# Numerical Simulation of Electric Field Distribution around an Instrumented Total Hip Stem
## 3 Results  
The results of the measurements on the cross section of the porcine femur perpendicular to the first electrode and the interface between the insulator and the implant have been shown in Table 1. As in a homogeneous medium the electric potential varies inversely proportional with the distance from the electrode, it could be roughly expected that measurements on line B starting from the interface between the implant and the insulator resulted in smaller values of the potential than measurements on line A starting from the first electrode. This holds true except for the measured values at a distance of 7 mm. The distinctive distribution of the electric potential demonstrates that the highest values of 1.68 V, 1.25 V, and 1.17 V (case studies 1-3) were obtained on line A. The investigation of the potential at the cross section of the bone resulted in a decay of 78% on line A (2-7 mm) and 72% on line B. In case study 1, the decay amounted to 68% along line A. For case study 2, it was 53% and for case study 3, it was 46%. In general, case study 3 came closest to the measured values, with deviations in the range of 0.01 V-0.25 V. Regarding the differences in measured and simulated potential values, one should keep in mind that there are several error sources both in measurements as well as in the numerical simulations. The most important error source in the simulations has to be attributed to the lack of data on dielectric tissue properties for porcine bone which is why the data from human bone needed to be taken. Additionally, there is rather high uncertainty in general in dielectric tissue properties in the low-frequency spectrum. Figure 2: Experimental setup with the connected hip stem. A raster of 10 different readout locations at the surface of the porcine femur was used. The distribution of the electric field strength and the electric potential in the numerical simulation shows a strong stimulation capacity of the surrounding bone tissue (Figures 3 and 4). The implant surface is also stimulated. When the tissue properties from [PERSON] et al. [22] for yellow bone marrow were used, its insulating effect on the electric field distribution became evident (see Figure 3a). In the case of using higher conductivity as of red bone marrow [23], the electric field reached a larger area of the surrounding bone and was more evenly distributed (see Figure 3b). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Potential (V)**} \\ \cline{2-6}  & **Distance to the** & & \multicolumn{4}{c}{**Simulation**} \\ \cline{3-6}  & **Implant (mm)** & **Experimental** & **Case Study 1** & **Case Study 2** & **Case Study 3** \\  & & & **[22]** & **[22]** & **[24]** \\ \hline \multirow{4}{*}{Line A starting from the first electrode} & 2 & 0.99 & 1.68 & 1.25 & 1.17 \\  & 4 & 0.76 & 1.24 & 0.95 & 0.87 \\ \cline{1-1}  & 5 & 0.49 & 0.57 & 0.73 & 0.63 \\ \cline{1-1}  & 7 & 0.22 & 0.54 & 0.59 & 0.47 \\ \cline{1-1}  & 2 & 0.81 & 1.19 & 0.90 & 0.80 \\ \cline{1-1} Line B starting from the implant-insulator interface & 4 & 0.52 & 1.10 & 0.78 & 0.69 \\ \cline{1-1}  & 5 & 0.42 & 0.65 & 0.63 & 0.53 \\ \cline{1-1}  & 7 & 0.23 & 0.53 & 0.54 & 0.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Electric potential measured on the cross-section of the bone perpendicular to the first electrode and the interface between implant and insulator. Figure 4: Measured and simulated electric potential values. Values are shown on readout locations L1–L5 of the raster followed by readout locations R1–R5 of the raster, each at a depth of (**a**) 5 mm and (**b**) 8 mm within the stimulated porcine femur. Figure 3: Distribution of the electric field strength in the transversal plane of the porcine femur. Conductivity values of (**a**) yellow bone marrow (case study 1) [22] and (**b**) red bone marrow (case study 3) [23] have been employed here. In case studies 2 and 3, the electric potential at the raster displays the same trend due to the similar potential values of red bone marrow and cancellous bone (Figure 4).