# Sensitivity Analysis of a Numerical Model for Percutaneous Auxicular Vagus Nerve Stimulation
## 4 Discussion
However, since the ratio of maximum to minimum values in Reference [28] is two orders higher than in our study (ratio of maximum to minimum is 7 and 500 for 0.1-0.7 S/m and 0.0002-0.1 S/m, respectively), we expect the induced electric field to change way less in our study compared to in Reference [28]. The effect of skin conductivity on the induced electric field for peripheral nerve exposure was also investigated in Reference [29] using a skin conductivity of 0.1 S/m and 0.2 S/m. Results of the study in Reference [29] show maximum changes in the electric field of 4%. However, the values reported in Reference [29] concern the maximum (99% value) induced electric field for an adult model completelyinside shielded whole-body x-, y-, and z-gradient coils. Furthermore, the ear conductivity is less likely to change a lot in the range of 0.1-0.7 S/m between individuals. Thus, dielectric properties of the ear have no effect on the stimulation thresholds and the axons' recruitment volume. Results of Figure 7 show that the stimulation thresholds increase with an increasing number of axons. By increasing the number of axons, we also increase the size of the axon population region and we expand the location of the axon population. Some axons will then be located in regions of lower electric fields. By increasing the size of the axon population region, we are more likely to find axons in different E-field iso-layers, which will enhance the differences between the axons' stimulation thresholds. The temperature and ear conductivity are the non-influential parameters in the specified range of values. Maximum change in the stimulation threshold is equal to 8 mV (0.9%) and 1 mV (0.1%) over the entire range for the temperature and ear conductivity, respectively. The electrodes' position is a more influential parameter with an SI equal to 6.5% over the entire range and less than 7 mV for 0.1 mm shift in the electrodes' position. The number of axons seems to be the more influential parameter than the axon diameter (18% is the maximum change in the stimulation threshold for 100% axon activation over the entire range). However, this parameter has a wider range of values than the axon diameter (number of axons is in the range 21-133 while the axon diameter is from 7 um to 12 um). If we adjust the SI with the range of values for each parameter, the axon fiber diameter sensitivity will become 1.5 mV for each axon and 25.6 mV for each 1 um diameter. The frequency distribution of the axon fiber diameters from 7-12 um shows that more than 60% of the ABVN axons have a diameter between 7 um and 8 um [24]. In this range, the maximum variation in the stimulation threshold for 100% axon activation is 32 mV, which represents a 3.2% relative variation. The electrodes' penetration depth is the most influential parameter with a maximum variation of 38 mV for each 0.1 mm penetration depth. Clinical data show that 38 mV is a rather small voltage change. Stimulations are typically applied with several 100 mV up to several Volts. In some cases, steps of approximately 50 mV can be perceived by the patients.