Enhanced magnetic transduction of neuronal activity by nanofabricated inductors quantified via finite element analysis

Devices were fabricated by electron beam lithography on glass or high resistivity silicon dies. A2/A4/A6 poly methyl-methacrylate (PMMA) 495 (Kayaku Advanced Materials Inc. MA, USA) was spin-coated on samples at 3000 RPM for 30 s and baked in a convection oven for 30 min. Direct write of inductor patterns was then performed by electron beam lithography (Elionix, Tokyo, Japan) followed by development of the resist using methyl isobutyl ketone/isopropyl alcohol (MIBK/IPA) (1:2). Ti/Au (1:10) was deposited by electron beam deposition followed by PMMA lift off in ultrasonicated acetone (5 min) at room temperature. Silicon oxide insulating layer was deposited by plasma-enhanced chemical vapor deposition. An additional nanolithography step was performed to define the ground pad and protruding pillars at the interface pad, followed by buffered oxide etching through the silicon oxide layer. Au protrusions were grown by electron beam deposition PMMA was lift off. Samples were then cleaned in IPA and cultured with neurons as described below to demonstrate biocompatibility (figure 1(b)). The device optimization described below uses a device geometry successfully fabricated in this way as a starting point.

Zoom In Zoom Out Reset image size

Primary cortical neurons were cultured on substrates following previously described protocols [35]. Glass or device surface was sterilized for 15 min in ethanol, then a portion of each sample was prepared with a 50 µl droplet of sterile filtered aqueous 0.1 mg ml⁻¹ poly-d-lysine (Gibco A38904-01) and 4 µg ml⁻¹ laminin (Gibco 23017-015). Coverslips sat for 60 min in incubator conditions (37 °C, 5% CO₂, 95% humidity), were rinsed three times with 1x phosphate buffered saline (PBS), then stored at 4 °C overnight. Primary cortical rat neurons (Gibco A10840-01, Lot 2111507) were thawed from dry ice (−80 °C) for 2 min without agitation in a 37 °C water bath. A 15 ml conical tube and 1 ml micropipette tip were rinsed with plating media (Neurobasal Plus, Gibco A3582901; 10% FBS Gibco 10437010; 1× GlutaMAX, Gibco 35050-061), the tip was used to transfer the cell suspension from the cryotube to the conical tube, 1 ml of plating media was added dropwise for a final concentration of 500 000 cells ml⁻¹, and 300 µl of cell suspension (150 000 cells) were plated onto each sample. The cultures sat in incubator conditions for 4 h before plating media was removed and 3 ml maintenance media (Neurobasal Plus, 1× B27 Plus Gibco A3582801, 1× GlutaMAX) were added to each 35 mm well. 1.5 ml media changes were performed every 3–4 days (Mondays and Fridays). Cells on devices were stained with 10 μg ml⁻¹ calcein AM (Invitrogen C3099) in media for 20 min at 37 °C followed by a 20 min rest in stain-free media at 37 °C before imaging for visualization (figure 1(b)).

At 24 days in vitro (DIV) samples on glass coverslips were removed from maintenance media and placed in extracellular solution (ECS; in mM, NaCl 145, KCl 5, MgCl₂ 1, CaCl₂ 1, HEPES 5, Glucose 5, Sucrose 20, D-serine 0.01, adjusted to pH 7.4 with NaOH and 315 mOsm with sucrose). All solutions were prepared with culture grade H₂O (Corning 25-055-CVC). Filamented glass pipettes (8250 Glass, A-M Systems 596800 were pulled on a P-97 pipette puller (Sutter Instruments, Novato, CA) to create 5–10 MΩ micropipettes. Pipettes were backfilled with intracellular solution (ICS; in mM, KCl 120, HEPES 10, ATP.Na 5, GTP.Na 0.2, EGTA 10, adjusted to pH 7.2 with KOH), mounted on a Sutter IPA Headstage with a Ag/AgCl coated wire driven by a Sutter Quad micromanipulator and connected to a Sutter Double IPA patch clamp amplifier for recording via SutterPatch (v. 2.04, Sutter Instruments, Novato, CA) within Igor Pro software (v. 8.04, WaveMetrics, Portland, OR) in current clamp configuration. For staining experiments, ICS included 20 µM of biocytin (Sigma B4261). Upon breaking through the plasma membrane, biocytin diffused into the cell, allowing imaging of the neuron processes for morphological registration used for simulations (figure 1(a)). Electrophysiology experiments were performed using Olympus BX51WIF microscope (Olympus America Inc., Waltham, MA) and ORCA-Flash4.0 V3 C13440 Digital sCMOS camera (Hamamatsu, Japan) for optical acquisition during biocytin injection.

Biocytin-injected neuron morphology (figure 1(a)) was traced to create a vector representation, which was imported into COMSOL multiphysics simulation environment (COMSOL Inc., Stockholm, Sweden). Geometry was extruded to a height of 1.1 µm (figure 1(c)). The membrane was modeled with exterior surface area 1450 μm², volume 14.39 μm³, relative permeability = 1, relative permittivity μ = 1, electrical conductivity σ = 1 × 10⁻¹³ S m⁻¹, surrounding the intracellular environment, surface area 1431.1 μm², volume 463.77 μm³, which was modeled using the electrical properties of cerebrospinal fluid, = 1.09 × 10², μ = 1, σ = 2 S m⁻¹. Representative action potential (AP) data was extracted from voltage traces of current clamp recordings (figure 3(a), sampling frequency = 6103.5 Hz, total recording time 23:51.768) and used as input for an electronic circuit simulation software (LTSPICE, Analog Devices, Norwood, MA). The cell-device interface was simulated as a 100 MΩ resistor in parallel with a 15 pF capacitor. The current was measured across this interface and downsampled to 20 key values, which were applied as inputs in COMSOL on one face of the neuron in a parametric sweep stationary study for simulations of magnetic flux density and field strength during APs to compare the response of the naïve model neuron to that of the modeled cell-device interface (figure 3(c)).

Simulations and optimizations of device response and device-neuron interface were performed in COMSOL. Patterns used for nanofabrication were imported and extruded along the z-axis. The electrical properties of the device were set to those of gold, = 1, μ = 1, σ = 1 × 10⁶ S m⁻¹. This gold layer thickness was tested at 100, 500, 1000, and 1500 nm. Lateral width of the inductor conducting turns was tested at 540, 730, 940, and 1020 nm using a constant center-to-center turn distance of 1478 nm. Given a constant outer diameter (75 µm edge-to-edge, 80 µm corner-to-corner), turn width (1.0 µm edge-to-edge, 1.1 µm corner-to-corner), and turn spacing (0.46 µm edge-to-edge, 0.50 µm corner-to-corner), the number of turns was varied and represented as the percentage of the total diameter left open at its core. The open core percentage was tested at 10.9% (23 turns), 22.6% (20 turns), 34.4% (17 turns), 46.2% (14 turns), 57.9% (11 turns), and 65.8% (9 turns). All device geometries were tested using representative current input of 1 nA through the interface pad at the center of the inductor. The optimized device geometry was used to model the magnetic response when coupled with the model neuron. The effects of various substrates were tested using the same input current by varying the material properties of a 25 × 50 × 100 µm block beneath the device between glass, = 4.7, μ = 1, σ = 2.3 × 10⁻²¹ S m⁻¹; polyimide, = 3.8 [36], μ = 1, σ = 6.7 × 10⁻¹⁸ S m⁻¹; parylene, = 3.1 [36], μ = 1, σ = 1.136 × 10⁻¹⁵ S m⁻¹; and silicon of various conductivities, = 11.68, μ = 1, σ = (0.01, 0.1, 1, 10, 100, 1000, 10 000, 100 000) S m⁻¹ (0.001 Ω cm to 10 000 Ω cm). Magnetic field values were extracted from the model either linearly across a 120 µm × 1 µm × 1 µm region of interest (ROI) centered at various Y coordinates on the Z = 0 plane, or volumetrically within a 40 µm × 40 µm × 10 µm ROI centered at the cell-device interface pad, in the X, Y, and Z axes. For linear scans, the mean and standard deviation of the absolute magnetic field magnitude were taken along the Y/Z axes within the ROI. Separately, absolute magnetic field amplitude was taken along a 20 µm, Y-aligned line on the Z = 0 plane, centered on the neurite 2 µm away from the input port (supplementary figure 1) to compare the magnetic field amplitude of the neuron with and without the presence of the device. Volumetric values averaged the Z component of the magnetic field across the ROI. For optimizations of device geometry and substrate testing, the Z component of the magnetic field output was extracted at an XZ slice of the model arena at the Y coordinate corresponding to the center of the coil and used to compare the output of each model instance.

In order to explore the feasibility of enhancing intrinsic NMFs by nanofabricated coils (nanocoils) interfaced with single neurons, we generated a realistic finite element model of a cell coupled to device and quantified the magnetic field response to current injected into the cell (figure 1). The model uses morphology extracted from primary cortical neurons injected with fluorescently labeled biocytin via patch micropipette electrodes (figure 1(A) and supplementary figure 2). Neurons grew on glass coverslips or nanofabricated devices for up to 24 DIV (figure 1(B)). We input a series of key current values into the model, extracted and calculated from a patch clamp recording of cells on coverslips (figure 3(c)), with a peak of 1.7 nA intracellular current in the model cell (figure 1(C)), resulting in intracellular electric fields of up to 1.2 mV µm⁻¹ and extracellular electric fields up to 30 µV mm⁻¹ within 2 µm of the neurite membrane (supplementary figure 2(C)), and the transmembrane electric field gradient reaching 11 mV nm⁻¹ as previously seen both in vitro and in vivo [37]. The absolute amplitude of the magnetic field observed near the neuron in response to current injection reached values of up to 0.51 nT and decays to <1% of peak signal within an average of 30 µm of the neuron, similarly to previous models of single-cell NMFs [11, 12]. We next quantified the magnetic field amplitude at a volume surrounding the same 1.7 nA current-injected neuron coupled to a nanocoil (figure 1(D)). The neuronal membrane was coupled to the interface pad in the middle of the nanocoil (figure 1(D), a). The magnetic field amplitude at various line scans across the X axis (figure 1(D), (a–e)) reached values of up to 1.6 nT and decayed to <1% of peak within an average of 19 µm from the outer turns of the nanocoil. In the case of line a (figure 1(D)), which crosses the interface pad, the magnetic field decayed to <1% of peak an average of 46 µm from the interface pad. We quantified the spatial distribution of NMFs in the naïve neuron not coupled to the device within a 1 µm by 1 µm cross sectional area around various line scans across the X axis and found that across three representative somatic and neurite compartments (figures 1(c), (a–c) and (E)) the full widths at half maximum (FWHM) of magnetic field magnitude were (a) 2.7 µm, (b, soma) 7.9 µm, and (c) 7.1 µm. In contrast, the spatial distribution of magnetic fields near a neuron coupled to a device across five representative regions (figures 1(D), (a–e) and (F)) was spatially enhanced with FWHM of (a) 67 µm, (b) 72 µm, (c) 62 µm, (d) 46 µm, and (e, ground pad) 16 µm. The magnetic field amplitude of the neuron itself was not significantly changed when coupled to the device, reaching levels of up to 0.60 nT in the neurite of the naïve neuron and 0.25 nT in the neurite of the neuron enhanced by the device, measured 2 µm from the neurite input port (supplementary figure 1), within the bounds of minimal magnetic interference. In summary, the magnetic field amplitude output by the device driven by cellular potentials is more than three times greater at its peak (1.6 nT vs 0.51 nT) across a ten times wider lateral distance (72 µm from the device vs 7.1 µm from the neurite) than the intrinsic NMF. Looking at a 40 × 40 × 10 µm voxel, discussed below, this results in a 250-fold spatial enhancement (640 pT vs 2.5 pT, see figure 3).

Based on the initial geometry used to quantify the magnetic response of a neuron-device interface, we performed optimizations of design features to explore maximal transduction while obeying nanofabrication limitations (figure 2). Three main parameters tested included the vertical thickness of the device metallization layer (figures 2(A)–(C)), the lateral width of the nanocoil turns (figures 2(D)–(F)), and the number of turns as represented by the open core percentage (figures 2(G)–(I)). For each parameter value, we compared the mean z-axis component of the magnetic flux density (B_z ) within a ROI across a XZ slice over the center of the device, spanning 50 µm along the x axis, and 12.5 µm along the z axis. The bottom of the slice was aligned to z = 0, coplanar with the bottom plane of the device (figures 2(A), (B), (D), (E), (G) and (H), bottom panel).

Zoom In Zoom Out Reset image size

We used the initial geometry (turn width of 334 nm, core 57.9%) and varied the vertical gold layer thickness by extruding the device to values of 100, 500, 1000, and 1500 nm (figures 2(A)–(C)), yielding average field strength B_z = 0.030 ± 0.013 nT, 0.086 ± 0.033 nT, 0.12 ± 0.04 nT, and 0.13 ± 0.05 nT, respectively. Proceeding with a 500 nm thick gold layer, we next quantified the effect of nanocoil turn width on the average magnetic field strength B_z at the device surface (figures 2(D)–(F)). Turn width was set to 540, 730, 940, and 1020 nm, yielding average field strength B_z = 0.11 ± 0.04, 0.13 ± 0.04, 0.14 ± 0.04 and 0.14 ± 0.05 nT, respectively (figure 2(F)). Predictably, the widest path induced the strongest magnetic field strength. We turned to testing the effect of the total number of turns, while maintaining a constant outer diameter (80 µm), neural interface pad diameter (when allowed by the core size, 14 µm), coil thickness (500 nm), turn width (1020 nm), and turn spacing (1478 nm) (figures 2(G)–(I)). We represent this as the ratio of the inner to the outer diameter, or the percentage of the outer diameter that makes up the open core of the nanocoil. We tested values 10.9% (23 turns), 22.6% (20 turns), 34.4% (17 turns), 46.2% (14 turns), 57.9% (11 turns), and 65.8% (9 turns), which yielded mean B_z = 0.27 ± 0.16, 0.25 ± 0.12, 0.22 ± 0.08, 0.18 ± 0.06, 0.14 ± 0.04 and 0.11 ± 0.03 nT, respectively (figure 2(I)). Predictably, smaller cores produced higher peak magnetic field strength perpendicular to the plane of the coil (peak B_z = 1.1, 0.85, 0.79, 0.73, 0.67 and 0.52) while the minimum field strength observed at the periphery of the ROI remained stable across different conditions (min B_z = 0.057, 0.058, 0.061, 0.064, 0.060, and 0.061 nT).

We analyzed the magnetic field developing at the neuron-device interface during a typical AP selected from a series of spontaneously occurring spikes recorded via patch clamp (figure 3(a)). Modeled magnetic field was averaged across a 40 × 40×10 µm voxel extending 20 µm to each side of the center of the coil, and 5 µm above and below the coil (figure 3(B)). The same voxel dimensions were used to average the modeled magnetic output of the naïve neuron. Absolute AP amplitude was 72 mV, and the after-hyperpolarization voltage was −8.2 mV (figure 3(c)). The AP voltage trace was run through the equivalent circuit of a neuron to derive the current trace (figure 3(c), purple). The current peaked at 1.7 nA during depolarization and had a minimum of −0.80 nA during the after-hyperpolarization stage. The magnetic field perpendicular to the plane of the neuron and nanocoil peaked at 2.5 pT for the naïve neuron, and at 640 pT for the neuron enhanced by the device. The magnetic field perpendicular to the plane of the geometry induced by the downswing current was −1.2 pT for the naïve neuron and −300 pT for the enhanced neuron. The overall spatial enhancement of the transduced magnetic field output within a voxel was 250-fold higher than the intrinsic NMF.

Zoom In Zoom Out Reset image size

To evaluate performance on substrates compatible with nanolithography that are commonly used for implantable devices, we quantified the magnetic transduction of nanocoils embedded on dielectric substrates including glass, parylene and polyimide, and on silicon with various levels of doping (figure 4). High resistivity silicon (1000 Ω cm and 10 000 Ω cm) and all dielectric substrates displayed strong induced magnetic fields (figure 4(A)) with average magnetic field strength of 0.23 ± 0.08 nT for dielectrics, 0.22 ± 0.07 nT for 10 000 Ω cm Si, and 0.22 ± 0.07 nT for 1000 Ω cm Si. Low resistivity silicon (0.001, 0.01, and 0.1 Ω cm) demonstrated predictable current shunting, and weak induced magnetic fields, with average field strength of 4.8 × 10⁻⁶ ± 3.8 × 10⁻⁴nT, 8.5 × 10⁻⁵ ± 2.1 × 10⁻⁴ nT, and 9.7 × 10⁻⁴ ± 7.1 × 10⁻⁴ nT, respectively). Silicon substrates with resistivities of 1, 10, and 100 showed an intermediate effect, with average field strength of 0.0080 ± 0.0048, 0.052 ± 0.022, and 0.16 ± 0.06 nT, respectively). Current density was largely in proportion to field strength, reaching maximal levels of 880 A m⁻², 2400 A m⁻², 2800 A m⁻², and 2800 A m⁻² for 1, 100, 1000 Ω cm Silicon and for Polyimide, respectively (figures 4(B)–(E)).

Zoom In Zoom Out Reset image size