# Detecting Malposition of Coil Couple for Transcutaneous Energy Transmission

Transcutaneous energy transmission technology based on coil coupling is widely required for various wireless powering implanted devices in human body. However, the coupling performance is commonly affected by malposition between coils in practice. It is difficult for users to know the actual position of the implanted receiver coil (RC) and how to realign the transmitter coil (TC) outside the body. This article proposes a detecting method of coil-coupling malposition based on a sensing board with coil array fitted on the TC. In this article, the sensing system and the data processing algorithm separating the sensing coil (SC) signals induced by TC and RC currents, respectively, are introduced. Then, an analytical model formulating the induction effect between the RC and SCs is given. Inverse computation algorithms of the malposition based on the processed sensing data and the induction effect model are presented at last. The proposed method is validated by experiments simulating malposition both in distance and concentricity on an actual coil couple. The results show that the sensing system can provide accurate parameterized guide for users to adjust the installation of the TC for good energy transmission performance.

From the State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, Peopleâ€™s Republic of China.

Submitted for consideration May 2015; accepted for publication in revised form September 2015.

Disclosure: The authors have no conflicts of interest to report.

This work was supported by the Natural Science Foundation of China (No. 51275461), the Science Funding for Creative Research Groups of the National Natural Science Foundation of China (No. 51221004), and International Cooperation Program (No. 2014DFR71220).

Correspondence: Haibo Xie, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Zheda Road 38, Hangzhou 310027, Peopleâ€™s Republic of China. Email: hbxie@zju.edu.cn.

How to supply power for electric-driven devices implanted in human body such as artificial heart is a challenging work. Use of a wire penetrating the skin increases the risk of the infection and affects usesâ€™ life. Transcutaneous energy transmission system (TETS) based on coil coupling is considered as an effective means to solve the problem. The TETS technology powers a transmitter coil (TC) outside the body with alternating current, which builds alternative magnetic field passing through the human skin and induces current on a receiver coil (RC) inside the body to supply power for the implanted device. As without any wires penetrating the userâ€™s skin, this technology can greatly prevent infections and improve the quality of usesâ€™ life.^{1} The AbioCor total artificial heart (Abiomed, Danvers, MA) and the LionHeart 2000 left ventricular assist device (Teleflex, Morrisville, NC) have been implanted into patients with TETS. Almost no device-related infections were reported, which demonstrated that the TETS was effective to reduce infections.^{2}

Reducing energy loss during the coil coupling is extremely important for TETS. The received energy by the device should not be too low for its normal running. In addition, the lost energyâ€“generating heat in the human body is potentially harmful to health.^{3} Through electrical resonance design between the TC and RC, the efficiencies of existing TETSs are generally above 70%, even above 80%, based on a premise that the coils are kept in coaxial and a proper distance.^{4} However, in actual applications, the malposition between the coils accompanying the skin peristaltic generated by breathing and various trunk actions is inevitable. Studies reported by Slaughter and Myers^{4} pointed out that the coil-couple malposition in practice may range from 3 to 15 mm in distance and from 0 to 20 mm in concentricity. As reducing the coil-coupling strength, serious malposition greatly reduces the efficiency of TETS.

In many TETSs, to ensure that the implanted device can receive enough power in practice, larger size TC is commonly used to make sure that the RC will still be strongly induced by its magnetic field even in malposition conditions.^{5},^{6} Nevertheless, this method is at the cost that larger part of the magnetic field does not interact with the RC. It means that more energy is wasted and accordingly induces more harmful current on the skin. Feedback control is another approach adopted by some TETSs to keep the received power in a relative stable level.^{7},^{8} The inputted current and resonant mode of the systems will be adjusted based on the feedback from detecting the induced current on the inside coil. An alarm circuit for the malposition was also proposed by Ozeki *et al*.^{9} In this study, when the change of the relative position of the coils was relatively small, the circuit was tuned by way of changing the resonant point; when the coils were in irregular position, a switch was turned on to alarm the user. Malposition on horizontal and vertical gaps can be alarmed by the circuit.

Obviously, it is better for user to know the exact relative position of the RC from TC, which can provide an accurate guide to adjust the installation of the TC for good energy transmission performance. In the TETS, the implanted RC itself produces secondary alternating magnetic field (under induction of current on the TC), which can be used for detecting the relative position of RC. Thus, this article presents a detecting method of the coil-coupling malposition using the magnetic field from RC. A sensing board, which is a printed circuit board having coil array on it in actual, is fitted on the TC. The induced currents on the sensing coils (SCs) are sampled and processed, then used to determine the relative position of the implanted RC with inverse computation. With this malposition-detecting system, users of the TETSs can know the actual malposition of the coils in real time and adjust the installation of the TC under parameterized guide for good wireless power transmission performance. The remainder of this article offers the following:

- â€“ The sensing system and the sampled data processing algorithm separating the SC signal induced by TC and RC currents, respectively, are introduced. Then, an analytical model formulating the induction effect between the RC and SCs is given. Two inverse computation algorithms of the malposition based on the processed sensing data and the induction effect model are presented at last, including one based on fast table search method and the other based on more accurate iterative optimization computation.
- â€“ The proposed method is validated by experiments simulating malposition both in distance (3â€“15 mm) and in concentricity (0â€“20 mm) on an actual coil couple developed in our laboratory.

## Detecting Method

Figure 1 illustrates the diagram of the proposed malposition-detecting system. As show in Figure 1A, alternative current is provided to TC from the direct current (DC) source through an inverter circuit and builds alternative magnetic fieldâ€“inducing current on the RC, which is used to power the implanted device after rectifying. The TC and RC work with capacitors C_{1} and C_{2}, respectively, in resonant modes at a same frequency, as designed by us in a previous study.^{10} A sensing board having coil array on it as shown in Figure 1B is fitted onto the TC to acquire the induced voltage information for further calculation of the implanted RCâ€™s position.

Both the current on TC and RC will induce voltage signals on the SCs of the sensing board. However, the relative position between the SCs and the TC is keeping unchanged. Thus, the mutual inductances between them remain constants. In contrast, the malposition between the TC and SCs accompanying the skin peristaltic generated by breathing and various trunk actions is inevitable. As a result, the coupling conditions from RC to both TC and SCs will change accordingly. These changes will cause varying induced voltages on SCs, which can be sampled and processed to determine the relative position of the RC by inverse computation.

### Parameter Derivation

The inductions between the coils are illustrated in Figure 2. According to the practice in actual TETS, sinusoidal current *I* _{1} *= A*sin (Ï‰*t*) is commonly supplied to the TC. Accordingly, the voltage on SC induced by TC and RC, respectively, that is, *U* _{13} and *U* _{23}, can be formulated as follows:

where *M* _{12}, *M* _{13}, and *M* _{23} are the mutual inductances between TC and RC, TC and SC, and RC and SC, respectively. *R* _{e} expresses the equivalent load of the implanted device powered by the RC current.

Therefore, the total induced voltage on SC *U* _{3} can be formulated as the linear superposition of *U* _{13} and *U* _{23}:

where *a* = Ï‰*M* _{13} *A* and *b* = Ï‰^{2} *M* _{12} *M* _{23} *A/R* _{e}. Thus, as long as the induced signal *U* _{3} is sampled, its amplitude *U* _{0} and its phase difference Ï• with *U* _{1} supplied on TC can be determined. Here, *U* _{1} has the same phase with *I* _{1} when the TC resonating with the capacitor *C* _{1}. Accordingly, the values of *a* and *b* can be calculated as follows:

For each position of the RC, the value of *b* for SC_{1}, SC_{2} â€¦ and SC_{m} shown in Figure 1B can be determined and form as a matrix as follows:

The mutual inductances between SCs and RC can be formed as a matrix *M* _{23}. According to previously mentioned equations, the factors Ï‰, *M* _{12}, *A*, and *R* _{e} are all same for different SCs. The relative position of RC can be computed as long as the values of the items in *M* _{23} are determined.

In practice, the values of the mutual inductances in *M* _{23} are affected not only by the relative positions between the SCs and RC, but also by some other factors, such as coil temperature changed by itself heating and human body heating.^{11} Thus, we use the distribution of the *M* _{23} in following computations of the malposition. It is the normalized results (by maximum item in the matrix) of *M* _{23} and *b*, which is described as *k* _{23} as follows:

### Induction Effect Formulation

As illustrated in Figure 3, the magnetic vector potential

at point *P* on the *j*th turn of SC, which is produced by the *n*th turn of RC with radius *R* _{n} and current *I* _{2}, is formulated as follows:

where

*R* _{n} and *r* _{j} represent radius of *n*th turn of RC and *j*th turn of SC, respectively. Selecting the center of the TC as the origin of coordinate system, (*x* _{i}, *y* _{i}, and *z* _{i}) and (*x*, *y*, and *z*) are the center coordinates of SC and RC, respectively.

,

, and

mean the direction vectors of *X*, *Y*, and *Z* coordinators, respectively.

The flux through the circle coil with radius *r* _{j} is given as follows:

where

Accordingly, the mutual inductance between *i*th SC on sensing board (Figure 1B) and RC can be formulated as follows:

where *N* _{1} and *N* _{2} represent the turns of RC and SC.

Theoretical mutual inductance between SCs and RC

can be formed as follows:

Accordingly, the theoretical mutual inductance distribution between SCs and RC is formulated as follows:

### Inverse Computation Method

With the theoretical model of

, the relative coordinate of RC can be determined by inverse calculation once its measured *k* _{23} was obtained. In this inverse computation, the main purpose is to find the coordinate (*x*, *y*, and *z*) where the computed

is closest to the measured *k* _{23}. Therefore, in this study, the coordinate leading to the minimum residual error Î” (according to Equation 15) of calculated result from its measured value is regarded as the coordinate of the RC. In the following text, two methods of inverse computation are offered for obtaining the position of RC.

#### Table search for fast primary determination

In the TETS, the malposition of the coil couple is about 3â€“15 mm in *z* direction and 0â€“20 mm in *x* and *y* directions. As described in Equation 12, the equation of mutual inductance between SC and RC includes *N* _{1} Â· *N* _{2} times of double integral to be calculated. Therefore, iterative computation taken in a wide domain will waste a lot of time for obtaining optimal solution. To save on inverse calculation time, a table, with theoretical mutual inductances between SCs and RC computed every other 1 mm in *x*, *y*, and *z* sitting, has been built. Once the measured *k* _{23} given, the residual error Î” of all the coordinates can be obtained by simple addition and subtraction. Hence, the coordinate in table leading to the minimum residual error Î” will be obtained quicker.

#### Further iterative computation for precise solution

As the precision of the solution is limited by the density of the table, iterative computation is operated for finding the optimal solution of RC coordinate around the result position from table search. In this detecting system, the general position of RC is calculated by the search method, which is considered close to the actual position of RC. According to the forward model previously mentioned, the solution for searching the minimum residual error Î” is a nonlinear problem. In conclusion, the iterative computation in this study is a nonlinear problem with a boundary condition. Therefore, the function *fmincon*, which is customized to find minimum of constrained nonlinear multivariable function in MATLAB (MathWorks, Natick, MA), is effective for searching the optimal coordinate of *x*.

Here, Î” is the optimization computation target, which is formulated by Equation 15. *P* _{0} is the start coordinate for iterative calculation, which is obtained by table search method. *P* _{0} âˆ’ Î”*P* and *P* _{0} + Î”*P* represent the lower and upper bounds of *P*. In following experiment, used as the largest solution error in primary table search method is below 2 mm.

## Experimental Validation

To validate the proposed detection method in the previous section, experiments simulating the TC and RC malposition in different directions have been implemented. The TC and RC were aligned on fitting blocks to keep parallel as shown in Figure 4A. The malposition is adjusted through three linear motions in *x*, *y*, and *z* directions, respectively. The sensing board, composed of 16 uniform SCs as shown in Figure 4B, was fixed tightly on the TC.

Air-core-type coils built of 600 strand AWG46 Litz wire were used in our study. The outer diameter of the TC and RC are 88 and 66 mm, with 23 and 16 turns, respectively, and the same inner diameter of 16 mm. At present, the existed wire winder machine is applied for fabricating helix coils (such as motor stator coil), not suitable for the flat spiral coils designed in our TETS. The machine should be custom designed for fabricating the coils used in this study, which is complex and troublesome. Hence, the TC and RC are fabricated by hand in this study. As shown in Figure 4B, 16 uniform printed SCs were fabricated in spiral shapes, with horizontal space and longitudinal space of coil center being 20 mm. The SCs were designed with inner diameter and outer diameter of 5 and 8.6 mm, respectively, built of 10 turns spiral printed wires, whose pitch was made of 0.4 mm, with coil space and width both of 0.2 mm.

With the previously mentioned experiment platform, the detecting for malposition between the TC and RC in radial direction (*x*-*y* plane) from 0 to 20 mm and *z* axial direction from 3 to 15 mm was tested. The signal-processing results, validations of the table search method, and iterative computation are presented below.

### Signal-Processing Results

Different malposition generates different signals on SCs. One example when the RC center is at position (*x* = 15 mm, *y* = 15 mm, and *z* = 7.5 mm) is presented here for introducing the solution procedure. Here, *R* _{L} is chosen of 20 Î© with output voltage of 24 V. Correspondingly, the input voltage and current of DC source are 46.5 V and 0.75 A. Signal on SC_{10} is given in Figure 5 as illustration. The voltage and phase information of the voltage signal on SC_{10} *U* _{3} and input voltage *U* _{1} on TC are sampled by Tektronix MSO 2024 (Tektronix, Beaverton, OR) mixed signal oscilloscope, whose amplitudes are 76.2 and 5.7 V with frequency of 600 kHz, as shown in Figure 5A. Hence, the amplitude *U* _{0} and phase Ï• can be obtained for computing *a* and *b* according to Equations 4 and 5. Correspondingly, the induced voltage on SC from TC and RC can be separated, as shown in Figure 5B. By detecting the voltages of all 16 SCs, the matrix *b* in Equation 6 can be determined as shown in Table 1. *k* _{23} also can be calculated according to Equation 8. Two representative points with the coil couple being at two extreme (farthest and closest) position are also presented in Table 1.

### Validation of Table Search Method

In this section, first, a table including the calculated

with *x*, *y* ranging from âˆ’5 to 25 mm, and *z* ranging from 0 to 20 mm is built, with same interval of 1 mm, as shown in Table 2 (here only a few points were given as examples). Once the measured value *k* _{23} is acquired by the signal-processing method, the residual error Î” between *k* _{23} and

of all coordinates in the table can be calculated according to Equation 15. Then, a loop program is operated in MATLAB for finding the targeting coordinate, which results the minimum Î”. On the exampled coordinate (*x* = 15 mm, *y* = 15 mm, and *z* = 7.5 mm), the computed coordinate result is *x* = 15 mm, *y* = 14 mm, and *z* = 8 mm, with minimum Î” of 0.0113.

Figure 6 shows the computed coordinate result against the actual position of RC. We implemented tests on *x*-*y* planes with *z* changed every 4 mm from 3 to 15 mm. The results at the positions every 5 mm from 0 to 20 mm on lines *y* = 0 and *y* = *x* of the plane were shown in the figure. Two two-dimensional figures in *x*-*y* and *x*-*z* planes are used to illustrate the coordinate comparisons in three-dimensional space. The left figures describe the computation results of *x* and *y* coordinates, meanwhile, the right figures shows the results of *z* coordinate. It can be found that the results from table search method are close to the actual position of RC, commonly less than 2 mm, which is effective for users to adjust the RC when malposition is happen.

### Validation of Iterative Computation

To get a more precise position of RC, iterative computation was performed. At the exampled coordinate (*x* = 15 mm, *y* = 15 mm, and *z* = 7.5 mm), *P* _{0} = [15, 14, 8] acquired from the table search method was used as the initial value, with calculating range Î”*P* = [2, 2, 2]. The optimized coordinate of RC is *P* = [15.12, 15.14, 7.86] with Î” = 0.0109. In comparison, the distance from the actual position is improved from 1.12 mm (table search method) to 0.4 mm (iterative computation), whereas Î” was only improved from 0.0113 to 0.0109. The value of the minimum Î” is relatively small for the computing data being normalized. Table 3 gives more results comparing the iterative computation and table search method with the actual coordinate. It can be found that 18% to 83% errors can be reduced by the iterative computation.

## Discussion

This study proposed a malposition-detecting method for TETS. In the TETS, power was delivered based on magnetic flux transmitted from TC to RC. When malposition of coil couple occurs, most of the effective magnetic path of the flux will not pass through RC, leading to the coupling efficiency decreased. As described in our previous article, the efficiency of the TETS was about 80% to 90% when TC is coaxial with RC. However, the efficiency was reduced to about 70% to 80% when malposition of the coil couple reached 20 mm in most working condition, dropping by about 10%.^{10} Obviously, the systemâ€™s efficiency can be improved by moving the TC outside the body to zero malposition if the position of the coil couple can be estimated with the proposed detecting system. With high efficiency, the battery will last much longer between charges, as well as the number of charge cycles will be decreased under same amount of the power transmission.

Two inverse computations, table search and iterative calculation, have been operated for comparison. The results can be obtained fast by table search method, ranging from about 0.1 to 0.3 seconds. However, the accuracy of the solution by table search method is limited by the resolution of the table. The density of the table can be increased to 0.5 mm or much higher, but it will greatly increase the data size. In the clinical application, the position of the coil couple does not need to be adjusted frequently, which is commonly adjusted when the malposition is obviously noticed (several times a day is enough). Iterative computation will cost much more time (more than 1,000 seconds) for calculation, but it improves the precision of the malposition solution, as shown in Table 3. The distance of example points from the corresponding points in the table built for searching is different, as the density of the table was 1 mm. For example, the closest point in the table search method for (15, 15, 7.5) and (14, 13, 11) is (15, 15, 7) or (15, 15, 8) and (14, 13, 11), respectively. Besides, the shapes of the coils were not completely regular, as TC and RC were handmade. Both of these factors leaded the percentage between two algorithm in Table 3 changing significantly.

This method can also be applied for the malposition detecting with an angle misalignment, and it just need to add the variables of the angles into the analytical model of the mutual inductances. Correspondingly, the theoretical value can be calculated and filled into the table based on analytical model. The methods for obtaining experimental value of mutual inductances, as well as the procedure of the iterative calculation, are the same as that without angle misalignment.

Errors are still observable in the detected results, which we believe are majorly caused by the RC being fabricated by hand leading to an irregularly shaped coil. The irregularly shaped coil can cause the theoretical model to be imprecise. In addition, initial installation error exists, which will probably bring a primitive error.

## Conclusion

A detecting method of the coil-coupling malposition for TETS was proposed in this article. In this method, a sensing board, which is a printed circuit board in actual and having coil array on it, is fitted on the TC. The induced currents on the SCs are sampled and processed and then used to determine the relative position of the implanted RC with inverse computation. With malposition experiment both in distance (3â€“15 mm) and concentricity (0â€“20 mm) on an actual coil couple developed in our laboratory, the proposed method was well validated. The detecting method in this study provides an effective way for malposition detection in TETS, which can help users to adjust the TC position for a better performance of energy transmission. It also can be applied to other coils-coupled or coil-permanent-magnet-coupled systems to monitor the relative position of the parts and improve the system performances in actual applications.

## Acknowledgment

The authors thank Miss H. M. Shen for her valuable suggestion in inverse computation.

## References

**Keywords:**

transcutaneous energy transmission; coil couple; malposition; sensing coil; inverse computation