Marija Cotic

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.

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.

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

BackgroundEpilepsy 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.MethodsHidden 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.ResultsSignificant 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.ConclusionsThe 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.

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

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.

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: 1–4Hz, 4–8Hz, 8–13Hz, 13–30Hz and 30–100Hz was studied. WPC was strongest in the 1–4Hz frequency range during both seizure and non-seizure activities; however, WPC values varied minimally between electrode pairings. The 13–30Hz 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.

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-Mg2 + /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-Mg2 + /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-Mg2 + /high-K + .

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.

INFLUENCE OF CELLULAR PROPERTIES ON THE ELECTRIC FIELD DISTRIBUTION AROUND A SINGLE CELL

Electric flelds have been widely used for the treatment of neurological diseases, using techniques such as non-invasive brain stimulation. An electric current controls cell excitability by imposing voltage changes across the cell membrane. At the same time, the presence of the cell itself causes a re-distribution of the local electric fleld. Computation of the electric fleld distribution at a single cell microscopic level is essential in understanding the mechanism of electric stimulation. In addition, the impact of the cellular biophysical properties on the fleld distribution in the vicinity of the cell should also be addressed. In this paper, we have begun by flrst computing the fleld distribution around and within a spherical model cell. The electric flelds in the three regions difiered by several orders of magnitude. The fleld intensity in the extracellular space was of the same order as that of the externally applied fleld, while in the membrane, it was calculated to be several thousand times greater than the applied fleld. In contrast, the fleld intensity inside the cell was greatly attenuated to approximately 1/133th of the applied fleld. We then performed a

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.

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.