# Magnetoelectric Nanoparticles for Wireless Peripheral Nerve Stimulation: A Computational Study
## 3 Results  
Figure 4 shows some examples of the electric potential \(\varphi\) elicited by the single MENP or MENPs cluster along the neural fiber when the dipolar distribution shows its maximum amplitude, i.e., \(\pm\)2.5 mV on each hemisphere. For the sake of readability, the images are focused on a segment of 500 \(\upmu\)m length along the fiber, centered on the [PERSON]'s node closer to the MENP or MENPs cluster. Figure 4a shows the case study of a single MENP positioned at 2R from the neural fiber, perpendicularly oriented. As expected, slightly negative values, i.e., an excitatory effect, are observed in correspondence to the MENP. Due to the specific dimensions of the MENP (80 nm) and the [PERSON]'s node length (1 \(\upmu\)m), the MENP stimulation solely affects the electric potential of the [PERSON]'s node, without affecting any other segments of the fiber model and resulting in a punctual stimulation typical of a nanoelectrode. As a comparison, Figure 4b,c illustrate the potential distribution elicited along the fiber when the stimulating source is an MENPs cluster with a diameter of 80 \(\upmu\)m placed at distance 2R and with perpendicular and parallel orientations, respectively. The graphs clearly show that the external potential perceived by the fiber is indeed affected by the orientation of the MENPs cluster. When the MENPs cluster is perpendicularly oriented (Figure 4b), the external potential behavior is similar to that in the case of the single MENP stimulation: an excitatory effect is observed along the neural fiber, with the negative peak in correspondence to the Ranvier's node. From the comparison of Figure 4a,b, it is evident that dissimilarities in the widening of the external potential peak are directly linked to the differences in the dimensions of both the single MENP and MENPs cluster. The influence over the perceived external potential of the fiber is wider by increasing the MENPs diameter. Looking at the single MENP, the fiber is excited over 75% of the peak value at a total length of almost 80 nm, while the 80 \(\upmu\)m MENPs cluster causes strong excitation in the micrometer range, i.e., an extension of 80 \(\upmu\)m along the fiber senses the external potential over 75% of its peak value. The magnitude of the two peaks is 0.8 mV for both the single MENP and the MENPs cluster when perpendicularly oriented. A very different behavior is observed for the MENPs cluster parallelly oriented (Figure 4c). For the latter, both negative values, i.e., an excitatory effect, and positive values, i.e., an inhibitory effect, are perceived along the fiber length. The total magnitude of the variation is 0.8 mV. Table 2 shows the \(MF\)s values, by discriminating the different MENPs' configurations. When considering a single MENP, placed at distance 1R from the fiber, the \(MF\) value is the same for both the perpendicular and the parallel orientations. Due to the similarity of the results, the following analysis of the influence of the MENP-fiber distance over the \(MF\) value was performed only for the MENP perpendicularly oriented. The \(MF\) value increases by increasing the MENP-fiber distance, growing from 4.8 for a 1R distance to 31.1 for a 3R distance. If considering clusters of MENPs whether perpendicularly or parallelly oriented, the \(MF\)s trend is consistent for each different configuration and mirrors the one observed when stimulating with a single MENP, i.e., the \(MF\) value increases by increasing the MENP-fiber distance. Exceptionally, the 500 \(\upmu\)m MENPs cluster parallelly oriented shows an opposite trend, decreasing the \(MF\) value from 23.5 for a 2R distance to 17.3 for a 3R distance. Moreover, the results evidence an influence of the clusters orientations and dimensions over the \(MF\) values. Typically, lower \(MF\)s are required to evoke an action potential when a cluster of MENPs is perpendicularly rather than parallelly oriented, with the exception of the MENPs cluster of 500 \(\upmu\)m at distance 3R.