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Sensors 2020, 20, 6087 9 of 13 5. Conclusions Batch-fabricated proof-of-concept 1800 μm diameter microcoils have been created. These 12 μm-thick coils demonstrate an inductance of 15.5 nH. In addition, these microcoils have achieved dimensions such that they may be implanted at the entrance of the cochlea, which has a 2 mm diameter [5]. Using AF analysis, the coils demonstrate potential to improve operating spatial resolution without exhibiting spread of excitation when compared to the conventional CIs as the coils utilize micromagnetic stimulation and the AF depolarization-hyperpolarization regions span 1.5 mm for each microcoil. Author Contributions: Conceptualization, P.B. and R.R.S.; modelling, R.R.S.; fabrication, R.R.S.; experimentation, R.R.S.; theoretical analysis, R.R.S.; investigation, P.B. and R.R.S.; methodology, P.B. and R.R.S.; validation, R.R.S.; writing—original draft preparation, R.R.S.; writing—review and editing, P.B.; visualization, P.B. and R.R.S.; supervision, P.B.; project administration, P.B.; funding acquisition, P.B. Both the authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the the National Science Foundation under grant CAREER ECCS 1055801, ECCS 1809334, and PFI-TT 1827321. Acknowledgments: Guidance was provided by Waymond Scott at the Georgia Institute of Technology, School of Electrical and Computer Engineering. Support and encouragement were provided by the other members of the Translational Biosystems Interface Lab at the Georgia Institute of Technology: Giovanni Calixte and Shambavi Ganesh. Conflicts of Interest: The authors declare no conflict of interest. Abbreviations The following abbreviations are used in this manuscript: CI Cochlear Implant FEM Finite Element Modelling MEMS Microelectromechanical Systems AJP Aerosol Jet Printing AF Activating Function ABS Acrylonitrile Butadiene Styrene UA Ultrasonic Atomizer CCM Cubic Centimetres per Minute Appendix A. Activating Function Calculation The activating function is generally calculated using the electric field induced by electrodes that utilize direct current; however, the underlying concept will be adapted to the case of of an external electric field resulting from a magnetic field. Axons arranged parallel with the generated electric fields will fire an action potential. Using the quasi-magnetostatics approximation of Maxwell’s equations [18], the activating function, Equation (A1), of the microcoils may be found through the relationships demonstrated in Equations (A2) and (A3). AF(x) = ∂2V (A1) ∂x2 E ̄ + ∂A = −∇V (A2) ∂t AF(x) = −∇Ex(x) (A3) Recall the electric field in quasi-magnetostatics is E ̄ = −∇V − ∂A , described by Larsson in ∂t Equation (32) [18]. Using the assumptions mentioned previously, and the approximation of the loops of the microcoil as concentric current-carrying rings, the calculation for the activating function of thePDF Image | Silver-Nanoparticle Microcoil via Aerosol Jet Printing
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