# Evaluation of Bone Consolidation in External Fixation with an Electromechanical System
## 2 Materials and Methods
### Experimental Models
This program enables the selection of movement type, choosing the linear velocity of the movement, the displacement distance, and the number of repetitions to be performed. Because the micromotor needed a power supply to ensure the mechanical stimulus, there was also a mechanical resistance, and the motor current consumption was related to the mechanical resistance. Although the resistance depends on several factors, such as the sliding friction among several surfaces, the resistance opposition in the osteotomy mainly contributes to the system's mechanical resistance. Hence, it is crucial to find a relationship between the rigidity of the osteotomy and the energy to supply to the motor that guarantees the necessary mechanical stimulus. Moreover, after calibration, the electromechanical system creates displacement relationships between the fixator clamp and the osteotomy. A support platform built-in Aluminum profile of Minite(r) (30 \(\times\) 30) was developed for the two models, allowing the positional adjustment of the components. This structure intended to replicate, in a simplified way, the positioning of the lower limb in the horizontal position, like in a bedridden patient. It included a fixed support, representing the position of knee connection, and a free axial support, which mimicked the relationship with the foot and guided the axial movement introduced in the assembly, as shown in Figure 3. The osteotomy's displacement was characterized using a Mitutoy(r) analogue comparator, with a measurement accuracy of 1 um and located on one of the faces of Sawbones(r) block. Figure 2: Connection of the electromechanical system into the external fixator Orthofix®. This study used the Sawbones(r) blocks (Sawbones(r), Malmo, Sweden, 2019) with different densities to simulate different osteotomy rigidities. According to the trademark, these materials allow for a good simulation of the mechanical characteristics of the regenerated bone in the many stages of bone callus growth [17], reproducing the variation in bone callus stiffness. The mechanical properties and the designation of the several materials are in Table 2. This material is applied in osteotomy to carry out advancement tests. These tests are intended to evaluate the resistance capacity of the material when subjected to compression. The Sawbones(r) materials have rigidities (stiffness expressed in Young's compression Modulus) between those of fibrous tissue, immature bone, and mature bone. Table 3 compares the Sawbones stiffness values at different densities with bone characteristics in the various phases. Several authors [19; 20] used these regenerated bone properties to represent bone regeneration in mathematical models, whereas other researchers created numerical models based on the same information [21; 22; 23]. The primary purpose of this experimental setup was to study the relationship between rigidity and micromovements on the osteotomy for the loading conditions defined at the micromotor. Moreover, it was also essential to evaluate the micromotor energy consumption (CEMotor) in forward and backward movements to determine its relationship with the material's stiffness at the osteotomy. Hence, three different displacements were imposed in the osteotomy, corresponding to 1, 1.5, and 2 mm, and, to guarantee repeatability and reproducibility, five tests for each displacement were performed. Several authors argue that the recovery time can be reduced if osteotomy stimulation is promoted with displacements of 1 mm/day [13; 24; 25; 26; 27; 28; 29].