Planar figure-8 coils for ultra-focal and directional micromagnetic brain stimulation

Abstract

Recently, white-matter fiber tract pathways carrying neural signals through the brain were shown to follow curved, orthogonal grids. This study focuses on how these white-matter fibers may be selectively excited using micromagnetic stimulation (μMS), a new type of neuronal stimulation, which generates microscopic eddy currents capable of directionally activating neurons. One of the most remarkable properties of this novel type of stimulation is that the μMS fields provide unique directional activation of neuronal elements not seen with traditional electrical stimulation. An initial prototype built with SU-8 based photolithography technology shows that the structure can be fabricated. The coil design was optimized through electrical resistance calculations and electric field simulations to elicit the brain's maximal focal and directional neural responses.

I. INTRODUCTION

Recently, white-matter fiber tract pathways carrying neural signals through the brain were shown to follow curved, orthogonal grids.¹ This study focuses on how these 3D fiber grids may be stimulated using micromagnetic stimulation (μMS), a new type of neuronal stimulation, which generates microscopic eddy currents capable of directionally activating neurons.^2–4 One of the most remarkable properties of this novel type of stimulation is that the orientation of the applied μMS fields provides unique activation of neuronal elements not seen with traditional electrical stimulation. Developed initially to stimulate single neurons, μMS uses ultraconductive microtraces capable of carrying current pulses large enough to elicit neural activation through electromagnetic (EM) induction. In this regard, the μMS mechanism of action is similar to transcranial magnetic stimulation (TMS). However, where TMS can generate broad and nonfocal activation, μMS has an ultrasmall dimension, inducing electric fields with a much higher spatial gradient, rendering it inherently more efficient to elicit focal neural activation.

Magnetic stimulation had shown several benefits while maintaining the therapeutic effects. It is shown that the therapeutic effect of magnetic stimulation is similar to conventional electric stimulation.⁵ Skach et al. and Ye et al.,^6,7 had shown that the microscopic magnetic stimulation could produce axonal blockage; however, the authors were using standard commercial coils. Bonmassar et al.⁸ also used the commercially available coils to show to enhance MRI safety. Golestanirad et al.⁴ studied the neuromodulation directionality properties of the micromagnetic stimulation, also using the commercial coils. Commercial coils are designed with high Q-factor, which optimizes the device inductances but unfortunately reduces the magnetic flux available for tissue stimulation.⁹ Lee et al.¹⁰ demonstrated that the implantable micromagnetic coil could be used for intracortical stimulation; however, the authors utilized a custom-made half-a-turn needle-shaped coil with a rather small magnetic flux. Our previous study showed that the planar spiral coil geometry produces a higher induced electric field in the tissue compared to the long solenoid design.^9,11 For the first time, this study introduces a custom-made figure-of-8 spiral coil geometry with high magnetic flux. We illustrated the advantages of this design over the single spiral coil geometry in terms of magnetic flux and induced electric field in the tissue.

This study aims to develop a microscaled neuromodulation device that could help focal and directional stimulation of the neural activity in the brain using a figure-of-8 coil design. The coils were designed to have an electrical resistance (DC) equal to or below 5 Ω. The electric field simulations were performed to optimize the coil design by maximizing the brain's neural responses. A prototype was built using a photolithography process on SU-8 and Cr/Au e-beam deposition.

The paper is organized as follows. First, the methods utilized in the fabrication and numerical simulation are described in Sec. II. Then, the results of fabrication and EM simulation are described in Sec. III. Finally, the discussion and conclusion are presented in Secs. IV and V.

II. MODELING

A. Theory

Neuronal processes such as axons parallel to the direction of the electric current density $\overrightarrow{J}$ [Fig. 1(a)] are depolarized or hyperpolarized depending on the direction and strength of $\overrightarrow{J}$, but the processes transverse to the $\overrightarrow{J}$ are not affected¹² [Fig. 1(b)]. Thus, the magnetic stimulation via μMS is capable of synaptically activating or inhibiting neurons in a spatially oriented manner. One aspect of the directionality of μMS was shown in vitro.² Depending on the magnetic field flux's direction, the axon of the ganglion cell beneath the coil showed the generation of action potentials recorded by the patch clamping technique. The following paragraph illustrates how resistance, inductance, capacitance, the quality factor (Q-factor), and the volume of activation (VOA) are estimated using the equations below.

FIG. 1.

Double figure-of-8 orientation-selective stimulation mechanisms (Refs. 3 and 4). (a) In the proposed figure-of-8 magnetic nerve stimulation, the same time-varying electric current is passed through both coils, generating two time-varying magnetic fields ( $\overrightarrow{\mathit{B}}$ ) around each coil. According to Faraday’s law of induction, these time-varying magnetic fields induce currents exciting the fiber (red fiber) by generating a virtual cathode (+) and anode (−), hyperpolarizing the neuron’s membrane in the anode’s end and depolarizing it in the cathode’s end. This induced current, however, is maximal along the side shared by both coils (since the $\overrightarrow{\mathit{E}}$ field is maximum around the rim of each coil). (b) The direction of this magnetically induced excitation depends on the orientation of the fiber, and thus, its stimulating effect on fibers parallel to the axis (center-to-center) of the figure-of-8 coil can be avoided (green fiber). (c) and (d) The double figure-8 coil configuration allows eliciting axons running with an orientation perpendicular (black arrow) to the axis of the active figure-of-8 coils (yellow), where the hyperpolarizing/depolarizing membrane net effect maximally occurs.

The trace resistance (Ω) was computed as

$$R_t={\displaystyle \frac{\rho l}{A},}$$ (1)

where (see Supplemental Table I) l is the trace length (m), A is the cross-sectional area (m²), and ρ is the resistivity (Ω m). The self-inductance L (H) of a coil is computed using the modified Wheeler formulas^13,14 to take into account the coil's square planar spiral shape

$$\begin{array}{cc}{L}_1=K_1{\mu }_0{\displaystyle \frac{N^2{\displaystyle \frac{(d_{\mathrm{in}}+d_{\mathrm{out}})}{2}}}{\left(1+K_2{\displaystyle \frac{d_{\mathrm{out}}-d_{\mathrm{in}}}{d_{\mathrm{out}}+d_{\mathrm{in}}}}\right)},K_1=2.34;K_2=2.75,}& \end{array}$$ (2)

We also considered a second modification to Wheeler formulas to take into account the coil's topology of the trace thickness¹⁵

$$L=L_1\left(-0.2\cdot \ln \left({\displaystyle \frac{h}{h_0}}\right)-0.27\right),$$ (3)

where μ₀ is the vacuum permeability (H/m), N is the number of turns, d_in is the inner diameter of the coil (m), d_out is the outer diameter of the coil (m), h is the trace height (m), and h₀ = 1 m.

The capacitance (F) of a coil is computed with the total sum of the capacities of each pair of contiguous turns provides as¹⁶

$$C={\displaystyle \frac{\pi {\epsilon }_0{\epsilon }_{r}l}{\ln \left({\displaystyle \frac{D}{2r_0}}\right)+\sqrt{{\displaystyle \frac{D^2}{2r_0^2}-1}}},}$$ (4)

where ${\epsilon }_0$ is the vacuum permittivity (F/m), ${\epsilon }_r$ is the relative permittivity of the trace insulator [i.e., in our design, Parylene C (Ref. 17)], r₀ is the wire radius (m), and D is the distance between a pair of turns (m).

The quality (Q) factor indicates how close the inductor is to an ideal inductor. The Q-factor is calculated using

$$Q={\displaystyle \frac{2\pi fL}{R_t},}$$ (5)

where f is the frequency (Hz), L is the inductance (H), and R_t is the trace resistance (Ω).

The importance of the quality factor for μMS is best understood as follows. The maximum energy that can be stored in the magnetic field of an ideal inductor is

$$\mathit{W}={\displaystyle \frac{1}{2}\int \int \int \mathit{J}(x,y,z)\cdot \mathit{A}(x,y,z)dxdydz={\displaystyle \frac{1}{2}{L}^{\ast }{i}^2,}}$$ (6)

where A is the magnetic potential (T m), the curl is the magnetic flux density (i.e., B = ∇ × A), and $L^{\ast }$ is the ideal inductance (H). In an actual inductor, $L^{\ast }>L$ due to magnetic field losses. However, the portion of the energy W that is lost is instead available for eliciting neuronal activity. Thus, by reducing the Q-factor and the inductance of the coil, we gain neuronal stimulation efficiency.

The VOA (m³) was estimated integral over the volume of the brain block

$$\mathrm{VOA}=\int \int \int ◯|E_b|\ge 2\left(\frac{V}{m}\right)dxdydz,$$ (7)

where $E_b$ is the estimated E-field (RMS) in the brain block (V/m).

In electric nerve stimulation, the pulsed voltages are required between two electrodes that induce electric current between two electrodes in contact with tissues. The different pulse shapes and parameters can be chosen to elicit nerves for the intended application.¹⁸ The monophasic square pulse was commonly used for deep brain stimulation (DBS) with a passive charge-balancing phase, whereas the biphasic pulse could actively balancing the phase of the pulse.¹⁹ The stimulation pulses width (p_w) traditionally using in DBS was relatively short (i.e., p_w = 60 μs), whereas the therapeutic potential of DBS was demonstrated with p_w as small as 20 μs.^20–22 Whereas the magnetic stimulation induces an electric field (E) to stimulate neurons, as per Faraday's law of induction,

$$\mathrm{\nabla }\times E=-{\displaystyle \frac{\mathrm{\partial }\mathrm{B}}{\mathrm{\partial }t},}$$ (8)

where E is the electric field (V/m), B is the magnetic field (T), and t is the time (s). Therefore, to obtain induced stimulation voltages, large time-varying currents of approximately I_peak= 10 A or more may be needed. However, large currents may damage the traces. Therefore, the fusing current for the single pulse was estimated using the modified-Onderdonk's equation²³

$$A_{\min }=6.45\times {10}^{-10}\cdot \sqrt{{\displaystyle \frac{0.15}{t}}}\cdot {(p_s\cdot I_{\mathrm{peak}})}^{-1}$$ (9)

where A_min is the minimum trace area required to avoid fusing (m²), t is the duration for pulse (s), $p_s$ is the pulse modifier (s^−0.5A⁻¹m⁻²) to account for the pulse shape (e.g., exponentially decaying pulse = 0.16, see for details Ref. 24), and I_peak is the peak current (A). Therefore, the minimum required trace area to avoid fusing in a 20 μs pulse with 10 A current in the above condition is estimated as 5.45 μm², below the proposed trace area (Table I).

TABLE I.

Physical and electrical properties of the proposed μMS coil.

Properties	Calculated results
Coil diameter (external/internal)	80/1 μm
Trace length	1.72 mm
Trace dimension (width, height, area)	2.60 μm, 2.25 μm, 5.85 μm2
Number of turns	11
Resistance	5 Ω
Inductance (nH)	3.91 nH
Capacitance (pF)	0.10 pF
Q-factor	4.91 × 10−5
Amin	5.45 μm2

B. Numerical simulation

Similar to our EM optimization,²⁴ we conducted a series of numerical simulations to optimize the μMS coil design for maximum focality and depth stimulation device by varying the physical and electrical parameters while maintaining low R (≤5 Ω). Sim4Life (ZMT, Switzerland) was used to solve Maxwell's equation using the finite element method (FEM) with a quasistatic low-frequency solver at 10 kHz.

The planar spiral coil geometry was designed with 11 windings within a rectangle of 80 μm width. The trace width of 2.60 μm and trace height of 2.25 μm and two planar spiral coils were aligned and mirrored (i.e., currents flowing in the same direction) to generate a figure-of-8 shape coil with a 2 μm gap (Fig. 2). The coils were placed 2 μm above a block with the gray matter electric properties²⁵ at 10 kHz (σ: 0.24 S/m, ε_r: 22,240) to estimate the EM fields in the brain. Simulations were conducted with an input current of 10 A and three coil diameters (80, 160, and 240 μm) and three coil windings (4, 8, and 11).

FIG. 2.

Numerical simulation setup of μMS coil with target dimension. (a) 11 windings were fitted within an 80 × 80 μm² rectangular geometry. (b) Side-view of the μMS coil and a block of the rat brain.

III. FABRICATION

The planar 2D coil array manufacturing was performed at the Center for Nanoscale Systems (CNS) at Harvard University. Figure 3 illustrates the cross-sectional layer design and materials used in the coil fabrication.

FIG. 3.

Design, dimensions of the μMS construction. The microcoils were built using nine different layers, traces, pads (Au in yellow, Cr in gray), substrates (SU-8 in violet, LOR in green), and dielectric (SPR 700 in orange) layers as shown.

The photolithography process was performed as follows. First, the lift-off photoresist (LOR) layer was applied to detach the planar coil from the silicon wafer. Next, SU-8 was deposited as a highly biocompatible²⁶ photoresist polymer with enough flexibility for being used as a neural implant,²⁷ and with high tensile strength (70 MPa) advantageous in many implantable devices.^28–30 The first metal layer (Fig. 3, layer 1) connected the center of the coil to the pad, and the second metal layer on the top (Fig. 3, layer 2), which was prepared to use as the seed/stencil approach for the thick plating process later to form 2D spiral coils with the target trace height. The two metal layers were insulated with a layer of photoresist SPR 700. A gold bath process was used in the electroplating in order to meet the ≤5 Ω resistance requirement. The Au plating experiment (TECHNIC Elevate Gold 7990 NBV, USA) was done separately to test the pulling condition and fabrication feasibility. A 100 nm thick Au layer was prepared as a seed layer using a silicon wafer. Photoresist sidewalls were prepared on top of the seed layer with 2.3 μm thickness as resist trenches to avoid shortage between windings of the trace. Au plating was processed with a current of 1 mA for 28 min to target 2.25 μm trace thickness.

IV. RESULTS AND DISCUSSION

A. Coil properties estimation

Table I shows the coil properties calculated from the equations in Sec. II A.

B. Numerical simulation

The results of the magnetic vector field were shown in Fig. 4, where the magnetic vector field is rotating perpendicular to the trace that is maximum at the center of the spiral coil geometry and decreases nonlinearly with the distance from the coil. The maximum absolute magnetic field was 4.94 × 10⁶ A/m at the center of the coil and 3.78 × 10⁶ A/m at the brain block. Thus, the time-varying magnetic field induces a current and an electric field perpendicular to the magnetic field.⁴

FIG. 4.

EM simulation results of the magnetic vector field at the central slice of the figure-of-8 coil. The numerical simulation result shows the magnetic field vector circulation around the traces at the central slice of the figure-of-8 coil.

The resulting E-field vectors from the single planar spiral coil and figure-of-8 coil were shown in Fig. 5. The single planar spiral coil geometry was estimated to generate a maximum E-field vector along the edge of the coil circulating along with the spiral trace geometry [Fig. 5(a)]. The maximum E-field vectors are generated along the center of adjacent traces between two planar spiral coils, as shown in Fig. 5(b) (white arrow), with an absolute magnitude E-field of 1.41-fold higher at the center of the figure-of-8 coil (i.e., 2.34 V/m) compared to the peak generated at the side of the coil (i.e., 1.66 V/m).

FIG. 5.

EM simulation results of single spiral and figure-of-8 coil. Electric vector field estimated from (a) a single spiral coil interacting with the brain block underlying the coil and (b) the figure-of-8 coil showing the maximum E-field vector strength between the two planar spiral coils.

Figure 6 shows the electric vector field on the surface of the brain block with three coils with different dimensions. The E-field focality is shown in the case of a larger dimension coil [Fig. 6(a)] compared to the case of a smaller coil [Fig. 6(c)] in the case of using the same 10 A input current. VOA was estimated 7.09 ×10⁻¹⁴ m³ for the size of 240 × 240 μm², 3.99 ×10⁻¹⁴ m³ for the size of 160 × 160 μm², and 3.25 ×10⁻¹⁵ m³ for 80 × 80 μm².

FIG. 6.

EM simulation results in three different coil dimensions. Electric vector fields estimation using three different figure-of-8 coil dimensions of (a) 240 × 240 , (b) 160 × 160, (c) 80 × 80 μm² in the surface view on the brain block, and cross-sectional view of the absolute E-field at the center of the coil with the dimension of (d) 240 × 240, (e) 160 × 160, and (f) 80 × 80 μm².

Figure 7 shows the estimated E-field penetration depth on the brain block with three different numbers of windings (i.e., 4, 8, and 11 windings) within 80 μm dimension. The higher number of windings in the spiral figure-of-8 coil produced higher E-field penetration on the underlying brain block. The trace resistance for the different number of windings was 1.82 Ω for the 4 winding, 3.65 Ω for the 8 windings, and 5 Ω for the 11 windings. Absolute E-field max was estimated at 0.96 V/m for 4 winding, 1.68 V/m for 8 windings, and 2.34 V/m for 11 winding in the brain block.

FIG. 7.

EM simulation results. Estimated absolute E-field penetration at the coil center across a different number of windings in 10 A input current (a) 4 windings, (b) 8 windings, (c) 11 windings with a trace width of 2.6 μm within the same dimension.

The field penetration depth at the center of the figure-of-8 coil is shown in Fig. 8. The magnitude of the E-field nonlinearly decreased with the distance from the coil.

FIG. 8.

EM simulation results. (a) The magnitude of the E-field as it penetrates the brain block and (b) absolute magnitude E-field plot over the distance from the coil.

C. Coil fabrication

The top layer (i.e., layer 2) was developed as a seed layer for electroplating. Figure 9 shows the optical and scanning electron microscope (SEM) images (Hitachi SU-8230, Japan) of the fabricated planar spiral μMS coils on a SU-8 substrate. The result with an optical microscope was shown in Fig. 9(a) before the wet-etching process of the top layer. Figure 9(b) shows the SEM images of the etched μMS coils with a zoomed-in view in Fig. 9(c).

FIG. 9.

Manufacturing results of the figure-of-8 coil at CNS. (a) Optical microscope images in the left show a 500 nm layer of SPR-700 on top before etching. (b) Top view of the 13 turns Au/Cr traces of the proposed planar figure-of-8 coil using scanning electron microscopy (SEM), (c) zoomed-in view of the coil on top of a SU-8 substrate SEM images of the 200 μm figure-of-8 coil.

Au plating was done separately with the target trace dimension (Table I). SEM images were done before and after the photoresist removal to see the growth of the trace with Au plating [Figs. 10(a)–10(c)]. In addition, noncontact optical profiler imaging (Taylor Hobson CCI HD, United Kingdom) was done to check the overall continuity and quality of the trace after Au plating [Fig. 10(d)].

FIG. 10.

Au plating results of the figure-of-8 coil. (a) and (c) Au traces with 11 turns of the proposed planar figure-of-8 coil was scanned from the top using SEM before and after the resist removal [dashed line in (a) indicates the location of the cross-sectional view], (b) cross-sectional view of the 11 turns Au traces of the proposed planar figure-of-8 coil using SEM showing the photoresist (PR) prepared for sidewalls, (d) perspective view of the figure-of-8 coil using a noncontact optical profiler.

D. Discussion

μMS has several advantages over electrical stimulation. First, μMS does not require charge-balanced stimulation waveforms as in electrical stimulation. In μMS, neither sinks nor sources are present when the time-varying magnetic field induces a current. Thus, μMS does not suffer from charge buildup as can occur with electrical stimulation.²⁴ Second, magnetic stimulation via μMS is capable of activating neurons with specific axonal orientations.⁴ Third, it is contactless, so biocompatible materials such as parylene will allow implantation with minimal or no reaction. Moreover, as the probes can be insulated entirely from the brain tissue, we significantly reduce the problem of excessive power deposition into the tissue during magnetic resonance imaging (MRI).⁸

Numerical simulations provide a crucial insight into the mechanisms of micromagnetic stimulation and should be used both during the design process and to interpret the neural responses. For example, the long solenoid coil design optimizes the Q-factor but renders the bulk of the magnetic energy inaccessible. An alternative uses spiral and figure-of-8 coils that maximize neuronal tissue access to the magnetic flux produced by μMS coil to optimize neural stimulation by focal and directional maximum E-field vector generation.

The effects of coil dimensions and the number of windings were compared using numerical simulation. As the size of the figure-of-8 coil decreases, a smaller and more focal E-field was observed in the brain block. The increase in the number of windings in the spiral geometry resulted in an increase in the induced E-field in the brain block. Although the increase in the number of windings results in an increase in the trace length and thickness, thicker traces were required to achieve a coil resistance ≤5 Ω. As previously shown,¹¹ a low Q-factor is preferable to maximize the flux in the tissue as in the planar coil geometry, and the μMS coil that we designed had a Q-factor less than 0.0002. Finally, the smaller coil design has the benefits of minimally damage the brain during implantation.

As previously reported by Golestanirad et al.,⁴ the alignment of the time-varying magnetic field generated by microscopic solenoids orthogonal to the axonal direction could elicit neural activities. Similarly, the proposed figure-of-8 design has the potential to target the orthogonally aligned axons in the brain. Furthermore, 2 × 2 arrays could enable the selective excitation of orthogonally aligned neurons.

The entire implant could be encapsulated in Parylene coating to prevent leakage. Parylene C is the best polymer for moisture resistance and is very flexible, and only Parylene C will contact the tissue.

Limitations. The proposed device was not tested preclinically in animal models to confirm the neuromodulation properties of this novel medical device. In the future, we expect to test the device implanted rodent's brain in the proximity of white-matter tracts to validate the expected directionality sensitivity of the micromagnetic fiber stimulation with the new figure-of-8 coil design.

V. SUMMARY AND CONCLUSIONS

White-matter fiber bundles in the brain may be selectively stimulated using a new type of neuronal stimulation: microscopic magnetic stimulation (μMS). One of the most remarkable properties of this novel type of stimulation is that the orientation of the applied μMS fields provides unique activation of neuronal elements not seen with traditional electrical stimulation. Developed initially to stimulate single neurons, μMS uses ultraconductive microtraces capable of carrying current pulses large enough to elicit neural activation through EM induction.

An initial prototype of the stencil was built using photolithography based on SU-8 technology, suggesting that the structure is manufacturable, and the numerical simulations indicated that the device is capable of directional and focal stimulation.

APPENDIX: EQUATION PARAMETERS USED IN COIL CHARACTERIZATION

Table II shows the equation parameter used in Sec. II A.

TABLE II.

Parameters used to calculate the resistance, inductance, capacitance, quality factor (Q-factor), and trace area required to avoid fusing current (A_min) are shown.

Parameters	Value
ρ	1.7 × 10−6 Ω cm (copper)
A	5.85 μm2
K 1	2.34
K 2	2.75
μ 0	4π × 10−7 H/m
d in	1 μm
d out	80 μm
H	2.25 μm
ɛ0	8.85 × 10−12 F/m
ɛr	2.42 (Parylene C)
L	1.72 mm
D	1.09 μm
r 0	1.23 μm
F	10 kHz
Rt	5 Ω
T	20 μs
ps	0.16 s−0.5 A−1 m−2
I peak	10 A

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.