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Power Link Optimization for a Neurostimulator in Nasal Cavity

International Journal of Antennas and Propagation , Volume 2017, pp 1-6; doi:10.1155/2017/9096217

Abstract: This paper examines system optimization for wirelessly powering a small implant embedded in tissue. For a given small receiver in a multilayer tissue model, the transmitter is ed as a sheet of tangential current density for which the optimal distribution is analytically found. This proposes a new design methodology for wireless power transfer systems. That is, from the optimal current distribution, the maximum achievable efficiency is derived first. Next, various design parameters are determined to achieve the target efficiency. Based on this design methodology, a centimeter-sized neurostimulator inside the nasal cavity is demonstrated. For this centimeter-sized implant, the optimal distribution resembles that of a coil source and the optimal frequency is around 15 MHz. While the existing solution showed an efficiency of about 0.3 percent, the proposed system could enhance the efficiency fivefold.1. IntroductionEfficient wireless power transfer to medical implantable devices is highly desirable. Removal of bulky energy storage components enables the miniaturization of devices and eliminates the need for additional surgeries to replace the battery. Instead of a battery, a receiver on the implant obtains energy provided by external sources. Among various means to deliver power wirelessly, such as using ultrasound, optical, or biological sources, wireless powering through radiofrequency (RF) electromagnetic waves is the most established [1–5].Most studies using electromagnetic waves for powering implantable devices utilize inductive coupling. Under these conditions, a coil structure is most commonly used as the source. In an effort to enhance the efficiency, resonant LC tanks have been used on both coils for impedance matching [4, 6]. Instead of using separate capacitors, one may use extra coils to match the impedance and maintain a high -factor [7].As another effort to increase the efficiency, the size and number of turns of a coil are tuned to maximize the power transfer efficiency [3, 8]. In most studies, the optimization is based on the mutual inductance relation between two coil structures [9]. This approach, however, relies on quasi-static approximation in which the electric field induced by time-varying magnetic field is ignored. Dissipated power loss in tissue due to the presence of electric field, therefore, cannot be correctly accounted for.Recently, optimization of the power transfer efficiency including tissue loss was performed based on full-wave analysis [10, 11]. It showed that, for any given receiver, the power transfer efficiency is upper-bounded because of the tissue loss, and the upper bound is analytically solvable. Specifically, for an implant with a size of few millimeters, the optimal frequency lies in the low gigahertz range [12]. At such a high frequency, the implant is no longer in the near-field regime from the source; hence, inductive coupling alone is not sufficient to explain the performance [13].This finding is the basis for a new design methodology of power delivery systems. For a given receiver, one can readily obtain achievable power transfer efficiency and design the overall system to meet the goal. The power transfer efficiency can often be increased dramatically compared to those of conventional inductive coupling mechanisms [10, 11]. Equipped with this highly efficient power delivery system, a millimeter-sized pacemaker has been built and tested in a rabbit [14].In this work, we apply the optimization technique for a few-centimeters-sized implantable device. This research is novel and important because most implantable devices are still of a size of a few centimeters. This work provides the maximum achievable efficiency for the receivers at a certain depth of tissue composition. As a specific application, the optimization was applied for a neurostimulator inside the cavity of the head [15]. The implant stimulates the sphenopalatine ganglion (SPG), a nerve bundle located behind the nose, to relieve the pain caused by cluster headache. For the same receiver size, our design methodology could improve the efficiency fivefold compared to previous design performance.2. Background Theory2.1. Power Transfer EfficiencyThe power transfer efficiency is defined as the ratio between the received power and the input power to the system.Power efficiency degrades because of various factors, such as ohmic loss due to finite conductivity of the source, radiation loss , and dielectric loss inside the lossy tissue. Among those, the ohmic loss and the dielectric loss often dominate the power loss in a system. The upper bound on for a given receiver structure can be analytically solved [11]. Obviously, this forms the upper bound for the power transfer efficiency.2.2. Tissue, Source, and Receiver ModelWe model the inhomogeneity of the tissue as a planar multilayered medium, as illustrated in Figure 1. Although actual tissue medium is not a strict planar structure, it is known that planar modeling is adequate to predict the power transfer efficiency [16]. The tissue properties are modeled by assigning a dielectric permittivity to each layer. The dependence of with frequency is obtained from the Debye relaxation model [12].Figure 1: The layered medium model for tissue consists of stacked layers, each of which is assigned a dielectric permittivity . The center of the source is positioned at the origin, and the receiver is placed at with the norm of in the layers.Over the planar structure, we look for a source that maximizes the power transfer efficiency. It is difficult, however, to optimize the source, since the shape of the source can be arbitrary in three-dimensional space. The problem can be greatly simplified by invoking the equivalence principle [17], according to which any arbitrary source can be represented by an equivalent surface (tangential) current density, , along a plane between the source and the medium, as shown in Figure 1. For the sake of convenience, is assumed to be placed at .As a result, without loss of generality, we model the source with surface electric current on in the rest of the paper:where . Finally, the receiver of miniature devices is modeled as a magnetic dipole with arbitrary orientation located at (Figure 1):where is the magnetic moment of the dipole and denotes the orientation of the magnetic dipole, which is tilted by from the -axis. For a given and , we want to find and that optimize the power transfer efficiency.2.3. Efficiency OptimizationFor the given magnetic dipole moment , power transfer occurs through the time-varying magnetic field component in the direction of the moment. In a phasor notation, the transferred power iswhere is the magnetic field generated by the source and represents the real part of a complex number . The electric and magnetic fields generated by a time-harmonic current density on the surface of the source conductor can be solved by decomposing the current density into its spatial frequency components. Finally, the efficiency can be written as [14]where and are the electric fields generated by the source and , respectively. Also, represents the imaginary part of a complex number . The above equation of efficiency is intrinsic to the fields in the tissue multilayer structure, excluding any power loss due to radiation or ohmic loss in the source. Therefore, this gives the upper bound on the efficiency that can be obtained. The choice of that maximizes (5) is the key to efficient power transfer. Remarkably, the solution to the optimization problem maximizing can be found in a closed form as a consequence of vector space structure of fields in the multilayer geometry of the medium [11].3. Application: Receiver in Nasal CavityA minimally invasive implantable device demands as small a size as possible. However, if the functions of an implant necessitate large amounts of power, the size of the receiver must reflect this requirement. In some cases, a relatively large implant can utilize a preexisting vacant space inside the human body and thus bypass the need for further miniaturization.A good example of such an occurrence is a commercial neurostimulator inside the head to relieve the pain caused by cluster headache, as shown in Figure 2(a), produced by Autonomic Technologies (ATI) [15]. The implant requires a large amount of power (~50 mW) to provide intense stimulation to the sphenopalatine ganglion (SPG), a nerve bundle located behind the nose. Therefore, miniaturization of the receiver is limited by the device power consumption. Fortunately, exploiting the nasal cavity for the placement of the cm-scale implant, 50 mW of power can be delivered to the cm-scale implant in a relatively noninvasive manner.Figure 2: (a) The neurostimulator implant inside the head to relieve headache pain. (b) Modeling of the receiver occupying the same volume and in the same position as the neurostimulator implant.However, despite the large size of the receiver, the system suffers from low power transfer efficiency. The existing power transfer system attempted minimization of absorption loss in tissue by operating in the range of hundreds of kHz. A Litz wire structure is adopted in the receiver to reduce the ohmic loss of the receiver, as in [7]. Nevertheless, small receiver size and long distance between transceivers reduce the efficiency significantly. As a result, the power transfer efficiency is about 0.3% for the existing wireless powering solution.We are interested in the improvement in power transfer efficiency without increasing receiver size. In order to determine this, we model the receiver as a multiturn loop occupying the same volume as the original receiver and place it at the depth at which the implant will be located, 3.4 cm below the air-tissue interface, as in Figure 2(b). Detailed composition of tissue found from the anatomy of human is tabulated in Table 1. The thickness of the last layer is assumed to be infinite to simplify the calculation. Th
Keywords: wireless power transfer / energy storage / Coil / optimal distribution / Wirelessly Powering / Multilayer Tissue / Small Receiver / Small Power / nasal cavity

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