## 4 Discussion  
In this study, a finite-element simulation model of a minipig mandible with an electro-stimulating implant without contact to the oral cavity could be built. This model enabled us to determine optimized stimulation parameters for the electro-stimulating setup. Furthermore, we could draw conclusions on the impact of changing material properties during bone healing. The simulation results lead to a recommendation for the stimulation parameters to be used in the in vivo experiments following this study. Applying the optimized parameters \(h_{\text{el}}=25\,\text{mm}\) and \(\varphi_{\text{stim,opt}}=0.523\,\text{V}\), nearly one half of the defect volume is being stimulated beneficially (Figure 6, case for \(\sigma_{\text{defect}}=0.078\,\text{S/m}\)). By specifying strict weighting of the objective function for overstimulation, in the optimized setting only 2% of the tissue receives unfavorable electric field strengths greater than \(70\,\text{V/m}\). It is favorable that the simulated volume of overstimulated tissue is generally much smaller than the volume of beneficially stimulated tissue. Otherwise, the related tissue damage would undo the healing impact of the electric stimulation in certain regions of the defect. However, we observed that the desired field threshold between 5 and \(70\,\text{V/m}\) is not only achieved in the bone, but also in the soft tissue (Figure 4b). The consequences of this need to be carefully studied in the in vivo experiments as the impact of such fields on soft tissue is not exactly known. Forcing the optimization to avoid overstimulation, a relatively low optimal stimulation amplitude of ca. \(\varphi_{\text{stim,opt}}=0.5\,\text{V}\) results. This is also favorable in terms of ensuring long lifetime of the battery being used in the planned animal experiments. Furthermore, [PERSON] et al. [66] observed profound  
Figure 6: Impact of changing the electrical conductivity \(\sigma_{\text{defect}}\) in the defect domain on the volume of stimulated tissue and the current flowing through the electrodes. electrolysis at stimulation potentials higher than \(1\,\mathrm{V}\). Therefore, in the planned electro-stimulating devices voltages as high as this should be avoided. In this context, comparative numerical test studies with higher stimulation amplitudes of \(\varphi_{\mathrm{stim}}=$1\,\mathrm{V}$\) and \(\varphi_{\mathrm{stim}}=$2\,\mathrm{V}$\) showed that the volume of beneficially stimulated tissue could be increased by \(11.0\%\) and \(15.6\%\) respectively, but these lead to a 5-fold or 11-fold increase respectively in the overstimulated volume. This brings us to the conclusion that the stimulation voltage should be monitored carefully and kept low to avoid possible tissue damage during application. To sum up, the optimized stimulation parameters \(h_{\mathrm{el}}=$25\,\mathrm{mm}$\) and \(\varphi_{\mathrm{stim,opt}}=$0.5\,\mathrm{V}$\) allow for an energy-efficient beneficial electrical stimulation of roughly one half of the defect volume with only very small regions of overstimulated tissue. The computed currents of \(1.244\,\mathrm{mA}\) flowing between electrode and tissue may be perceptible according to [67] (reproduced in [68]); however, this value is far from the threshold for muscular reactions (\(5\,\mathrm{mA}\)[67]). Consequently, the electric currents present in the optimized stimulation setup may be acceptable for long-term stimulation. However, in the end only the in vivo experiments can reveal the actual impact. Analyzing the consequences of changing conductivity in the defect domain allowed us to roughly estimate how the stimulation impact might change over the whole treatment time. For the in vivo experiments this might extend over 6-12 weeks. We draw the conclusion that a corresponding adjustment in the stimulation parameters is necessary to ensure proper stimulation throughout the entire therapy.