Dependence of excitability indices on membrane channel dynamics, myelin impedance, electrode location and stimulus waveforms in myelinated and unmyelinated fibre models

Neuronal excitability is determined in a complex way by several interacting factors, such as membrane dynamics, fibre geometry, electrode configuration, myelin impedance, neuronal terminations This study aims to increase understanding in excitability, by investigating the impact of these factors on different models of myelinated and unmyelinated fibres (five well-known membrane models are combined with three electrostimulation models, that take into account the spatial structure of the neuron). Several excitability indices (rheobase, polarity ratio, bi/monophasic ratio, time constants) are calculated during extensive parameter sweeps, allowing us to obtain novel findings on how these factors interact, e.g. how the dependency of excitability indices on the fibre diameter and myelin impedance is influenced by the electrode location and membrane dynamics. It was found that excitability is profoundly impacted by the used membrane model and the location of the neuronal terminations. The approximation of infinite myelin impedance was investigated by two implementations of the spatially extended non-linear node model. The impact of this approximation on the time constant of strength-duration plots is significant, most importantly in the Frankenhaeuser-Huxley membrane model for large electrode-neuron separations. Finally, a multi-compartmental model for C-fibres is used to determine the impact of the absence of internodes on excitability

SECONIC : towards multi-compartmental models for ultrasonic brain stimulation by intramembrane cavitation

Objective. To design a computationally efficient model for ultrasonic neuromodulation (UNMOD) of morphologically realistic multi-compartmental neurons based on intramembrane cavitation.Approach. A Spatially Extended Neuronal Intramembrane Cavitation model that accurately predicts observed fast Charge Oscillations (SECONIC) is designed. A regular spiking cortical Hodgkin-Huxley type nanoscale neuron model of the bilayer sonophore and surrounding proteins is used. The accuracy and computational efficiency of SECONIC is compared with the Neuronal Intramembrane Cavitation Excitation (NICE) and multiScale Optimized model of Neuronal Intramembrane Cavitation (SONIC).Main results. Membrane charge redistribution between different compartments should be taken into account via fourier series analysis in an accurate multi-compartmental UNMOD-model. Approximating charge and voltage traces with the harmonic term and first two overtones results in reasonable goodness-of-fit, except for high ultrasonic pressure (adjusted R-squared >= 0.61). Taking into account the first eight overtones results in a very good fourier series fit (adjusted R-squared >= 0.96) up to 600 kPa. Next, the dependency of effective voltage and rate parameters on charge oscillations is investigated. The two-tone SECONIC-model is one to two orders of magnitude faster than the NICE-model and demonstrates accurate results for ultrasonic pressure up to 100 kPa.Significance. Up to now, the underlying mechanism of UNMOD is not well understood. Here, the extension of the bilayer sonophore model to spatially extended neurons via the design of a multi-compartmental UNMOD-model, will result in more detailed predictions that can be used to validate or falsify this tentative mechanism. Furthermore, a multi-compartmental model for UNMOD is required for neural engineering studies that couple finite difference time domain simulations with neuronal models. Here, we propose the SECONIC-model, extending the SONIC-model by taking into account charge redistribution between compartments

Setting reference level in the human safety guidelines via nerve activation intercomparison at IF

International guidelines/standards have been published for human protection from electromagnetic field exposure. The research in the intermediate frequencies (IF: 300 Hz-10 MHz) is scattered unlike for other frequencies, and thus the limit prescribed in the guidelines/standards are different by a factor of 10. The IEEE International Committee on Electromagnetic Safety has published a research agenda for exploring the electrostimulation thresholds. However, the consistency of the excitation models for specific target tissue needs to be revised. For this purpose, we present the first intercomparison study using multiphysics modelling to investigate stimulation thresholds during transcranial magnetic stimulation (TMS). To define the stimulation threshold, a noninvasive technique for brain stimulation has been used. In this study, by incorporating individual neurons into electromagnetic computation in realistic head models, stimulation thresholds can be determined. The study case of one subject showed that the allowable external magnetic field strength in the current guidelines/standard is conservative

Comparison between direct electrical and optogenetic subthalamic nucleus stimulation

Subthalamic nucleus deep brain stimulation is a treatment for Parkinson’s disease. In this study, a computational model of a plateau-potential generating subthalamic nucleus neuron (Otsuka-model) and a four-state ChR2(H134R) model (Williams-model) are combined, in order to compare electrical and optogenetic neuromodulation capabilities. The impact of the stimulation modality (optogenetic or electric) on firing rates, strength-duration curves and action potential shape is investigated. First, in contrast to electrical stimulation, mean instantaneous firing rates saturate for optical stimulation at intensities higher than 0.1 W/cm2. Second, rheobase and chronaxie are 175% and 9.6% larger in optogenetic stimulation compared to electrical stimulation, respectively. Third, action potential shape is not significantly impacted by the neurostimulation modality

Investigation of the stimulation capabilities of a high-resolution neurorecording probe for the application of closed-loop deep brain stimulation

Deep brain stimulation is an established surgical treatment for several neurological and movement disorders, such as Parkinson's disease, in which electrostimulation is applied to targeted deep nuclei in the basal ganglia through implanted electrode leads. Recent technological improvements in the field have focused on the theoretical advantage of current steering and adaptive (closed-loop) deep brain stimulation. Current steering between several active electrodes would allow for improved accuracy when targeting the desired brain structures. This has the additional benefit of avoiding undesired stimulation of neural tracts that are related to side effects, e.g., internal capsule fibres of passage in subthalamic nucleus deep brain stimulation. Closed-loop deep brain stimulation is based on the premise of continuous recording of a proxy for pathological neural activity (such as beta-band power of measured local field potentials in patients with Parkinson's disease) and accordingly adapting the used stimulus parameters. In this study, we investigate the suitability of an existing highresolution neurorecording probe for high-precision neurostimulation. If a subset of the probe's recording electrodes can be used for stimulation, then the probe would be a suitable candidate for closed-loop deep brain stimulation. A finiteelement model is used to calculate the electric potential, induced by current injection through the high-resolution probe, for different sets of active electrodes. Volumes of activated tissue are calculated and a comparison is made between the highresolution probe and a conventional stimulation lead. We investigate the capability of the probe to shift the volume of activated tissue by steering currents to different sets of active electrodes. Finally, safety limits for the injected current are used to determine the size of the volume in which neurons can be activated with the relatively small electrodes patches on the highresolution probe

Brain cortical stimulation thresholds to different magnetic field sources exposures at intermediate frequencies

Permissible field strengths in the international guidelines/standard for human protection are derived from peripheral nerve system stimulation at the intermediate frequencies where electrostimulation (attributable to axon activation) is more dominant than thermal effect. Recently, multiscale computation has been used to investigate neuron stimulation thresholds by incorporating individual neurons into realistic head models. However, the consistency of excitation models and permissible levels to specific target tissues (central nervous system) needs to be clarified. This article aims to investigate brain cortical stimulation thresholds using a multiscale computational approach for different scenarios of magnetic field exposures. The magnetic exposures include transcranial magnetic stimulation, uniform exposure, and wireless power transfer systems. Our results confirmed the consistency of the multiscale computations of the cortical thresholds between two independent groups for electromagnetic exposure of transcranial magnetic stimulation (thresholds in the range of motor cortex activation). We also quantified the conservativeness of permissible field strengths of international guidelines/standards at intermediate frequencies. Finally, with the multiscale approach, we confirmed that 10 000 kW of transmitting power of wireless power transfer (WPT) in an electric vehicle charging system may not induce an adverse effect for cortical activation

Sensitivity study of neuronal excitation and cathodal blocking thresholds of myelinated axons for percutaneous auricular vagus nerve stimulation

Objective: Excitation of myelinated nerve fibers is investigated by means of numerical simulations, for the application of percutaneous auricular vagus nerve stimulation (pVNS). High sensitivity to axon diameter is of interest regarding the goal of targeting thicker fibers. Methods: Excitation and blocking thresholds for different pulse types, phase durations, axon depths, axon-electrode distances, temperatures and axon diameters are investigated. The used model consists of a 50 mm long axon and a centrally located needle electrode in a layered medium representing the auricle. Neuronal excitation is simulated using the Frankenhaeuser-Huxley equations for all combinations of parameter values. Results and conclusion: Multiple modes and locations of excitation along the axon were observed, depending on the pulse type and amplitude. When increasing the axon-electrode distance from 1 mm to 2 mm, sensitivity of thresholds to axon depth decreased with ca. 50%, while sensitivity to axon-electrode distance, axon diameter and phase duration each increased with ca. 15% to 20%, except from monophasic anodal pulses, showing a 45% decrease for axon-electrode distance. These trends for axon diameter and axon-electrode distance allow for more selective stimulation of thicker target fibers using monophasic anodal pulses at higher axon-electrode distances. Cathodal monophasic pulses did not perform well due to blocking of the thicker fibers, which was only rarely seen for other pulse types. Significance: Sensitivities of stimulation thresholds to these parameters by numerical simulation reveal how the stimulation parameters can be changed in order to increase therapeutic effect and comfort during pVNS by enabling more selective stimulation