No abstract

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.

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.

SUMMARYObjective: 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.

BackgroundWhen 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.MethodsUsing 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.ResultsThe 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.ConclusionsThe 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.