Electrical stimulation is a promising therapeutic approach for the regeneration of large bone defects. Innovative electrically stimulating implants for critical size defects in the lower jaw are under development and need to be optimized in silico and tested in vivo prior to application. In this context, numerical modelling and simulation are useful tools in the design process. In this study, a numerical model of an electrically stimulated minipig mandible was established to find optimal stimulation parameters that allow for a maximum area of beneficially stimulated tissue. Finite-element simulations were performed to determine the stimulation impact of the proposed implant design and to optimize the electric field distribution resulting from sinusoidal low-frequency ( $f=20\mathrm{Hz}$ ) electric stimulation. Optimal stimulation parameters of the electrode length $h_{\mathrm{el}}=25\mathrm{m}\mathrm{m}$ and the stimulation potential ${\phi }_{\mathrm{stim}}=0.5\mathrm{V}$ were determined. These parameter sets shall be applied in future in vivo validation studies. Furthermore, our results suggest that changing tissue properties during the course of the healing process might make a feedback-controlled stimulation system necessary.

Objective: Electrical stimulation is known to enhance bone healing. Novel electrostimulating devices are currently being developed for the treatment of critical-size bone defects in the mandible. Previous numerical models of these devices did not account for possible uncertainties in the input data. We present the numerical model of an electrically stimulated minipig mandible, including optimization and uncertainty quantification (UQ) methods that allow us to determine the most influential parameters. Methods: Uncertainties in the optimized finite element model are quantified using the polynomial chaos method that is implemented in the open-source Python toolbox Uncertainpy. The volumes of understimulated, beneficially stimulated, and overstimulated tissue are considered quantities of interest because they may significantly impact the expected healing success. Further, the current is a substantial quantity, limiting the lifetime of a battery-driven stimulation unit. With sensitivity analyses, the most critical parameters in the numerical model can be identified. Thus, we can learn which parameters are particularly relevant, for example, when conceptualizing the stimulation unit or planning the manufacturing process. Results: The results of this study show that the parameters of the electrode-tissue interface (ETI), as well as the conductivity within the defect volume, have the most significant impact on the model results. Conclusions: The UQ results suggest that careful characterization of the ETI and the dielectric tissue properties is crucial to reduce these uncertainties. Significance: The numerical model regarding uncertainties yields important implications for reliable implant design and clinical translation.

Fractures or other major bone defects in the mandible are commonly treated by mounting a reconstruction plate at the fracture site. To avoid complications due to loosening of the implant or the fixation screws, electrical stimulation presents a possibility to accelerate bone healing. The aim of this study was to investigate different combinations of activated electrodes and plate designs regarding their feasibility for electrostimulation of the mandibular bone. The electric field distribution for multiple implant designs was computed using the finite element method. The results suggest that the electrode insulation renders a crucial parameter, which influences substantially the stimulation impact and its power consumption.

The reproducibility of scientific results gains increasing attention. In the context of biomedical engineering, this applies to experimental studies of three different kinds: in-vivo, in-vitro, and in-silico. Numerical modelling and finite element simulation of bio-electric systems are intricate processes involving manifold steps. A typical example of this process is the electrical stimulation at alloplastic reconstruction plates of the mandible. During the bio-electric modelling and simulation process, diverse methods realised in various software tools are exploited. To comprehensibly render how the final model has been developed requires a thorough documentation. We exploit the W3C provenance model PROV to structure this process and to make it accessible for modellers and for automatic analyses. Different entity types, such as data, model, software, literature, assumptions, and mathematical equations are distinguished; roles of entities within an activity are revealed as well as the involved researchers. In addition, we identify five process patterns: 1) information extraction from the literature; 2) generation of a geometrical model which uses data as input; 3) composition of several geometrical or mathematical models into a combined model; 4) parameterisation, which augments the input model by additional properties; and, finally, 5) refinement, which uses a model in addition to an assumption and generates an enhanced model. By modelling provenance information of a typical bio-electric modelling and simulation process as well as identifying provenance patterns, we provide a first step towards a better documentation of academic investigations in that scientific field.

Smart implants are intended to achieve a longer lifespan in the future through integrated sensory and therapeutic functions. In this way, insufficient osseointegration and loosening of uncemented total hip replacements should be prevented by electrodes attached to the femoral stem, specifically stimulating bone growth to improve fixation and thus avoiding revision. For this function, an energy source is necessary, whereby an internal, autonomous one is desirable. Accordingly, in a previous study, a piezoelectric element was integrated into an uncemented hip stem to convert mechanical energy into electrical energy. However, the electrical output has only been calculated computationally, while in practical applications, energy losses occur during energy storage. Moreover, there is a lack of research on total hip and knee replacements with integrated piezoelectric elements that evaluate electrical power generation during everyday activities other than gait. Therefore, the present study aimed to experimentally determine the generated average electrical power of an uncemented revision hip stem with equipped piezoelectric element during different everyday activities. Furthermore, the storable energy during the most promising activities was evaluated with a standard energy harvesting (SEH) circuit. A simplified test rig was set up for these measurements. The results indicate that jogging and walking, with an average electrical power of 204 µW and 75 µW, respectively, convert the most energy, followed by stairs up and stairs down. After 20 min of jogging, 20.7 mJ were stored in a 330 µF capacitor, while one hour of walking yielded 12.9 mJ in a 470 µF capacitor. The energy required for two 1 cm long stimulation electrodes is estimated to range from 0.1 mJ (10 µA, 1000 Hz) to 254 mJ (100 µA, 20 Hz) for the recommended daily protocol of three 45 min sessions. Accordingly, the harvested energy of 12.9 mJ may be sufficient to support electrical bone stimulation at up to 20 µA over 20−1000 Hz. To increase the stored energy, significant energy losses in the SEH circuit due to impedance mismatch must be minimized by improving the energy harvesting circuitry.

Objective: Electrical stimulation is known to enhance bone healing. Novel electrostimulating devices are currently being developed for the treatment of critical-size bone defects in the mandible. Previous numerical models of these devices did not account for possible uncertainties in the input data. We present the numerical model of an electrically stimulated minipig mandible, including optimization and uncertainty quantification (UQ) methods that allow us to determine the most influential parameters. Methods: Uncertainties in the optimized finite element model are quantified using the polynomial chaos method that is implemented in the open-source Python toolbox Uncertainpy. The volumes of understimulated, beneficially stimulated, and overstimulated tissue are considered quantities of interest because they may significantly impact the expected healing success. Further, the current is a substantial quantity, limiting the lifetime of a battery-driven stimulation unit. With sensitivity analyses, the most critical parameters in the numerical model can be identified. Thus, we can learn which parameters are particularly relevant, for example, when conceptualizing the stimulation unit or planning the manufacturing process. Results: The results of this study show that the parameters of the electrodetissue interface (ETI), as well as the conductivity within the defect volume, have the most significant impact on the model results. Conclusions: The UQ results suggest that careful characterization of the ETI and the dielectric tissue properties is crucial to reduce these uncertainties. Significance: The numerical model regarding uncertainties yields important implications for reliable implant design and clinical translation.