# Magnetoelectric Nanoparticles for Wireless Peripheral Nerve Stimulation: A Computational Study
## 3 Results
For example, when stimulating  
with a MENPs cluster of 80 \(\upmu\)m, the \(MF\) value ranges from 5.8 to 34.2 for the perpendicular orientation, whereas it ranges from 7.9 to 85.8 for the parallel orientation. Regarding the MENPs' dimensions, \(MF\) generally decreases by increasing the cluster diameter. As an example, \(MF\)s of 7.9, 6.3, and 3.9 are needed for cluster diameters of 80, 250 and 500 \(\upmu\)m, respectively, parallelly oriented. A recurring opposite trend is visible for the MENPs cluster of 500 \(\upmu\)m at distance 3R for both orientations, and for the same cluster when oriented parallelly and placed at distance 2R. Figure 5 shows a representation of the recruited volume of a 1000 \(\upmu\)m fascicle hypothesized to be injected with the MENPs. The fascicle diameter was comprised within the range of peripheral fascicle diameters [32]. The image illustrates the cross-section view, and reports the different MENP configurations considered. More specifically, the figure shows the \(MF\) values needed to activate the neural fibers in the circular areas of 1R, 2R and 3R around the MENPs. Due to the definition of the MENP-fiber distance, the activated region with radius 1R is barely visible. When considering the single 80 nm nanoparticle placed in the middle of the fascicle, even if using an \(MF\) equal to 31.1, i.e., multiplying the potential on the surface of the MENP by more than thirty times, the fibers recruited \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **MENPs-Fiber Distance** & **Perpendicular Orientation** & **Parallel Orientation** \\ \hline \multirow{4}{*}{MENP 80 nm} & 1R & 4.8 & 4.7 \\  & 2R & 13.7 & \\  & 3R & 31.1 & \\ \hline \multirow{4}{*}{Cluster 80 \(\upmu\)m} & 1R & 5.8 & 7.9 \\  & 2R & 16.7 & 67.9 \\  & 3R & 34.2 & 85.8 \\ \hline \multirow{4}{*}{Cluster 250 \(\upmu\)m} & 1R & 5.7 & 6.3 \\  & 2R & 13.2 & 22 \\  & 3R & 21.9 & 45 \\ \hline \multirow{4}{*}{Cluster 500 \(\upmu\)m} & 1R & 2.9 & 3.9 \\  & 2R & 7.4 & 23.5 \\ \cline{1-1}  & 3R & 27.8 & 17.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Multiplication factors for different MENPs dimensions and orientations. Figure 4: Comparison of electric potential \(\varphi\) along the neural fiber for different MENPs’ configurations. (**a**) Single MENP at distance 2R with perpendicular orientation; (**b**) 80 \(\upmu\)m MENPs cluster at distance 2R perpendicularly oriented; (**c**) 80 \(\upmu\)m MENPs cluster at distance 2R parallelly oriented. The Ranvier’s node middle point, highlighted in the plots, is aligned to the MENP or MENPs cluster center. by the stimulations are confined in a very narrow volume around the nanoparticle. If considering clusters of MENPs, the recruitment volumes are larger with lower \(MF\) values: for the 80 \(\upmu\)m cluster in the perpendicular configuration, about a quarter of the fascicle volume was recruited with \(MF\) equal to 34.2, while for the 250 \(\upmu\)m in the perpendicular configuration, two thirds of the volume of the fascicle are recruited with lower \(MF\), equal to 21.9. The different behavior of the equivalent current \(I^{int}\) injected in the intracellular space along the fiber length varying MENPs' dimension is detailed in Figure 6, where Figure 6a,b shows the equivalent current when the stimulating source is a single MENP and a 500 \(\upmu\)m cluster, respectively. In both cases, the source is perpendicularly oriented and placed at a distance 1R from the fiber. For the sake of readability, the extension along the fiber length is the same as in Figure 4, and the timeframe covers the whole stimulus duration. As expected, when stimulating with a single MENP perpendicularly oriented, the injected current is localized in the [PERSON]'s node, which comprises the MENP and its two adjacent MYSA segments, whereas it is zero in all the other segments. The maximum amplitudes in absolute value of the current injected in the [PERSON]'s node are 47.7 nA, 47.2 and 47.5 nA for distances 1R, 2R and 3R, respectively.