Effects of knee flexion on the structural properties of the rabbit femur-anterior cruciate ligament-tibia complex (FATC)

Many studies have been conducted to determine the biomechanical properties of the anterior cruciate ligament (ACL). The method of holding the femur-ACL-tibia complex (FATC) test specimen, the strain rate applied, the angle of knee flexion and the direction of the applied loads have an important effect on the outcome. It is felt that the tensile properties and strength of the ligament should be measured by applying the tensile force along the axis of the ligament. A versatile clamp was designed to accomplish this purpose. Fifty-seven rabbit knee specimens were tested at angles of flexion of 0 degrees, 30 degrees or 90 degrees. In addition, a comparative study of 25 pairs of rabbit legs were performed, whereby loading was either along the ligament or along the tibial axis. Cyclic hysteresis, ultimate load, energy absorbed, and stiffness were determined. The ultimate load values for the FATC decreased with increased knee flexion for those loaded along the tibial axis, while no such change was detected for FATC tested along the ligament axis. Other structural properties measured followed similar trends. It is concluded that the structural properties of the rabbit FATC change minimally with knee flexion (from 0 to 90 degrees) when loaded along the ligament axis, but decrease significantly with knee flexion when loaded along the axis of the tibia. Therefore, the data obtained in this field of study can be compared only if the direction of loading with respect to the ACL is similar.     

Coupled motions under compressive load in intact and ACL-deficient knees: a cadaveric study

Knowledge of the coupled motions, which develop under compressive loading of the knee, is useful to determine which degrees of freedom should be included in the study of tibiofemoral contact and also to understand the role of the anterior cruciate ligament (ACL) in coupled motions. The objectives of this study were to measure the coupled motions of the intact knee and ACL-deficient knee under compression and to compare the coupled motions of the ACL-deficient knee with those of the intact knee. Ten intact cadaveric knees were tested by applying a 1600 N compressive load and measuring coupled internal-external and varus-valgus rotations and anterior-posterior and medial-lateral translations at 0 deg, 15 deg, and 30 deg of flexion. Compressive loads were applied along the functional axis of axial rotation, which coincides approximately with the mechanical axis of the tibia. The ACL was excised and the knees were tested again. In the intact knee, the peak coupled motions were 3.8 deg internal rotation at 0 deg flexion changing to -4.9 deg external rotation at 30 deg of flexion, 1.4 deg of varus rotation at 0 deg flexion changing to -1.9 deg valgus rotation at 30 deg of flexion, 1.4 mm of medial translation at 0 deg flexion increasing to 2.3 mm at 30 deg of flexion, and 5.3 mm of anterior translation at 0 deg flexion increasing to 10.2 mm at 30 deg of flexion. All changes in the peak coupled motions from 0 deg to 30 deg flexion were statistically significant (p<0.05). In ACL-deficient knees, there was a strong trend (marginally not significant, p=0.07) toward greater anterior translation (12.7 mm) than that in intact knees (8.0 mm), whereas coupled motions in the other degrees of freedom were comparable. Because the coupled motions in all four degrees of freedom in the intact knee and ACL-deficient knee are sufficiently large to substantially affect the tibiofemoral contact area, all degrees of freedom should be included when either developing mathematical models or designing mechanical testing equipment for study of tibiofemoral contact. The increase in coupled anterior translation in ACL-deficient knees indicates the important role played by the ACL in constraining anterior translation during compressive loading.     

Estimation of in vivo ACL force changes in response to increased weightbearing

Accurate knowledge of in vivo anterior cruciate ligament (ACL) forces is instrumental for understanding normal ACL function and improving surgical ACL reconstruction techniques. The objective of this study was to estimate the change in ACL forces under in vivo loading conditions using a noninvasive technique. A combination of magnetic resonance and dual fluoroscopic imaging system was used to determine ACL in vivo elongation during controlled weightbearing at discrete flexion angles, and a robotic testing system was utilized to determine the ACL force-elongation data in vitro. The in vivo ACL elongation data were mapped to the in vitro ACL force-elongation curve to estimate the change in in vivo ACL forces in response to full body weightbearing using a weighted mean statistical method. The data demonstrated that by assuming that there was no tension in the ACL under zero weightbearing, the changes in in vivo ACL force caused by full body weightbearing were 131.4 ± 16.8 N at 15 deg, 106.7 ± 11.2 N at 30 deg, and 34.6 ± 4.5 N at 45 deg of flexion. However, when the assumed tension in the ACL under zero weightbearing was over 20 N, the change in the estimated ACL force in response to the full body weightbearing approached an asymptotic value. With an assumed ACL tension of 40 N under zero weightbearing, the full body weight caused an ACL force increase in 202.7 ± 27.6 N at 15 deg, 184.9 ± 22.5 N at 30 deg, and 98.6 ± 11.7 N at 45 deg of flexion. The in vivo ACL forces were dependent on the flexion angle with higher force changes at low flexion angles. Under full body weightbearing, the ACL may experience less than 250 N. These data may provide a valuable insight into the biomechanical behavior of the ACL under in vivo loading conditions.     

Cruciate coupling and screw-home mechanism in passive knee joint during extension--flexion

The screw-home mechanism and coupling between forces in cruciate ligaments during passive knee joint flexion were investigated for various boundary conditions, flexion axis alignments and posterior cruciate ligaments (PCL)/anterior cruciate ligament (ACL) conditions. A developed non-linear 3D finite element model was used to perform detailed elasto-static response analyses of the human tibiofemoral joint as a function of flexion angle varying from 10 degrees hyper-extension to 90 degrees flexion. The tibia rotated internally as the femur flexed and externally as the femur extended. The re-alignment of the flexion axis by +/-5 degrees rotation about the axial (distal-proximal) axis, transection of the ACL and changes in cruciate ligament initial strains substantially influenced the 'screw-home' motion. On the other hand, restraint on this coupled rotation diminished ACL forces in flexion. A remarkable coupling was predicted between ACL and PCL forces in flexion; forces in both cruciate ligaments increased as the initial strain or pretension in one of them increased whereas they both diminished as one of them was cut or became slack. This has important consequences in joint functional biomechanics following a ligament injury or replacement surgery and, hence, in the proper management of joint disorders.     

In vitro forces in the normal and cruciate-deficient knee during simulated squatting motion

Three orthogonal components of the tibiofemoral and patellofemoral forces were measured simultaneously for knees with intact cruciate ligaments (nine knees), following anterior cruciate ligament resection (six knees), and subsequent posterior cruciate ligament resection (six knees). The knees were loaded using an experimental protocol that modeled static double-leg squat. The mean compressive tibial force increased with flexion angle. The mean anteroposterior tibial shear force acted posteriorly on the tibia below 50 deg flexion and anteriorly above 55 deg. Mediolateral shear forces were low compared to the other force components and tended to be directed medially on both the patella and tibia. The mean value of the ratio of the resultant tibial force divided by the quadriceps force decreased with increasing flexion angle and was between 0.6 and 0.7 above 70 deg flexion. The mean value of the ratio of the resultant tibiofemoral contact force divided by the resultant patellofemoral contact force decreased with increasing flexion and was between 0.8 and 1.0 above 55 deg flexion. Cruciate ligament resection resulted in no significant changes in the patellar contact forces. Following resection of the anterior cruciate ligament, the tibial anteroposterior shear force was directed anteriorly over all flexion angles tested. Subsequent resection of the posterior cruciate ligament resulted in an approximately 10 percent increase in the quadriceps tendon and tibial compressive force.     

The effects of flexion and rotation on the length patterns of the ligaments of the knee

Measurements have been made of the lengths of the ligaments in human knee joint specimens. The ligaments considered were the lateral collateral, medial collateral, anterior cruciate and posterior cruciate. The ligament length patterns were determined for twelve specimens at flexions of 0, 30, 60, 90 and 120°, in neutral, internal rotation and external rotation at each angle. The collateral ligaments steadily diminished by about 20 per cent in length from 0 to 120° flexion, rotation having little effect. The anterior cruciate gradually increased 10 per cent from 0 to 120° flexion and the posterior cruciate, was 10 per cent longer at 0° flexion than at all other angles for which length was constant. The action of the cruciates was therefore somewhat reciprocal. Rotation had a significant effect on cruciate lengths, affecting the anterior more than the posterior cruciate. Computations were made of the change in length of the anterior and posterior fibres of each cruciate ligament, in relation to the central fibres. Reciprocal functions between fibres were demonstrated.     

Recruitment of knee joint ligaments

On the basis of earlier reported data on the in vitro kinematics of passive knee-joint motions of four knee specimens, the length changes of ligament fiber bundles were determined by using the points of insertion on the tibia and femur. The kinematic data and the insertions of the ligaments were obtained by using Roentgenstereophotogrammetry. Different fiber bundles of the anterior and posterior cruciate ligaments and the medial and lateral collateral ligaments were identified. On the basis of an assumption for the maximal strain of each ligament fiber bundle during the experiments, the minimal recruitment length and the probability of recruitment were defined and determined. The motions covered the range from extension to 95 degrees flexion and the loading conditions included internal or external moments of 3 Nm and anterior or posterior forces of 30 N. The ligament length and recruitment patterns were found to be consistent for some ligament bundles and less consistent for other ligament bundles. The most posterior bundle of each ligament was recruited in extension and the lower flexion angles, whereas the anterior bundle was recruited for the higher flexion angles. External rotation generally recruited the collateral ligaments, while internal rotation recruited the cruciate ligaments. However, the anterior bundle of the posterior cruciate ligament was recruited with external rotation at the higher flexion angles. At the lower flexion angles, the anterior cruciate and the lateral collateral ligaments were recruited with an anterior force. The recruitment of the posterior cruciate ligament with a posterior force showed that neither its most anterior nor its most posterior bundle was recruited at the lower flexion angles. Hence, the posterior restraint must have been provided by the intermediate fiber bundles, which were not considered in the experiment. At the higher flexion angles, the anterior bundles of the anterior cruciate ligament and the posterior cruciate ligament were found to be recruited with anterior and posterior forces, respectively. The minimal recruitment length and the recruitment probability of ligament fiber bundles are useful parameters for the evaluation of ligament length changes in those experiments where no other method can be used to determine the zero strain lengths, ligament strains and tensions.     

Estimation of ACL forces by reproducing knee kinematics between sets of knees: A novel non-invasive methodology

In situ force in the anterior cruciate ligament (ACL) has been quantified both in vitro in response to relatively simple loads by means of robotic technology, as well as in vivo in response to more complex loads by means of force transducers and computational models. However, a methodology has been suggested to indirectly estimate the in situ forces in the ACL in a non-invasive, non-contact manner by reproducing six-degree of freedom (six-DOF) in vivo kinematics on cadaveric knees using a robotic/UFS testing system. Therefore, the objective of this study was to determine the feasibility of this approach. Kinematics from eight porcine knees (source knees) were collected at 30 degrees , 60 degrees , and 90 degrees of flexion in response to: (1) an anterior load of 100 N and (2) a valgus load of 5 N m. The average of each kinematic data set was reproduced on a separate set of eight knees (target knees). The in situ forces in the ACL were determined for both sets of knees and compared. Significant differences (rho<0.05) were found between the source knees and the target knees for all flexion angles in response to an anterior load. However, in response to valgus loads, there was no significant difference between the source knees and the target knees at 30 degrees and 90 degrees of flexion. It was noted that there was a correlation between anterior knee laxity (the distance along the displacement axis from the origin to the beginning of the linear region of the load-displacement curve) and internal-external rotation. These data suggest that in order to obtain reproducible results one needs to first match knees to knees with comparable anterior knee laxity. Thus, an estimate of the in situ forces in the ACL during in vivo activities might be obtainable using this novel methodology.     

Increasing quadriceps loads affect the lengths of the ligaments and the kinematics of the knee.

The relationships between the lengths of the ligaments and kinematics of the knee and quadriceps load, for low to physiologic levels of quadriceps loads, have not previously been studied. We investigated the effects of increasing levels of quadriceps force, necessary to balance increasing levels of externally applied flexion moments, on the kinematics of the tibiofemoral joint and on the separation distances between insertions of selected fibers of the major ligaments of the knee in twelve cadavera. Static measurements were made using a six-degree-of-freedom digitizer for flexion angles ranging from 0 to 120 deg in 15 deg increments. Quadriceps generated extension of the knee was performed by applying loads to the quadriceps tendon to equilibrate each of four magnitudes of external flexion moments equivalent to 8.33, 16.67, 25.00, and 33.33 percent of values previously reported for maximum isometric extension moments. The magnitude of quadriceps force increased linearly (p < 0.0001) as external flexion moment increased throughout the entire range of flexion. Anterior translation, internal rotation, and abduction of the tibia increased linearly (p < 0.0001, p < 0.001, p < 0.001) as external flexion moment and, hence, quadriceps load increased. For the fibers studied, the anterior cruciate ligament (p < 0.0076), posterior cruciate ligament (p < 0.0001), and medial collateral ligament (p < 0.0383) lengthened linearly while the lateral collateral ligament (p < 0.0124) shortened linearly as quadriceps load increased. Based on these results for low to physiologic levels of quadriceps loads, it is reasonable to assume that the ligament lengths or knee kinematics expected with higher quadriceps loads can be extrapolated.     

The symmetry of the medial collateral and anterior cruciate ligament properties: a biochemical study in the rat hind limb

The medial collateral (MCL) and the anterior cruciate ligament (ACL) of the rat's knee are frequently used in biomedical research and occasionally in ligament healing studies. The contralateral normal ligament serves as a control. In this study the presence of symmetry in the biomechanical properties of the MCL and the ACL was investigated. Bilateral femur-MCL-tibia and femur-ACL-tibia preparations were obtained from the hind limbs of sixty rats and were subjected to tensile testing to failure under the same loading conditions. Tensile load to failure, stiffness and energy absorption capacity were measured and the mode of failure was recorded. All biomechanical parameters were not significantly different between the two knees of the same animal, although significant individual variation was evident. The most common mechanism of failure was mid-substance tear. Symmetry seems to exist in the biomechanical properties of the MCL and the ACL in the rat knee. When ligament healing is evaluated, increased group size is necessary and the use of a normal control group may be advisable. The contralateral normal knee ligament may serve as a control when the properties of an injured ligament are evaluated and when the parameters of tensile testing failure under similar load conditions are applied.     

The effects of knee motion and external loading on the length of the anterior cruciate ligament (ACL): a kinematic study

A six-degrees-of-freedom mechanical linkage device was designed and used to study the unconstrained motion of ten intact human cadaver knees. The knees were subjected to externally applied varus and valgus (V-V) moments up to 14 N-m as well as anterior and posterior (A-P) loads up to 100 N. Tests were done at four knee flexion angles; 0, 30, 45, and 90 deg. Significant coupled axial tibial rotation was found, up to 21.0 deg for V-V loading (at 90 deg of flexion) and 14.2 deg for A-P loading (at 45 deg of flexion). Subsequently, the knees were dissected and the locations of the insertion sites to the femur and tibia for the anteromedial (AM), posterolateral (PL), and intermediate (IM) portions of the ACL were identified. The distances between the insertion sites for all external loading conditions were calculated. In the case when the external load was zero, the AM portion of the ACL lengthened with knee flexion, while the PL portion shortened and the intermediate (IM) portion did not change in length. With the application of 14 N-m valgus moment, the PL and IM portions of the ACL lengthened significantly more than the AM portion (p less than 0.001). With the application of 100 N anterior load, the AM portion lengthened slightly less than the PL portion, which lengthened slightly less than the IM portion (p less than 0.005). In general, the amount of lengthening of the three portions of the ACL during valgus and anterior loading was observed to increase with knee flexion angle (p less than 0.001).     

Effect of the posterior cruciate ligament on posterior stability of the knee in high flexion

Most biomechanical studies of the knee have focused on knee flexion angles between 0 degrees and 120 degrees. The posterior cruciate ligament (PCL) has been shown to constrain posterior laxity of the knee in this range of flexion. However, little is known about PCL function in higher flexion angles (greater than 120 degrees ). This in vitro study examined knee kinematics before and after cutting the PCL at high flexion under a posterior tibial load and various muscle loads. The results demonstrated that although the PCL plays an important role in constraining posterior tibial translation at low flexion angles, the PCL had little effect in constraining tibial translation at 150 degrees of flexion under the applied loads.     

Three-dimensional finite element modelling of the human ACL: simulation of passive knee flexion with a stressed and stress-free ACL

In this study, a three-dimensional finite element model of the human anterior cruciate ligament (ACL) was developed and simulations of passive knee flexion were performed. The geometrical model of the ACL was built from experimental measurements performed on a cadaveric knee specimen which was also subjected to kinematics tests. These experiments were used to enforce the particular boundary conditions used in the numerical model. A previously developed transversely isotropic hyperelastic material model was implemented and the ability to pre-stress the ligament was also included. The model exhibited the key characteristics of connective soft tissues: anisotropy, nonlinear behaviour, large strains, very high compliance for compressive or bending loading along the collagen fibres and incompressibility. Simulations of passive knee flexion were performed, with and without pre-stressing the ACL. The resultant force generated by the ACL was monitored and the results compared to existing experimental data. The stress distribution within the ligament was also assessed. When the ACL was pre-stressed, there was a good correlation between the predicted and experimental resultant forces reported in the literature over the entire flexion-extension range. The stress distribution in the pre-stressed and stress-free ACL were similar, although the magnitudes in the pre-stressed ACL were higher, particularly at low flexion angles.     

Circumferential measurement and analysis of strain distribution in the human ACL using a photoelastic coating method

Large variable deformations of the ligament cannot be adequately quantified by one-dimensional and/or localized measurements. To obtain accurate measurement of non-uniform strains over the entire surface of anterior cruciate ligament (ACL), we used a photoelastic coating technique and a method that allowed us to photograph an ACL around its longitudinal axis. A cadaver knee was modified to expose its ACL for observation, and the ligament was then coated with a photoelastic material. The knee was locked in a jig that allowed simulation of natural knee motion. The jig containing the knee was then mounted on a stand, which allowed the exposed ACL to be photographed from any angle around its longitudinal axis while set at a chosen degree of knee flexion. The jig itself was rotated on its stand so as to obtain a panoramic view of the ACL at a given knee angle. The obtained images of the photoelastic fringe patterns yielded significant information for understanding how the strain distributions along the fiber bundles change in association with knee motion. From the results we obtained using the photoelastic measuring method, we reached the following conclusions. Reciprocal functioning between the anterior and the posterior bundles from extension to flexion of the knee does occur. Strain distribution is not uniform even along the same bundle. The strain behavior of the ACL under uniaxial tensile test does not duplicate the conditions in which the ACL is damaged during knee motion. The differences in strains on the ACL under active and passive knee motions may not be as large as those reported previously in the literature.     

Design and validation of an unconstrained loading system to measure the envelope of motion in the rabbit knee joint

An unconstrained loading system was developed to measure the passive envelope of joint motion in an animal model commonly used to study ligament healing and joint arthritis. The design of the five-degree-of-freedom system allowed for unconstrained knee joint loading throughout flexion with repeated removal and reapplication of the device to a specimen. Seven New Zealand White rabbit knees were subjected to varus, valgus, internal and external loads, and the resulting envelopes of motion were recorded using an electromagnetic tracking device. Intra-specimen reproducibility was excellent when measured in one specimen, with maximal rotational differences of 0.6 and 0.3 deg between the fourth and fifth testing cycles for the varus (VR) and valgus (VL) envelopes, respectively. Similarly, the maximal internal (INT) and external (EXT) envelope differences were 0.5 and 0.4 deg, respectively, between the fourth and fifth cycles. Good inter-animal envelope reproducibility was also observed with consistent motion pathways for each loading condition. A maximal VR-VL laxity of 17.9 +/- 2.3 deg was recorded at 95 deg flexion for the seven knees tested. The maximal INT-EXT laxity of 75.2 +/- 4.8 deg occurred at 50 deg flexion. Studies on measurement reproducibility of re-applying individual testing components demonstrated a maximal error of 1.2 +/- 0.7 deg. Serial removal and re-application (test-retest) of the complete measuring system to one cadaveric knee demonstrated maximal envelope differences of less than 0.7 deg for VR-VL rotation and 2.1 deg for INT-EXT rotation. Our results demonstrate that the measuring system is reproducible and capable of accurate evaluation of knee joint motion. Baseline in vitro data were generated on normal joint kinematics for future in-vivo studies with this system, evaluating ligament healing and disease progression in arthritis models.     

Movements of the Forearm and Shoulder Performed against the Gravitation Force: Target Positioning under Kinesthetic Control

In humans, we tested targeted movements of the forearm and shoulder performed in the vertical direction (in a parallel manner with respect to the sagittal plane). Movements were realized, first, with the possibility for visual control of the coincidence of the angle of the limb link axis vs the vertical and the target angle value (using an optic system and video recording), and, second, in the absence of the above control. Movements including flexion (i.e., movement against the gravitation force) – extension of the limb link with an individually selected convenient velocity were initiated and terminated according to the presentation of permissive sound signals; simultaneously, EMGs were recorded from a few muscles flexing and extending the elbow and shoulder joints. We analyzed systematic errors of target positioning of the forearm and shoulder in movements realized exclusively under kinesthetic control. In the case of isolated flexion of the forearm for a 90 deg target angle, such errors in all members of the examined group (n = 11) were positive. These errors were, on average, 8.1 ± 0.7 deg without loading and reached 11.2 ± 0.9 deg with introduction of a 10 to 30 N additional loading on the forearm. Isolated movements of the shoulder for a 70 deg target angle (performed without loading, with full extension of the forearm and its voluntary fixation) were accompanied by positive errors of 18.3 ± 1.1 deg, on average. Both the movements and positioning were performed due to changes in the levels of activity of the flexor muscles, with minimum involvement of the antagonists. The nonlinear properties of the receptor apparatus responsible for the formation of a kinesthetic estimate of the joint angle (first of all, of muscle spindles) are a fundamental reason for positive errors of target positioning of the limb links realized under kinesthetic control in the absence of the visual one.     

Effect of changes in cruciate ligaments pretensions on knee joint laxity and ligament forces

The knee joint cruciate ligaments are reconstructed with the rationale to avoid joint instability, recurrent injury, damage to soft tissues and osteoarthritis. Wide range of procedures with different stiffness, pretension, orientation and insertion locations have been proposed with the primary goal to restore the joint laxity. Apart from the general lack of success in preservation of force in the reconstructed ligament itself, the concern, not yet addressed, arises as to the effect of such perturbation on the other intact cruciate ligament. The interaction between cruciate ligament forces is hypothesized in this work. Using a 3-D nonlinear finite element model of the tibiofemoral joint, we examined this hypothesis by quantifying the extent of coupling between cruciate ligaments while varying the prestrain in each ligament under flexion with and without anterior-posterior (A-P) loads. A remarkable coupling was predicted between cruciate ligament forces in flexion thus confirming the hypothesis; forces in both cruciate ligaments increased as initial strain or pretension in one of them increased whereas they both diminished as one of them became slack. Moreover, changes in laxity and in ligament forces as a cruciate ligament prestrained or pretensioned varied with flexion angle and external loads. These findings have important consequences in joint functional biomechanics following a ligament injury or replacement surgery and in selection of laxity matched or ligament force matched pretensioning protocols.     

An analytical approach to determine the in situ forces in the glenohumeral ligaments.

The purpose of this study was to use an analytical approach to determine the forces in the glenohumeral ligaments during joint motion. Predictions from the analytical approach were validated by comparing them to experimental data. Using a geometric model, the lengths of the four glenohumeral ligaments were determined during anterior-posterior loading simulations and forward flexion-extension. The corresponding force in each structure was subsequently calculated based on length data via load-elongation curves obtained experimentally. During the anterior loading simulation at 0 deg of abduction, the superior glenohumeral ligament carried up to 71 N at the maximally translated position. At 90 deg of abduction, the anterior band of the inferior glenohumeral ligament had the highest force of 45 N during anterior loading. These results correlated well with those found in previous experimental studies. We believe that this validated analytical approach can be used to predict the forces in the glenohumeral ligaments during more complex joint motion as well as assist surgeons during shoulder repair procedures.