Transcranial magnetic stimulation (TMS) is a non-invasive neuromodulation technique extensively used in clinical applications and basic research. During TMS, a coil is placed over the scalp. A brief high-intensity current pulse passes through the coil producing a time-varying magnetic field (B-field). The B-field further induces an electric field (E-field) inside the brain, which modulates brain activities [1, 2]. Despite the widespread use of TMS for treating neurological and neuropsychiatric conditions such as depression [3–6], obsessive-compulsive disorder [7, 8], migraine [9], stroke [10], epilepsy [11], schizophrenia [12], and autism [13], the underlying mechanisms of its effects remain largely unclear. Animal models are essential for investigating such underlying mechanisms since they allow more comprehensive electrophysiological recordings and invasive experiments that are difficult or impractical on humans. However, most commercial TMS coils are designed for humans. The large geometric size of human TMS coils will cause non-focal high-intensity stimulation, which are not applicable to small animal studies [14–16]. Therefore, there is a strong need for miniaturized TMS coils in neuroscience, neural engineering, and clinical research communities.

Several miniaturized TMS coils have been developed for rodent studies, among which circular coil is one of the most popular designs. For example, a circular coil (8 mm outer diameter) with 300 turns of copper wire around an iron core was built to achieve a maximum B-field of 12 mT [17, 18]. By increasing the windings to 780 turns, it produced a maximum B-field of 120 mT and an E-field of 12.7 V m−1 on the brain surface at ∼1 mm below the coil [19]. A similar circular coil (9.2 mm outer diameter) with 70 turns of copper wire around a soft ferrite core produced a maximum B-field of 180 mT and an E-field of 2.5 V m−1 at 2 mm below the coil [20]. In another circular coil (5 mm outer diameter) with 50 turns of copper wire around a tapered iron powder core [21], a maximum B-field of 685 mT and an E-field of 15 V m−1 at the base of the coil were generated. However, the maximum E-field of circular coils has a circular shape under the coil perimeter thus is not focal (figure 1(A)) [22, 23]. In several recent studies, figure-eight coils were built for focal TMS in rodents. For example, a figure-eight coil with 9 turns of copper wire in each wing (19 mm outer diameter) could produce more focal B-field (300 mT as maximum) and E-field (0.55 V m−1 as maximum) [24]. A more powerful figure-eight coil (25 mm outer diameter) was designed to use a commercial stimulator to generate B-field and E-field intensities similar to those of human TMS coils that could elicit unilateral motor evoked potentials (MEPs) in rats, which was not achieved in most rodent studies [25]. With the aid of convex optimization for TMS in realistic rat head models [26, 27], the figure-eight coil could be further optimized with windings extending to a wide region (116 mm by 84 mm) to achieve minimum energy without sacrificing the stimulation focality [28]. To date, figure-eight coils in conjunction with specially modified flat electrodes or probes have been used to assess brain circuitry and function [29, 30]. However, the figure-eight coil cannot be easily combined with standard electrophysiology since it is difficult to implant a straight penetrating electrode under the center of the coil (where maximum stimulation intensity exists) while keeping the coil close to the brain surface (figure 1(B)). Other alternative designs [31–34] improved the stimulation focality using analytical models but at the same time generated E-field distributions different from those of circular or figure-eight coils, which are most commonly used in humans. Consequently, the neural responses elicited with these coils cannot be directly compared with those in human TMS studies.

Figure 1.  E-fields simulated with different TMS coils in free space. (A) A circular coil generated a non-focal maximum E-field under its perimeter. Standard multi-electrode array (MEA) could be implanted to the location with high E-field without obstruction. (B) A figure-eight coil generated a focal maximum E-field under the center of the coil. However, standard MEA could not be vertically implanted under the center of the coil unless the coil was far apart or tilted at a very large angle, which might result in weak or different E-field distribution. (C) A C-shaped coil generated a focal maximum E-field under the center of the coil. Standard MEA could be implanted to the focal point with the coil or the MEA slightly tilted.

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To develop a TMS coil that can (1) generate focal B- and E-fields similar to those of human figure-eight coils, and (2) is compatible with standard electrophysiological recording and stimulation, we designed, fabricated, characterized, and evaluated a novel C-shaped miniaturized coil for use in small animals [35, 36] (figure 1(C)). This coil consisted of insulated copper wires around a C-shaped iron powder core, which allowed convenient implantation of electrophysiological recording and stimulation electrodes between the two bases of the coil. The resulting B- and E-fields were simulated with finite element modeling and further characterized with experimental measurements. The efficacy of this TMS coil in neuromodulation was validated with electrophysiological recordings of single-unit activities (SUAs), somatosensory evoked potentials (SSEPs), and MEPs before and after repetitive TMS (rTMS) in rats using single electrodes and multi-electrode arrays. This novel miniaturized coil and the associated experimental paradigm enabled the combination of TMS, electrophysiological recording, and electrical stimulation in rat brains. Using this paradigm, we for the first time observed distinct modulatory effects on SUAs, SSEPs, and MEPs with the same rTMS protocol in anesthetized rats. It provided a useful tool to investigate the neural responses as well as the underlying neurobiological mechanisms of TMS in small animal models.

2.1. TMS coil design

A miniaturized TMS coil was built by winding 30 turns of insulated 23-gauge copper wire on a C-shaped magnetic core. The core was made from an iron powder toroid (T60-26, Micrometals, Anaheim CA, USA). The toroid has an outer diameter of 15.2 mm, an inner diameter of 8.5 mm, and a height of 6.0 mm. A small gap was cut on the toroid to form the C-shaped geometry. The angle and shortest distance between the two bases of the C-shaped coil were 150° and 5 mm, respectively. The winding at each base of the coil was rectangular with a dimension of 7 mm × 4 mm. The core material was composed of ferromagnetic particles coated with organic compounds to ensure electrical insulation. This insulation makes the core tolerant of thermal aging and provides high saturation flux density with low loss [21, 37, 38]. The permeability of the core material is 75 times that of the air, which greatly increases the magnetic flux density of the coil. The TMS coil was dip-coated with conformal silicone coating (422C, MG Chemicals, Canada) to provide extra protection and insulation. To characterize the electrical properties of the coil, the coil resistance and inductance were measured via a precision LCR meter (Keysight E4980AL, Santa Rosa, CA, USA) at 1 V input voltage from 20 Hz to 100 kHz (201 points in log scale).

2.2. TMS circuit design

A custom-made stimulator was designed to generate TMS pulses through the coil (figure 2). A DC voltage source (Kungber SPS605 Variable DC Power Supply, Shenzhen, China) was used as the power supply to drive the circuit. Its voltage could be adjusted to control the amplitude of the TMS pulse. The maximal output of the DC voltage source (60 V) was used for all experiments. Two aluminum electrolytic capacitors (capacitance: 680 F; voltage: 200 VDC) and one polymer film capacitor (capacitance: 40 F; voltage rating: 500 VDC) were connected in parallel for generating the pulses. Since electrolytic capacitors had larger capacitance and resistance compared to film capacitor, the combination of those capacitors improved performance by providing high capacitance at low frequencies while providing low resistance at high frequencies. Two N-channel metal–oxide–semiconductor field-effect transistors (MOSFETs; IRF540, Vishay, Malvern PA, USA) were used to control the charging and discharging of the capacitors. When the voltage applied at the gate terminal was below the threshold voltage, the MOSFET was off, and the capacitors was charged up to the supplied DC voltage. When the voltage applied at the gate terminal was above the threshold voltage, the flow of current through the MOSFET led to discharging of capacitors. As a result, a current pulse was generated in the TMS coil. A Schottky diode (SR560, EIC semiconductor, Bangkok, Thailand) parallelly connected to the coil was used to protect the MOSFETs from damage. The gate voltage of the MOSFET was determined by the output of an operational amplifier (OPA548, Texas Instruments, Dallas TX, USA). The noninverting input terminal of the amplifier was connected to an Agilent 33500B arbitrary waveform generator (Keysight, Santa Rosa, CA, USA), which could be programmed to generate monophasic waveforms as the stimulator's input. The inverting input terminal of the amplifier was connected in feedback to a sense resistor (0.05 Ω) and the source terminal of the MOSFET. The high forward gain and differential input nature of the amplifier made it a voltage-to-current converter that drove the gate of the MOSFET. When it was above the threshold, the voltage of the input signal appeared across the sense resistor. The current passing through the sense resistor would appear in the drain of the MOSFET and the TMS coil. Two identical MOSFET circuits were used and connected in parallel to double the coil current. Therefore, the coil current was measured as the sum of currents across two sense resistors in the circuit.

Figure 2. Simplified schematic of the driving circuit of the TMS coil. The stimulation pattern was generated with a waveform generator as the input to the circuit. The voltage signal was converted into current with two operational amplifiers. The output voltages controlled the on and off conditions of two MOSFETs in parallel. When the MOSFETs were off, the capacitors were charged up to the voltage of the DC power supply. When the MOSFETs were on, the capacitors were discharged, and a current pulse was generated in the TMS coil.

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To evaluate the performance of the stimulator, Gaussian pulses with different peak amplitudes (0–10 V) but the same standard deviation (30 µs) were generated as input signals to the circuit. The coil current was measured at each intensity in an incremental order with steps of 0.2 V. In addition, the coil current was measured when the Gaussian pulses were delivered at different frequencies (1, 5, 15, and 20 Hz) with the same peak amplitude of 7.5 V and standard deviation of 30 µs. To further test the flexibility and real-time capability of the device, arbitrary stimulation patterns of Gaussian pulses with random peak amplitude (3–8 V) and frequency (1–20 Hz) were generated via real-time Standard Commands for Programmable Instruments (SCPI) commands sent to the arbitrary waveform generator. The coil current was recorded simultaneously.

2.3. Measurements of magnetic and electric fields

To characterize the C-shaped TMS coil (figure 3(A)) driven by the stimulator, experimental measurements of B- and E-fields were performed with a stereotaxic system in a Faraday cage. The center point between two bases of the coil was defined as the origin of the 3D coordinates. The x-, y-, and z-component of B-field () produced by the TMS coil were measured using a two-loop search coil (radius r= 1.15 mm, number of turns N= 2) (figure 3(B)). The search coil was placed above the base of the TMS coil and oriented to the direction of each measured component. Voltage V was induced in the search coil during stimulation and amplified 100 times with a Model 1700 Differential AC Amplifier (A-M systems, Sequim WA, USA). The B-field was sampled with a 1 mm spatial resolution. The induced voltages along each direction () in the transverse (x–y) plane were captured with an Axon Digidata 1322 A acquisition system (Molecular Devices, Sunnyvale CA, USA). Assuming the B-field was homogeneous over the search coil, Faraday's law of induction was used to calculate each component of B-field [39]:

Figure 3.  B- and E-field measurement. (A) Photograph of the miniaturized C-shaped TMS coil. (B) Schematic of the set-up for B-field measurement. Three types of search coils were placed above the coil to measure the B-field in x-, y- and z-directions. (C) Schematic of the set-up for induced E-field measurement. Two dipole probes were placed above the coil and oriented to measure the E-field in x- and y-directions within saline.

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The corresponding x- and y-component of E-field () were measured using a dipole probe in saline (figure 3(C)). The dipole probe consisted of two twisted insulated wires with a 3 mm separation at the exposed ends [40, 41]. The TMS coil was placed underneath a glass beaker that was filled with sodium chloride solution (0.9%). The dipole probe was placed in the solution and oriented to the direction of each component. A biphasic waveform was measured via the dipole probe during stimulation. It was amplified 1000 times with a DAM50 differential amplifier (World Precision instruments, Sarasota FL, USA). The E-field was sampled with a 2 mm spatial resolution. The induced voltages along each direction in the transverse plane were measured with the Axon data acquisition system. Assuming the induced E-field was approximately constant between the exposed ends of the twisted wires [40], the x- and y-components of E-field were calculated as:

where was the first peak of the biphasic waveform measured along x- and y-direction, respectively; was the known distance of the exposed ends along each direction.

2.4. Finite element modeling of magnetic and electric fields

Finite element modeling was conducted using Multiphysics 6.0 (COMSOL, Burlington MA, USA) to simulate the B- and E-fields induced by the TMS coil. The magnetic core was constructed as a half circle (−105° to 105°) with a rectangular transection (6 mm × 3 mm). Relative permeability of the core material was set to 75; the electrical conductivity was set to 0 due to the dielectric coating of iron powder; the winding was simulated as a single copper conductor with a diameter of 0.2 mm. The 30-turn helical coil was evenly distributed on the core. In the frequency domain analysis, the coil current, , was modeled as a sinusoidal current at frequency, , with the same peak amplitude, , and the same maximum rate of change at time, :

As a result, the TMS coil was injected with a 142 A sinusoidal current at 3217 Hz to replicate the maximum time derivative of 2.87 A s−1 in measured Gaussian current pulse.

For comparison with the experimental measurements, the B-field was simulated in the air; the E-field was simulated in saline. A cylinder with a height of 60 mm and a diameter of 60 mm was created to approximate the saline solution in the beaker. Its isotropic electrical conductivity was set at 1.45 S m−1 [42]. The simulated TMS coil was positioned underneath the cylinder as in the experimental setup. B- and E-fields were calculated using COMSOL Magnetic and Electric Fields (mef) interface. Complete meshes of B- and E-fields consisted of 204 3805 and 492 000 elements, respectively.

To estimate the B- and E-fields induced in the brain, a 3D rat brain model was built based on an existing model [43], which was constructed from 240 cross-sectional magnetic resonance imaging slices. Electrical conductivity of the brain was set to 0.106 S m−1 corresponding to gray matter [41, 44, 45]. The TMS coil was positioned 1.5 mm above the right hemisphere and rotated 15° as in the experimental setup. The complete mesh consisted of 188 150 elements.

2.5. Animal surgery

Female Sprague-Dawley rats (n = 32, 11–12 weeks, 220–250 g) were used in this study; eight animals were used for single-unit recordings from the primary somatosensory cortex (S1); eight animals were used for single-unit recordings from the primary motor cortex (M1); eight animals were used for SSEP recordings while another eight animals were used for MEP recordings.

Animals were anesthetized with ketamine-xylazine (K, 75 mg kg−1; X, 10 mg kg−1; intraperitoneal administration) following a rapid inhalational induction with 3%–4% isoflurane. Anesthesia was maintained with additional boluses of 36 mg kg−1 ketamine. The animal was mounted on a stereotaxic frame with Parafilm-wrapped ear bars and nose cone in a Faraday cage. Neural recordings were conducted when the anesthesia state was stable. Physiological status of animals (pedal reflex, body temperature, breathing rate, etc) was monitored throughout the experiments. A craniotomy was performed to expose the right sensorimotor cortex. One burr hole was incised to attach the ground wire over the occipital bone.

2.6. Single-unit recordings

To conduct single-unit recordings, a multi-electrode array (Neuronexus A8x8-Edge-5 mm-50-150-177, Ann Arbor MI, USA) was implanted in the S1 (AP: 0.00 mm; ML: 3.80 mm) or the M1 (AP: 2.40 mm; ML: 3.00 mm) regions (figure 4(A)). SUAs were recorded and sorted via OmniPlex neural recording system (Plexon, Dallas TX, USA).

Figure 4. TMS combined with electrophysiological recording and stimulation. (A) Experimental set-up for single-unit recordings. Single-unit activities were recorded with the MEA implanted in the S1 and the M1 regions. The coil was placed above the sensorimotor cortex over the craniotomy window. The location of MEA placement was verified with an implantation lesion (S1 layer 4–5 and M1 layer 5). (B) Experimental set-up for SSEP recording. SSEPs elicited by electrical stimulation in the forelimb were recorded with the microelectrode implanted in the S1 region. Microelectrode location was verified with an electrolytic lesion (S1 layer 2–3). (C) Experimental set-up for MEP recording. MEPs elicited by electrical stimulation in the M1 were recorded with needle electrodes inserted in the forelimb. Stimulating microelectrode location was verified with an electrolytic lesion (M1 layer 5).

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By connecting the recording system with implanted electrodes, wire loops between electrodes were formed [30, 41]. During TMS, the changing magnetic field would induce current in the loop. The injected current via electrodes might evoke neural responses at high amplitude. To estimate the amount of TMS-induced current in the recording electrode, the induced electromotive force around the wire loop formed with the recording assembly and coupled to the maximal B-field during TMS without any offset was calculated [41]:

where is the induced electromotive force; is the magnetic flux through the loop; is the maximal B-field during TMS; S is the area of the loop formed by the recording electrode and reference electrode; is the standard deviation of the Gaussian-shaped pulse. The induced current in the loop could be converted using the input impedance of the headstage (40 M) yielding 120 nA. It is unlikely to induce significant neural responses via microsimulation at this amplitude [46, 47], and the induced current could be even smaller due to the offset of the wire loop. Similarly, the induced current in the ground electrode could be converted using the impedance of the rat body with a larger loop area. However, the injected current density via ground electrode could be negligible due to a large contact area.

2.7. Somatosensory evoked potentials (SSEPs)

To record SSEPs, a single platinum–iridium microelectrode (PI2PT30.5A5, Microprobes, Gaithersburg MD, USA) was implanted in the S1 (AP: −0.25 mm; ML: 3.80 mm) (figure 4(B)). The microelectrode and ground wire were connected to the DAM50 differential amplifier (gain: 1000). Two subdermal needle electrodes (Natus, Middleton WI, USA) were inserted into the contralateral forelimb to stimulate the median nerve [48]. Another needle electrode was inserted into the tail as the ground for a STG1004 stimulator (Multi Channel Systems, Reutlingen BW, Germany). A biphasic square current pulse (pulse amplitude: ±0.8 mA; pulse width: 0.1 ms) was applied every 5 s to evoke SSEPs. All signals were recorded with the Axon data acquisition system.

2.8. Motor evoked potentials (MEPs)

To record MEPs, a single microelectrode was implanted in the M1 (AP: 1.25 mm; ML: 3.00 mm) (figure 4(C)). The microelectrode and ground wire were connected to the STG1004 stimulator. Two biphasic current pulses (pulse amplitude: ±0.8 mA; pulse width: 0.5 ms; inter-pulse interval: 2 ms) were applied every 5 s to evoke MEPs. To record muscle activities, two subdermal needle electrodes were inserted into the biceps brachii muscle and the finger pad of the contralateral forelimb as the recording and reference electrode, respectively [30, 48]. A third needle electrode was inserted to the tail as the ground. MEPs were recorded with the DAM50 differential amplifier (gain: 1000) and Axon data acquisition system.

2.9. Repetitive transcranial magnetic stimulation (rTMS)

rTMS in all animal experiments were delivered as Gaussian input pulses with a peak amplitude of 7.5 V and standard deviation of 30 µs at 10 Hz. During single-unit or evoked potential recordings, the TMS coil was placed ∼1.5 mm above the cortex. It was rotated 15° to make the tip of the electrode align with the coil center. Following 5 min baseline recordings, subthreshold rTMS (3 min, 10 Hz) or control condition (rTMS turned off) was delivered to the sensorimotor cortex (n = 5, rTMS groups; n = 3, control groups). To evaluate the time-course of rTMS effects, neural signals were monitored for 15 min after stimulation.

2.10. Temperature measurement

To evaluate the heating effects produced by the coil, the temperature of the coil and the brain surface before and after rTMS (3 min, 10 Hz) was measured three times using a thermometer (Famidoc, Guangdong, China) in three animals. The temperature of the coil was measured to be 23.8 °C before rTMS (10 Hz) and increased to 46.7 0.3 °C after 3 min of rTMS (n = 3). Meanwhile, the temperature of rat brain surface was measured to be 35.8 0.2 °C before rTMS and slightly increased to 36.2 0.2 °C after 3 min of rTMS (n = 3).

2.11. Histology

Histology was performed to verify the implantation site in the brain. For evoked potential recordings, an electrolytic lesion was created by delivering a constant current (amplitude: 0.3 mA; duration: 10 s) to the implanted microelectrode. For single-unit recordings, no electrolytic lesions were created since the multi-electrode array could not be used to deliver a strong enough current. Perfusion was performed using 10% formalin solution (Sigma-Aldrich, Burlington MA, USA) via the vascular system. After the brain was extracted and dehydrated with 18% sucrose solution, brain slices (50 μm) were cut on a coronal plane with a Cryostat (Leica, Buffalo Grove IL, USA). Nissl staining was applied on the brain slices to visualize the neuron populations and implantation lesions.

2.12. Data processing and statistical analyses

All neural recordings were imported and processed in MATLAB (MathWorks, Natick MA, USA). The baseline of the neural recordings was defined as the 5 min recording when the animal was under a stable anesthesia state prior to rTMS. For single-unit recordings, a 250 Hz highpass filter was first applied to the data. Spike sorting was performed in the Plexon offline sorter (Plexon, Dallas TX, USA) to extract the timestamps of neuronal firing. The mean firing rate of each neuron was calculated and averaged with a one-minute bin size. For evoked potential recordings, timestamps of current stimulus artifacts were captured by setting a threshold using MATLAB function 'findpeaks'. The DAM50 amplifier was set with a bandpass filter of 0.1 Hz–10 kHz, and no other filter was applied to the evoked potentials. After the timestamps of each stimulus artifact were obtained, a 100 ms window following the artifact was extracted to isolate the evoked potentials. The individual peak-to-peak amplitude was calculated as the difference between the highest and the lowest value in each evoked potential. The individual latency was calculated as the duration between the stimulus artifact and the first negative peak of each evoked potential. The peak-to-peak amplitude and latency of each evoked potential were further averaged every minute (12 consecutive sweeps).

All values were normalized with their corresponding 5 min baseline recordings and reported as the mean ± standard error of the mean (SEM). Two-tailed t-tests with a significance level of 0.01 were conducted to compare the normalized neural signals before and after rTMS or control condition.

3.1. Characterization of TMS coil

Gaussian pulses (peak amplitude: 7.5 V; standard deviation : 30 µs) were generated as input signals to the circuit (figure 5(A)). The corresponding coil current was measured across the sense resistors (figure 5(B)). The current had the same shape as the input pulse and a peak amplitude ( at 142 A. The current as a function of time could be approximated by the following equation:

Figure 5. Electrical properties of the TMS coil. (A) A Gaussian voltage pulse generated by a waveform generator was used as the input signal. (B) Coil current. (C) E-field waveform measured in saline. (D) Output (coil) current as a function of input signals. (E) Output current relative to current measured at 1 Hz as a function of rTMS frequency. (F) Coil resistance measured via a precision LCR meter. (G) Representative arbitrary stimulation pulse patterns generated by the coil. Top: stimulation pattern with multi-level amplitudes and frequencies. Bottom: stimulation pattern with random amplitudes and intervals.

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The induced E-field waveform was proportional to the first derivative of the coil current. The resulting biphasic waveform was measured via a dipole probe in saline (figure 5(C)). The induced E-field waveform as a function of time could be approximated by the following equation:

where was measured to be 5.2 V m−1 when the dipole probe was placed ∼3.5 mm from the center of the coil. The input–output curve demonstrates the relationship between the input signal and the output (coil) current (figure 5(D)). The response of the circuit was linear when the input signal was within the range of 3–8 V. The lower limit (3 V) was determined by the gate-source threshold voltage of the MOSFET (2–4 V). However, saturation occurred when the input signal was greater than 8 V. In addition, the output current was affected by the rTMS frequency (figure 5(E)). The coil current decreased as the frequency increased. At 20 Hz, the coil current dropped to 95% of the value at 1 Hz. Furthermore, the resistance and inductance of the coil were measured via a precision LCR meter at 1 V input voltage from 20 Hz to 100 kHz. The resistance remained at 0.1 Ω when the frequency was lower than 10 kHz (figure 5(F)). This limit was much higher than the frequency of the input pulse (3217 Hz); therefore, the skin and proximity effects, which reduced the effective area of the copper wire and increased the overall resistance [49], were not obvious during stimulation. The inductance of the coil was measured to be constant at 11.7 µH when the input frequency is between 100 Hz and 10 kHz, which was similar to the simulated inductance of 13.4 µH in the finite element modeling. However, the inductance might vary with the amplitude of the coil current due to the use of the magnetic core which could introduce nonlinearity at high amplitude [50]. The TMS coil was able to deliver arbitrary stimulation patterns (figure 5(G)) via the custom-made stimulator. The pulse amplitude and frequency were precisely controlled through real-time SCPI commands sent to the arbitrary waveform generator.

3.2. Comparison of simulated and measured field distributions

B-field induced by the coil in the air was measured on benchtop and simulated with finite element modeling method. The measured and simulated B-fields were highly consistent (figure 6(A)). At the center of the TMS coil, the peak strength of x-component of B-field was measured and simulated to be 227 mT and 247 mT, respectively. Both measurement and simulation showed two smaller peaks with opposite polarity at the bases of the coil. The measurement showed a slightly larger peak at the right base (south pole) compared with the left base (north pole). This deviance in magnitude might be due to the slight asymmetry of the handcrafted magnetic core. The y-component of B-field had four peaks with different polarity, which were apparent in both measurement and simulation. Among the four peaks, each pair of the diagonal peaks shared the same polarity. The combination of x- and y-component was shown in the quiver plots. The measurement and simulation showed near identical B-field distributions. The minimum points existed at the base of the coil. The main B-field vectors pointed from the north pole to the south pole. The z-component was the dominant component of B-field in the transverse plane. The simulation showed that the north pole and the south poles had peak strengths of 446 mT and −455 mT, respectively. The measurement showed that the north pole and south pole had peak strengths of 406 mT and −473 mT, respectively.

Figure 6.  B- and E-field distributions from measurement and simulation. (A) Measured (top) and simulated (bottom) B-field profiles in the transverse plane. The x-, y-, and z-components of B-field and their combination of x- and y-components of B-field were in the air when the TMS coil was placed ∼0.5 mm away. (B) Measured (top) and simulated (bottom) E-field profiles in the transverse plane. The x- and y-components of B-field and their combination were in saline when the TMS coil was placed ∼4.5 mm away. In addition, normalized measured and simulated x-component (top) and y-component (bottom) of E-field as a function of depth along the z-direction showed consistent decay rates.

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E-field induced by the coil in saline was further measured and simulated. The dipole probe was placed ∼4.5 mm from the base of the coil considering the glass thickness (∼3.5 mm). The measured and simulated E-fields were also highly consistent (figure 6(B)). The x-component of E-field had four peaks with different polarity in both measurement and simulation. Similar to the y-component of B-field, each pair of the diagonal peaks shared the same polarity, and each pair of the adjacent peaks had opposite polarity. At the center of the TMS coil, the peak strength of y-component of E-field was measured and simulated to be 3.7 V m−1 and 3.9 V m−1, respectively. Both measurement and simulation showed two smaller peaks with opposite polarity at the base of the coil. The combination of x- and y-component was shown in the