Effect of Perturbing a Simulated Motion on Knee and Anterior Cruciate Ligament Kinetics

Abstract

Current surgical treatments for common knee injuries do not restore the normal biomechanics. Among other factors, the abnormal biomechanics increases the susceptibility to the early onset of osteoarthritis. In pursuit of improving long term outcome, investigators must understand normal knee kinematics and corresponding joint and anterior cruciate ligament (ACL) kinetics during the activities of daily living. Our long term research goal is to measure in vivo joint motions for the ovine stifle model and later simulate these motions with a 6 degree of freedom (DOF) robot to measure the corresponding 3D kinetics of the knee and ACL-only joint. Unfortunately, the motion measurement and motion simulation technologies used for our project have associated errors.

The objective of this study was to determine how motion measurement and motion recreation error affect knee and ACL-only joint kinetics by perturbing a simulated in vivo motion in each DOF and measuring the corresponding intact knee and ACL-only joint forces and moments. The normal starting position for the motion was perturbed in each degree of freedom by four levels (−0.50, −0.25, 0.25, and 0.50 mm or degrees).

Only translational perturbations significantly affected the intact knee and ACL-only joint kinetics. The compression-distraction perturbation had the largest effect on intact knee forces and the anterior-posterior perturbation had the largest effect on the ACL forces.

Small translational perturbations can significantly alter intact knee and ACL-only joint forces. Thus, translational motion measurement errors must be reduced to provide a more accurate representation of the intact knee and ACL kinetics. To account for the remaining motion measurement and recreation errors, an envelope of forces and moments should be reported. These force and moment ranges will provide valuable functional tissue engineering parameters (FTEPs) that can be used to design more effective ACL treatments.

Introduction

Knee soft tissue injuries are very common and can cause osteoarthritis even after surgical treatment. With as many as 250,000 ACL injuries occurring annually [1], ACL tears are among the most common knee injuries [2], especially during sports activities [3,4]. While success rates exceeding 90% have been reported for ACL reconstruction [5,6], native knee kinematics are not restored, leading to abnormal knee joint laxity and instability [7–9]. The inability to restore normal ACL knee kinematics can alter joint contact regions which, in theory, can cause wear of the articular cartilage and increase the risk for the early onset of osteoarthritis [10,11]. In fact, several studies have indicated no difference in the long term prevalence of knee osteoarthritis between ACL reconstructed and conservatively treated patients following an ACL injury [12–14]. Therefore, more effective treatment strategies are required in order to restore normal knee biomechanics and delay or prevent the onset of osteoarthritis following an ACL injury.

One factor which may contribute to the inability of current ACL reconstructions to restore normal knee biomechanics is the limited knowledge of normal knee and ACL biomechanics for activities of daily living (ADLs). Normal ACL biomechanics have been traditionally determined in vitro by applying displacements or loads which reproduce clinical examinations (e.g., anterior drawer or pivot shift tests [15–17]). Investigators have also attempted to determine the in vivo forces in the human knee and ACL using noninvasive methods [18,19]. However, these methods require simplifying the complex structure and function of the knee and ACL in order to develop computational models. Alternatively, investigators have attempted to directly measurement the ACL force and strain using surgically implanted sensors. However, these direct measurements usually involve subjects with existing joint injury and are susceptible to the sensor location, orientation, and calibration [20]. Therefore, our knowledge of knee and ACL biomechanics during ADLs remains limited.

Improved measurement and motion recreation technologies now provide the capabilities to record and simulate knee kinematics for ADLs to determine corresponding ligament and joint kinetics. However, an appropriate preclinical animal model is required to accurately acquire both the in vivo and in vitro measurements. The ovine stifle joint is an attractive model for these studies because it is a suitable orthopaedic injury and surgical model for the human knee joint and its soft tissue structures [21–23]. The sheep and human ACL are both primary restraints to anterior tibial translation [15,22], although transecting the ACL and loading the knee with an anterior force produces a much more dramatic anterior tibial translation change in the sheep (600% increase) than in the human (200% to 300% increase) [22]. Therefore, the ovine stifle joint provides a challenging mechanical environment for the preliminary

in vivo evaluation of ACL reconstructions. Lastly, full 3D knee kinematics have been measured for the ovine model [24].

Our long term research goal is to measure in vivo motions for the ovine stifle model and recreate these motions using a 6 degree of freedom (DOF) robot to measure intact knee and ACL-only joint kinetics. Unfortunately, both measurement and motion simulation technologies have associated errors, which could significantly affect the forces and moments recorded in both the intact knee and ACL-only joints. The implication of the associated errors is that, depending on the position on the force-displacement curve (toe or linear region) where the joint or ACL functions for the ADL, small positional errors could have a large effect on the force or moment measurements. The objective of this study is to determine how perturbing a simulated in vivo motion affects the 3D intact knee and ACL-only kinetics. We hypothesized that small translational or rotational perturbations of the motion would significantly affect the intact knee force but not the ACL-only joint force, based on previous studies in animal models which indicated that knee structures can achieve up to 40% of failure strength for ADLs [25] while the ACL functions at less than 10% of its failure strength [26]. This research contributes to our long term goal of quantifying functional tissue engineering parameters (FTEPs) to more effectively repair damaged load-bearing structures such as the ACL [27].

Design and Methods

Experimental Design.

Six (3 left and 3 right; no pairs) hind limbs from skeletally-mature, mixed breed female sheep (3–4 yrs old; 110–170 lbs) were used. A Kuka robot (KR210, Kuka Robotics Corp., Clinton Township, MI) with a 6-axis load cell (Theta Model, ATI Industrial Automation, Apex, NC) was used to recreate a 6 DOF ovine in vivo motion adapted from Tapper et al. [24]. The intact knee joint was subjected to 10 cycles of this gait path while joint forces and moments were recorded. We determined the effects of perturbation by comparing the forces and moments recorded for the intact knee joint when the motion was applied at the normal starting position versus a perturbed tibial starting position. For each of the 6 degrees of freedom (translations along and rotations about the X, Y, and Z axes of the tibial joint coordinate system), the intact knee joint was first exposed to 10 cycles of the ovine gait path at the normal starting position and subsequently perturbed by four levels (−0.50, −0.25, 0.25, and 0.50 mm or degrees). This range of translational and rotational perturbations approximately bounded the errors associated with our motion measurement system (Liberty, Polhemus (estimated translation error: 0.17 mm, estimated rotational error: 0.37 deg)) and recreation technologies (KR210, Kuka Robotics Corp. (translation error: 0.15 mm, rotational error: 0.15 deg)).

The sources of error associated with our methodology and their average measurement errors are presented in Table 1. These values were determined from preliminary experiments which were conducted using the robot. All preliminary experiments and perturbation tests were conducted in the same working volume. Thus, changes in the robot pose and direction of loads should be minimal. Protocols were developed to register and apply motions to a limb using the robot (unpublished preliminary study funded by the Department of Defense). The first preliminary study was needed to examine how registering the limb in the robot at different installations affected the force and moment data. Right and left hind limbs from 11 subjects were used to examine our method for limb registration within the robot. These limbs were prepared for testing and attached to the robot using the same methods used in this study. Each limb was subjected to 10 cycles of a 6 DOF gait path in a sheep model [24]. Forces and moments were analyzed in each anatomical direction according to the joint coordinate system established by Grood and Suntay [28]. Each limb was removed from the robot setup and reattached two days later and the registration technique was repeated. We found that our limb registration technique resulted in no significant force or moment differences between registrations (p < 0.05). The position and path repeatability of the robot are minimal in comparison to the level of perturbations. The compliance of the robot was determined by comparing loaded and unloaded conditions throughout the in vivo motion. The motion was applied without a joint attached (i.e., the unloaded condition) and the measured displacements and rotations for each anatomical direction were compared to the actual testing condition used in the study (i.e., the loaded condition), which involves securing an ovine stifle joint to the robot and applying the same motion used for the unloaded condition. The difference in the displacement or rotation produced by the added load was determined for each direction. The values in Table 1 indicate that the robot is suitable for the use of evaluating the effect of sub-millimeter and sub-degree perturbations.

Table 1.

Sources of error

Source of error	Average measurement error (mean ± SEM)
Faro CMM	Single point accuracy	± 0.025 mma
EM motion tracking system	Error (rotations)	0.37°
	Error (translations)	0.17 mm
Limb registration	Force difference	6.80 ± 7.20 N
	Moment difference	0.19 ± 0.23 Nm
Robot path repeatability	Error (rotations)	1.4 × 10−4 ± 1.5 × 10−4°
	Error (translations)	2.2 × 10−3 ± 2.5 × 10−3 mm
Robot position repeatability	Error (rotations)	3.5 × 10−2 ± 1.2 × 10−2°
	Error (translations)	6.4 × 10−3 ± 2.0 × 10−3 mm
Robot compliance	Error (rotations)	5.8 × 10−4 ± 1.2 × 10−3°/N
Error (translations)	1.5 × 10−4 ± 1.1 × 10−4 mm/N

^aCMM single point accuracy provided by Faro Technologies Inc.

Detailed Methods

Joint Preparation and Robot Setup.

Ovine limbs were obtained from a local vendor. Since the joint preparation and robot setup procedures have been previously reported [29], a summarized version is presented. Each limb was dissected free of all muscles and tendons, leaving the knee joint capsule, the collateral and cruciate ligaments, and both menisci intact. The proximal half of the tibia was secured in a specially-designed fixture using polymethyl methacrylate. The tibial fixture was used to establish the tibial anatomical coordinate system [28], using the previously reported methodology [29]. The tibial fixture was then attached to the load cell on the 6 DOF robot and adjusted to align the tibial coordinate system with the robot and load cell axes, as previously reported [29]. The centroid of the tibial ACL insertion site was selected as the tibial joint center point and digitized using a 3D coordinate measurement machine (CMM) (Faro Digitizer F04L2, FARO Technologies Inc., Lake Mary, FL). The translations and rotations are reported according the tibial coordinate system [28]. The forces and moments are reported in the tibial reference frame, based on the tibial coordinate system.

The hanging femur was then guided onto the base fixture and the load cell was tared before securing the femur. The joint was then positioned at a 60.5 deg flexion angle and small translational adjustments were made in the robot to minimize forces and moments to <5 N and <1 Nm, respectively. At the average starting position, forces and moments were 0.5 N and 0.1 Nm, respectively. The 60.5 deg flexion angle was selected because it corresponds to the midpoint of knee flexion for the selected motion path, where we believe that the forces and moments would be minimal. Our final setup has been shown in a previous publication [29].

Robot Testing.

All testing was performed at room temperature. With the joint in the starting position, a set of 10 gait cycles (8.22 s cycle duration) was applied to precondition the joint. We then applied another 10 gait cycles and recorded the forces and moments. We then perturbed the starting position in each DOF by each level (−0.50, −0.25, 0.25, and 0.50 mm or degrees). The 10 cycles were repeated following each perturbation while the forces and moments were recorded. Finally, we removed the soft tissue structures and the distal portion of the femoral condyles, leaving the ACL as the only structure transmitting force across the joint. The testing procedure was repeated for the ACL-only condition.

Data Analysis

Robot perturbation experiments.

For the intact knee and ACL-only joints, we examined the forces along and the moments about each anatomical axis. The stance and swing phases were separately analyzed. The 8th and 9th gait cycles of the 10 cycle test were used for analysis to minimize the initial cycle effects. The 8th and 9th gait cycles were averaged and normalized to consecutive heel strikes. The forces and moments were averaged across subjects for the normal condition and each level of perturbation. Forces were analyzed in the tibial reference frame, along the anterior-posterior (A-P), medial-lateral (M-L), and compression-distraction (C-D) anatomical axes of the tibial coordinate system [28]. Moments were also analyzed in the tibial reference frame according to the abduction-adduction (Ab-Ad), flexion-extension (F-E), and internal-external (I-E) anatomic rotations about the A-P, M-L, and C-D axes, respectively.

Statistical analysis.

For each direction of force and moment, a one-way repeated measures analysis of variance (ANOVA) was performed to determine if perturbations produced a significant load difference during the stance or swing phase of gait. In each direction of load, the four perturbation levels were compared to one another and to the normal starting point. All data was normal and homoscedastic.

Post hoc comparisons were made using the Bonferroni method. The significance level for all comparisons was set at p < 0.05.

Results

Intact Knee.

Only translational perturbations significantly affected the intact knee kinetics (Table 2). The C-D perturbation had the largest effect on the intact knee forces throughout the gait cycle (Fig. 1), with the full range of the C-D perturbation (distraction to compression shift) significantly increasing (p < 0.05) the force in the compression direction throughout gait (stance: −359.4 ± 8.5 (SEM) N; swing: −220.2 ± 26.5 N). The other translational perturbations only significantly affected (p < 0.05) the intact knee forces during swing (Table 2; the A-P perturbation is shown in Fig. 2).

Table 2.

Effect of perturbations on the intact knee (C/D = compression/distraction; A/P = anterior/posterior; M/L = medial/lateral). Post hoc analysis was performed using ANOVA (p < 0.05).

	Perturbed direction	Significantly different conditions			Significance	Increased force(s)/moment(s)
Stance	C/D	Neutral 0.25 mm distraction	≠	0.50 mm compression	p < 0.041	Compression force
		0.25 mm distraction 0.50 mm distraction	≠	0.25 mm compression
		Neutral	≠	0.50 mm distraction			p < 0.008	Distraction force
		0.50 mm distraction	≠	0.50 mm compression	p < 0.034	Posterior and compression forces extension moment
		Swing	A/P	0.25 mm posterior 0.50 mm posterior	≠	0.50 mm anterior	p < 0.036	Anterior force
				0.50 mm posterior	≠	0.25 mm anterior
				M/L	0.25 mm medial 0.50 mm medial	≠			0.50 mm lateral	p < 0.029	Lateral force
0.25 mm medial 0.50 mm medial	≠		0.25 mm lateral
C/D	Neutral 0.25 mm distraction		≠		0.50 mm compression	p < 0.040	Compression force extension moment
	0.25 mm distraction 0.50 mm distraction		≠	0.25 mm compression
	Neutral		≠	0.50 mm distraction	p < 0.002			Distraction force
	0.50 mm distraction		≠	0.50 mm compression	p < 0.046	Lateral and compression forces extension moment

Fig. 1.

Compression-distraction (C-D) force recorded for different levels of C-D perturbations in the intact knee. The C-D perturbations significantly affected the C-D forces in the intact knee throughout the gait cycle (mean (N = 6) ± SEM).

Fig. 2.

Anterior-posterior (A-P) force recorded for different levels of A-P perturbations in the intact knee. The A-P perturbations significantly affected the A-P forces in the intact knee only during swing (mean (N = 6) ± SEM).

ACL-Only Joint.

Only the A-P and C-D perturbations affected the ACL-only joint kinetics (Table 3). The A-P perturbation had the greatest effect, particularly on the ACL A-P forces (Fig. 3) and the F-E moments, as the full range of perturbation (posterior to anterior shift) significantly increased (p < 0.05) the ACL A-P forces in the anterior direction (stance: 7.7 ± 1.8 N; swing: 39.7 ± 3.4 N) and the F-E moments in the flexion direction (stance: 0.5 ± 0.1 Nm; swing: 2.7 ± 0.2 Nm). All significant effects of the perturbations on the ACL-only joint forces and moments are shown in Table 3.

Table 3.

Effect of perturbations on the ACL (A/P = anterior/posterior; C/D = compression/distraction). Post hoc analysis was performed using ANOVA (p < 0.05).

	Perturbed direction	Significantly different conditions			Significance	Increased force(s)/moment(s)
Stance	A/P	Neutral 0.25 mm posterior 0.50 mm posterior	≠	0.50 anterior	p < 0.033	Anterior, medial, distraction forces flexion moment
							Swing	A/P	Neutral	≠	0.50 anterior	p < 0.049	Anterior force flexion moment
0.25 mm posterior	≠	0.50 anterior	p < 0.008	Anterior and medial forces flexion and adduction moments
0.50 mm Posterior	≠	0.50 anterior	p < 0.019	Anterior, medial, distraction forces flexion and adduction moments
0.25 mm posterior	≠	0.25 mm anterior	p < 0.021	Anterior force flexion moment
0.50 mm posterior	≠	0.25 mm anterior	p < 0.015	Anterior and medial forces flexion and adduction moments
C/D	0.50 mm distraction	≠	0.50 mm compression	p < 0.032	Posterior force extension moment

Fig. 3.

Anterior-posterior (A-P) force recorded for different levels of A-P perturbations in the ACL-only joint. The A-P perturbations significantly affected the A-P forces in the ACL-only joint throughout the gait cycle (mean (N = 6) ± SEM).

Discussion

Only translational perturbations significantly affected the intact knee and ACL-only joint kinetics. The majority of perturbations that significantly altered intact knee and ACL-only joint forces exhibited a linear change (see Figs. 1–3). The C-D and A-P perturbations had the greatest effect on the forces and moments in the intact knee and ACL-only joint kinetics. During stance, only the C-D perturbations affected the intact knee kinetics and only the A-P perturbations affected the ACL-only joint kinetics. During swing, all translational perturbations significantly altered the intact knee kinetics while the A-P and C-D perturbations significantly altered the ACL-only joint kinetics. Our finding that the C-D perturbations had the largest effects on the intact knee forces was anticipated since small translations in the compression direction can substantially increase the joint contact force. As expected, the A-P perturbation has the largest effect on the ACL-only joint forces since the primary function of the ACL is to resist anterior tibial translation. The skewed alignment of the ACL and its complex function is illustrated by: (1) the A-P perturbation changing the ACL-only joint forces in all directions, along with altering the F-E and Ab-Ad moments, and (2) the C-D perturbation affecting the ACL-only joint A-P forces.

During stance, the pattern of compression peaks for the intact knee (see Fig. 1) parallel those previously reported for human gait, with peaks occurring at heel-strike and near toe-off [30,31]. The peak knee compression force magnitudes (<1.3 BW) measured in this study were less than those previously estimated for ovine (≈2.1 BW [32]) and human (≈2.6–3.2 BW [30,31]) gait on a walkway. We would expect the intact knee compression force to be less in a quadruped since the body weight is supported by more limbs throughout the gait cycle.

This study had several limitations. The starting position was established at a zero load, zero moment condition whereas in vivo, the joint may experience load throughout gait. This may account for the lower peak knee compression force magnitudes reported in this study. Additionally, depending on the native laxity of the joint, the definition of this starting position may have some variations in the translations and rotations. In this study, an average motion was applied to all ovine stifle joints. In our future studies, we will apply subject-specific motions to each limb to ensure that the specific joint positions are reproduced, thereby reducing this variability. Next, deformation of the tibia and femur were not measured to determine if there was any effect on the measured joint or ACL-only joint loads. In future studies, these deformations will be determined by measuring points on each bone using the CMM at various positions in the motion path. Finally, we applied the simulated motion at a slower speed than actually recorded. Due to the speed limitations of our serial robot, the time interval for the simulated in vivo motion (8.22 s gait cycle) was an order of magnitude longer than the actual recorded gait cycle. However, speed should not significantly alter the intact knee and ACL kinetics during a simulated walking motion, based on findings that soft tissue samples experience similar forces when tested at two strain rates differing by an order of magnitude [33].

We will continue to develop strategies that will allow us to measure joint forces and moments which better resemble the in vivo condition. First, a calibration factor will be developed for the knee kinematics of each subject in order to improve the motion recording accuracy. For future studies, we also plan to record the in vivo knee joint motion for each subject and subsequently apply this motion to the same limb using our robot. We expect that applying the subject-specific in vivo motions to each knee will allow us to measure forces and moments that more closely resemble the in vivo kinetics and potentially minimize the effect of recording errors since each joint will encounter native joint positions. To further address the remaining translational errors, an envelope of forces and moments will be measured for each specimen by perturbing the motion path in each translational degree of freedom for both the intact knee and ACL-only joints. These force and moment ranges will serve as design parameters for designing more effective ACL treatments. While the subject-specific ovine stifle kinematics have been previously measured and reproduced in a hexapod robot [34], the corresponding kinetics have not yet been reported. In addition, the reproduced motions were not independently validated. We are currently implanting arthroscopically implantable force probes into the ovine ACLs. We plan to validate our reproduced motions by comparing the voltage patterns recorded for the simulated motions to the voltage patterns recorded in vivo.

This research contributes to our long term goal of quantifying functional tissue engineering parameters (FTEPs) to more effectively repair damaged load-bearing structures [27]. In pursuit of this goal, we plan to use the ovine model to characterize knee and ligament function for various levels of gait and to investigate the effects of injuries and treatments. This novel platform will allow us to establish design criteria and evaluation benchmarks for traditional and tissue engineered ACL reconstructions.