( A ) Plots of the electric fields (middle) and the field gradients (right) arising from the microcoil (left) in the x direction (dEx/dx) along the x axis for three different vertical cross sections through the coil. The red dashed lines in the gradient plot indicate estimated threshold levels from earlier studies with transcranial magnetic stimulation coils (see text). ( B ) Plots of the electric fields (middle) and the spatial gradients (bottom) in the x direction (dEx/dx) along the y axis for three horizontal cross sections. ( C ) Extracted portion of the field gradient profiles for different amplitudes along the x axis for values of x ≥ 0. ( D ) Similar to (C), but for the field gradients along the y axis for values of y ≤ 0. ( E ) Contour plots of suprathreshold gradient areas for different current amplitudes.

Although the spatially narrow regions of activation estimated in Fig. 1 are highly attractive for applications in which focal activation is required, it is well established that prolonged implantation into the cortex induces a foreign body response that can lead to the formation of a high-impedance glial sheath around the implant with a resultant increase in distance to targeted neurons ( 11 , 12 ). Migration of neurons away from the implant can also occur as part of the foreign body response ( 22 ), and migration distances of ~75 μm were reported even for implants that did not deliver stimulation. The increased distance to viable neurons raises the possibility that the spatially narrow fields and gradients arising from low-amplitude stimuli may not extend far enough for the coil to remain effective following prolonged implantation. We therefore examined how the spatial extent of the induced fields and gradients was altered by changes to the amplitude of stimulation. We started by more closely examining the profiles of fields and gradients for the same 1-mA stimulus used in Fig. 1 . One-dimensional plots of fields and vertical gradients (dEx/dx) were generated for multiple sections through the coil in both the vertical and horizontal directions ( Fig. 2 , A and B, respectively; the red dashed line in each plot of gradients represents the previously reported threshold level of 11,000 V/m 2 ). The portions of the trace in which the gradient exceeds the threshold provide an estimate of the approximate extent over which activation would occur. Because activation will be limited to only those regions that are external to the coil perimeter, we restricted our focus to the region to the left of the blue dotted line in Fig. 2A and outside the two blue dotted vertical lines in Fig. 2B . With this approach, the extracted portion of dEx/dx along the x axis is plotted in Fig. 2C (black) for a 1-mA stimulus, whereas the relevant portion of dEx/dx along the y axis is plotted in Fig. 2D (black). We performed a similar analysis for larger stimulus amplitudes (10, 25, 50, and 100 mA) and overlaid the corresponding traces (red, blue, green, and pink, respectively). Comparison of the individual plots reveals not only that the suprathreshold region increases with amplitude but also that it is asymmetric in the x and y directions; for example, for an amplitude of 100 mA, the suprathreshold region extends ~151 μm along the x axis and 414 μm along the y axis. To better visualize the full extent of this region, we developed a two-dimensional contour plot for all amplitudes ( Fig. 2E ). The plots confirm the sensitivity of this region to changes in amplitude as well as the relatively wide spatial extent over which the field gradient is suprathreshold for higher stimulus amplitudes. Note that even the largest stimulus amplitude used in Fig. 2 is well below the levels used in the original in vitro ( 13 ) and in vivo studies ( 23 ). Thus, the model results suggest that implanted microcoils will be able to effectively activate neurons over a spatially extensive region, for example, beyond the extent over which gliosis and cellular migration occur. Because magnetic fields pass readily through even high-impedance materials, the ability of implanted coils to reach these more distant regions may not be adversely affected, even by severe gliosis, the way that they can with electrodes.

The coil shown in Fig. 1A is still considerably larger than existing cortical implants, so we explored whether even smaller designs could also generate suprathreshold fields and gradients. Consistent with electromagnetic theory, the peaks in dEx/dx were localized to the corners of the coil, that is, the regions containing sharp bends in the flow of current, and therefore we considered the possibility that even a single sharp bend of a wire might generate fields and gradients strong enough for activation. Accordingly, we considered the design of Fig. 1B (left, red thick trace). The 100-μm width of this coil would fit within a single cortical column and would be comparable in size to existing electrode implants, suggesting that it could be implanted safely into the cortex. The peak strength of the field gradient calculated for this coil was 49 kV/m 2 ( Fig. 1B , middle and right panels), almost identical to that of the larger single loop; the spatial extent over which the gradient exceeded the threshold for the 1-mA stimulus was again narrowly confined, extending only ~60 μm.

( A ) Surface (middle) plot of the electric field gradients in the x direction (dEx/dx) arising from the 500-μm square coil on the left (red). Note that the horizontally oriented peaks in the surface plot indicate the peak gradients in a direction normal to the cortical surface, that is, up and down in the cortical column representation on the left. Right: Two-dimensional profile of the gradients in the vertical (dEx/dx, top) and horizontal (dEz/dz, bottom) directions; the “0” on the abscissa corresponds to the bottom right corner of the coil. The horizontal lines indicate estimated threshold levels from earlier studies with much larger coils (see text). Dashed vertical lines indicate the width of the suprathreshold region. ( B ) Similar to (A), except for a 100-μm trapezoidal coil.

To better understand whether coils that are small enough to be implanted can activate cortical neurons, we modeled the fields arising from a single loop of the inductor used in previous microcoil studies ( 13 , 14 , 19 ). The dimensions of the loop were 500 μm × 500 μm, and the wire thickness was 10 μm ( Fig. 1A , left). After deriving the magnetic and electric fields that arose from the single loop (Materials and Methods), we calculated the gradient of the electric field along three orthogonal dimensions; the strength of the gradient along the length of a neuron or axon is known to underlie activation ( 5 , 20 ), so surface plots that displayed the field gradient across the region surrounding the coil ( Fig. 1A , middle) could be used to quickly assess potential effectiveness. We were especially interested in the component of the gradient oriented normal to the cortical surface (dEx/dx using the axes of Fig. 1 ), because this represents the driving force for activation of vertically oriented PNs. Whereas the peak amplitude of the stimulus current through the coil in previous studies could exceed 1 A, here we found that an amplitude of 1 mA produced a peak field gradient of ~50,000 V/m 2 ( Fig. 1A , right), a value well above the 11,000-V/m 2 threshold previously reported for stimulation of peripheral axons with a transcranial magnetic stimulation coil ( 21 ). This therefore suggests that even a single loop of appropriately aligned coil could be effective for activating PNs. The spatial extent over which the peak field exceeded the threshold extended for only ~75 μm from the coil ( Fig. 1A , top right) and therefore suggests that activation could be confined to only a few nearby cells. For the orientation of the coil in Fig. 1A , the component of the gradient that was parallel to the passing axons of layers 1 and 4 (dEz/dz) was 0 V/m 2 ( Fig. 1A , bottom right), suggesting that those axons or similarly oriented processes would not be activated.

Fabrication of microcoil probes and in vitro experiments

To verify that the new microcoils could activate cortical neurons, we microfabricated the coil design of Fig. 1B for use in physiological experiments (Materials and Methods; Fig. 3A). The coil consisted of a copper trace (10 μm wide × 2 μm thick) on a silicon substrate that had a cross-sectional area of 50 μm × 100 μm and a length of 2000 μm. The coil assembly had a dc resistance of ~15 ohms and was insulated with 300 nm of SiO 2 (Materials and Methods) to prevent the leakage of electric current into the tissue. A second, similarly sized microcoil was also constructed by carefully bending a 50-μm-diameter copper wire (Fig. 3B). Although this second coil did not have as sharp a bend as the microfabricated coil, the thicker cross-sectional area of the wire allowed stronger currents. Five-micrometer polyurethane/polyamide insulation prevented the leakage of electrical current from this second coil into the bath or tissue. Its resistance was ~13 ohms.

Fig. 3 Microcoils activate cortical PNs in vitro. (A) Schematic of the microfabricated coil consisting of a copper trace (red) on a silicon substrate (yellow). (B) Illustration of the bent-wire microcoil. The 50-μm copper wire (red) is surrounded by 5-μm polyurethane/polyamide insulation. (C) Responses to subthreshold (left) and suprathreshold stimulation (right) in the presence of synaptic blockers (top traces) and with TTX added (bottom traces). The blue curves were computed by subtracting the TTX traces from the corresponding traces in the top panels. The asterisk indicates the evoked action potential. (D) Action potentials (APs) could also be extracted without the use of TTX by subtracting a response without a presumed spike (artifact only) from a response with a spike; the black trace is such a spike [different cell from (C)]. A spontaneous spike from the same cell is overlaid (green). (E) Schematic of the in vitro experimental setup. A cell-attached patch electrode was used to record from the soma of an L5 PN in response to stimulation from the microcoil; the long axis of the coil could be positioned either normal to (top) or parallel to the slice surface (bottom). In all cases, the tip of the coil was positioned over the proximal axon. The red dashed and solid horizontal arrows represent weak and strong (respectively) electric fields induced along the length of the axon. AIS, axon initial segment. (F) Typical responses for each orientation. Stimulation was delivered at a rate of 100 Hz; the stimulus artifact indicates the timing of each pulse. The prominent after-hyperpolarizations seen following each pulse in the bottom traces are reliable indicators of elicited spikes. (G) Probability of eliciting an action potential as a function of stimulation current amplitude for control artificial cerebrospinal fluid (aCSF) (left, n = 7 cells) and with synaptic blockers added (right, n = 4 cells). (H) Onset latencies of evoked spikes were plotted for 10 consecutive pulses delivered at 100 Hz in 11 individual neurons. All spikes were elicited within 0.3 to 0.7 ms after onset of the stimulus. (I) Same as (H), but with synaptic blockers added to the perfusion bath (n = 4 cells). (J) Schematic of the experimental setup showing the coil positioned over the apical dendrites in either a perpendicular (top) or a parallel orientation (bottom). (K) Typical responses to apical dendrite stimulation for each orientation. The red horizontal bar indicates the duration over which stimulation was applied.

Fabricated microcoils were first tested for their ability to activate cortical neurons during in vitro experiments using coronal brain slices from mice (Materials and Methods; Fig. 3, C to K). A loose-seal cell-attached patch-clamp electrode was positioned on the soma of a targeted layer 5 (L5) PN within the whisker (motor) cortex and used to record action potentials elicited by magnetic stimulation from the microcoil (Materials and Methods). Patch-clamp recordings have proven effective for allowing visualization of elicited action potentials in previous studies with electric stimulation because the amplifiers are not saturated by the stimulus; for example, the electrical artifact associated with the stimulus does not preclude observation of neuronal responses (24, 25). The coil was positioned close to the targeted cell with the tip centered over the proximal axon, the portion of the cell that was thought to have the highest sensitivity to stimulation (26, 27). To ensure that observed responses arose from direct activation of the cell itself, that is, not secondary to activation of one or more presynaptic neurons, we added 10 μM 2,3-dihydroxy-6-nitro-7-sulfamoyl-benzo[f]quinoxaline (NBQX), 10 μM bicuculline, and 50 μM d-2-amino-5-phosphonopentanoic acid (d-APV) to the perfusion bath in some experiments to block synaptic input to the cell. Stimulation at relatively low amplitude levels produced an electrical artifact that consisted of a short-duration biphasic waveform that persisted for ~0.4 ms (Fig. 3C, top left). Increasing the amplitude of stimulation slightly produced a similar artifact but now continued into a more prolonged waveform (Fig. 3C, top right). The addition of 1 μM tetrodotoxin (TTX) to the bath eliminated the prolonged part of the response (Fig. 3C, bottom right, red trace), suggesting that it was an action potential, and subtraction of the response in TTX from the corresponding control response revealed a waveform (blue trace) that was highly similar to those action potentials that arose spontaneously. Elicited action potentials could also be extracted from the raw recordings (without the use of TTX) by subtracting responses that contained the artifact only from those that contained an artifact plus an action potential (Fig. 3D, black); this process revealed a waveform that again had amplitude and kinetics that were nearly identical to those from a spontaneous action potential (Fig. 3D, green trace). This suggests that the direct subtraction method for identifying action potentials is comparably effective to the use of TTX. Together, these experiments indicate that magnetic stimulation from microcoils can elicit action potentials through direct activation of L5 PNs.

To explore the ability of the coils to selectively target neurons, we ran experiments in which the orientation of the coil was varied relative to the orientation of the targeted PN. Initially, the plane of the coil was held perpendicular to the surface of the slice (Fig. 3E, top), resulting in a weak electric field and gradient along the length of the neuron. As expected, this configuration was not effective (Fig. 3F, top), even for the strongest amplitude that could be delivered by our system. The coil was then reoriented with its flat surface approximately parallel to the slice surface (Fig. 3E, bottom); this orientation is similar to that which would arise during insertion of the microcoil into the intact cortex and resulted in a strong gradient along the length of the neuron that led to robust spiking (Fig. 3F, bottom); note that the presence of the positive-going after-hyperpolarization that closely follows each stimulus provides a clear marker for the presence of an elicited action potential (24). With direct activation, individual stimuli could each induce a single action potential at even the fastest rates tested (up to 100 Hz; n = 11 of 11; Fig. 3F, bottom). Similar to electric stimulation, stronger levels of magnetic stimulation increased the likelihood that a given pulse would elicit a spike (Fig. 3G, left; n = 7) and revealed thresholds of 44.21 ± 7.31 mA (SD) for direct activation. The sensitivity to stimulation in these cells was not significantly affected by the addition of synaptic blockers to the perfusion bath (Fig. 3G, right; n = 4). The ability to extract and visualize individual spikes also allowed the timing of individual spikes to be precisely determined and revealed onset latencies of ≤1.0 ms (Fig. 3H). As expected from spikes that are directly activated, latencies were not sensitive to the addition of synaptic blockers (Fig. 3I).

Repositioning the coil such that its tip was over the apical dendrite of the targeted neuron (Fig. 3J) allowed the sensitivity of this portion of the neuron to be explored as well. Once again, orienting the plane of the coil perpendicular to the slice surface (Fig. 3J, top) resulted in very weak electric fields along the neuron and did not produce spiking (Fig. 3K, top). However, alignment of the coil parallel to the surface of the slice (Fig. 3J, bottom) produced robust spiking (n = 8; Fig. 3K, bottom). The onset latencies of spikes elicited by stimulation over the apical dendrite were not well correlated to individual stimuli and were typically ≥3 ms, suggesting that spikes were mediated through the activation of the surrounding neural network. The addition of pharmacological blockers of excitatory synaptic input to the perfusion bath [10 μM CNQX (6-cyano-7-nitroquinoxalene-2,3-dione) and 50 μM d-APV] eliminated these responses, thereby confirming their presynaptic origin. The thresholds for indirect activation were 46.50 ± 11.78 mA (SD), and therefore both modes of activation had similar thresholds. Consistent with previous electric stimulation studies (6, 28, 29), it was not possible to elicit an individual action potential for each stimulus via indirect activation, even at the highest stimulus amplitudes. We did not attempt to identify the specific presynaptic neuron(s) activated by stimulation over the apical dendrite, but the high sensitivity of L5 PNs to vertically oriented electric fields raises the possibility that another vertically oriented neuron is activated; L2/3 PNs are an obvious possibility, especially because they are known to make excitatory synapses to L5 PNs. It is, of course, possible that multiple neuronal types are activated by stimulation from the microcoil, and further testing will be required to identify the specific types activated as well as to elucidate the subsequent synaptic interactions that occur.

For direct activation, thresholds were generally lowest when the tip of the coil was situated over the proximal axon at a distance of ~50 μm from the soma. Previous studies with electric stimulation have shown that the threshold for direct activation is minimized when the electrode is precisely centered over the dense band of sodium channels within the spike initiation zone of the proximal axon (26, 30), and it is likely that the lowest thresholds here arise because of the proximity to this location. However, we did not typically expend the considerable time and effort required to determine the exact location at which threshold is minimized (26), and so the 44.21-mA value reported here may not represent the absolute minimum threshold that can be obtained. For indirect activation, thresholds were generally lowest when the coil was over the apical dendrite at a distance of ~200 μm from the soma, although once again we did not systematically attempt to find the location for which threshold was minimized. Despite the fact that the values obtained here do not necessarily represent the absolute minimum thresholds, the levels that are reported here are still considerably lower than those reported with the previous microcoil for in vitro activation (13, 19). For example, previous work with the original microcoil (inductor) required thresholds of 717 mA for activation (13), whereas the thresholds for in vitro activation here were 44.21 mA (~16× reduction; see fig. S1 for further comparison of power levels). The lower threshold levels that were observed here likely arose because the smaller size of the coil not only generated stronger fields but also allowed for closer proximity to targeted neurons. Note also that for the responses that arose through indirect activation (Fig. 3K, bottom), the electrical artifact arising from the stimulus was quite small. This is consistent with the spatially narrow extent of the induced electric fields (Fig. 2) versus the relatively large separation between the coil and the recording electrode. Minimization of the stimulus artifact is a highly attractive feature, especially for efforts in which it is essential to record the response to artificial stimulation (31).

To better explore the spatial extent of magnetic stimulation as well as its ability to selectively activate specific orientations, we ran an additional series of experiments using brain slices from GCaMP6 mice (Materials and Methods). Cortical PNs from these animals express a calcium indicator that increases its level of fluorescence in response to spiking; similar to previous reports (32, 33), we observed low levels of fluorescence in the somas of individual L5 PNs (Fig. 4, A and C). Before measuring the responses to magnetic stimulation, we first examined the responses that arose from electric stimulation delivered via a conventional implantable electrode (Materials and Methods). At low levels of stimulation, there was little change in fluorescence, but as the amplitude of stimulation increased, the region over which fluorescence increased became progressively larger (Fig. 4B); this is consistent with results from previous studies of electric stimulation in vivo (6). At the highest level of stimulation tested here, a 200 μm × 200 μm region of the slice was strongly activated and uniformly extended in all directions. Similar to electric stimulation, low levels of magnetic stimulation also produced little change in the level of fluorescence, and higher levels resulted in increasing areas of activation (Fig. 4D). However, the spatial extent of activation was more narrowly confined with magnetic stimulation, and the location over which cells were activated was consistent with the predictions that arose from computational modeling (Figs. 2 and 4F). Although the responses shown in Fig. 4 (B and D) reflect the fluorescence of both somas and the surrounding neuropils (that is, axons and dendrites), the analysis could also be restricted to evaluate fluorescence changes in somas only (6, 32, 33). For the strongest stimulus tested here (52 mA), somas up to a distance of 160 μm from the coil exhibited robust increases (ΔF/F > 5 to 10%) in fluorescence (Fig. 4E), whereas smaller increases (ΔF/F > 1 to 3%) in fluorescence were exhibited by cells even further away. Thus, consistent with the modeling predictions of Fig. 2E, magnetic stimulation from these coils can modulate activity well beyond the region over which encapsulation and cell migration are expected to occur (11, 22, 34, 35), thereby suggesting that these coils can remain viable during chronic implantation.

Fig. 4 Comparison of spatial extent of excitation. (A) Light microscope photograph of a microelectrode situated over a V1 coronal slice from Thy1-GCaMP6f transgenic mice. The somas of individual neurons from L5 can be observed. (B) The change in fluorescence in response to three different levels of stimulation from an electrode. The tip of the electrode is seen as a downward-pointing triangle at the top of each image. The yellow triangle and the dashed line indicate the approximate orientation of cortical columns. (C) Similar to (A), showing the microcoil implanted over the V1 slice. The approximately semicircular tip of the coil is seen at the top of the image. (D) The change in fluorescence in response to three different levels of magnetic stimulation. (E) A region of interest (ROI) was defined for individual PNs on the basis of the somatic outline and used to calculate the cellular calcium fluorescence transients in each cell. Red neurons show strong calcium transients (ΔF/F >5%); yellow and green neurons indicate moderate (ΔF/F > 3%) and weak calcium transients (ΔF/F > 1%), respectively. Blue neurons indicate no observable increase in calcium fluorescence. (F) Schematic diagram illustrating the region over which PNs are predicted to be activated by stimulation from the coil. The proximal axon of PNs at location A (blue soma) is aligned with the region for which the induced field gradient (along the length of the neuron) is suprathreshold (yellow circular region); the apical dendrites of other neurons (location B, red soma) also extend into the suprathreshold region and become activated as well; and the processes of neurons that do not extend into the strong gradient region (location C, green soma) do not become activated. (G) Average calcium transient responses for the L5 PNs depicted in (F).

To eliminate the possibility that nonmagnetic factors contributed to the spiking responses observed here, we performed a series of control experiments, similar to the ones performed with the larger microcoil in earlier studies (13, 19). For example, the integrity of the coil insulation was tested regularly by measuring the impedance to ground; values were typically ~1 gigohm and were always greater than 200 megohms, thereby eliminating the possibility of direct electric stimulation contributing to observed responses. We also monitored the temperature in the bath as well as in the surrounding brain tissue during magnetic stimulation and observed increases of less than 1°C, well below the threshold for thermal activation of neurons (36–38). Capacitive currents can be transmitted through the coil insulation and have previously been shown to be effective for neuronal activation (39). However, there was no return electrode in the recording chamber in our experiments, and hence currents were not “forced” through the tissue as they were in a previous study (39). Although this greatly reduces the potential likelihood of capacitive activation, we nevertheless ran a control experiment in which a large transient current was used to “burn” a small portion of the coil, thereby leaving an open circuit; the transient current was not strong enough to also burn through the surrounding insulation, and thus there remained no potential for direct electrical activation. The subsequent delivery of stimulation to the “broken” coil produced a voltage differential across the open circuit, essentially acting as a capacitor. However, this approach was not effective for eliciting neural activity and therefore suggests that the observed responses were not mediated through capacitive activation. Finally, to eliminate the possibility that one or more (noncoil) hardware elements from our experimental setup might be generating the fields that are responsible for neuronal activation, care was taken to leave all hardware components in a fixed position across all experiments. In this manner, the only component that was not spatially fixed across trials was the orientation of the coil relative to targeted cells. Because some experiments induced neuronal responses whereas others did not, it is unlikely that any of the noncoil hardware components contributed meaningfully to activation, and we conclude that the fields arising from an appropriately oriented microcoil were the primary source of activation.