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

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.