In 6 surrogate specimens, a standardized transverse fracture model with a fracture gap of 3 mm was created, as described previously [1, 2]. The cylindrical bone surrogates were manufactured using polyoxymethylen-copolymerisat with a Young's modulus of 3.1 GPa (diameter 30 mm, wall thickness 7 mm, cylinder length 120 mm). Osteosynthesis was performed using a bridge-plating configuration with a standard 11-hole, 3.5-mm locking compression plate (Synthes, Oberdorf, Switzerland). Plates were fixed with 3 locking screws (55 mm) on each fragment placed in the second, third, and fourth hole from the fracture site (Figure 7). All screws were tightened to 1.5 Nm, with the plate elevated 2 mm from the surrogate surface. Specimens were inserted into a special testing frame mounted on a testing machine (Zwick 2.5 KN; Ulm, Germany) and an axial load of up to 100 N with a constant rate of 10 mm/min was applied. Measurements of the micromotion of the fragments were performed using a self-made high-accuracy tactile measurement system made of 3 digital dial indicators and an optical measurement system.
Optical measurement system
For measuring the 3D fracture motion we used the optical analysis system PONTOS 5 M (GOM - Optical Measuring Techniques, Braunschweig, Germany). The system is offered in 4 different configurations (5 M, 4 M, 12 M or High Speed) with several camera resolutions (up to 4096 × 3072 pixel) and frame rates (up to 5000 Hz) to cope for diverse applications. The individual system consists of two CCD cameras. For the detection of the motion passive markers are required. These passive markers are simple white dots. The size is adapted to the object size and camera resolution. The points are recorded and tracked by the PONTOS software (Figure 8). The accuracy of the measurements is directly addicted by the resolution of the cameras. Each passive marker is detected in the single image as ellipses in the size of several pixels. The center of the marker can therefore be determined in the sub-pixel space by evaluation of a best fit at the contour of the ellipses, which is done automatically by the software. The PONTOS 5 M system was set up and calibrated for a measurement volume of 350 × 280 × 280 mm according to the manufacturers documentation. The geometrical setup as well as the optical distorsion factors of lenses are considered in the calibration procedure. The frame rate was 4 Hz. We used white self-adhesive dots with a diameter of 2 mm. At least 3 points per object are needed. For a higher accuracy we used all in all about 200 passive markers. It is not necessary to add the points in a special pattern. But doing that, the system could learn to identify the objects with the help of the different patterns. A group of points functions like a six degrees of freedom (6DoF)-sensor. The high number of points allowed fitting two cylindrical geometry elements which represent the physical cylindrical fracture fragments. The 6DoF motion could therefore be directly represented at the location in the centre of the fracture gap for each fragment. Relative motion in all six degrees of freedom where analysedrespectively.
Reference measurement system
For reference measurements we used digital indicators from the company MAHR (Marcator 1086; Mahr, Goettingen, Germany). To date, dial indicators represent the gold standard in measuring motion in the range of micrometers. We used 3 digital indicators. Each dial gauge can specify one degree of freedom. The resolution of the individual gauge was 1 μm (Span of error 5 μm, Repeatability 2 μm). This accuracy is ensured by the company. For positioning the 3 dial indicators to the osteosynthesis two cranks were constructed and made for measure using a cnc milling machine (Figure 6). The measurement set up was developed in cooperation with the German Aerospace Center (DLR, Oberpfaffenhofen, Germany). The dial indicators were connected to a computer system by an usb interface. The data recording was carried out using the supplied software from Mahr. Due to the placement of the indicators far from the fracture gap, the interfragmentary motion could not be detected directly. Instead, interfragmentary motions were indirectly measured by analyzing the motion of the measuring spindle of the dial indicators. The motion at the fracture gap has to be calculated using the geometry of the cranks and the values of the dial indicators. Using the values of digital indicator 1 and 2 it was possible to calculate the z deviation (Δz) and the angle alpha (Δα) between the both cylinder axis (fracture fragments) (Figure 6). Using digital indicator 3 it was possible to calculate the y deviation (Δy). To compare the accuracy of the two measurement systems (PONTOS 5 M vs tactile measurement system), we conducted an additional measurement. For this purpose, the passive markers of the optical measurement system were attached directly to the spindles of each of the 3 indicators (Figure 5). With this set up the motion of the spindles could be detected with the optical measurement system, by measuring the point to point motion. Both values (digital indicator and PONTOS) could be compared. Simultaneous data collection was achieved by trigger points. A total of 3 data-sets, 200 values per set, were collected, 1 for each dial indicator.
Statistical analysis
For analyzing the agreement between the optical measurement system PONTOS 5 M and the indirect measuring by the dial indicators Bland-Altman-Plots were calculated. For each comparison we checked the assumption of uniform differences and uniform variability. If these assumptions were violated a regression approach was applied. We used a Generalized Estimation Equation Model (GEE) to account for the different measurements made in one specimen (the force was varied between 0 and 100 N in increments of 10 N for each specimen, which results in 11 measurements per specimen). The results of this model were used to calculate mean differences and 95% limits of agreement as described by Bland and Altman [17, 18].