Determination of the accuracy of the 3D motion-capture system
The accuracy of the measurement setup was determined under the same conditions as the pelvis specimen test was performed. A rigid steel framework equipped with 10 digital high-speed cameras (6 cameras Vicon MX13+, 4 cameras Vicon T40, Vicon, Oxford, UK) was placed around a Servo-hydraulic testing machine (MTS Bionix 858, MTS Eden Prairie, MN, USA). The framework was screwed to the concrete floor and walls of the room to avoid movement of the cameras and have the 10 cameras in the same stable position during measurements. A 3D linear stage (M-461-XYZ-M, Newport Spectra-Physics GmbH, Darmstadt, Germany) equipped with three manually-driven differential micrometres (DM-13, Newport Spectra-Physics GmbH, Resolution 0.0001 mm) was mounted to the table of the Servo-hydraulic testing machine. A Z-shaped steel frame was screwed to the 3D linear stage to hold five dome-shaped, passive reflecting markers with a diameter of 6.5 mm (Prophysics AG, Zürich, CH) (Figure 1). The markers were glued to the Z-shaped frame so that they could be tracked either by 2, 3, 6, or 10 cameras during the accuracy-determination procedure. Three additional markers, visible to all 10 cameras, were placed on to the base of the 3D linear stage as a static reference. The accuracy determination procedure consisted of a 3D-displacement curve with a step function with five steps up and five steps down per axis. Two procedures were performed, each with three independent repetitions. The first procedure had a 0.01 mm displacement in each axis per step and a second of 0.1 mm. The order of the displacement was done by moving the 3D linear stage first in the sagittal (Y), then the transverse (X), and finally in the longitudinal (Z) axes. The new 3D position was then held for a minimum of 5 s before proceeding to the next steps.
Before performing the accuracy determination procedure, the cameras were calibrated as described in the Vicon Handbook using the 120 mm 3-marker calibration wand and the Ergo-Calibration Frame equipped with 9 mm and 9.5 mm markers respectively. The sampling rate of the cameras was set at 60 Hz and the hydraulic pump of the Servo-hydraulic testing machine was running in order to get conditions identical to the 3D-deformation measurements with the pelvic specimen. The recorded 3D video data of the reflecting markers were tracked using the tracking software Vicon Nexus (Vicon, Oxford, UK) without using any filter function and then exported in to Microsoft Excel (Microsoft Corporation, Redmond, WA, USA). The 3D accuracy of the spatial resolution of the each marker was determined during the three middle seconds of the stationary phase after each 3D-displacement step. A simultaneous calculation of the three static markers was done.
Test procedure with the pelvic specimen
The test object consisted of a complete pelvic specimen including the individual proximal parts of both femora (n = 3). The specimen was fresh-frozen and stored at -25°C. After thawing to room temperature, soft tissues were removed cautiously, leaving the joint capsule, the ventral and dorsal sacroiliac ligaments, the sacrotuberal and sacrospinal ligaments, and the obturator membrane intact. The femora were then fixed with polymethyl methacrylate (PMMA, Beracryl, Swiss-composite, Jegenstorf, CH) in the holding fixture, which was mounted on the table of the Servo-hydraulic testing machine to simulate a two-leg standing position. The load was applied vertically onto the sacrum by the axial actuator of the testing machine with an adjustable fixture at the sacrum, allowing unconstrained rotational and transverse motion [17]. After adjusting the pelvis on the testing machine, 80 reflecting markers (diameter: 6.5 mm, Prophysics AG) were fixed at anatomically defined positions on the bone with cyanoacrylate (Loctide 401; Henkel & Cie AG, Pratteln, CH). Additionally, five quadruple-markers fixed on a T-shaped steel needle were placed at the most lateral point of the iliac crest and the greater trochanter (both sides), and at the proximal spinous tubercles of sacrum. These quadruple-markers were used as a ridge reference system for the different parts of the pelvic specimen during the dynamic loading procedure (Figure 2).
The dynamic sinusoidal loading of the pelvic specimen consisted of 100 loading cycles at 1 Hz with amplitudes between 100 N and either 0.5, 1, or 1.5 × body weight. During sinusoidal loading, the 3D-movement of the reflecting markers was recorded synchronously by 10 high-speed digital cameras. The displacement of the axial cylinder and the applied load were recorded simultaneously on the Vicon System at the same sampling rate of 60 Hz (Figure 3).
Data processing of the 3D marker data of pelvic specimen
The recorded 3D video data of the reflecting markers were reconstructed and tracked using the Vicon Nexus software without using any filter function. Each tracked marker was seen simultaneously by a minimum of 3 cameras. The dataset of each loading condition consists of the global 3D coordinates of all the markers and the applied load. It was exported into a CSV file for further use like in graphical animation software or displacement computation.
Analysis of the 3D-displacement of markers was done using Microsoft Excel. Calculation of the 3D distance change between two markers was done using the following equation:
Where Δd(t) is the temporal distance between the different spatial coordinates (xi(t); yi(t); zi(t)) of two markers over the loading cycles.