## 1 Introduction  
Electrical stimulation of bone has received a lot of attention in recent decades. It can be employed to improve bone healing in the case of fractures [1; 2; 3; 4; 5], non-unions [6; 7], or other bone defects [8; 9; 10] such as those resulting after tumor resection. A further benefit could be stimulation of osseous healing capacities especially in compromised situations such as irradiated sites or patients with systemic intake of antiresorptive drugs [11; 12]. The reason for the therapeutic effect of electrical stimulation is seen in the imitation of the electric fields that occur naturally in bone as a bioelectric tissue. The bioelectricity of bone has been an object of study for a long time. One example is in long bones showing the accumulation of charges when exposed to mechanical stress or strain: On the concave side negative charges accumulate and bone formation can be observed, whereas positive charges and bone resorption occur on the convex side [13]. These effects are attributed to streaming potentials [14; 15; 16] and piezoelectricity [17; 18; 19]. Also, some studies hypothesize strong interdependencies between both phenomena [20; 21]. Taking advantage of bone's bioelectric properties, electrical stimulation for bone regeneration was attempted as early as in the 1950s with [PERSON] [22] as the \"pioneer\" in the field of bone bioelectricity and stimulation. Since then, accelerated bone regeneration due to electrical stimulation has been widely investigated in numerous in vitro, in vivo, in silico, and clinical studies [23; 24]. The naturally occurring electric fields in loaded bone contribute to a complicated signaling network involved in bone modelling and remodeling that has not yet been fully understood. However, cell experiments showed that stimulation of osteoblasts with low-frequency electromagnetic fields induces enhanced collagen synthesis [25]. [PERSON] et al. observed significantly enhanced DNA production following electric stimulation of bone cells [26]. Further in vitro studies could prove effects of electric stimulation on processes such as proliferation, differentiation, and migration of bone mesenchymal stem cells [27] and osteoblasts [28]. There are many ways of applying certain types of stimulating signals, for example constant, pulsed or alternating currents or fields (electric, magnetic, electromagnetic). These signals may be coupled to the tissue directly, capacitively, or inductively [29; 30]. The diverse stimulation parameters applied in different studies are mainly used empirically or phenomenologically. This is because the complex physiological processes of bone remodeling are still not fully decoded. In clinical practice, low-frequency stimulation with sinusoidal electromagnetic fields between 5 and 70 V/m at \(f=20\) Hz empirically led to improved healing results [31]. Consequently, it is assumed that electric field strengths above 70 V/m might lead to harmful tissue damage due to overstimulation, whereas field strength below 5 V/m would show no supportive effect on bone regeneration. The method established by [PERSON] and [PERSON] [31] has been further developed. [PERSON] et al. proposed the \"pipolar induction screw system\" (BISS) [32] that became an established method and that has been applied mainly to patients with loosened hip endoprostheses or femoral head necrosis. These findings were also supported by recent in vitro studies: Cell experiments applying an AC sinusoidal signal (\(f=20\) Hz) on human osteoblasts showed voltage-dependent enhanced differentiation of the cells [33]. Using the BISS system, electromagnetic fields in combination with additional alternating electric fields at 20 Hz and 700 mV potential difference between the electrodes of the screw showed a positive impact on bone cell viability and differentiation [34]. As for the development of electro-stimulating implants for bone regeneration, numerical simulation is a useful tool in the design process.