Simulation-Based Optimization of Figure-of-Eight Coil Designs and Orientations for Magnetic Stimulation of Peripheral Nerve

Investigation of the mechanisms for wireless nerve stimulation without active electrodes

Electric-field stimulation of neuronal activity can be used to improve the speed of regeneration for severed and damaged nerves. Most techniques, however, require invasive electronic circuitry which can be uncomfortable for the patient and can damage surrounding tissue. A recently suggested technique uses a graft-antenna-a metal ring wrapped around the damaged nerve-powered by an external magnetic stimulation device. This technique requires no electrodes and internal circuitry with leads across the skin boundary or internal power, since all power is provided wirelessly. This paper examines the microscopic basic mechanisms that allow the magnetic stimulation device to cause neural activation via the graft-antenna. A computational model of the system was created and used to find that under magnetic stimulation, diverging electric fields appear at the metal ring's edges. If the magnetic stimulation is sufficient, the gradients of these fields can trigger neural activation in the nerve. In-vivo measurements were also performed on rat sciatic nerves to support the modeling finding that direct contact between the antenna and the nerve ensures neural activation given sufficient magnetic stimulation. Simulations also showed that the presence of a thin gap between the graft-antenna and the nerve does not preclude neural activation but does reduce its efficacy.

Magnetic stimulation of the sciatic nerve using an implantable high-inductance coil with low-intensity current

Objective.Magnetic stimulation using implantable devices may offer a promising alternative to other stimulation methods such as transcranial magnetic stimulation (TMS) or electric stimulation using implantable devices. This alternative may increase the selectivity of stimulation compared to TMS, and eliminate the need to expose tissue to metals in the body, as is required in electric stimulation using implantable devices. However, previous studies of magnetic stimulation of the sciatic nerve used large coils, with a diameter of several tens of mm, and a current intensity in the order of kA.Approach.Since such large coils and high current intensity are not suitable for implantable devices, we investigated the feasibility of using a smaller implantable coil and lower current to elicit neuronal responses. A coil with a diameter of 3 mm and an inductance of 1 mH was used as the implantable stimulator.Main results.Beforein vivoexperiments, we used 3D computational models to estimate the minimum stimulus intensity required to elicit neuronal responses, resulting in a threshold current above 3.5 A. Inin vivoexperiments, we observed successful nerve stimulation via compound muscle action potentials elicited in hind-limb muscles when the applied current was above 3.8 A, a significantly reduced current than that used in conventional magnetic stimulation.Significance.We report the feasibility of magnetic stimulation using an implantable millimeter-sized coil and low current of a few amperes to elicit neural responses in peripheral nerves. The proposed method is expected to be an alternative to TMS, with the merit of improved selectivity in stimulation, and to electrical stimulation based on implantable devices, with the merit of avoiding the exposure of conducting metals to neural tissues.

Electrical Stimulation Induced Current Distribution in Peripheral Nerves Varies Significantly with the Extent of Nerve Damage: A Computational Study Utilizing Convolutional Neural Network and Realistic Nerve Models

Electrical stimulation of the peripheral nervous system is a promising therapeutic option for several conditions; however, its effects on tissue and the safety of the stimulation remain poorly understood. In order to devise stimulation protocols that enhance therapeutic efficacy without the risk of causing tissue damage, we constructed computational models of peripheral nerve and stimulation cuffs based on extremely high-resolution cross-sectional images of the nerves using the most recent advances in computing power and machine learning techniques. We developed nerve models using nonstimulated (healthy) and over-stimulated (damaged) rat sciatic nerves to explore how nerve damage affects the induced current density distribution. Using our in-house computational, quasi-static, platform, and the Admittance Method (AM), we estimated the induced current distribution within the nerves and compared it for healthy and damaged nerves. We also estimated the extent of localized cell damage in both healthy and damaged nerve samples. When the nerve is damaged, as demonstrated principally by the decreased nerve fiber packing, the current penetrates deeper into the over-stimulated nerve than in the healthy sample. As safety limits for electrical stimulation of peripheral nerves still refer to the Shannon criterion to distinguish between safe and unsafe stimulation, the capability this work demonstrated is an important step toward the development of safety criteria that are specific to peripheral nerve and make use of the latest advances in computational bioelectromagnetics and machine learning, such as Python-based AM and CNN-based nerve image segmentation.

Development and Characterization of a Micromagnetic Alternative to Cochlear Implant Electrode Arrays

To stimulate the auditory nerve, cochlear implants directly inject electrical current into surrounding tissue via an implanted electrode array. While many cochlear implant users achieve strong speech perception scores, there remains significant variability. Since cochlear implant electrode arrays are surrounded by a conductive fluid, perilymph, a spread of excitation occurs. The functionality of the cochlea is spatially dependent, and a wider area of excitation negatively affects the hearing of the user. Importantly, magnetic fields are unaffected by the material properties of biological components. To utilize the electromagnetic properties of the human ear, a microcoil array was developed. The microcoils are 4-turn solenoids with a 250-μm turn radius and a 31.75-μm wire radius, coated with Parylene-C. The efficient design was implemented to accelerate testing. The obtained results describe stimulation capabilities. Functionality was validated using a frequency response analyzer to measure how the generated electromagnetic power radiates in space. 99.8% power loss was observed over a 100-μm separation between a pair of identical microcoils. Obtained through finite-element modeling, the microcoils can be driven by a 60 mA, 5 kHz, sinusoidal input for 10 minutes before predicted inflammation. Rattay's activating function was calculated to evaluate the magnetic stimulation effect of external fields on target neurons. Combined with the frequency response analysis, magnitude and spatial effects of the generated potential is established. As a result, each microcoil requires a 400-μm-wide area for each independent stimulation channel, which is 84% narrower than a commercial cochlear array channel, thereby suggesting greater spatial selectivity.

Coil efficiency for inductive peripheral nerve stimulation

Magnetic stimulation of peripheral nerves is evoked by electric field gradients caused by high-intensity, pulsed magnetic fields created from a coil. Currents required for stimulation are very high, therefore devices are large, expensive, and often too complex for many applications like rehabilitation therapy. For repetitive stimulation, coil heating due to power loss poses a further limitation. The geometry of the magnetic coil determines field depth and focality, making it the most important factor that determines the current required for neuronal excitation. However, the comparison between different coil geometries is difficult and depends on the specific application. Especially the distance between nerve and coil plays a crucial role. In this investigation, the electric field distribution of 14 different coil geometries was calculated for a typical peripheral nerve stimulation with a 27mm distance between axon and coil. Coil parameters like field strength and focality were determined with electromagnetic field simulations. In a second analysis, the activating function along the axon was calculated, which quantifies the efficiency of neuronal stimulation. Moreover, coil designs were evaluated concerning power efficacy based on ohmic losses. Our results indicate that power efficacy of magnetic neurostimulation can be improved significantly by up to 40% with optimized coil designs.

Electrical Stimulation Induced Current Distribution in Peripheral Nerves Varies Significantly with the Extent of Nerve Damage: A Computational Study Utilizing Convolutional Neural Network and Realistic Nerve Models

Although electrical stimulation is an established treatment option for multiple central nervous and peripheral nervous system diseases, its effects on the tissue and subsequent safety of the stimulation are not well understood. Therefore, it is crucial to design stimulation protocols that maximize therapeutic efficacy while avoiding any potential tissue damage. Further, the stimulation levels need to be adjusted regularly to ensure that they are safe even with the changes to the nerve due to long-term stimulation. Using the latest advances in computing capabilities and machine learning approaches, we developed computational models of peripheral nerve stimulation based on very high-resolution cross-sectional images of the nerves. We generated nerve models constructed from non-stimulated (healthy) and over-stimulated (damaged) rat sciatic nerves to examine how the current density distribution is affected by nerve damage. Using our in-house numerical solver, the Admittance Method (AM), we computed the induced current distribution inside the nerves and compared the current penetration for healthy and damaged nerves. Our computational results indicate that when the nerve is damaged, primarily evidenced by the decreased nerve fiber packing, the current penetrates deeper inside the nerve than in the healthy case. As safety limits for electrical stimulation of biological tissue are still debated, we ultimately aim to utilize our computational models to determine refined safety criteria and help design safer and more efficacious electrical stimulation protocols.

Electrode Spacing and Current Distribution in Electrical Stimulation of Peripheral Nerve: A Computational Modeling Study using Realistic Nerve Models

Electrical stimulation of peripheral nerves has long been used and proven effective in restoring function caused by disease or injury. Accurate placement of electrodes is often critical to properly excite the nerve and yield the desired outcome. Computational modeling is becoming an important tool that can guide the rapid development and optimization of such implantable neural stimulation devices. Here, we developed a heterogeneous very high-resolution computational model of a realistic peripheral nerve stimulated by a current source through cuff electrodes. We then calculated the current distribution inside the nerve and investigated the effect of electrodes spacing on current penetration. In the present study, we first describe model implementation and calibration; we then detail the methodology we use to calculate current distribution and apply it to characterize the effect of electrodes distance on current penetration. Our computational results indicate that when the source and return cuff electrodes are placed close to each other, the penetration depth in the nerve is shallower than the cases in which the electrode distance is larger. This study outlines the utility of the proposed computational methods and anatomically correct high-resolution models in guiding and optimizing experimental nerve stimulation protocols.

Focality-Oriented Selection of Current Dose for Transcranial Direct Current Stimulation

Background: In transcranial direct current stimulation (tDCS), the injected current becomes distributed across the brain areas. The objective is to stimulate the target region of interest (ROI) while minimizing the current in non-target ROIs (the 'focality' of tDCS). For this purpose, determining the appropriate current dose for an individual is difficult. Aim: To introduce a dose-target determination index (DTDI) to quantify the focality of tDCS and examine the dose-focality relationship in three different populations. Method: Here, we extended our previous toolbox i-SATA to the MNI reference space. After a tDCS montage is simulated for a current dose, the i-SATA(MNI) computes the average (over voxels) current density for every region in the brain. DTDI is the ratio of the average current density at the target ROI to the ROI with a maximum value (the peak region). Ideally, target ROI should be the peak region, so DTDI shall range from 0 to 1. The higher the value, the better the dose. We estimated the variation of DTDI within and across individuals using T1-weighted brain images of 45 males and females distributed equally across three age groups: (a) young adults (20 ≤ x ˂ 40 years), (b) mid adults (40 ≤ x ˂ 60 years), and (c) older adults (60 ≤ x ˂ 80 years). DTDI's were evaluated for the frontal montage with electrodes at F3 and the right supraorbital for three current doses of 1 mA, 2 mA, and 3 mA, with the target ROI at the left middle frontal gyrus. Result: As the dose is incremented, DTDI may show (a) increase, (b) decrease, and (c) no change across the individuals depending on the relationship (nonlinear or linear) between the injected tDCS current and the distribution of current density in the target ROI. The nonlinearity is predominant in older adults with a decrease in focality. The decline is stronger in males. Higher current dose at older age can enhance the focality of stimulation. Conclusion: DTDI provides information on which tDCS current dose will optimize the focality of stimulation. The recommended DTDI dose should be prioritized based on the age (>40 years) and sex (especially for males) of an individual. The toolbox i-SATA(MNI) is freely available.