# Sensitivity Analysis of a Numerical Model for Percutaneous Auxicular Vagus Nerve Stimulation
## 4 Discussion  
For the first time, a sensitivity study of a numerical model for pVNS has been performed. Electric field distribution shows that highest electric field values appear near the needle with a fast decline over distance, which is due to the point effect on the needle. Locations of the N2 branches shows higher electric fields compared to the N1's branches locations. Results show decreasing stimulation thresholds with increasing axon fiber diameter (a decrease of 17% over the entire range of 7-12 m for N2). An examination of Equations (3)-(5) shows that the three components \(C_{m},~{}G_{a}\), and \(G_{m}\) are proportional to fiber diameter \(d\) (\(G_{a}\propto d\) since \(L\propto d\)) [19]. Since \(C_{m},~{}G_{a}\), and \(G_{m}\) occur only in Equation (1) as ratios, changes in the axon fiber diameter affect the solution only through its relation to the internodal distance \(L\). The only effect of the changing axon diameter is then in the calculation of the external potential at the nodes. For a point electrode (in situ) and homogenous current distribution, the external nodal potential is given by [19]  
\[V_{e}=\frac{I\rho_{e}}{4\pi r} \tag{7}\]  
where \(\rho_{e}\) is the resistivity of the external medium surrounding the neuron, \(I\) is the stimulus current, and \(r\) is the electrode-node distance. The induced voltage along the nodes and thus the associated transmembrane voltage will be decreased quite considerably for the 7 m axon diameter compared to the 12 m axon diameter since the internodal distance \(L\) is greater in the latter case. Thus, the excitability will be decreased for the axons of lower diameter. Biphasic stimulation requires slightly less amplitude to stimulate the nerves than the monophasic pulses. This indicates that bend-mode and end-mode stimulation may dominate as well as that the single-phase duration is sufficiently long for excitation to develop. The axon population around N2 was slightly more sensitive in the monophasic configuration than in the biphasic configuration. Similar behavior was also recorded in our previous study and explained by the additional chance for stimulation at the reversal phase for the biphasic pulses compared to the monophasic pulses [12]. Since cathodic stimulation has lower thresholds than anodic stimulation (in the straight-mode stimulation), the varying polarity of stimulus (biphasic stimulus) increases the probability of firing in comparison with the constant polarity (monophasic stimulus). N2 was activated with lower amplitudes than N1 using both monophasic and biphasic patterns. This is due to its branches being at the location with higher electric field values compared to the branches of N1 (Figure 2). N2 was more sensitive to the axon fiber diameter than N1. This can be explained by its exposure to higher electric field values; thus, the effect of small changes in the axons' diameters can be enhanced by these higher values of E-fields. However, due to the decreasing behavior of the plots in Figure 3, one can see that SI depends only on the stimulation thresholds for 7 m and 12 m. Thus, SI will mostly reflect changes occurring between these two edges of the axon diameter interval. In the range of interval between 0.1 S/m and 0.7 S/m, the ear conductivity has the lowest effect on the stimulation thresholds among all the parameters (change of 0.1% over the entire range of 0.1-0.7 S/m). In fact, as suggested by [PERSON] et al. [27], any value of the skin in the range 0.1-0.7 S/m will not considerably alter the E-fields. Works on the effect of skin conductivity in a low frequency exposure assessment for peripheral nerve tissue [28] show that the choice of skin conductivity significantly affects the induced electric field, resulting in an increasing factor of three in the induced electric field when using a skin conductivity of 0.0002 S/m instead of 0.1 S/m.