Specimens
Seven right human, native and non-fixed knee specimens with soft tissue and skin were used for the experiments. These were stored at − 18 °C and thawed for the investigations slowly during 12 h at room temperature. The specimens were administered via Science Care (SCIENCE CARE, Arizona Headquarters, 21,410 N. 19th Ave., Suite 126, Phoenix, AZ 85027, United States, Fax: 602.331.4344).
Robot
A robotic 6-degree-of-freedom setup (KUKA KR 60–3 robot, Augsburg, Germany; reproducibility: ±0.06 mm) including a universal force/torque sensor (ATI UFS: Theta SI1000–120; resolution: 0.25 N and 0.025 Nm) was used to perform axially loaded knee flexion.
Screws
4.5 Mm cannulated, self drilling screws with long thread, available in lengths from 20 to 80 mm (article number X14.620–672, Synthes GmbH, Oberdorf, Switzerland) were used for screw osteosynthesis
Experimental procedure
Osteotomies of the femur and tibia were performed 25 cm above / below the joint space. At a distance of about 8 cm distal / proximal to the osteotomy, the bones were completely cleaned of periosteum and embedded in 2-component resin (RenCast© FC 53 isocyanate/FC 53 polyol, Gößl & Pfaff GmbH, Karlskron, Germany) (see Fig. 1). The settings of the robot used for previous studies with non human specimens [13] were adapted to the larger human knee joints. Fixation within aluminum cylinders in the robot, axes definition and recording of the passive path remained unchanged as described in previous studies [13, 14].
First, an antero-lateral approach to the knee joint was performed as is usually done in lateral tibial fractures, to prevent access-related falsification of the measured values [15]. Then the approach was closed by suture to prevent dehydration during the measurement. In the next step recording of the individual passive flexion path was performed [16, 17], which is required for further measurements. Passive path is described as a flexion way of minimal resistance unique for each knee joint [16].
Axial compressive load of 400 N (approximate half of the body weight) was applied to the femur during the recording (higher loads leads to specimen failure). Subsequently, the first measurement of the DE was performed on the ‘native’ knee, traversing the measured path and plotting friction torque against the flexion angle. From the area enclosed within the hysteresis curve the DE can be calculated.
Second, we reopened the joint and prepared the lateral soft tissues in order to induce a lateral tibial split fracture (AO: 41-B1, Schatzker Typ I [18], Tscherne u. Lobenhofer P1 [19]) After pre-drilling, two screws were inserted from the lateral side into the intact bone and were removed after fluoroscopic control. The resulting screw holes later enabled optimal fracture reduction. The fracture zone was marked with Kirschner wires exactly in the center of the lateral compartment under fluoroscopic control, because a too lateral fracture planning resulted in a covering of the fracture by the meniscus and too medial approach resulted in complex tibial fractures in preliminary experiments.
Subsequently, the bone fracture was induced using a chisel: Initially, the chisel was inserted in a sagittal plane into the lateral tibia without affecting the lateral cortical bone or the joint. Rotation of the chisel then resulted in fracture of the chondral and subchondral structures, as well as the lateral cortical bone. Great care was taken not to touch the surface structures with the chisel to ensure a fracture line as realistic as possible and to avoid intra-articular injuries with the chisel, which might later influence the measured DE.
Third, the fracture was reduced anatomically and the screws inserted into the existing holes (see Fig. 2a). The DE could thus in a next step be measured in the condition we labelled ‘even’. Thereafter, the fracture gap was simulated with two 1 mm washers, which were inserted anteriorly and posteriorly into the fracture gap (see Fig. 2b) and the DE measured for this condition called ‘1 mm gap’. To enlarge the fracture gap, a further washer was added in each side (‘2 mm gap’) and again DE was measured (see Fig. 2c).
Finally, we removed the screws and enlarged the screw holes in the lateral fragment in an oblong direction to obtain a displacement distance of the fragment of 4 mm. Subsequently, the fragment was fixed again in the ‘step up’ / ‘step down’ condition with the screws and washers and we carried out the corresponding measurement (see Fig. 2d). During the whole experiment, for each measurement, the approach was closed again with sutures to prevent the dehydration of the specimen and to preserve the synovial fluid.
Data analysis
The knee flexion movement varies for ±10° about the central flexion angle of approximately 60°. The axis of rotation varies with the vertical load, the reduction condition and with the flexion angle. The intersegmental force and moment are functionally meaningful if they are defined at the “joint center” that lies on the axis of rotation [20]. Therefore the screw axis identification method was used to determine the instantaneous screw axis parameter for each displacement
from position
to
using the robot coordinates of the tool center point. The point on the helical axis and the unit vector of the helical axis with reference to Pn are then transformed back to Cartesian base coordinates. This is done for a complete cycle in flexion angle steps of 1°. The median helical axis defines the lateral axis of the new reference system. The wrench vectors consisting of the forces and moments at the base frame are transformed to the new reference frame. The calculations were done using an open source robotics toolbox for MATLAB [21].
A low pass filter was used to plot the torque values of the force / torque sensor. Figure 3 shows the torque-time diagram and the corresponding hysteresis curve for the condition ‘step up’. The DE is represented by the area within the hysteresis curve. The DE for one cycle is calculated with Formula. The measurement was done for 40 cycles. The first two cycles were omitted in the calculation of the mean dissipated energy per cycle. The integral was calculated using the Simpson integration rule from unfiltered torque values since the white noise compensates during integration and the median DE of 38 cycles was calculated for further analysis using SPSS-Statistics (IBM, Version 25.0.0.1).
Formula
$$ E(dis)={\oint}_{\varphi }M\ d\varphi $$
E (dis): dissipated energy.
M: torque.
φ: flexion angle.
Formula 1: Calculation for the dissipated energy