## 1 Introduction  
Understanding and controlling biomechanical influences are essential factors for the long-term success of dental implants [1]. In this context, it is well known that the mechanical stress acting at the junction between implant and bone influences osseointegration [2; 3; 4]. Furthermore, the force transmission from the implant to the peri-implant bone depends on the design of the junction, the direction of the force (axial or non-axial), the length and diameter of the implant, the implant design, and the quality of the bone [5; 6; 7; 8]. Currently, research in the literature has examined the transmission of forces from the superstructure to the bone via the implant; however, the resulting conclusions remain limited [2; 9; 10]. Highly complex methods are required to measure the mechanics that occur in a system consisting of the bony implant site, implant, and superstructure (possibly with abutment and screw) [9; 10]. Two previously established conventional methods are currently available for this purpose. One method is the virtual and computer-based finite element method (FEM), which is used for deformation simulation. Complex geometric shapes are broken down into simpler bodies (finite elements) such as cuboids, tetrahedra, or cubes and represented within software. The deformation behavior of the original structures can be calculated approximately in the software model on the basis of these shapes and the resulting simplified mathematical relationships [11]. In this way, solid bodies such as bones or implants, but also soft tissue, can be examined in dentistry. The advantages of the FEM are its 3D representation of the simulated processes and its relatively simple implementation feasibility [12; 13; 14]. However, a disadvantage is that the FEM is only a simulation and a simplification and, therefore, its transfer to actual biomechanical processes in the human organism is difficult [15; 16]. The second established method is the use of strain gauges. This is used in dentistry, for example, in the detection of deformations of dental prostheses [17; 18] or of the peri-implant bone [19]. Strain gauges are electrical sensors in the form of meander-shaped conductors connected to a current source and placed at each of the measuring points to be examined. Their specific resistances and electrical voltages change according to changes in their lengths and cross sections due to a change in the shape of the measuring point location [20]. This corresponds to the deformation at the measuring point when used correctly [21]. The exact calculation of the change in length is based on the change in resistance and thus the change in stress, accounting for a material-specific proportionality constant. The calculation is assisted by a signal amplifier and software. This conversion must be performed individually for each measured value and is synchronized with the corresponding force value that caused the deformation [20; 22]. Strain gauges are an established method for measuring surface deformations in dental research, and they are currently the only adequate measurement method [6; 23; 24; 25; 26]. A disadvantage of using strain gauges is the high technique sensitivity of the method. Thus, bonding at the measurement site is very costly--especially in the context of in vivo investigations. In addition, only 1D measurements are possible with linear strain gauges. Therefore, not only is the exact positioning on the measuring point of great importance, but also the spatial alignment is important for correctly recording the direction of a shape change [27; 28; 29; 30]. Sufficient temperature control is also necessary for quantifying the measurement results, since even small temperature changes can lead to changes in the shape of the strain gauges due to their very fine structure. Thus, strain gauges are prone to falsified, temperature-related measured values [30]. Even when used in accordance with the process, inherent errors, such as hysteresis and nonlinearity, have been described when using strain gauges [31].