The influence of tissue conductivity uncertainty on the nerve activation thresholds in non-invasive electrical phrenic nerve stimulation

Non-invasive phrenic nerve stimulation can be used to overcome diaphragm insufficiency caused by mechanical ventilation. Detailed models and electromagnetic simulations are used to suggest appropriate stimulation parameters, but require accurate tissue properties. However, a wide range of electrical conductivity values is known from the literature. Here, we aim to perform an uncertainty analysis of the nerve activation threshold and the potential distribution along the phrenic nerve due to uncertain tissue conductivites. We built a generalized polynomial chaos (gPC) model to calculate the phrenic nerve activation threshold. It was based on a reduced order model of a detailed anatomical finite element model of the neck including 13 tissue types to calculate the potential distribution, followed by a biophysiological nerve model. The tissue conductivity values investigated here were for the compartments of fat, muscle, nerve, and soft tissue. Their influence on the nerve activation threshold was investigated by changing conductivity values of the single tissues and all tissues at a time within a Monte Carlo analysis using the gPC model. The phrenic nerve activation threshold varied between 33.8mA and 46.9mA for the combined variation of the conductivity values. Sobol indices and global sensitivity coefficients indicated the highest influence for muscle conductivity value, followed by soft tissue, fat, and nerve tissue. Our results may have implications for understanding the experimentally observed variation in individual phrenic nerve activation thresholds affected by physiological and pathological conductivity changes. Accurate electric properties of muscle and soft tissue and detailed geometric representations should be considered in electromagnetic simulations.