## 1 Introduction
It allows testing of possible stimulation setups and the exclusion of unfeasible designs already at an early stage. In this context, electro-stimulating implants for a hip revision system were developed and numerically optimized [35; 36; 37; 38]. Furthermore, electrically stimulating dental implants were designed and examined in vivo [39] and in silico [40]. However, large bone voids such as critical size defects in the mandible (lower jaw) have not been considered so far. Such defects extend over several centimeters and thus do not heal spontaneously without plastic reconstruction. Critical size defects occur mainly after partial resection of the mandible due to tumors, and are of great clinical relevance with over 3100 surgeries per year in Germany alone [41]. These defects are conventionally treated with a combination of bone replacement material and an osteosynthesis plate to keep the material in position with the help of screws. Unfortunately, this approach is frequently accompanied with complications that may make a revision surgery necessary. These complications include fracture of the plate, loosening of the fixation screws, or dehiscence [42; 43; 44]. To avoid such a second surgery with its additional risks for the patient, our aim is to use electrical stimulation as an approach to achieve faster bone healing and better fixation of bone and implant. Although we already proposed preliminary numerical models of an electrically stimulated human mandible [45; 46], the current work for the first time examines an electrical stimulation system for the regeneration of critical size defects in mandibular bone suitable for practical application in validation experiments. Specifically, in the current study we focus on a numerical model of a porcine, i.e., minipig mandible. This was chosen because of planned in vivo experiments with minipigs that will follow this numerical study. Compared to the human mandible, minipigs provide a similar geometry of the lower jaw. For the minipig mandible, a critical size defect is stated to be 2 cm [47]. The aim of the present study is to develop and numerically examine electro-stimulating devices that directly stimulate the tissue in the defect region. In this way, no external primary coil--in contrast to the BISS method [28; 32]--is necessary. This would increase the patient's comfort and ensure patient compliance. In this context, this work introduces the procedure to numerically simulate and optimize an electro-stimulating device for a critical size defect in the lower jaw of a minipig. The conducted finite-element simulation studies constitute an important first step in preparation for in vivo experiments. These experiments will be described in the future. In our current study, we hypothesize that the proposed design of a bipolar electro-stimulating device allows for a suitable region of beneficially stimulated tissue in the lower jaw of a minipig with a critical size defect. To support this hypothesis, the stimulation impact is estimated with the help of a finite-element simulation model. In addition, we assume that the resulting numerical model enables us to determine optimal stimulation parameters such as electrode length and stimulation potential for a given stimulation frequency of \(f=20\,\mathrm{Hz}\) to achieve a maximum beneficially stimulated area. To optimize the electro-stimulating implant with respect to best possible electric field distribution within the defect region, the finite-element method was used. Prior to simulation, a 3D model of a minipig mandible with a critical size defect, surrounding soft tissue, and an electro-stimulating implant was created. The implant parameters, i.e., the length of the electrodes and the applied voltage were optimized. In addition, we assessed the impact of varying the electric conductivity assigned to the defect and concluded important requirements for the application and further development of future electro-stimulating implants.