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Analysis of the capacitance of minimally insulated parallel wires implanted in biological tissue

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Abstract

State of the art bioelectronic implants are using thin cables for therapeutic electrical stimulation. If cable insulation is thin, biological tissue surrounding cables can be unintentionally stimulated. The capacitance of the cable must be much less than the stimulating electrodes to ensure stimulating currents are delivered to the electrode-tissue interface. This work derives and experimentally validates a model to determine the capacitance of parallel cables implanted in biological tissue. Biological tissue has a high relative permittivity, so the capacitance of cabling implanted in the human body depends on cable insulation thickness. Simulations and measurements demonstrate that insulation thickness influences the capacitance of implanted parallel cables across almost two orders of magnitude: from 20 pF/m to 700 pF/m. The results are verified using four different methods: solving the Laplacian numerically from first principles, using a commercially available electrostatic solver, and measuring twelve different parallel pairs of wires using two different potentiostats. Cable capacitance simulations and measurements are performed in air, a porcine blood pool and porcine muscle tissue. The results do not differ by more than 30% for a given cable across simulation and measurement methodologies. The modelling in this work can be used to design cabling for minimally-invasive biomedical implants.

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Acknowledgment

The authors would like to thank Weikang Chen and Huilin Xue for their assistance with the experimental verification. A. Aldaoud formulated the problem description, proposed the experimental set up, measured the cables in porcine blood and wrote the manuscript. R.-J. Tsai wrote the MATLAB code and performed all numerical simulations and measured the cables in porcine muscle. A. Aldaoud and R.-J. Tsai share first authorship for this manuscript. The rest of the authors were responsible for co-writing the manuscript and experimental discussions.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, Australia

    Rong-Jhen Tsai

  2. School of Physics, University of Melbourne, Parkville, Australia

    Ammar Aldaoud, David J. Garrett & Steven Prawer

  3. Department of Electrical Engineering and Computer Science, University of Liège, Liége, Belgium

    Jean-Michel Redoute

  4. Department of Biomedical Engineering, The University of Melbourne, Parkville, Australia

    David B. Grayden

Authors
  1. Rong-Jhen Tsai
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  2. Ammar Aldaoud
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  3. Jean-Michel Redoute
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  4. David J. Garrett
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  5. Steven Prawer
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  6. David B. Grayden
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Correspondence to Ammar Aldaoud.

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Appendix A

Appendix A

Figure 7 repeats the data presented in Fig. 6 with some minor differences in how the numerical results were obtained. The numerical curves in Fig. 6 were obtained using 𝜖i = 3 such that the curve could be smooth. However, the cables used have insulation permittivity ranging from 1.9 to 3.4. For each cable the numerical method is performed with its specific insulation permittivity. Each wire geometry and permittivity is detailed in Table 1.

Fig. 7
figure 7

Comparison of the numerical and experimental methods used to determine the capacitance of twelve different pairs of parallel wires in air, a porcine blood pool and porcine tissue. C1 to C12 denote a pair of insulated parallel wires with properties detailed in Table 1

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Tsai, RJ., Aldaoud, A., Redoute, JM. et al. Analysis of the capacitance of minimally insulated parallel wires implanted in biological tissue. Biomed Microdevices 22, 14 (2020). https://doi.org/10.1007/s10544-019-0467-9

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