# Electromagnetic Analysis, Characterization and Discussion of Inductive Transmission Parameters for Titanium Based Housing Materials in Active Medical Implantable Devices

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## Abstract

**:**

## 1. Introduction

## 2. FEM Impedance Parameter Estimation

## 3. Physical Coil Impedance Model

## 4. Transfer Function with Housing

## 5. Eddy Current Distribution in the Housing

## 6. Parameter Discussion

## 7. Realization of a Communication Link for an Implantable Infusion Pump

## 8. Results

## 9. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AC | Alternating Current |

AIMD | Active Medical Implantable Device |

ASIC | Application-Specific Integrated Circuit |

BVTF | Backward Voltage Transfer Function |

CP | Continuous Phase |

DC | Direct Current |

DQPSK | Differential Quadrature Phase Shift Keying |

ECD | External Controlling Device |

ESR | Equivalent Series Resistance |

FEM | Finite Element Method |

FEMM | Finite Element Method Magnetics [6] |

FVTF | Forward Voltage Transfer Function |

IIP | Implantable Infusion Pump |

MRI | Magnetic Resonance Imaging |

PCB | Printed Circuit Board |

QPSK | Quadrature Phase Shift Keying |

RTC | Real Time Clock |

SNR | Signal to Noise Ratio |

## Appendix A. Estimation of Coil Parameters by Measurement

Name | C | D | H | K | A | B |
---|---|---|---|---|---|---|

$\mathit{N}$ | 10 | 10 | 25 | 25 | 200 | 200 |

${\xd8}_{\mathit{W}}/\mathrm{mm}$ | $0.4$ | $0.4$ | $0.2$ | $0.2$ | $0.1$ | $0.1$ |

${\mathit{L}}_{\mathit{s}}/\mu \mathrm{H}$ | $18.36$ | $18.55$ | $111.4$ | $120.7$ | 6909 | 6829 |

${\mathit{R}}_{\mathit{s}}/\Omega $ | $0.2845$ | $0.2818$ | $3.223$ | $3.212$ | $101.1$ | $98.36$ |

${\mathit{R}}_{\mathit{p}}/\mathrm{k}\Omega $ | $55.94$ | $55.44$ | $42.44$ | $62.30$ | $312.8$ | $354.8$ |

${\mathit{C}}_{\mathit{p}}/\mathrm{p}\mathrm{F}$ | $33.18$ | $31.38$ | $51.22$ | $34.88$ | $75.03$ | $67.14$ |

${\mathit{f}}_{\mathbf{0}}/\mathrm{kHz}$ | 6448 | 6598 | 2107 | 2453 | $221.0$ | $235.0$ |

## Appendix B. Description of the FEM Housing Model

**Figure A1.**FEM model of the housing and the coils for the estimation of transmission parameters with dimensions, based on a prototype housing of an implantable infusion pump. This model is axially symmetric to the z-axis.

## Appendix C. Complete Reformulation of the Transformer Equations for Three Windings

## References

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**Figure 1.**FEM model of an axially symmetric magnetic problem setup, with two coils, ${L}_{1}$ and ${L}_{2}$ (red) and a titanium tube T around ${L}_{2}$ (blue). (

**a**) shows the three-dimensional model of the setup in a polar coordinate system where z is the symmetry axis; (

**b**) shows the the setup in FEMM, where the green semicircle is the boundary region and the legend describes the used parameters.

**Figure 2.**Lumped element model of a simple coil impedance Z, consisting of the main inductance ${L}_{1}$, the equivalent series resistance ${R}_{1}$, the parallel resistance ${R}_{p}$ and the parasitic parallel capacitance ${C}_{p}$.

**Figure 3.**Correction factors ${\xi}_{L}$ for the main inductance (

**a**) and ${\xi}_{R}$ for the equivalent series resistance (

**b**). Additionally, in (

**b**), the alternating current (AC) resistance factor ${\xi}_{Rac}$ without housing is plotted in dashed green, which shows the dominance of the skin- and proximity effect above the frequency ${f}_{ac}=1\phantom{\rule{0.166667em}{0ex}}\mathrm{MHz}$. The parameters, belonging to coil ‘A’ are ${N}_{A}=200$ and ${\xd8}_{W\phantom{\rule{0.222222em}{0ex}}A}=0.1\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ (see also Table A1).

**Figure 4.**Comparison of the calculated (- -) and measured (–) absolute impedance frequency response for serial (

**a**) and parallel (

**b**) tuned coils to $125\phantom{\rule{0.166667em}{0ex}}\mathrm{kHz}$. The different parameters of the coils ‘B’, ‘D’, ‘K’ are ${N}_{B}=200$, ${\xd8}_{W\phantom{\rule{0.222222em}{0ex}}B}=0.1\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$, ${N}_{D}=10$, ${\xd8}_{W\phantom{\rule{0.222222em}{0ex}}D}=0.4\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$, ${N}_{K}=25$ and ${\xd8}_{W\phantom{\rule{0.222222em}{0ex}}K}=0.2\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ (see also Table A1).

**Figure 5.**Correction factor for the mutual inductance ${\chi}_{M}$, split into real part (

**a**) and imaginary part (

**b**) for coil configuration ‘A’ (${N}_{A}=200$ and ${\xd8}_{W\phantom{\rule{0.222222em}{0ex}}A}=0.1\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$, see also Table A1).

**Figure 6.**Schematic of typical inductive resonant transmission for the estimation of the transfer function, by using a modified transformer. ${L}_{1}^{\prime}$ and ${L}_{2}^{\prime}$ represent the coils, which include the correction factors of the housing.

**Figure 7.**Comparison of the forward voltage transfer function into the implant (

**a**) and the reverse voltage transfer function out of the implant (

**b**) in a typical inductive transmission without housing (nH) in black and with conductive housing (wH) in blue, – for the measured (m) and - - for the calculated (

**c**) results. The used coil parameters for coils ‘A’ and ‘B’ are ${N}_{B}={N}_{A}=200$, ${\xd8}_{W\phantom{\rule{0.222222em}{0ex}}A}={\xd8}_{W\phantom{\rule{0.222222em}{0ex}}B}=0.1\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ (see also Table A1) and the distance between the coils increases from $10\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ over $50\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ to $90\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$.

**Figure 8.**Resulting magnetic field vector distribution, caused by eddy currents in the housing, while exciting ${L}_{2}$, split into real part (Re(B)) and imaginary part (Im(B)) of the field. The field strength is normalized to the maximum field strength ${B}_{max}$ and shown in color, according to the colorbar.

**Figure 9.**Resulting magnetic field vector distribution, caused by eddy currents in the housing, while exciting ${L}_{1}$, split into real part (Re(B)) and imaginary part (Im(B)) of the field. The field strength is normalized to the maximum field strength ${B}_{max}$ and shown by the color, according to the colorbar.

**Figure 10.**Schematic representation of the inductive link application, with the External Controlling Device (ECD) outside the body (

**blue**), the Implantable Infusion Pump (IIP) inside the abdominal cavity (

**green**) and the indicated transmission coils (

**red**).

**Figure 11.**Block diagram of the complete electronics of the implantable infusion pump system, with the IIP on the left side and the ECD on the right side. The main transmission components are the micro-controller ($\mathsf{\mu}\mathrm{C}$), the QPSK-ASIC, the analog frontend circuit and the coil. Additionally, the IIP has sensors, actors, a flash memory and a wake-up unit. The ECD has a touch display, where all commands are handled. Both devices are powered by batteries.

**Table 1.**Discussion of advantages and disadvantages of different parameters for titanium encapsulated implantable devices with inductive data and power link.

Type | Parameter | Advantages | Disadvantages |
---|---|---|---|

electrical | higher frequency f | increased data rate | smaller skin depth $\delta $, therefore higher attenuation and smaller range |

lower frequency f | bigger skin depth $\delta $, therefore smaller attenuation and bigger range | decreased data rate | |

higher transmission power | increased range | hard to realize inside the implant, because of the limited power source | |

higher modulation rank | increased data rate | requires higher bandwidth, or reduces the Signal to Noise Ratio (SNR) | |

coil | increased geometric coil size | increased range | usually limited by the overall size of the implant and the space inside the housing |

higher quality factor | increased range | reduced bandwidth which leads to lower data rate | |

lower quality factor | increased bandwidth which allows higher data rate | smaller range | |

using litz wire instead of solid wire for coil windings | reduces proximity and skin effect, which reduces the ohmic losses and increases power transmission | usually more expensive | |

intermediate resonant coil outside the housing, under the skin | increases range | more expensive, complicated setup, additional encapsulation necessary | |

housing | reduced conductivity of the material | increases skin depth, which reduces the attenuation and increases power transmission and range | approval for material usage necessary, eventually reduced mechanical properties |

reduced wall thickness | decrease attenuation by eddy currents, which increases power transmission and range | reduced mechanical strength | |

non conductive material | no eddy currents, hence no negative effects of the housing | smaller longevity, biocompatibility and mechanical strength | |

reducing hot spots of eddy currents | reduced attenuation, which improves power transmission and range | more complexity in housing and big effort to find the hot spots | |

ferrite plate below the coil inside housing | deviation of the magnetic field and reduction of eddy currents, which improves power transmission and range | problematic for Magnetic Resonance Imaging (MRI) scans | |

coil outside the housing | improved power transmission and range | lead through and additional encapsulation of coil with non conductive material necessary |

Parameter | Description | Value |
---|---|---|

${U}_{in}$ | input voltage | $1.8\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ to $3.6\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ |

f | operating frequency | $12\phantom{\rule{0.166667em}{0ex}}\mathrm{MHz}$ |

${f}_{0}$ | carrier frequency | $125\phantom{\rule{0.166667em}{0ex}}\mathrm{kHz}$ |

B | bandwidth | ≈$10\phantom{\rule{0.166667em}{0ex}}\mathrm{kHz}$ |

R | data rate | ≈$10\phantom{\rule{0.166667em}{0ex}}\mathrm{kBit}/\mathrm{s}$ |

modulation | CP-DQPSK | |

${I}_{TX}$ | current for sending | <$6\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\mathrm{A}$ |

${I}_{stby}$ | current in standby | <$4\mu \mathrm{A}$ |

d | transmission range | $10\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ to $60\phantom{\rule{0.166667em}{0ex}}\mathrm{mm}$ |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gruenwald, W.; Bhattacharrya, M.; Jansen, D.; Reindl, L.
Electromagnetic Analysis, Characterization and Discussion of Inductive Transmission Parameters for Titanium Based Housing Materials in Active Medical Implantable Devices. *Materials* **2018**, *11*, 2089.
https://doi.org/10.3390/ma11112089

**AMA Style**

Gruenwald W, Bhattacharrya M, Jansen D, Reindl L.
Electromagnetic Analysis, Characterization and Discussion of Inductive Transmission Parameters for Titanium Based Housing Materials in Active Medical Implantable Devices. *Materials*. 2018; 11(11):2089.
https://doi.org/10.3390/ma11112089

**Chicago/Turabian Style**

Gruenwald, Waldemar, Mayukh Bhattacharrya, Dirk Jansen, and Leonhard Reindl.
2018. "Electromagnetic Analysis, Characterization and Discussion of Inductive Transmission Parameters for Titanium Based Housing Materials in Active Medical Implantable Devices" *Materials* 11, no. 11: 2089.
https://doi.org/10.3390/ma11112089