A Study of Flex Miniaturized Coils for Focal Nerve Magnetic Stimulation

Abstract

Background:

Peripheral Magnetic Stimulation (PMS) is emerging as a complement to standard electrical stimulation of the peripheral nervous system. PMS may stimulate sensory and motor nerve fibers without the discomfort associated with the electrical stimulation used for standard nerve conduction studies. The PMS coils are the same ones used in Transcranial Magnetic Stimulation and lack focality and selectiveness in the stimulation.

Purpose:

This study presents a novel coil for PMS, developed using Flexible technologies, and characterized by reduced dimensions for a precise and controlled targeting of peripheral nerves.

Methods:

We performed hybrid electromagnetic (EM) and electrophysiological simulations to study the EM exposure induced by a novel miniaturized coil (or mcoil) in and around the radial nerve of the neuro-functionalized virtual human body model Yoon-Sun, and to estimate the current threshold to induce magnetic stimulation of the radial nerve. Eleven healthy subjects were studied with the mcoil, which consisted of two 15 mm diameter coils in a figure-of-eight configuration, each with a hundred turns of a 25 μm copper-clad four-layer foil. Sensory nerve action potentials (SNAPs) were measured in each subject using two electrodes and compared with those obtained from standard electrical stimulation. The SNAPs conduction velocities were estimated as a performance metric.

Results:

The induced Electric field was estimated numerically to peak at a maximum intensity of 39 V/m underneath the mcoil fed by 70 A currents. In such conditions, the electrophysiological simulations suggested that the mcoil elicits SNAPs originating at 7 mm from the center of the mcoil. Furthermore, the numerically estimated latencies and waveforms agreed with those obtained during the PMS experiments on healthy subjects, confirming the ability of the mcoil to stimulate the radial nerve sensory fibers.

Conclusion:

Hybrid EM-electrophysiological simulations assisted the development of a miniaturized coil with a small diameter and a high number of turns using flexible electronics. The numerical dosimetric analysis predicted the threshold current amplitudes required for a suprathreshold peripheral nerve sensory stimulation, which was experimentally confirmed. The developed and now validated computational pipeline will be used to improve the performances (e.g., focality and minimal currents) of new generations of mcoil designs.

1. Introduction

Since the pioneering studies by D'Arsonval in the early 19^th century^1,2, magnetic devices became a powerful tool for non-invasive magnetic stimulation (MS)³ in medicine. MS induces an electric field in neurons or nerves by a time-varying magnetic field, resulting in depolarization. MS is of interest due to its superiority in reduced pain and muscle contraction over electrical stimulation (ES) since it activates the nerves with reduced stimulation of the various types of superficial skin receptors and polymodal nociceptive nerve fibers⁴. Also, contrary to MS, ES injects radial currents, which activate pain nerves in the skin more severely^5-9. Stemming from the pioneering work of Barker and colleagues in the early '80s⁵, MS is commonly used to stimulate the central nervous system (CNS), and this technique is known as Transcranial magnetic stimulation (TMS), which has enabled breakthroughs in clinical^10-15 and basic neuroscience research^16-18. Several TMS devices have been approved by the Food and Drugs Administration (FDA) to treat numerous conditions¹⁹, including refractory depression²⁰ and obsessive-compulsive disorder²¹.

Furthermore, TMS can cause brief and controllable disruption of cortical activity in a specific brain region, allowing the exploration of brain-behavior relationships^22-27. MS uses similar TMS devices to target the peripheral nervous system (PNS) or Peripheral Magnetic Stimulation (PMS) for investigational nerve conduction studies^28-31, to treat different neurological^32-34 and musculoskeletal impairments^34,35,36-41. In a typical PMS session, a standard figure-of-eight or a circular coil is applied over specific muscles or nerves, such as the trapezius and the deltoid, to treat migraine^34,42,43, or the sacral nerve to treat urinary and fecal incontinence^44-46. Furthermore, PMS is increasingly being studied for stimulating both the spinal root and the peripheral nerve levels in treating neuropathic pain^33,47.

Besides already existing TMS devices, other coil geometries have been proposed, such as the parabolic coil, used to administer PMS as an adjuvant therapy to reduce skeletal muscle reflex activity³⁵ or the elliptical coil as a monotherapy for the treatment of lumbar radiculopathy⁴⁸. Newly approved devices developed explicitly for PMS are also available to treat particular conditions, such as stress urinary incontinence (SUI), neuropathic pain, and peripheral neuropathy. The main therapeutic targets for SUI conditions are the pelvic and/or pudendal nerves on the pelvic floor muscles, and an armchair-embedded coil has been FDA approved^41,49,50. A clinical trial is currently undergoing to study Axon Therapy by NeuraLace Medical Inc. initially based on two clinical reports^47,51. Even though MS has advantages over ES, principally the reduced cutaneous pain sensation, MS has limitations. First, uncomfortable muscle contraction and noxious stimulation of nociceptors in muscle, fascia, and tendons^7,32 may occur when high-intensity coil currents (about 2 kA, corresponding to a stimulation given at the motor threshold³²) stimulate deep regions. Second, the dimensions of large coils make their application to small sites difficult⁵², which can be addressed by adopting miniaturized stimulators. Several small coils are commercially available or present in literature^53-59. However, these coils typically stimulate the brain of small animals, such as mice and rats, and have several weaknesses⁶. First is the reduced efficiency since the induced electric field rapidly falls off with distance. Thus, larger driving currents (about 20 kA⁶⁰) are required to induce an electric field strong enough for stimulation⁶, generating excessive heat and large Lorentz forces that may damage conventional wires⁶¹. As far as we know, only very few examples of small coils for magnetic stimulations have been proposed in humans. For instance, Mori et al. describe a small round coil to stimulate suprahyoid muscles obtaining hyoid elevation in patients affected by dysphagia but lacking technical details^52,62,63.

This paper presents the validated results of multi-physics electromagnetic and electrophysiological in silico experiments used to characterize and improve the performances of a new type of miniaturized coil (mcoil) with an improved stimulation profile in terms of focality by using microstrips instead of wires. In these simulations, a detailed model of the mcoil was placed in correspondence to the superficial branch of the radial nerve over the arm of the Yoon-Sun anatomical body model (IT'IS Foundation, Zurich, Switzerland) functionalized with principal nerve trajectories. The radial nerve at the superficial branch level of the wrist was selected as a target. In practice, it is hard to stimulate this particular nerve using TMS without stimulating the surrounding muscles. Thus, a novel system designed to stimulate the peripheral nervous system, the focal non-invasive magnetic stimulation (f-NIMS) system, was built and tested to validate the numerical FEM simulations. The f-NIMS includes class-D amplifiers and a miniaturized multi-layered mcoil with high focality constructed from a flexible printed circuit board (flex PCB). The mcoil consisted of two coils paired together and fed currents in counter-phase to form the so-called figure-of-eight coil. Successively, we stimulated the superficial radial nerve of healthy subjects and recorded sensory nerve action potentials (SNAPs), comparing the efficacy and focality of the mcoil with standard peripheral nerve electric stimulation. We hypothesized that the new mcoil system would have similar efficacy as conventional electrical stimulation but without the discomfort associated with it and could induce an electric (E-) field capable of stimulating superficial peripheral nerves.

2. Methods and materials

2.1. The mcoil

Maximizing the cross-sectional area (A) was a crucial requirement in coil design as it reduces heating and peak voltages in the driving system; however, it increases the overall size of the coil. A rectangular cross-section allows for thinner coil designs over circular sections with the same area A since increasing the trace height (h) while decreasing the trace thickness (t=A/h) maintains the area A of the trace constant. The mcoil represents a different strategy from previous coil designs, using a polyimide Flex PCB with four micro-traces instead of copper^6,54,55,64 or litz wires^65-67. The mcoil (Fig. 1 A) was composed of two coils paired together to form the so-called figure-of-eight configuration.

Figure 1.

Validation of the mcoil model. (A) The physical mcoil and the measured Z-component of the B-field (Bz). (B) The numerical model of the mcoil and the computed Z-component of the B-field (Bz). The insets show the geometrical details of the physical coil (blue) and its model (yellow), composed of 4 planar loops vertically stacked.

2.1.1. Geometry and validation of the mcoil model

Hybrid EM and electrophysiological simulations were executed using the Sim4Life v5.0 (ZMT Zurich Medtech AG, Zurich, Switzerland) platform for life science investigations. Each of the four copper traces that compose the mcoil was modeled as a planar loop coil of 123 turns, an inner radius of 0.35 mm, corresponding to the radius of the brass pin, and an outer radius of 7.5 mm. Each loop was placed in the middle of the corresponding trace, and the space between consecutive loops was 1.5 mm (Fig. 1 B). The overall height of the mcoil model was 4.5 mm (Fig. 1B, yellow inset). The geometry was modeled closely to the figure-of-eight mcoil built and tested (Fig. 1 A). We validated the numerical model experimentally by comparing the measured vs. the simulated magnetic ∣B_z∣ field component intensity distribution. Measurements were conducted using an integrated monoaxial analog magnetic field sensor (AAK001-14E, NVE Corporation), characterized by 1.1 mm × 1.1 mm dimensions and mounted on a PCB. The sensor was accurately calibrated with a commercial Hall-effect magnetic field sensor on a known and stable magnetic field source. The NVE sensor precisely measures sense fields up to 400 mT with a highly linear behavior of up to 250 mT.

The magnetic field sensor was placed on a rigid support and was oriented orthogonally to the surface of the mcoil to detect ∣B_z∣. The magnetic field sensor was moved transversally along the X and the Y directions with a 5 mm spatial step to scan an area of 5 cm × 2.5 cm.

2.1.2. The FEM simulations modeling the peripheral nerves stimulation experiments

The stimulation target was the superficial sensory branch of the radial nerve, one of the forearm's nerve branches, consistent with one of the first TMS studies performed in the mid-1980s⁶⁸. The first step of the dosimetric analysis was to estimate the distribution of the E-field induced by the mcoil over the forearm and the radial nerve. The mcoil was placed over the wrist of the virtual female human body model Yoon-Sun, as shown in Fig. 2 A.

Figure 2.

Modeling the experiments. (A) Position of the mcoil model over the wrist of the neuro-functionalized model Yoon-Sun (position of the stimulation area and recording site are shown). (B) Position of the mcoil over the wrist of one subject (left).

EM solutions were computed using the Sim4life's Low Frequency (LF) Magneto-Quasi Static (MQS) solver considering a 1.9 kHz sinusoidal pulse and 70 A as the feeding current in Supplementary Fig. S3 C. The MQS estimates the B and E-fields by decoupling the B and E field under quasi-static conditions (see eq. S4-S6 in Supplement Material). The E field was solved using the FEM method in a uniform isotropic grid of 1 mm × 1 mm × 1 mm that discretized the entire simulation domain with prescribed Neumann boundary conditions. The dielectric properties of Yoon-Sun's virtual model were assigned according to the LF IT'IS database⁶⁹ (Table 1). Furthermore, the ViP neuro-functionalized models included a series of splines representing the nerve fibers surrounded by a homogeneous nerve model layer, with a conductivity of 0.030 S/m, ensuring an electrical continuity condition around the nerve. The neuroelectric response to magnetic stimulation was computed in Sim4Life using the T-Neuro solved interfaced with Yale's NEURON solver⁶⁹. In T-Neuro, axon trajectories were modeled as McIntyre-Richardson-Grill (MRG) electrophysiological model^70,71, which describes the axon as a double cable modeling myelin and an underlying internodal axolemma. The parameters used in the MRG model were chosen consistent with sensory fibers⁷². First, we estimated the mcoil current threshold for fiber excitation by conducting a titration study. The titration procedure estimated the minimal current intensity to initiate a membrane depolarization larger than 80mV within each fiber in the model, using a bisection scheme.

Table 1.

The electric conductivity of the simulated tissues.

Tissue	σref (S/m)
Skin	0.17
Fat	0.042
Muscle	0.329
Nerve	0.030
Tendon	0.384
Bone	Cortical: 0.020
	Cancellous: 0.082
	Marrow: 0.003
Blood	0.7

The threshold was defined as the minimal mcoil current intensity that evoked an action potential (AP) in the fiber.

2.2. The mcoil fabrication and the f-NIMS driving system

Due to manufacturing limitations, the thickness of each copper trace was fixed to multiples of 8.7 μm or ¼ oz. For a good trade-off between overall coil height and the number of turns, the trace thickness was selected equal to 35 μm or 1 Oz., which allowed a single trace height of 1 mm with a 2.847 m in length and overall target resistance of 1.4 Ω. Supported by previous FEM numerical simulations⁷³, we fabricated the mcoil as four copper micro traces (four-layered) etched using photolithography on a polyimide substrate (Fig. S.1). The overall height of the mcoil was only 5.1 mm, given the trace-to-trace spacing of just 0.38 mm (Fig. 3 A). The Flex micro traces were wound in 123 turns around a copper rod of OD=1mm, yielding a final diameter of 15 mm (Fig. 1). The inductance of each layer (see Supplementary Material) was 67 μH. We achieved a figure-of-eight coil geometry - which enables more focal stimulation - by pairing two single mcoils side-by-side (as shown in Fig. 3 B). The mcoil has a maximum dimension of only 30 mm, much smaller than standard TMS figure-of-eight coils (Fig. 3 B).

Figure 3.

The mcoil and the feeding f-NIMS system. (A) mcoil design. (B) Comparison between the mcoil and a typical larger figure-of-eight coil. Inset shows the dimensions of a single mcoil. (C) Connection scheme of the f-NIMS system.

The architecture of the entire f-NIMS system is shown in Fig. 3 C. The system was composed of a controller (i.e., Microsoft PC running Windows 10), a scope (Tektronix MDO3014) with high voltage active probes (Tektronix THDP0200), a generator (Tektronix AFG1062), two digital thermometers (TC01, National Instrument), and class-D amplifiers (Behringer iNUKE NU12000). The inductance of each layer was higher than the typical TMS coil to compensate for the smaller size (see Supplementary Fig. S2). Thus, we decided to use a different driving system than the standard TMS energy-storage capacitor system. Instead, a Class-D amplifier was selected to drive the mcoil since this audio amplifier can drive loads with large inductance, such as loudspeakers. Our approach was to drive the coils with four high power (i.e., peak power value of 12 kW) stereo amplifiers (i.e., peak power value of 6 kW/channel), one for each of the four layers, and connect the right and left channels to the right and left figure-of-eight coils. In this way, it was possible to obtain a versatile driving system that generated controllable pulses in pulse shape (i.e., sinusoidal or square), amplitude, and pulse width⁷⁴. The block diagram of a Class-D amplifier (Fig. S4 A) and a more detailed description are presented in the Supplementary Material. The amplifier input signal level on the front panel was set to maximum. The built-in crossover switch in the back panel enabled the amplifier to operate either in bi-amp mode (i.e., sending low-frequency to passive subwoofers and high-frequency to tweeter speakers) or full-range, while the crossover switch was set to full-range.

The arbitrary signal generator (ASG) was set to output two sinusoid pulses with amplitudes up to 5 Vpp, and a frequency of 3 kHz since standard TMS systems induce excitable tissue stimulation through biphasic magnetic pulses⁷⁵, approximated by a damped sinusoid at 3 kHz^76,77. The custom-made LabView program controlled the ASG and generated two sinusoids of inverted polarity to induce two opposite currents as in the standard figure-of-eight coils. It allowed the selection of other pulse shapes, amplitudes, and widths. The left and right inputs to Class-D amplifiers were connected to the two ASG output channels using BNC cables/adapters, and the outputs were fed to the various mcoil layers (Fig. 3C). The amplified voltage provided to each layer was measured using a differential high voltage probe (TDHP0200, Tektronix, Inc.). The current pulse flowing in each layer was measured using a Hall-effect current sensor (ACS772 200B series, Allegro Microsystems, Inc.). When the 5 Vpp sinusoidal pulse was fed at the input of each amplifier, the output signal reached voltage and current peaks of approximately 150 V and 70 A (Fig. S4 B-C), resulting in distortion and decreasing the frequency band from around 3 kHz to 1.9 kHz.

2.3. The f-NIMS System Safety

The high power in the class-D amplifiers raised the concerns of potential burns by Joule heating when our subjects were in contact with the mcoils⁶, which have trace resistances of approximately 1.5 Ω (Fig. S.2). In order to mitigate the risks of skin burns, sensors in each coil monitored the surface temperature of the mcoil continuously. The LabView code was programmed to automatically switch off the class-D amplifiers whenever the temperature and the exposure time reached a threshold⁷⁸, as per the CEM43 standard⁷⁹ (see Supplementary Material for further details). A second potential electrical safety concern is electropathology when currents from the class-D amplifiers' output flow directly into the subject. The risk of electrocution was substantially reduced by first applying a silicone conformal coating (PN 422B, MG Chemicals) followed by 25μm of Parylene C conformal coating, which confers a dielectric strength of 5kV and it is biocompatible.

Another potential safety concern, which is typically associated with TMS systems, is tinnitus or hearing loss⁸⁰. In general, the interaction between large currents passing through a circular coil and the induced high magnetic fields generate radially inward and outward Lorentz forces. The compressional waves propagate in the surrounding air⁸¹ toward every direction around the coil forming high-pitched sounds with potentially high sound pressure levels (SPL), which in the case of TMS tend to be harmful since they are too short (typically 400μs) to be perceived as loud noises. We performed SPL measurements (see Supplementary Materials) on the mcoil and found that the intensity was no louder than the SPL of a verbal conversation (≈ 60 dB), and such a low SPL intensity poses less than minimal risk to participants to either tinnitus or hearing loss.

2.4. The validation experiments on healthy subjects

The protocol was IRB-approved by the committee for clinical investigations at Beth Israel Deaconess Medical Center in accordance with The Code of Ethics of the World Medical Association (Declaration of Helsinki) for experiments involving humans. Eleven healthy volunteers between 18 and 50 years old were recruited to assess the safety and efficacy of the mcoil. Of the eleven participants, six were female, and five were male. Demographically, seven were white, three were Asian, and one was multiracial. The experimental sessions consisted of an initial nerve conduction study (NCS) test to assess nerve function and identify the location of the radial nerve using two recording electrodes, one at the level of the snuff and one at the level of the thumb at a distance of 5.5 cm and 7.5 cm from the stimulation site (Fig. 4 B). SNAPs were obtained using standard technique and both threshold and supramaximal stimulation intensity. This procedure was repeated with a handheld electrical stimulator cathode, as shown in Fig. 4 A. The mcoil stimulation was then applied to the same site (Fig. 5 C) to characterize and compare the electrical and magnetic's evoked responses and conduction velocities. Electromyography recording electrodes were placed over the thumb and the snuff areas to record the SNAP propagation over the superficial branch of the radial nerve (Fig. 4B) using the Synergy software.

Figure 4.

The experiments on healthy volunteers. (A) Position of stimulating electrodes to detect the radial nerve. (B-C) Position of the mcoil and recording electrodes during the stimulation.

Figure 5.

Distribution of ∣E∣. Left: ∣E∣ on the surface of nerve and muscles (cyan inset shows detail below the coil). Center and Right: ∣E∣ on two cross-sectional planes of the arm - sagittal (Right) and transversal (Center) - that pass through the center of the mcoil.

3. RESULTS

3.1. Numerical modeling of the human peripheral nerve experiments

Figures 1 A and B compare the measured and the simulated z-component of the B field (B_{z_meas} and B_{z_sim}) generated by the mcoil, with the z-axis defined as the axis orthogonal to the coil plane. The experimental and numerical results were in good agreement, differing by 10% with B_{z_meas} = 200 mT and B_{z_sim} = 220 mT and with a similar spatial extent of 5 cm × 2.5 cm.

In Figure 5, the EM exposure within the Yoon-Sun model for a 70 A current at 1.9 kHz is shown. The induced E-field map along the longitudinal and transversal planes, crossing the coil's center, is reported in panels B and C. E-field intensities between 45 V/m and 48.71 V/m (i.e., the maximum value reached on the skin) were confined in a small area, 3 mm deep below the skin. Panel A shows a focal distribution of the E-field on the surface of the target nerve and the underlying tissues of fat, muscle, and bone. An induced E-field of 39 V/m (E_max,nerve) was estimated on the nerve below the center of the coil, rapidly decreasing intensity longitudinally. The electrophysiological simulations estimated that this E-field was able to elicit fibers' sensory action potentials (Fig. 6, lilac panel), confirming the efficacy in generating SNAPs at the level of the snuffbox. The simulations indicated that the first action potential was located 7 mm far from the center of the coil, which was consistent with the derivative of the tangential E-field over the nerve trajectory (dE_s/ds) – proportional to the activation function (AF)⁸² -, as reported in Fig. 6, blue panel. Finally, the dosimetry analysis estimated a minimum driving current of 58 A, suggesting that the f-NIMS system had enough peak current (i.e., 70 A) to elicit the radial nerve stimulation. The simulations also indicated that the electric field distribution such that E-field > E_max,nerve/2 was shorter than 1 cm in length, while the E-field ≅ E_max,nerve had a distance along the nerve of less than 5 mm. We investigated the impact of inter-subject variability of the arm anatomy on the stimulation threshold by repeating the EM-hybrid simulation on the Jeduk anatomical model (IT'IS Foundation, Zurich, Switzerland).

Figure 6.

The numerical model of the experiments. Lilac sub-panel shows the action potential computed for the suprathreshold stimulation at the recording site. The Blue sub-panel panel shows the (top) distribution of ∣E∣ on the surface of the nerve. Two spheres represent the center of the coil and the first action potential (AP) position, as computed from NEURON (bottom).

The models differed in wrist diameter and depth of the superficial branch of the radial nerve (3 mm vs. 6 mm, respectively). Such differences lead to variations in the stimulation threshold of 27% (Fig. 7).

Figure 7.

Sagittal and coronal view of the two anatomical models Jeduk and Yoon-Sun. Blue splines represent the deep branch of the radial nerve. Red splines represent the superficial branch of the radial nerve. Grey spheres show the location of the numerically estimated stimulation site.

Furthermore, a variability analysis was conducted to estimate the effects of mcoil displacements on the nerve stimulation efficacy. When shifting and tilting the mcoil from the reference position, simulations showed a stimulation threshold change up to 160 % (Fig. 8 and Supplementary material).

Figure 8.

The box plot representation of the distribution of Δ_max (maximum variation concerning the m-Coil position) computed over the 20 superficial fibers available in the model (red splines). The box's top and bottom lines are the 1^st and 3^rd quartile, and the x represents the mean value. The vertical lines (or whiskers) show maximum and minimum values. Inner points and outliers are also reported. Arrows indicate the direction of longitudinal shifting (blue), transversal motion (orange), tilting (grey), and lifting (yellow).

3.2. Peripheral nerve stimulation in healthy volunteers

All participants tolerated the f-NIMS sessions without any adverse effects. Specifically, none of the eleven subjects studied reported skin redness, discomfort, hearing changes, or perceived tinnitus after inquiry. All experiments were conducted with the assistance of a neuromuscular neurologist using standard nerve conduction study techniques. The ES and mcoil stimulation evoked SNAP waveform shapes (Fig. 9 A-D) were similar at the snuffbox and the thumb level. Since the exact location of depolarization of the magnetic stimulation site was unknown, latencies were computed as differential measurements between responses recorded from the snuffbox and at the thumb. Nevertheless, Δt = 0.35 ms resulted in both stimulation methods.

Figure 9.

The recorded sensory nerve action potentials (SNAPs). (A)-(B) ES and mcoil stimulation on the same subject: recording from snuff (black trace) and the thumb (red trace). (C) mcoil stimulation: different recordings from the snuff of the same subject. (D) mcoil stimulation: recording from the snuff of different subjects.

Furthermore, the thumb conduction velocity of sensory nerve action potentials was 61 m/s for the ES. In comparison, it was 49 m/s when stimulated with the mcoil, which was slightly below 50 m/s or the lowest conduction velocity in healthy individuals⁸³. However, contrary to ES, the subject's wrist was cooled by the device (i.e., ice pack) used to cool off the mcoil, and cold is known to slow down conduction velocities.

Additionally, the responses achieved on multiple trials for a given subject were stable in amplitude and onset time (Fig. 9 C), while variability was visible among subjects (Fig. 9 D).

4. DISCUSSION

Many forms of treatment are available for neuropathic and musculoskeletal diseases in general, including oral medications, targeted blocks with local anesthetics and steroids, and neuromodulation, which broadly encompasses the use of energy to modify neural circuits and pain pathways. Neuromodulation devices can be invasive and non-invasive and based on ES or MS. Compared to invasive medical devices, non-invasive devices used to treat neuropathic diseases will provide a much safer treatment option, allowing for a more considerable number of candidates- including children- to access state-of-the-art diagnostic systems, including Magnetic Resonance Imaging (MRI). A non-invasive therapy option will provide a valuable tool in the treatment armamentarium for many neuropathic diseases. There are several ways by which non-invasive peripheral nerve stimulation could be achieved. Transcutaneous electrical stimulation (TES) is readily available but is limited by activation of skin nociceptors^8,9,51,52 and attenuation of current by tissue impedance. Thus, achieving high levels of stimulation in the target regions with high spatial resolution is challenging. Another way is using MS of the peripheral nervous system, also known as PMS, which has gained further attention over the years as a possible therapeutic tool for treating different neurological and musculoskeletal diseases^32,84. The principle mechanism of action behind PMS is Faraday's law of induction. Pulsed current i(t) flowing inside a stimulating coil generates a pulsed magnetic field that induces an electric field (i.e., proportional to di(t)/dt) inside excitable tissues to depolarize nerve fibers^5,85. Therefore, the major advantages of PMS over transcutaneous TES are that it doesn't require strong and prolonged skin contact and is almost painless. PMS is typically administered with large coils that induce inside deep nerves and muscles a stimulating E-field to elicit the therapeutic effect^34,42-45,47. However, a focal PMS stimulation of superficial nerves without concomitant muscle stimulation is challenging to achieve. The most straightforward approach to attain a focal stimulation would be to reduce the size of the coil. Nevertheless, this comes with physical caveats, such as excessive Joule heating and large Lorentz forces⁶. For this reason, several studies proposed alternative methods to improve focality, which consist of a compromise between focality and energy efficiency without reducing the coil size. This optimal design can be achieved with focal transcranial magnetic stimulation on a single brain area⁸⁶, but it is less suitable for smaller sites commonly targeted with PMS^51,52,63. For instance, Mori and co-workers designed a smaller coil specifically for suprahyoid muscles^52,62,63. Such a device has an overall dimension of 94 mm × 84 mm and can reach a maximum B-field intensity of 0.8 T below its surface. All the other small coils in the literature were explicitly designed and realized for preclinical applications^54-56,59; thus, they were never tested on humans. Therefore, we decided to study a small coil designed expressly for stimulating the superficial branch of peripheral nerves in humans. The mcoil was manufactured using novel Flexible technology, minimizing the dimensions (i.e., OD=30 mm) while maximizing the number of turns (i.e., N=123). A figure-of-eight coil with similar overall dimensions to the mcoil was developed by Tang et al.⁵⁴, which induced an E-field intensity below 10 V/m at a depth of 1 mm from its surface and was therefore used for subthreshold stimulation of rats' brain⁸⁷. However, the mcoil can induce a four-fold increase in E-field (i.e., approximately 40 V/m, as shown in Fig. 5) at a triple of the depth (i.e., 3 mm) or a depth of the superficial branch of the radial nerve ⁸⁸. Due to the different technological approaches and the reduced mcoil dimensions, the overall impedance was higher than that of standard TMS coils (Supplementary Fig. S2), thus requiring a different feeding system. The non-invasive magnetic stimulator or f-NIMS consisted of two waveform generators connected to the left and right channels of four class-D amplifiers, which were then attached to the left and right figure-8 coils components of the mcoil, as shown in Fig. 3C. Additionally, a set of high-voltage probes and thermometers monitored the system's output and temperature for safety purposes (Fig. 3C). To validate the numerical simulations and demonstrate the efficacy of the f-NIMS system, we focused on the stimulation of a superficial branch of the radial nerve of healthy subjects (Fig. 4). The volunteers' radial nerve stimulation experiments reveal similar SNAP shapes and amplitudes of the electric vs. the magnetic stimulation with the mcoil (Fig. 9A-B). However, magnetic stimulation amplitudes were up to 10 times smaller, indicating that fewer fibers were excited with magnetic vs. electric stimulation. Although, the relative latencies recorded at two different locations (snuffbox and thumb) yielded similar velocities. The experimental results were in satisfying agreement with in-silico simulations using neuro-functionalized anatomical models. The simulations also revealed that the f-NIMS system could deliver to the mcoil a current up to 12 A (i.e., 58 A vs. 70A) above the threshold (Fig. 6). Although the power was a limitation of the f-NIMS system since we could elicit SNAPs only in 3 out of 11 subjects studied (Fig. 9D). The simulations also indicated high focality of the E-field on the nerve (i.e., E-field > E_max,nerve/2 was shorter than 1 cm in length along the nerve, Fig. 5). Among the many factors that contribute to the SNAPs threshold, including individual sensitivities⁴, we have focused on two main factors that may have affected the efficacy of the mcoil in our human studies. First was the subject's anatomy (Fig. 7), as a wider arm circumference and increased subcutaneous tissue would displace the nerve deeper inside the arm, thus being exposed to lower E-field intensities. The second confounding factor was the precision of the mcoil placement over the nerve. In order to achieve efficient stimulation, the nerve should be below the center of the mcoil. Nevertheless, precise targeting was challenging and constituted a limitation of this study. To examine how such factors could affect the stimulation, we numerically conducted a variability study on the stimulation threshold estimated through the titration analysis (more details are reported in the Supplementary material), which exhibited variations up to 160% (Fig. 8). The variation analysis results were in line with our experience gained during the human studies, predicting that adjusting the coil position by even 1-2 mm would lead to the consistent presence or absence of significant SNAPs, thus further supporting the notion of focality.

5. CONCLUSIONS

In this work, in silico models were used to predict the stimulation performances of a new small coil (mcoil) design with an intrinsic high focality. Human experiments confirmed that the mcoil elicited sensory action nerve potentials (SNAPs) on the superficial branch of the radial nerve located in the wrist. The numerical study showed that the maximum power currently available from the proposed f-NIMS system was above, albeit close, to the PNS stimulation threshold numerically predicted for the manufactured coil applied to the ViP model Yoon-Sun. Nevertheless, the computational modeling demonstrated how the predicted threshold was strongly influenced by factors such as the individual anatomy or the coil placement, justifying that the test performed on healthy volunteers succeeded on three out of eleven subjects. In future studies, an upgraded version of the f-NIMS system and the mcoil will be developed to increase the available power to attain stimulation of subjects with larger arms or lower sensitivity while maintaining the current safety levels discussed in this manuscript.