Determination of Current Flow Induced by Transcutaneous Electrical Nerve Stimulation for the Treatment of Migraine: Potential for Optimization

Introduction: Transcutaneous electrical nerve stimulation (TENS) for migraine involves the application of pulsatile stimulation through electrodes placed on the forehead to target the underlying trigeminal nerves. It is a simple, safe modality and has secured clinical approval in several markets including the European Union and the United States. Despite nearing almost 7 years of use (postclinical approval), the exact mechanism of action is not fully known. Guided by the need to stimulate the trigeminal nerves bilaterally, electrode dimensions are simply required to extend enough to cover the underlying nerves. The goal of this study is to examine induced current flow [magnitude and spatial distribution of electric field (EF)] and another driver of stimulation [activating function (AF)] due to TENS therapy for migraine for the first time. We further consider the effect of changing the electrode dimension and shape and propose a design modification to deliver optimal flow.Methods: We developed the first ultra-high-resolution finite element (FE) model of TENS for migraine incorporating the target supratrochlear (ST) and the supraorbital (SO) nerves. We first simulated the clinically approved V-shaped geometry. We then considered three additional designs: extended V-shaped, idealized pill-shaped, and finally an extended V-shaped but with greater contact spacing (extended V-shaped +CS).Results: Our findings revealed that the clinically approved electrode design delivered substantially higher mean current flow to the ST nerve in comparison with the SO nerves (Medial: 53% and Lateral: 194%). Consideration of an extended design (~10 mm longer and ~ 4 mm shorter) and a pill-like design had negligible impact on the induced current flow pattern. The extended V-shaped +CS montage delivered relatively comparable current flow to each of the three target nerves. The EF induced in the ST nerve was 49 and 141% higher in the Medial and Lateral SO nerve, respectively. When considering maximum induced values, the delivery of comparable stimulation was further apparent. Given the existing electrode design's established efficacy, our results imply that preferential targeting of the ST nerve is related to the mechanism of action. Additionally, if comparable targeting of all three nerves continues to hold promise, the extended V-shaped +CS montage presents an optimized configuration to explore in clinical studies.

Influence of limiting the duration of the armature winding current on the operating indicators of a linear pulse electromechanical induction type converter

Introduction. Linear pulse electromechanical converters of induction type (LPECIT) are used in many branches of science and technology as shock-power devices and electromechanical accelerators. In them, due to the phase shift between the excitation current in the inductor winding and the induced current in the armature winding, in addition to the initial electrodynamic forces (EDF) of repulsion, subsequent EDF of attraction also arise. As a result, the operating indicators of LPECIT are reduced. The purpose of the article is to increase the performance of linear pulse electromechanical induction-type converters when operating as a shock-power device and an electromechanical accelerator by limiting the duration of the induced current in the armature winding until its polarity changes. Methodology. To analyze the electromechanical characteristics and indicators of LPECIT, a mathematical model was used, in which the solutions of equations describing interrelated electrical, magnetic, mechanical and thermal processes are presented in a recurrent form. Results. To eliminate the EDF of attraction between the LPIECIT windings, it is proposed to limit the duration of the induced current in the armature winding before changing its polarity by connecting a rectifier diode to it. It was found that when the converter operates as a shock-power device without limiting the armature winding current, the value of the EDF pulse after reaching the maximum value decreases by the end of the operating cycle. In the presence of a diode in the armature winding, the efficiency criterion, taking into account the EDF pulse, recoil force, current and heating temperature of the inductor winding, increases. When the converter operates as an electromechanical accelerator without limiting the armature winding current, the speed and efficiency decrease, taking into account the kinetic energy and voltage of the capacitive energy storage at the end of the operating cycle. In the presence of a diode in the armature winding, the efficiency criterion increases, the temperature rise of the armature winding decreases, the value of the maximum efficiency increases, reaching 16.16 %. Originality. It has been established that due to the limitation of the duration of the armature winding current, the power indicators of the LPECIT increase when operating as a shock-power device and the speed indicators when the LPECIT operates as an electromechanical accelerator. Practical value. It was found that with the help of a rectifier diode connected to the multi-turn winding of the armature, unipolarity of the current is ensured, which leads to the elimination of the EDF of attraction and an increase in the performance of the LPECIT.

The Magnetic Response of Starphenes

The aromaticity of [n]starphenes (n = 1, 4, 7, 10, 13, 16), as well as starphene-based [19]dendriphene, is addressed by calculating the magnetically induced current density and the induced magnetic field, using the pseudo-π model. When an external magnetic field is applied, these systems create diatropic currents that split into a global peripheral current surrounding the starphene skeleton and several local currents in the acene-based arms, resulting in large shielding cones above the arms. In particular, the arm currents are smaller than their linear analogs, and in general, the strengths of the ring currents tend to weaken as the starphene get larger.