# Study of Electrical Neural Stimulation Effects Using Extraneural and Intraneural Electrodes
## 2 Materials and Methods
### FEM Models of the Human Median Nerve and Neural Electrodes  
The human median nerve simplified models were obtained starting from the anatomical image used in our previous works [3; 5]. In Figure 1, a schematic view of the used procedure is shown. According to the considered electrode type, two different nerve dimensions were modeled, depending on the median nerve region where the electrodes were implanted. Geometrical properties of the human median nerve related to nerve and fascicle dimensions were set according to the data reported in [11]. To create and locate circle-section inner fascicles in the nerve boundary model, the nerve model with the ds-FILE electrode had an anatomical boundary shape. The nerve model with the cuff had a circular shape section according to the electrode section. The 3D nerve models were developed in Comsol Multiphysics(r) v.5.3 (Comsol S.r.l., Brescia, Italy); all the models had a length of 15 mm. Different tissue classes were assigned to each region of the nerve model according to the human anatomy. Three tissues were considered: endoneurium, perineurium, and epineurium. Conductivities related to each tissue were 0.00088 S/m and 0.0826 S/m for perineurium and epineurium. Endoneurium has an anisotropic conductivity tensor with a transverse value of 0.00826 S/m and a longitudinal value of 0.0571 S/m [6]. A cylindrical region with saline solution properties and a diameter of 76 mm was considered to simulate the intraoperative environment. [PERSON]'s equations in media were solved using finite element methods, using Dirichlet boundary conditions with \(V=0\) at infinity. To implement this approximation in Comsol, the diameter of the saline cylindrical region was set larger than the nerve dimension. The AC/DC module of Comsol Multiphysics(r), physics of Electric Currents, was used. A quasi-static approximation of [PERSON]'s equations was considered [13] for the study of the electric potential in the tissues  
\[\
abla\cdot(\sigma\
abla V)=0 \tag{1}\]  
where \(V\) and \(\sigma\) are the electric potential and the conductivity of the medium, respectively. Comsol Multiphysics(r) allows us to solve the following equations:  
\[\
abla\cdot\vec{J}=Q_{J} \tag{2}\]where \(\vec{j}\) is the current density and \(Q_{j}\) is the current source,  
\[\vec{J}=\sigma\vec{E}+\vec{J_{e}} \tag{3}\]  
where \(\vec{E}\) is the electric field and \(\vec{J_{e}}\) is the external current density,  
\[\vec{E}=-\
abla V \tag{4}\]  
\(Q_{j}\) and \(J_{e}\) are set to zero in all the space in the model and [PERSON]'s equations are solved in quasi-static approximation. Tetrahedral elements are used to mesh the geometry of the model.  
Nerve dimensions in the models with ds-FILE and CUFF electrodes are different according to their dimensions and to the region of the nerve where the electrode was implanted in experimental studies. Two different nerve regions were considered at two different heights along the median nerve, those regions have section dimensions of minor and major diameters of 2.99 \(\pm\) 0.66 mm and 6.27 \(\pm\) 0.85 mm for the first region and 3.35 \(\pm\) 1.39 mm and 7.07 \(\pm\) 1.29 mm for the second region, as reported in [11].