Witricity charger design with FEM simulation and corresponding experiment verification for recharging the deep brain stimulation

Abstract

In this paper, a wireless charger based on the novel witricity technology has been proposed for implanted deep brain stimulation (DBS). The simulation structure and the experiment model have been illustrated respectively. And the inductance, the resistance, the coupling coefficient have been compared between the simulation results and the measured results. Finally, the charger for implanted DBS power supply was proposed. The simulations have been done for coils with different copper tape arrangements to select the well match. Then a fabricated small “box” for the receiver has been designed and a head phantom has been constructed for the study of electrical energy delivery. The experiments have been carried out and the input voltage, input current, charging voltage and charging current have been measured for verification. In the end, the electric distributions have been studied to make sure its safety for human beings.

Keywords

Wireless charger witricity technology deep brain stimulation copper tape arrangements transmitter receiver

1. Introduction

In the current design of clinical neural implants, electric energy transmission plays a critical role in essentially all intelligent man-made prosthetic devices, from artificial hearts to brain implants [1, 2, 3, 4]. The deep brain stimulation (DBS) device is a typical example of a useful device and provides an excellent vehicle for further developments in more general applications [5, 6, 7, 8, 9].

For some artificial medical devices like artificial limb, the power might be up to several watts. The continuous power supply problem is a dominant factor causing high cost of the current implantable devices. Currently, the battery is sealed within the implantable pulse generator so that the entire device must be surgically replaced once the battery is out of power. The battery can last for a period ranging from a few month to several years. The combined cost for an implanted device replacement surgery is approximately $30,000. Although inductive wireless power technology has been studied by many researchers [10, 11, 12, 13, 14, 15], it cannot be applied efficiently in practice to charge the DBS due to its disadvantages of short transmission and strong electromagnetic radiation [16, 21].

The primary goal of this paper is to develop a DBS device charger based on witricity technology [22, 27]. This technology based on magnetic resonance coupling can transfer the electric energy or power over a distance without the use of wires. By considering the experiment condition and the complexity, one novel DBS charger was proposed in this paper. It was analyzed by FEM simulations and corresponding experiments to illustrate the great potential performance. The witricity system with the feature of high energy transfer efficiency is based on a new magnetic-resonance principle. A novel simulation model for full-wave 3-dimensional (3-D) electromagnetic (EM) field computation using HFSS will be developed as a powerful tool to efficiently analyze the performance of the device. Corresponding verifying experiments and measurements have been carried out to test the charger.

2. Self-inductance, mutual inductance and coupling coefficient

The analysis presented in this paper is evaluated based on a circular Witricity model, since such coil shape is particularly well suited for power transfer of implantable devices. An equivalent circuit is presented in Fig. 1 and a formula expressing the power transfer theory from the transmitter to the receiver is derived as well.

Figure 1.

Relative position of the circular coils.

Figure 2.

The diagram of a circular coil.

Figure 1 shows the diagram of the relative position of the two single-turn coils, where R1 and R2 are the radius of the primary coil and the secondary coil, h is the vertical distance of the two coils, and t is the horizontal displacement of the two coils. Figure 2 is the diagram of a circular coil.

Suppose R is the radius of the coil (like R1 or R2 in Fig. 1) and r is the radius of the wire. The filamentary circuit L1 has the same structure with the L2. So the external self-inductance of the L1 is the same as the L2. According to Ampere circuital theorem, the external self-inductance is

$\displaystyle L_{e}=\frac{\mu}{4\pi}\oint_{1}{\oint_{2}{\frac{d\vec{l}_{1}% \cdot d\vec{l}_{2}}{r}}}=\frac{\mu}{4\pi}\int_{0}^{2\pi}{d\phi\int_{0}^{2\pi}{% \frac{R\left({R-r}\right)\cos(\phi-\lambda)d\lambda}{r}}}$ (1)

Since the radius of the wire is much smaller than the curvature radius of the loop, the current is evenly distributed in the wire cross section. Thus, the internal self-inductance of the coil with one turn is

$\displaystyle L_{e}=\frac{\mu_{0}}{8\pi}\left({2\pi R}\right)$ (2)

The following equations can be attained

$\displaystyle\begin{array}[]{l}\mathord{\buildrel\lower 3.0pt\hbox{$% \scriptscriptstyle\rightharpoonup$}\over{R}}_{1}=R_{1}\cos\theta{\kern 1.0pt}{% \kern 1.0pt}\vec{x}+R_{1}\sin\theta{\kern 1.0pt}{\kern 1.0pt}\vec{y},\\ \mathord{\buildrel\lower 3.0pt\hbox{$\scriptscriptstyle\rightharpoonup$}\over{% R}}_{2}{\kern 1.0pt}{\kern 1.0pt}{=}{\kern 1.0pt}{\kern 1.0pt}R_{2}\cos\left({% \theta+\varphi}\right)\vec{x}+\left[{R_{2}\sin\left({\theta+\varphi}\right)+t}% \right]\vec{y}+h\vec{z}\\ \end{array}$ (3) $\displaystyle\left|{\mathord{\buildrel\lower 3.0pt\hbox{$\scriptscriptstyle% \rightharpoonup$}\over{R}}_{2}-\mathord{\buildrel\lower 3.0pt\hbox{$% \scriptscriptstyle\rightharpoonup$}\over{R}}_{1}}\right|=\sqrt{\begin{array}[]% {l}\left[{R_{2}\cos\left({\theta+\varphi}\right)-R_{1}\cos\theta}\right]^{2}\\ +\left[{R_{2}\sin\left({\theta+\varphi}\right)+t-R_{1}\sin\theta}\right]^{2}+h% ^{2}\\ \end{array}}$ (4) $\displaystyle d\vec{l}_{1}\cdot d\vec{l}_{2}=R_{1}R_{2}\cos\varphi{\kern 1.0pt% }d\theta{\kern 1.0pt}d\varphi$ (5)

According to Neumann formula [28], the mutual inductance between these two coils can be derived by

$\displaystyle M=\frac{\mu}{4\pi}\int_{0}^{2\pi}{d\theta\int_{0}^{2\pi}{\frac{R% _{1}R_{2}\cos\varphi{\kern 1.0pt}d\varphi}{\left|{\mathord{\buildrel\lower 3.0% pt\hbox{$\scriptscriptstyle\rightharpoonup$}\over{R}}_{2}-\mathord{\buildrel% \lower 3.0pt\hbox{$\scriptscriptstyle\rightharpoonup$}\over{R}}_{1}}\right|}}}$ (6)

The electromagnetic fields of the charger which include two resonant coils, a transmitter and a receiver can be approximated by

$\displaystyle\text{F}\left({r,t}\right)\approx a_{S}\left(t\right)\text{F}_{% \text{S}}\left(r\right)+a_{D}\left(t\right)\text{F}_{\text{D}}\left(r\right)$ (7)

Where $\text{F}_{\text{S}}\left(r\right)$ , $\text{F}_{\text{D}}\left(r\right)$ are the eigenmodes of the transmitter and the receiver respectively. Then the fields $\dot{a}_{S}$ and $\dot{a}_{D}$ can be shown to satisfy [29]

$\displaystyle\dot{a}_{S}=\left({j\omega_{S}-\Gamma_{S}}\right)a_{S}\left(t% \right)+j\kappa_{SD}a_{D}\left(t\right)+f\left(t\right)$ (8) $\displaystyle\dot{a}_{D}=\left({j\omega_{D}-\Gamma_{D}}\right)a_{D}\left(t% \right)+j\kappa_{DS}a_{S}\left(t\right)$ (9)

The eigen-frequency is

$\displaystyle\omega=\frac{\omega_{S}+\omega_{D}+\sqrt{4\kappa^{2}-\left({% \Gamma_{S}-\Gamma_{D}+j\omega_{D}-j\omega_{S}}\right)^{2}}}{2}+j\frac{\Gamma_{% S}+\Gamma_{D}}{2}$ (10)

Where $\omega_{S,D}$ are the eigen-frequency for the transmitter and receiver, $\Gamma_{S,D}$ are the resonance width depending on the intrinsic losses, and $\kappa_{S,D}$ are the coupling coefficient.

When the system is at resonance, it can be obtained $\kappa_{S}=\kappa_{D}=\kappa$ , $\omega_{S}=\omega_{D}=\omega_{0}$ , and the working frequency is the real part of the eigen-frequency as follows

$\displaystyle\omega=\omega_{0}\pm\sqrt{\kappa^{2}-\left({\frac{\Gamma_{S}-% \Gamma_{D}}{2}}\right)^{2}}$ (11)

Moreover

$\displaystyle\frac{\left|{a_{D}}\right|^{2}}{\left|{a_{S}}\right|^{2}}=\frac{% \kappa^{2}}{\left({\omega-\omega_{0}}\right)^{2}+\Gamma_{D}^{2}}=\frac{\kappa^% {2}}{\kappa^{2}-\left({\frac{\Gamma_{S}-\Gamma_{D}}{2}}\right)^{2}+\Gamma_{D}^% {2}}$ (12)

The system is under strong coupling when the coupling rate is much faster than the whole loss rates. the ratio $\kappa\mathord{\left/{\vphantom{\kappa{\sqrt{\Gamma_{S}\Gamma_{D}}}}}\right.% \kern-1.2pt}{\sqrt{\Gamma_{S}\Gamma_{D}}}$ can be used to represent that condition. If $\kappa\mathord{\left/{\vphantom{\kappa{\sqrt{\Gamma_{S}\Gamma_{D}}}}}\right.% \kern-1.2pt}{\sqrt{\Gamma_{S}\Gamma_{D}}}>>1$ , the desired regime can be called as a strong-coupling regime.

The conducting wires have a radius r, and the distance between the two coils is H. For the rate of energy transfer between the two coils S and D with a distance H, $\kappa$ is given through the frequency splitting of the combined system

$\displaystyle\kappa=\frac{\omega M}{2\sqrt{L_{1}L_{2}}}$ (13)

Where $M$ is the mutual inductance of the two coils, and it is $M\approx{\pi\mathord{\left/{\vphantom{\pi{2\mu_{0}(r_{S}r_{D})^{2}}}}\right.% \kern-1.2pt}{2\mu_{0}(r_{S}r_{D})^{2}}}\mathord{\left/{\vphantom{{\pi\mathord{% \left/{\vphantom{\pi{2\mu_{0}(r_{S}r_{D})^{2}}}}\right.\kern-1.2pt}{2\mu_{0}(r% _{S}r_{D})^{2}}}{H^{3}}}}\right.\kern-1.2pt}{H^{3}}$ in Fig. 1. That means $\omega\mathord{\left/{\vphantom{\omega{2\kappa}}}\right.\kern-1.2pt}{2\kappa}% \sim\left({H\mathord{\left/{\vphantom{H{\sqrt{r_{S}r_{D}}}}}\right.\kern-1.2pt% }{\sqrt{r_{S}r_{D}}}}\right)^{3}$ .

The source coil and the receiver coil are the same, that means R1 $=$ R2 $=$ RS and L2 $=$ L1 $=$ L. The Q factor of each coil is [18]

$\displaystyle Q=\frac{\omega L}{R_{s}}$ (14)

From equations above, the maximum power gain can be gotten [12]

$\displaystyle G_{\max}(Q,k)=1+\frac{2}{Q^{2}k^{2}}-2\sqrt{\frac{1}{Q^{4}k^{4}}% +\frac{1}{Q^{2}k^{2}}}$ (15)

Figure 3.

Coupling coefficient versus horizontal displacement based on rectangular shapes of primary and secondary coils.

Figure 4.

The coil, the copper tape arrangements, and the magnetic flux distributions.

It is important to be aware of the difference between such a resonant-coupling inductive scheme and the well-known non-resonant inductive scheme for energy transfer. Using the coupled-mode theory (CMT) it is easy to show that, if keeping the geometry and the stored energy in the source coil constant, the resonant inductive mechanism allows for more power delivered for work than the traditional non-resonant mechanism. Actually, capacitive-loaded conductive loops are being widely used also as resonant antennas (for example in cell phones), but those operate in the far-field regime and the radiation Q are intentionally designed to be small to make the antenna efficient, making it inappropriate for energy transfer.

Suppose the diameter of circular coils is 50 mm, the vertical distance h between the two circular coils is 3 mm, and the radius of the wire is 1 mm. The result is shown in Fig. 3. It can be seen that the curve of the coupling coefficient of circular coils drops regularly as the horizontal displacement increases from 0 mm to 40 mm.

The coupling coefficients between circular coils is 0.1494, as the horizontal displacement is 25 mm. Therefore, the circular coils have enough stability with the horizontal displacement variation.

3. The transmitter design

Hitherto Witricity works at the frequency in MHz range; hence some undesirable problems become inevitable. Firstly, high frequency devices are much more expensive than their low frequency counterparts. High-frequency circuits and digital circuits are often sharing the same circuit board, constituting mixed signals or cross talks. High-frequency circuits are sometimes unstable as the digital circuits are starting up because the noise generated by the digital circuit could affect the normal functions of high frequency circuits. Also, realization of inductive charging at high frequencies results in relatively more radiation and heat generation in the vicinity of the electrical device.

If the resonant frequency can be reduced, that will be highly desirable in overcoming the aforementioned shortcomings of Witricity chargers. Some simulations on the transmitter with different copper tape arrangements have been conducted to compare the performances in order to reduce the resonant frequency. Finite element analysis (FEA) and corresponding experiments have been carried out to showcase the performance of the transmitter. Figure 4a–e present the coil, the copper tape arrangements, and the magnetic flux distributions at the position of 2 cm above the coil. And the dimension is shown in Table 1.

Table 1
Dimension parameters of the transmitter coil

Shape of winding	Spiral
Number of turns	10
Radius of the spiral (mm)	136.5
Thickness of copper (mm)	0.04
Width of copper (mm)	4
Copper track separation (mm)	1.18
Width of the strip (mm)	18
Length of the strip (mm)	25.4
Number of the strips	20

Figure 5.

The simulated resonant frequencies and the unloaded Q factors of the five coils with different copper tapes. A – Four copper tapes, B – Four separated copper tapes, C – Four separated copper tapes with small angular misalignment, D – Four copper tapes with large angular misalignment, and E – Twenty copper tapes.

The resonant frequencies and the unloaded Q factors of the five coils with different copper tapes have been shown in Fig. 5. It can be seen that the last one with twenty copper tapes has the similar resonant frequency and magnetic flux distributions with others but the highest unloaded Q factor. Its self-inductance is about 2.2 uH based on the analytical calculation and the simulation results. When using network analyzer, the measured unloaded Q factor of the last model is about 356, slightly different from the simulation results.

4. The receiver box design

To increase the transmission efficiency, the size of the resonator at the receiving side is expected to be as large as possible in order to capture more magnetic flux produced by the resonator at the power source. However, in medical applications, the size of the receiving resonator is usually limited by the size of the parent device. In order to make the receiver much smaller but with the same resonant frequency of the transmitter, a fabricated small “box” is built and shown in Fig. 6, which contains two spiral coils on the two top surfaces and a connected helix between the coils. The dimension parameters were shown in Table 2. The simulated and measured resonant frequencies of the “box” are about 7.961 MHz and 8.152 MHz, respectively.

Table 2
Dimension parameters of the receiver box

The helix	Shape of winding	Helix
	Number of turns for helix	30
	Radius of the helix (mm)	22
	Radius of the wire (mm)	0.4
	Height of the helix (mm)	16
The two spirals	Shape of winding	Spiral
	Number of turns	36
	Radius of the wire (mm)	0.14
	Copper track separation (mm)	1.18

Figure 6.

A fabricated small “box” for the receiver.

The simulated unloaded Q factor of the receiver box is about 227 and the measured one is near to 200. Its self-inductance is about 11.6 uH.

5. System design

Through the discussion above, it can be obtained that the transmitter and the receiver box have different resonant frequencies, which will make the system non-resonant. In order to make them work under resonance, the transmitter must be revised to make it have the same resonant frequency with the receiver box. Then, external capacitors have been added. Table 3 presents the resonant frequencies and the unloaded Q factors with different external capacitors.

Table 3
The resonant frequencies and the Q factors with different external capacitors

Capacitance (pF)	Resonant frequency (MHz)	Unloaded Q factor
100	18.583	402.60
110	15.884	389.77
120	13.708	375.90
130	11.816	363.48
140	10.357	352.53
150	9.012	342.73
160	8.221	334.49
170	7.570	327.23
180	7.043	322.68
190	6.734	318.80
200	6.472	314.71

Table 3 tells that when the external capacitor is 160 pF, the resonant frequency of the transmitter is about 8.221 MHz, quite near to the receiver’s. Then adjust the position of the copper tapes on the coil to make its resonant frequency to be about 8.152 MHz.

Using the transmitter and the receiver box studied above, a simple platform has been built. The network analyzer was employed to measure the S parameters and get the Smithchart at resonant frequency of 8.0742 MHz, presented in Fig. 7. It can be got from the S parameters that the transmitting efficiency is the highest when the frequency is the resonant frequency. The Smithchat was used to match impedance according to the most energy received by the receiver when the system is in a state of impedance matching. Matlab fsolve(@) has been implemented to calculate the coupling coefficient k, transmitter’s self-inductance L1 and the receiver’s self-inductance L2 under normal condition. Gmax was also calculated through Eq. (15) and the unloaded Q factor was given in Table 4.

Table 4

Calculated data based on the measured S parameters

Resonant frequency (MHz)	$k$	$L_{1}$ (uH)	$L_{2}$ (uH)	$G$ max	Unloaded Q factor (System’s)
8.0742	0.1783	2.37	13.25	0.3324	117

Figure 7.

The measured S parameters and smithchart for the platform.

In the witricity systems for implantable devices, the transmitter and receiver coils are separated by skin and tissue with a distance of 20 mm to 60 mm. The coils are usually misaligned, due to anatomical constraints and their coupling efficiency is inevitably impaired. Because of changes in the coupling rate, lateral misalignment and angular misalignment may cause fluctuations in output voltage, output power and transmission efficiency, leading to instability in the witricity system. These effects therefore must be fully addressed in order to enhance the stability of the system. Careful parameter design is also necessary, especially for energy transmission over a relatively large distance.

During the evaluation, the external witricity transmitter is placed at different distances and angles from the head phantom implanted with the witricity cell, and the output voltages have been measured and compared to the results obtained from computer simulation. In order to facilitate measurements, impedance matched RF circuits, cables and probes have been utilized to obtain relevant data. Figure 8 shows the schematic and experimental diagram of the measurement circuit.

Figure 8.

The schematic and experimental diagram of the measurement circuit.

Figure 9.

Simulation and measured receiver output voltages vs. frequency with a distance of 20 mm.

Figure 10.

Receiver output voltages. (a) Lateral misalignments of 10 mm. (b) Angular misalignment of 20 ${}^{\circ}$ .

Figure 11.

Maxwell ML 2032 rechargeable battery.

Figure 12.

The phantom for the performance verification of the proposed witricity system.

Figure 13.

The completed head phantom.

Figure 14.

The result of the experiment. (a) Input voltage from the rectifier bridge. (b) Input current from the rectifier bridge.

Figure 15.

Electric distributions in the head phantom at different distance between the receiver box and the plane. (a) at the center of the receiver box, (b) at the distance of 10 mm below, (c) at the distance of 20 mm, (d) at the distance of 30 mm, (e) at the distance of 40 mm, (f) at the distance of 50 mm, (g) at the distance of 60 mm, (h) at the distance of 70 mm.

Figure 9 presents both the measured and the simulation data of the output voltages when the frequency rangs from 2 MHz to 16 MHz. It is clear that when the operating frequency is at or near the resonant frequency, the output voltage of the receiver reached to the highest value. For the simulation result, it is about 383.8 mV at 7.877 MHz; and for the measured result, that value is up to 327.4 mV at 8.102 MHz.

Output voltages with lateral and angular misalignments have been shown in Fig. 10a and b, respectively. The output voltage of the receiver is recorded in Fig. 10a at the frequency of 8.102 MHz and the lateral misalignment is 10 mm when the distance between the transmitter and the receiver is changed from 20 mm to 60 mm. When the angular misalignment between the transmitter and the receiver is fixed at 20 ${}^{\circ}$ , the receiver’s output voltage decreases from its peak value of 265 mV to 10 mV at 8.102 MHz resonant frequency and the distance between the transmitter and the receiver is changed from 20 mm to 60 mm as shown in Fig. 10b. It can be seen that the output voltages are about 250 mV even with 10 mm lateral misalignments or 20 ${}^{\circ}$ angular misalignment, which is enough for supplying the DBS.

In order to make the charger applicable for practical applications and getting experiences of device design, a wireless charger was built for demonstration and doing corresponding experiments. The charger is designed to charge the battery, Maxwell ML 2032 shown in Fig. 11, the rated voltage and power capacity are 3 V, 65 mAh respectively for DBS device.

Based on the design requirements, the charger provides invariable current to charge the battery. For the witricity study, where the operating frequency is much higher, the model should be constructed considering the material composition to make it for the intended frequency range.

The electrical properties of this model are verified; the encapsulated witricity cell with ML 2032 rechargeable battery was implanted within the skull and relevant experiments were conducted. The construction of the head model was intended to be used at a frequency of up to 10 MHz. In order to simplify the experimental setup, a partial scalp model has been used to cover the implant as we did in our previous volume conduction power delivery experiments.

A head phantom has been constructed for the study of electrical energy delivery between an external transmitter and an internal receiver (Here is the small “box”). This phantom, which geometrically resembles the upper portion of a human head, simulates the geometry and electrical properties of the brain, skull and scalp, which is shown in Fig. 12. Both the intracranial contents and scalp of this model were made of agar and conductive agents, and the skull was made from a mixture of carbon black epoxy and barium titanate (BaTiO3). A series of molding procedures was used to accurately construct the head components. Figure 13 presents the completed head phantom.

Figure 14 shows the result of the experiment above. Figure 14a and b present the curves of input voltage and current from the rectifier bridge. It can be verified that the load charging equipment can receive stable voltage 2 V and current 30 mA with this witricity charger system from this experiment.

The resonant frequency of the coils in this project is near to 8 MHz. So it is needed to study the electric distribution in the head phantom to make sure whether the method is harmful to the patients or not. According to the actual structure of the head phantom and the external transmitter and the internal receiver, the simulation model is established. Figure 15 is the simulation results of the electric field distributions in the phantom.

$\displaystyle\textit{SAR}=\int\limits_{\textit{Brain}}{\frac{\sigma\left(r% \right)\left|{E\left(r\right)}\right|^{2}}{\rho\left(r\right)}}dr$ (16)

The results shows, the highest density occurred at the center of the receiver box and it is up to 2e-4 V/m. And the highest value is about 1e-4 V/m at the distance of 20 mm and 5e-5 V/m at 30 mm. The electric distribution is only 1e-6 V/m when the distance is larger than 40 mm. Based on Eq. (16), SAR values can be calculated and it is found that even the peak SAR values are much lower than the US standard (1.6 W/kg) and the EU standard (2 W/kg). Therefore, it is safe to use this resonant method to transfer power for the implanted medical devices like DBS.

6. Conclusion

Based on the witricity concept and the study, one application method for charging DBS is proposed and studied through simulations and experiments. In addition, wave network equations for calculating the Gmax and Q factors have been introduced as well. The self-inductance, mutual-inductance, and the maximum possible efficiency of the proposed system have been analyzed. The design of the structure parameters is discussed. Experimental results are presented to evaluate the performance of the derived prototype.

Footnotes

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (Grant Number 51507114), in part by the Natural Science Foundation of Hubei Province (Grant Number 2014CFB272).

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Witricity charger design with FEM simulation and corresponding experiment verification for recharging the deep brain stimulation

Abstract

Keywords

1. Introduction

2. Self-inductance, mutual inductance and coupling coefficient

Table 1 Dimension parameters of the transmitter coil

Table 2 Dimension parameters of the receiver box

Table 3 The resonant frequencies and the Q factors with different external capacitors

Footnotes

Acknowledgments

References

Table 1
Dimension parameters of the transmitter coil

Table 2
Dimension parameters of the receiver box

Table 3
The resonant frequencies and the Q factors with different external capacitors