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Sensors 2020, 20, 6087 6 of 13 To better understand the impact of micromagnetic stimulation on neurons, the AF was calculated for excitable tissue located a distance z away from the microcoil (Figure 5a). The calculation is detailed in Appendix A. The results demonstrate the spatial capability of the microcoil to stimulate excitable tissue in the cochlea. Observing AF(x) at z = 300 μm away from the microcoils, the approximate distance of excitable tissue from the implant, any neurons with axons arranged along the direction of the electric field will demonstrate stimulation represented by the activating function, AF(x), where η is wave impedance, κ is the wavenumber, R is the radius of the largest coil loop, and I(t) is the time-dependent input current. Depolarization occurs at one location along the axon, where AF(x) > 0. In Figure 5, neurons oriented along the electric field, located along the x-axis where the peaks occur will be more likely to be stimulated. ηκ3 3R2 2R2 R2 AF(x)=−4π π R2+ 4 + 4 + 4 I(t) √22 j 1 jκ|x|e−jκ x+z κ(x2+z2)− √2 2 j 1 |x|e−jκ x2+z2 √ x2 κx+z 1000zx2+z2 z2+1 √ + 2 2−√ κ(x+z) κx2+z2 27x2+1 3/2 z2 √22 κ(x2 +z2) 1000xz x2 +1 z (1) x 2jx |x|e−jκ x+z − 3− 2] 2 κ(x2 +z2)2 μ I(t)R2 √ 2 2 e−jκ x+z +jω 0 4 x(x2 +z2 −jωx4 +x2 z2 +R2+2x4 +x2 z2 −R2−z4 −R2z2 z2|z|(x2 +z2 +R2)5/2 x2 +13/2 |x| z Figure 5. (a) Diagram and coordinate system for activating function; (b) AF(x) plot demonstrating spatially where neurons are more likely to be stimulated, when the maximum amplitude of the current is 1 A and coil distance, z, is varied from 100 to 400 μm. Neurons located at x = 0 will likely not be stimulated by the coil. 3.2. AJP Coil Miniaturization and Characterization The inkjet coils have been miniaturized by 97% using AJP techniques (Figure 6). The resulting thickness of the traces is between 11 and 14 μm, shown in Figure 7. After miniaturizing the coils, one primary challenge that persists is that the coils are fragile in the sense that if its surface is scraped by a remotely sharp object, such as a small copper wire edge, the silver can be removed, creating shortsPDF Image | Silver-Nanoparticle Microcoil via Aerosol Jet Printing
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