## 4 Discussion
Specifically, decreasing the conductivity in the defect domain (Figure 6) revealed that with the same amplitude of the signal driving the stimulation a higher percentage of the defect region could be stimulated beneficially. What this implies is that a lower stimulation potential would be sufficient to obtain the same volume of beneficially stimulated tissue, or that the healing stimulation would reach further into the tissue, enabling a better growth of new tissue into the volume. However, substantially increased overstimulation could also be observed in this case. Therefore, the ideal stimulation unit would be feedback--controlled and able to adjust the stimulation signal during the treatment. As the flowing current decreases with the healing progress, the power consumption is reduced as well. This may allow for a longer lifetime of the battery. For the future application in vivo--and later also in the clinic--a stimulation unit that will control and monitor the stimulation signal is under development. Regarding the design of the circuitry, the electrical impedance of the electrodes in the biological tissue is an important measure. For the optimized stimulation configuration the impedance is \(Z=\frac{\varphi_{\mathrm{stim,opt}}}{I}=\frac{0.523\,\mathrm{V}}{1.244\,\mathrm{mA }}=$420.4\,\mathrm{\Omega}$\). Ex vivo experiments are planned to validate the numerical results. These experiments will include impedance measurements as well as measurements of the electric potential around the electrode in a porcine mandible. Regarding the assumptions and limitations of the numerical study, there are different aspects to be noted. With respect to the dielectric tissue properties, we chose to include only the conductivity but not the permittivity. This has the advantage of simplifying the mathematical and numerical model and thus reducing computational demands. This decision is well justified since it is the conductivity which has the main impact when simulating electric stimulation of biological tissue [69]. A limitation of all such numerical studies on bioelectric effects is given by the fact that the dielectric properties of biological tissues available in the literature vary strongly among different species and also depend on the experimental conditions and the specific anatomic site [70; 71; 72]. Furthermore, the tissue properties depend on age [73] and health conditions of the subject: osteoporosis [74; 75] will have an impact, for example. In addition, we assumed the defect to be filled purely with cancellous bone. In practice however, the cancellous bone material that is taken from another part of the body will be molded to fit into the defect, and equipped with growth factors. Hence, the cancellous bone will not be available in its original structure, thus having an unknown effect on its dielectric properties. Aside from that, we assumed each single sub-domain of the model that is representing one kind of tissue to be homogeneous and isotropic, neglecting the possible impact on the dielectric properties due to tissue heterogeneity and composition. To better capture the impact of the latter assumptions and the only vaguely known dielectric tissue properties, our future studies will include _Uncertainty Quantification_ (UQ) methods in the numerical model. With this, the impact of the uncertain input parameters, especially the electric conductivity, on the obtained stimulation parameters could be identified. UQ methods are currently gaining in importance for this reason in numerical simulations of biological tissues [76; 77; 78]. In addition to the uncertainties in tissue parameters, geometrical uncertainties resulting from different jaw geometries or from manufacturing limitations of the implant could be estimated in terms of stochastic measures as well.