Increasing the posterior tibial slope lowers in situ forces in the native ACL primarily at deep flexion angles

High tibial osteotomy is becoming increasingly popular but can be associated with unintentional posterior tibial slope (PTS) increase and subsequent anterior cruciate ligament (ACL) degeneration. This study quantified the effect of increasing PTS on knee kinematics and in situ forces in the native ACL. A robotic testing system was used to apply external loads from full extension to 90° flexion to seven human cadaveric knees: (1) 200 N axial compressive load, (2) 5 Nm internal tibial + 10 Nm valgus torque, and (3) 5 Nm external tibial + 10 Nm varus torque. Kinematics and in situ forces in the ACL were acquired for the native and increased PTS state. Increasing PTS resulted in increased anterior tibial translation at 30° (1.8 mm), 60° (1.7 mm), and 90° (0.9 mm) flexion and reduced in situ force in the ACL at 30° (57.6%), 60° (69.8%), and 90° (75.0%) flexion in response to 200 N axial compressive load. In response to 5 Nm internal tibial + 10 Nm valgus torque, there was significantly less (39.0%) in situ force in the ACL at 90° flexion in the increased compared with the native PTS state. Significantly less in situ force in the ACL at 60° (62.8%) and 90° (67.0%) flexion was observed in the increased compared with the native PTS state in response to 5 Nm external tibial + 10 Nm varus torque. Increasing PTS affects knee kinematics and results in a reduction of in situ forces in the native ACL during compressive and rotatory loads at flexion angles exceeding 30°. In a controlled laboratory setting PTS increase unloads the ACL, affecting its natural function.

The frontal alignment is determined by the morphology of both the proximal tibia and the distal femur. 6 Increasing varus alignment has been shown to increase peak contact pressure in the medial tibiofemoral compartment, result in a higher degree of medial meniscal extrusion, and increase ACL forces by up to 74% compared with neutral alignment. 3,11 As a result, high tibial osteotomy (HTO) in the medial opening wedge (MOW-HTO) technique has been recommended in varus malalignment to protect the articular cartilage in the medial compartment and reduce the risk of ACL graft failure in case of ACL reconstruction. 2,11,12 However, MOW-HTO has also been associated with an unintentional increase in PTS, which subsequently leads to ACL fiber degeneration. [13][14][15] Moreover, PTSincreasing osteotomies are performed in patients with posterior cruciate ligament insufficiency without knowing the effects of PTS change on the native ACL. 16,17 Yet, HTOs with both intentional and unintentional PTS changes, are becoming increasingly popular to counteract negative effects of frontal and sagittal plane malalignments. [18][19][20][21][22] However, these osteotomy procedures alter the bony morphology, moving the position of tibial ACL insertion site relative to the femoral ACL insertion site, and causing a change of the in situ forces in the native ACL. Altered, nonphysiologic in situ forces in the ACL may result in ACL fiber degeneration and subsequent injury.
The purpose of this study was to quantify the effect of increasing PTS on knee kinematics and the in situ forces in the native ACL in human cadaveric knees using a 6 degrees of freedom (6 DOF) robotic testing system. It was hypothesized that increasing PTS would increase anterior and proximal tibial translation, while maintaining medial-lateral tibial translation and internal-external, and varusvalgus tibial rotation. It was further hypothesized that increasing PTS would decrease the in situ force in the native ACL.

| Specimen preparation
Seven fresh-frozen human cadaveric knees (mean age 51.9 ± 19.8 years; range, 21-75 years; 71% male) were used for this controlled laboratory study, which was approved by the institutional review board of the University of Pittsburgh (CORID #331).
Specimens were thawed at room temperature for 24 h before testing. Before testing, each specimen underwent manual, fluoroscopic, and arthroscopic examination. Specimens were excluded if ligamentous injuries, meniscal injuries, cartilage injuries greater than Grade 2 according to the International Cartilage Repair Society grading system, 23 or osteoarthritis greater than Grade 2 to according to the Kellgren-Lawrence grading scale 24 were detected. In addition, specimens with a medial PTS greater than 12°as determined on strict lateral radiographs were excluded. The threshold value of 12°was chosen based on previous research showing that only 3% of a population between 18 and 92 years have a medial PTS ≥ 12°. 25 The femur and tibia were cut 20 cm proximal and distal from to the joint line, respectively. All soft tissue was removed 10 cm proximally and distally from the joint line and the fibula was fixed to the tibia using a bicortical screw to maintain its anatomical position. Subsequently, an epoxy compound (Bondo; 3 M) was used to pot the femoral and tibial bone.

| PTS states and surgical procedures
Two PTS states were assessed for each specimen: (1) osteotomized knee with native PTS, (2) osteotomized knee with increased PTS.
Both PTS states were assessed after the osteotomy was performed to avoid any influence of the surgical approach on the primary outcome measures (kinematics, forces). As a result, the detected changes in knee kinematics and in situ forces in the ACL could exclusively be attributed to the change in PTS.
After potting and before the experimental testing protocol started, an external fixator (Hoffmann 3 Modular External Fixation; Stryker GmbH) was attached to the proximal tibia. Under fluoroscopic guidance, one pin (ø 6 mm) each was placed in the subchondral bone parallel to the PTS of the medial and lateral tibial plateau. A third pin was placed centrally in the epoxy compound cylinder of the tibia. Each subchondral pin was connected to the pin in the epoxy compound cylinder of the tibia by a connecting rod (ø 11 mm) via pin-to-rod couplings. As a result, the external fixator formed a triangle for rigid force transmission along the long axis of the tibia without affecting knee kinematics and in situ forces in the ACL ( Figure 1). 2,5,26,27 F I G U R E 1 Schematic illustration of the osteotomy. Osteotomized knee with native posterior tibial slope (PTS) state (A) and osteotomized knee with increased PTS state (B). A supra-tuberositary anterior opening wedge osteotomy with a posterior cortical hinge was performed. To increase the PTS an epoxy compound wedge (blue) was placed in the osteotomy gap. The osteotomy was secured with an external fixator. The quadriceps tendon, patella, and patellar tendon were removed in this figure to show the level and orientation of the osteotomy. Next, a 3-5 cm longitudinal incision 3 cm medial and lateral to the tibial tuberosity was made. The patellar tendon and its insertion zone at the tibial tuberosity were exposed. The cortical bone of the tibia proximal to the tibial tuberosity and distal to Gerdy's tubercle was visualized. The tibial insertion of the medial collateral ligament (MCL) had to be slightly released (less than one-third of the tibial insertion site) for the subsequent osteotomy. Two K-wires (one medial, one lateral to the patellar tendon) were drilled from anteriorinferior to posterior-superior to guide the subsequent osteotomy. To increase the PTS, the proximal pin-to-rod couplings of the external fixator were released and the osteotomy gap was gradually opened. A custom-made epoxy compound wedge (wedge base height, 10 mm) was placed in the osteotomy gap until the base of the wedge touched the anterior tibial cortex and the proximal pin-torod couplings of the external fixator were resecured. Accordingly, the osteotomy gap was opened by 10 mm (anterior cortex), resulting in a knee size-dependent change in PTS. 16,28 To decrease the PTS, the steps were performed in reverse order. After each PTS change, a layer-by-layer wound closure was performed.

| Experimental setup and protocol
Specimens were attached to a 6 DOF robotic testing system (MJT model FRS2010) using custom-made aluminum clamps. Femur and tibia were attached to the lower and upper plates of the robotic manipulator, respectively. A universal force/moment sensor (UFS; ATI Delta IP60 model SI-660-60), located on the upper manipulator of the robotic testing system, was used to provide feedback to the controller. The robotic testing system was controlled using a LabView Program (Technology Services Inc). The translational and rotational position repeatability of the robotic testing system was shown to be less than ±0.015 mm and ±0.01°, respectively. The measurement uncertainty of the UFS was found to be approximately 1% of full scale. 29 The medial-lateral translation axis and flexion-extension rotation axis were defined by the femoral insertion sites of the medial and lateral collateral ligament. The proximal-distal translation axis and internal-external rotation axis were defined by the anatomical tibial shaft axis. The anterior-posterior translation axis and varus-valgus rotation axis were defined as the cross-product of the two mentioned axes. 30 Given that a supra-tuberositary HTO was performed, the anatomical tibial shaft axis and therefore the joint coordinate system was not affected by the HTO.
The path of passive flexion-extension from full extension (defined as 1 Nm extension moment) to 90°of knee flexion of the osteotomized intact knee with the native PTS state (i.e., external fixator attached, surgical approach, MCL release, and osteotomy performed) was determined. Minimized forces and moments (within 0.5 N and 0.2 Nm, respectively) across all axes of the defined coordinate system throughout the range of motion were required to determine the path of passive flexion extension. [31][32][33][34] Three loading conditions were applied to the osteotomized intact knee with the native PTS state while continuously flexing the knee from full extension to 90°of knee flexion, and the resulting 6 DOF kinematics were recorded. The three loading conditions were (1) 200 N axial compressive load, (2) 5 Nm internal tibial torque combined with 10 Nm valgus tibial torque, and (3) 5 Nm external tibial torque combined with 10 Nm varus tibial torque. The loading conditions were chosen as it has been shown that axial compressive loads and tibial rotational torques affect the in situ forces in the ACL. [35][36][37][38] In addition, the combined loading conditions have recently been confirmed as appropriate biomechanical loading conditions to evaluate in situ forces in the ACL. 34,39 To control for viscoelasticity of the soft tissues, each loading condition was repeated five times, and the data from the fifth cycle were used for final analysis.
After acquisition of the 6 DOF kinematics for each loading condition of the osteotomized intact knee with the native PTS state, the specimen was removed from the robotic testing system leaving the connecting clamps attached and thus maintaining the previously defined coordinate system. The PTS was increased and the osteotomized intact knee with the increased PTS state was mounted to the robotic testing system. The testing protocol was repeated as for the native PTS state.
After the 6 DOF kinematics of the intact knee were recorded for both PTS states (osteotomized knee with native PTS, osteotomized knee with increased PTS) and all three loading conditions, the ACL was arthroscopically removed. In the ACL deficient knee, the previously acquired 6 DOF kinematics for each loading condition of the osteotomized intact knee with the increased PTS state were repeated using the position-control mode. The new forces and moments were measured by the UFS and the in situ forces in the ACL in the osteotomized knee with the increased PTS state were calculated by applying the principle of superposition. 40,41 Next, the native PTS state was restored and the previously acquired 6 DOF kinematics for each loading condition of the osteotomized knee with the native PTS state were repeated using the position-control mode.
Again, the new forces and moments were measured by the UFS and the in situ forces in the ACL in the osteotomized knee with the native PTS state were calculated by applying the principle of superposition (Table 1). 40,41 Given the ability of the robotic testing system to accurately replicate knee kinematics after ACL removal (i.e., positioncontrol mode), it is possible to determine the magnitude and direction of the in situ force of the removed ACL. This can be done by quantifying the change in force vector before and after ACL removal. 40,41 The specimens were kept moist throughout the entire testing protocol using physiological saline solution. 42

| PTS measurements and repeatability of PTS adjustment
PTS measurements were performed on strict lateral radiographs using a previously described technique (Figure 2). 18 To apply the principle of superposition to calculate in situ forces in the ACL in both PTS states within the same specimen, the two PTS states need to be precisely and reliably restored. Preliminary testing displayed good to excellent repeatability of multiple PTS adjustments to an accuracy of ±0.2°and measurements of the in situ force in the ACL within the repeatability of the robotic testing system, enabling the principle of superposition to be applied reliably.
To ensure reliable PTS adjustments during testing, a three-step protocol was followed for each PTS change: (1) The two PTS states were marked on the pins and connecting rods of the external fixator to ensure that the pin-to-rod couplings were always at the exact same level for the corresponding PTS state.

| RESULTS
The experimental protocol was successfully completed in all seven fresh-frozen human cadaveric knees without complications such as posterior cortical hinge fracture, tibial plateau fracture, or osteotomy fixation failure.
The native PTS before osteotomy was 9.

| DISCUSSION
The most important finding of this study was that an isolated increase in PTS in a native knee joint affected translational and rotatory knee kinematics and resulted in a significant reduction of the in situ forces in the native ACL, primarily noted at flexion angles exceeding 30°.
In line with the hypothesis of this study, an isolated increase in PTS was shown to cause anterior and proximal tibial translation, which is consistent with previous research. 1,28,45,46 One study evaluated changes in knee kinematics in 10 human cadaveric knees after increasing the PTS by 4.4°. In response to a 200 N axial compressive load, a significant increase in anterior tibial translation by 2 mm was observed at 30°and 90°flexion. 45  which is reflected by lower in situ forces. This finding is supported by previous studies. 28,46 One study investigated the native ACL in nine human cadaveric knees in response to a 200 N axial compressive load and found a significant reduction in native ACL strain after gradually F I G U R E 3 In situ forces in the native ACL. In situ force in the ACL versus flexion angle in the native and increased posterior tibial slope (PTS) state in response to 200 N axial compressive load (A), 5 Nm internal tibial torque + 10 Nm valgus tibial torque (B), and 5 Nm external tibial torque + 10 Nm varus tibial torque (C). *Statistically significant difference between the native and increased PTS state (p < 0.05). ACL, anterior cruciate ligament.
increasing the PTS from 5°to 15°. 46 This was confirmed by another study that showed a 120% decrease in the native ACL strain after increasing the PTS by an average of 9.6°in four intact human cadaveric knees. 28 However, it should be questioned whether a reduction in native ACL strain of more than 100% is physiologically feasible considering the inability of ligamentous structures to transmit compressive loads. Of note, the reduced in situ forces in this study were primarily observed at flexion angles exceeding 30°, where typical cutting or pivoting maneuvers would not be expected.
This may be related to the smaller radii of the femoral condyles at higher flexion angles, resulting in an even more pronounced approximation of the ACL insertion sites. Taken  Noncontact ACL injuries most commonly occur during athletic tasks, associated with considerably higher loads. 54 Therefore, it might be possible that certain effects of PTS increase were masked in this study owing to low external loads applied.

| CONCLUSION
In this study, an isolated increase in PTS by an anterior opening wedge HTO affected both translational and rotatory knee kinematics and resulted in a reduction of in situ forces in the native ACL by up to 75% in response to isolated compressive and combined rotatory loads. Increasing the PTS in a controlled laboratory setting unloads the ACL, affecting its natural function.

ETHICS STATEMENT
This study was approved by the Institutional Review Board of the University of Pittsburgh (CORID #331).