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 abstracted 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. Introduction
Efficient 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 Theory
2.1. Power Transfer Efficiency
The 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 Model
We 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].
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 Optimization
For 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 Cavity
A 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.
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(b)
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. This simplification is justified because the signal reflection from deeper layers is negligible. Following the theory in Section 2, the bound on efficiency is calculated as the black curve in Figure 3 for this receiver structure and configuration. Note that the frequency sweeping ends early at tens of MHz, after which the receiver is not modeled as a subwavelength (electrically small) structure. Equation (3) does not hold when the dimensions of the structure become comparable to the wavelength.
The optimal source that achieves the bound on efficiency in the frequency range from 100 kHz to 10 MHz is shown in Figure 4(a). It resembles a single rotational source and can be easily synthesized as a loop source, as in Figure 4(b). However, the simulated efficiency of a loop source made of copper using a commercial EM simulation tool [18] (blue curve in Figure 3) shows a vast departure from the theoretical bound due to the finite conductivity of copper. While the ohmic loss in the source is taken into account in the simulation of the loop source, the theoretic bound considers only the dielectric loss in tissue as the loss in the system. If the material of the source is replaced by a perfect conductor (PEC), the efficiency of the loop source borders the bound as expected (dashed blue curve in Figure 3).
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Without a PEC in hand, we aim to build a copper source possessing an efficiency that approaches the bound as close as possible. Therefore, the operating frequency should be chosen to be around 15 MHz (shaded region in Figure 3) to achieve the desired efficiency.
4. Experiment
An experiment is performed to measure the power transfer efficiency to the implant inside the tissue and to verify the theoretical and the simulated results. The optimal source is realized with a multiturn loop, as shown in Figure 4(c). A matching circuit is included to match the impedance of the loop to the output impedance of a power source instrument, 50 Ω, at 15 MHz.
The receiver is implemented with a multiturn loop, as shown in Figure 5(a), fitting inside the same cover used in the existing product [15]. The circuit model for the receiver is shown in Figure 6, in which the capacitance values for the rectifier are specified. The multiturn loop in a receiver can be modeled as an induced alternating voltage source connected with resistance and . Unlike the resistance , the inductance of the receiver coil is not sensitive to the surrounding medium. The inductance , therefore, can be easily measured using a network analyzer when the receiver is outside the tissue. The inductance of the loop μH could be successfully resonated out with = 15 pF and the rectifier.
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As turkey breast mimics the tissue structure of the human cheek (Figure 5(c)), it is used as the experimental substrate. The receiver is inserted 3.4 cm into the turkey breast. The available received power can be deduced by in Figure 6. The measurement of and , however, is challenging for small-scale structures. For example, to measure , the standard method to use the deembedding structure is not suitable when the size of the deembedding structure is comparable to the structure of interest. The electromagnetic coupling between the deembedding structure and the structure of interest degrades the measurement accuracy.
Instead, an optical approach has been proposed [19]. It makes use of the nonlinearity of the rectifier to accurately characterize power receiving structures. For this purpose, an LED and the charge pulse control unit to drive the LED are included in the receiver. In this method, the LED blinking period is closely related to the amount of received power. Explicitly, by measuring the LED blinking periods for two distinct input power levels, we can estimate and deduce the available received power [14, 19]. The LED blinking period is measured outside the tissue through an optical cable connecting the LED and the National Instruments (NI) machine (Figure 5(b)). The measured power transfer efficiency is then calculated as the ratio between the input power and the received power.
The result of measurement is shown in Figure 7. In the measurement, to make the LED blinking at a designated period indicating that the available power at the receiver is 0.1 mW, the transmit power was needed to be 2.85 mW. From this ratio, the available power transfer efficiency is measured to be 3.5% and denoted by a red dot in Figure 7. It shows that the efficiency closely matches the simulation result. In practice, the efficiency should degrade further during the AC-DC conversion in a rectifier. In this experiment, the AC-DC conversion efficiency is about 44% due to the small power level. This results in the overall power transfer efficiency from the input source to the load being 1.5%. Nevertheless, this is five times higher efficiency than that of the existing solution, which is denoted by a blue dot. The existing solution exceeds the simulation results (blue curve) at corresponding frequency (~800 kHz) because a Litz wire is used [15] instead of a plain coil, as was used in simulation. As stated in Section 3, Litz wire has a reduced AC resistivity and hence improves the efficiency. However, Litz wire typically has a resonant frequency of a few MHz and cannot be used for our new operating frequency. Our design methodology demonstrates that it is a better choice to discard the Litz wire and increase the operating frequency. This yields much higher efficiency than the existing solution. In other words, by following the design methodology driven by the bound provided by the theory, one can dramatically improve the power transfer efficiency.
5. Conclusions
The theoretic bound of power transfer efficiency is derived for a centimeter-sized implantable device. Simulation is performed to verify the theory; guided by the theory, a power delivery system for a centimeter-sized neurostimulator in the head is designed. For this moderate-sized implant, the optimal frequency for power delivery system is at 15 MHz. Also, the optimal current distribution resembles that of a simple coil source, which is the most commonly used source structure for inductive coupling. Lastly, the experiment is performed for a receiver placed inside a turkey breast. The measured performance improves fivefold compared to that of the previous design.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by grants from Kyung Hee University in 2016 (KHU-20160593).