify individual neural rhythms in signals containing large amplitude spikes and other artifacts. NRE is capable of discriminating signal features sharing similar time or frequency localization, as well as extracting low-amplitude, low-power rhythms otherwise masked by spectrally dominant signal components. The algorithm allows for independent retention and reconstruction of rhythmic features, which may serve to enhance other analysis techniques such as independent component analysis (ICA), and aid in application-specific tasks such as detection, classification or tracking.

Transmembrane potential induced in a spherical cell model under low-frequency magnetic stimulation.

Time-varying magnetic fields can induce electric fields in the neuronal tissue, a phenomenon that has been recently explored in clinical applications such as peripheral nerve stimulation and transcranial magnetic stimulation. Although the transmembrane potential induced during direct electric stimulation has already been the subject of a number of theoretical studies, an analytical solution for the magnetically induced transmembrane potential change is still unavailable. In addition, although several studies have analyzed the impact of stimulation parameters, including stimulation intensity and frequency, as well as coil design and position, on the amount of tissue polarization, the effects of tissue non-homogeneity on cell polarization have not been fully elucidated. In this study, we have derived an analytical expression for the transmembrane potential induced by a low-frequency magnetic field in a spherical neuronal structure. This model is representative of a spherical cell body or any neuronal structure of a similar shape. The model cell is located in an extracellular medium and possesses a low-conductive membrane and an internal cytoplasm. These three regions represent the basic tissue non-homogeneity of a neuron at a microscopic level. The sensitivity of the induced transmembrane potential to the coil position and to the geometrical and electrical parameters of the model structure was studied in a broad physiologically relevant range. Our results demonstrate that the structure is regionally polarized, with the pattern of polarization depending on the relative positioning between the model cell and the stimulation coil. In addition, both the geometrical and electrical parameters of the structure affect the amount of polarization. These results may be generalized to other neuronal tissues that possess similar non-homogenous properties, but different shapes, such as an axon. Our results support the idea that aside from coil design and position, tissue non-homogeneity could play an important role in determining the effects of magnetic stimulation.