The contribution of the cruciate ligaments to the load-displacement characteristics of the human knee joint

Stability Analysis and Input Design of a Two-Link Planar Biped

A two-link planar biped system under the influence of holo nomic ( connection) constraints with constraints not in effect and in effect is investigated in this paper. The use of quadratic Lyapunov functions to construct the feedback strategies for maintaining stability in the vicinity of an operating point is presented. The role of the different inputs in opposing gravity, maintaining connection constraints, and moving the system is delineated. Finally, the effectiveness of this methodology and one of its applications are demonstrated via some digital computer simulations.

A comparison of material characterizations in frequently used constitutive models of ligaments

Longitudinal tensile and simple shear stress-strain curves of human medial collateral ligaments (MCL) were fitted by six frequently used constitutive relations of ligaments using two different fitting methods for determining which was the best fitting method and the most preferable constitutive model for describing the ligament properties. According to the results of fitting goodness, two typical constitutive models were further analyzed by FEM to investigate the effect of the variation in MCL constitutive models under some physiological loads (i.e., 4.5 Nm external tibial and 10 Nm valgus tibial torques). It was found that different fitting methods induced great variations in describing the simple shear behavior whereas no obvious difference in the longitudinal tensile behavior. The most accurate description of both the longitudinal tensile and simple shear behaviors was obtained from the constitutive model with ground substance defined by an exponential function when the parameters were fitted by the two test data, respectively. Although the distributions of maximal principal stress were almost the same, the variation in MCL constitutive models affected the highest value of the stress greatly when MCL was under the complex physiological loads.

The Effect of the Variation in ACL Constitutive Model on Joint Kinematics and Biomechanics Under Different Loads: A Finite Element Study

The biomechanics and function of the anterior cruciate ligament (ACL) have been widely studied using both experimental and simulation methods. It is known that a constitutive model of joint tissue is a critical factor in the numerical simulation. Some different ligament constitutive models have been presented to describe the ACL material behavior. However, the effect of the variation in the ligament constitutive model on joint kinematics and biomechanics has still not been studied. In this paper, a three-dimensional finite element model of an intact tibiofemoral joint was reconstructed. Three ACL constitutive models were compared under different joint loads (such as anterior tibial force, varus tibial torque, and valgus tibial torque) to investigate the effect of the change of the ACL constitutive model. The three constitutive models corresponded to an isotropic hyperelasticity model, a transversely isotropic hyperelasticity model with neo-Hookean ground substance description, and a transversely isotropic hyperelastic model with nonlinear ground substance description. Although the material properties of these constitutive equations were fitted on the same uniaxial tension stress-strain curve, the change of the ACL material constitutive model was found to induce altered joint kinematics and biomechanics. The effect of different ACL constitutive equations on joint kinematics depended on both deformation direction and load type. The variation in the ACL constitutive models would influence the joint kinematic results greatly in both the anterior and internal directions under anterior tibial force as well as some other deformations such as the anterior and medial tibial translations under valgus tibial torque, and the medial tibial translation and internal rotation under varus torque. It was revealed that the transversely isotropic hyperelastic model with nonlinear ground substance description (FE model III) was the best representation of the realistic ACL property by a linear regression between the simulated and the experiment deformation results. But the comparison of the predicted and experiment force of ligaments showed that all the three ACL constitutive models represented similar force results. The stress value and distribution of ACL were also altered by the change in the constitutive equation. In brief, although different ACL constitutive models have been fitted using the same uniaxial tension curve and have the similar longitudinal material property, the ACL constitutive equation should still be carefully chosen to investigate joint kinematics and biomechanics due to the different transverse material behavior.

Alterations in knee joint laxity during the menstrual cycle in healthy women leads to increases in joint loads during selected athletic movements

BACKGROUND

It has been speculated that the hormonal cycle may be correlated with higher incidence of ACL injury in female athletes, but results have been very contradictory.

HYPOTHESIS

Knee joint loads are influenced by knee joint laxity (KJL) during the menstrual cycle.

STUDY DESIGN

Controlled laboratory study.

METHODS

Serum samples and KJL were assessed at the follicular, ovulation, and luteal phases in 26 women. Knee joint mechanics (angle, moment, and impulse) were measured and compared at the same intervals. Each of the 26 subjects had a value for knee laxity at each of the 3 phases of their cycle, and these were ordered and designated low, medium, and high for that subject. Knee joint mechanics were then compared between low, medium, and high laxity.

RESULTS

No significant differences in knee joint mechanics were found across the menstrual cycle (no phase effect). However, an increase in KJL was associated with higher knee joint loads during movement (laxity effect). A 1.3-mm increase in KJL resulted in an increase of approximately 30% in adduction impulse in a cutting maneuver, an increase of approximately 20% in knee adduction moment, and a 20% to 45% increase in external rotation loads during a jumping and stopping task (P < .05).

CONCLUSION

Changes in KJL during the menstrual cycle do change knee joint loading during movements. Clinical Relevance Our findings will be beneficial for researchers in the development of more effective ACL injury prevention programs.

Influence of modern studded and bladed soccer boots and sidestep cutting on knee loading during match play conditions

BACKGROUND

The influence of modern studded and bladed soccer boots and sidestep cutting on noncontact knee loading during match play conditions is not fully understood.

HYPOTHESIS

Modern soccer boot type and sidestep cutting compared with straight-ahead running do not significantly influence knee internal tibia axial and valgus moments, anterior joint forces, and flexion angles.

STUDY DESIGN

Controlled laboratory study.

METHODS

Fifteen professional male outfield soccer players undertook trials of straight-ahead running and sidestep cutting at 30 degrees and 60 degrees with a controlled approach velocity on a Fédération Internationale de Football Association (FIFA) approved soccer surface. Two bladed and 2 studded soccer boots from 2 manufacturers were investigated. Three-dimensional inverse dynamics analysis determined externally applied internal/external tibia axial and valgus/varus moments, anterior forces, and flexion angles throughout stance.

RESULTS

The soccer boot type imparted no significant difference on knee loading for each maneuver. Internal tibia and valgus moments were significantly greater for sidestep cutting at 30 degrees and 60 degrees compared with straight-ahead running. Sidestep cutting at 60 degrees compared with straight-ahead running significantly increased anterior joint forces.

CONCLUSION

Varying soccer boot type had no effect on knee loading for each maneuver, but sidestep cutting significantly increased internal tibia and valgus moments and anterior joint forces.

CLINICAL RELEVANCE

Sidestep cutting, irrespective of the modern soccer boot type worn, may be implicated in the high incidence of noncontact soccer anterior cruciate ligament injuries by significantly altering knee loading.

Validation of the soft tissue restraints in a force-controlled knee simulator

In vitro testing of total knee replacements (TKRs) is important both at the design stage and after the production of the final components. It can predict long-term in vivo wear of TKRs. The two philosophies for knee testing are to drive the motion by displacement or to drive the motion by force. Both methods have advantages and disadvantages. For force control an accurate simulation of soft tissue restraints is required. This study was devised to assess the accuracy of the soft tissue restraints of the force-controlled Stanmore knee simulator in simulating the restraining forces of the anterior cruciate ligament (ACL) and posterior cruciate ligament (PCL). In order to do this, human cadaver knee joints were subjected to the ISO Standard Walking Cycle. The resulting kinematics were monitored when the soft tissue structures were intact, when the ACL and PCL were resected, and when they were simulated by springs positioned anteriorly and posteriorly. The stiffness of the springs was determined from the literature. Two different stiffnesses of springs were used which were 7.24 N/mm (designated as soft springs) and 33.8 N/mm (designated as hard springs). All the intact knees showed displacements that were within the range of the machine. Cutting the ACL and PCL resulted in anterior and posterior motion and internal external rotation that were significantly greater than the intact knee. Results showed that when the ACL and PCL were cut hard springs positioned anterior and posterior to the knee returned the knee to near normal anterior-posterior (AP) motion. Using hard springs in the posterior position in any condition reduced rotational displacements. Therefore using springs in a force-controlled simulator is a compromise. More accuracy may be obtained using springs that are of intermediate stiffness.

The mechanical consequences of dynamic frontal plane limb alignment for non-contact ACL injury

This study investigated the mechanical consequences of differences in dynamic frontal plane alignment of the support limb and the influence of anticipatory muscle activation at the hip and ankle on reducing the potential for non-contact ACL injury during single-limb landing. A frontal plane, three-link passive dynamic model was used to estimate an ACL non-contact injury threshold. This threshold was defined as the maximum axial force that the knee could sustain before the joint opened 8 degrees either medially or laterally, which was deemed sufficient to cause injury. The limb alignment and hip and ankle muscle contractions were varied to determine their effects on the ACL injury threshold. Valgus or varus alignment reduced the injury threshold compared to neutral alignment, but increasing the anticipatory contraction of hip abduction and adduction muscle groups increased the injury threshold. Increasing anticipatory ankle inversion/eversion muscle contraction had no effect. This study provides a mechanical rationale for the conclusion that a neutral limb alignment (compared to valgus or varus) during landing and increasing hip muscle contraction (abductors/adductors) prior to landing can reduce the possibility of ACL rupture through a valgus or varus opening mechanism.

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.

Pedestrian injuries: viscoelastic properties of human knee ligaments at high loading rates

OBJECTIVE

Accidents involving pedestrians are very common, and often lead to severe injuries to the lower extremities. In a large portion of pedestrian-automobile collisions, knee ligament injuries are sustained. In this study, the viscoelastic properties of the four major human knee ligaments were investigated at loading rates representative for pedestrian-automobile collisions.

METHODS

Bone-ligament-bone specimens were tested in knee distraction loading. The collateral ligaments and the separate functional bundles of the cruciate ligaments were tested in the anatomical position corresponding to a fully extended knee. A series of step-and-hold tests and ramp tests at different rates were conducted to characterize the time-dependent behavior of the knee ligaments for deformation rates associated with the pedestrian impact loading environment. The quasi linear viscoelastic (QLV) theory was used to describe the structural response of the knee ligaments and averaged parameters for this model were determined.

RESULTS

The QLV theory was found to be applicable for the time range that is relevant for pedestrian-automobile collisions. The structural behavior of the knee ligaments was found to be particularly rate-sensitive for high elongation rates, as occur during these collisions. The ligament stiffness was found to increase with age for both the collateral ligaments and with weight for the medial collateral ligament.

CONCLUSIONS

For the loading conditions that are relevant for pedestrian-automobile collisions, the use of the QLV model for the description of the mechanical behavior of knee ligaments is appropriate. The rate-sensitivity is particularly important for these extreme loading conditions. The relaxation behavior was found to be consistent between different ligament types and samples. Variations due to donor anthropometry were found predominantly for the instantaneous elastic behavior.

The effect of femoral attachment location on anterior cruciate ligament reconstruction: graft tension patterns and restoration of normal anterior-posterior laxity patterns

The issue of the best place to attach an anterior cruciate ligament graft to the femur is controversial, and different anatomic or isometric points have been recommended. It was hypothesised that one attachment site could be identified that would be best for restoring normal anterior-posterior laxity throughout the range of knee flexion. It was also hypothesised that these different attachment sites would cause different graft tension patterns during knee flexion. Using six cadaver knees, an isometric point was found 3 mm distal to the posterior edge of Blumensaat's line, at the 10:30-11:00 o'clock position in right knees, at the antero-proximal edge of the anatomic ACL attachment. Anterior-posterior laxity was measured at +/-150 N draw force at 20-120 degrees flexion with the knee intact and after anterior cruciate ligament transection. The graft was placed at the isometric point, and AP laxity was restored to normal at 20 degrees flexion, then measured at other angles. Graft tension was measured throughout, and also during passive flexion-extension. This was repeated for four other graft positions around the isometric point in every knee. Laxity was restored best by grafts tensioned to a mean of 9 +/- 14 N, positioned isometrically and 3 mm posterior to the isometric point. Their tension remained low until terminal extension. Grafts 3 mm anterior to the isometric point caused significant overconstraint, and had higher tension beyond 80 degrees knee flexion. Small changes in attachment site had large effects on laxity and tension patterns. These results support an isometric/posterior anatomic femoral graft attachment, which restored knee laxity to normal from 20 to 120 degrees flexion and did not induce high graft tension as the knee flexed. Grafts attached to the roof of the intercondylar notch caused overconstraint and higher tension in the flexed knee.

Finite Element Analysis of the Human ACL Subjected to Passive Anterior Tibial Loads

In this study, a constitutive law based on a nearly incompressible transversely isotropic hyperelastic potential is proposed to describe the mechanical behaviour of the anterior cruciate ligament (ACL). The constitutive formulation is valid for arbitrary kinematics (finite elasticity) and is thermodynamically admissible. Based on anatomic measurements performed on a human cadaveric knee specimen, a three-dimensional continuum finite element model of the ACL was developed. The numerical model was used to simulate clinical procedures such as the Lachman and drawer tests, which are performed to assess the existence and severity of an ACL injury. Finite element analyses showed that the two procedures have distinct effects on the behaviour of the ACL and provided new insights into the stress distributions. Moreover, good qualitative and quantitative agreement was found between the present study and results obtained experimentally in comparable conditions.

Development and Validation of a 3-D Model to Predict Knee Joint Loading During Dynamic Movement

The purpose of this study was to develop a subject-specific 3-D model of the lower extremity to predict neuromuscular control effects on 3-D knee joint loading during movements that can potentially cause injury to the anterior cruciate ligament (ACL) in the knee. The simulation consisted of a forward dynamic 3-D musculoskeletal model of the lower extremity, scaled to represent a specific subject. Inputs of the model were the initial position and velocity of the skeletal elements, and the muscle stimulation patterns. Outputs of the model were movement and ground reaction forces, as well as resultant 3-D forces and moments acting across the knee joint. An optimization method was established to find muscle stimulation patterns that best reproduced the subject’s movement and ground reaction forces during a sidestepping task. The optimized model produced movements and forces that were generally within one standard deviation of the measured subject data. Resultant knee joint loading variables extracted from the optimized model were comparable to those reported in the literature. The ability of the model to successfully predict the subject’s response to altered initial conditions was quantified and found acceptable for use of the model to investigate the effect of altered neuromuscular control on knee joint loading during sidestepping. Monte Carlo simulations (N=100,000) using randomly perturbed initial kinematic conditions, based on the subject’s variability, resulted in peak anterior force, valgus torque and internal torque values of 378 N, 94 Nm and 71 Nm, respectively, large enough to cause ACL rupture. We conclude that the procedures described in this paper were successful in creating valid simulations of normal movement, and in simulating injuries that are caused by perturbed neuromuscular control.

On the coupling between anterior and posterior cruciate ligaments, and knee joint response under anterior femoral drawer in flexion: a finite element study

OBJECTIVE

To investigate the extent of coupling between the anterior and posterior cruciate ligaments as well as the role of the posterior cruciate ligament in the knee joint response under anterior femoral force at different flexion angles.

DESIGN

A developed finite element model of the tibiofemoral joint is used to perform non-linear elastostatic analyses.

BACKGROUND

The structural properties of the posterior cruciate ligament subsequent to an injury (either left untreated or replaced by a graft) would likely change, an event that alters the function of not only the ligament itself but also the other intact cruciate ligament and the entire joint.

METHODS

The model consists of two bony structures and their articular cartilage layers, menisci and four principal ligaments. Under 100 N anterior femoral load at different flexion angles from 0 degrees to 90 degrees, kinematics, forces in ligaments and contact forces in the fully unconstrained joint were computed in intact cases and following alterations in joint ligaments.

RESULTS

Collateral ligaments were the primary structures to resist the force at full extension under 100 N anterior femoral load with a moderate contribution from the posterior cruciate ligament. With joint flexion up to 90 degrees, however, force in the posterior cruciate ligament substantially increased whereas that in collateral ligaments diminished.

CONCLUSIONS

A remarkable coupling was found between the posterior cruciate ligament and the anterior cruciate ligament in flexion; a structural alteration in one of them significantly influenced the mechanical role of both ligaments and not just the one affected. A tauter or stiffer ligament increased the force in both ligaments while an excessive laxity or rupture in one diminished forces in both.

RELEVANCE

Alterations in ligament stiffness or initial tautness during reconstruction surgery or following injuries markedly influence the normal role of both cruciate ligaments. Consideration of cruciate ligaments coupled together rather than in isolation should be the rule in the management of ligament injuries towards a successful long-term outcome.

Biomechanics of passive knee joint in drawer: load transmission in intact and ACL-deficient joints

A non-linear 3D finite element model of the passive human tibiofemoral knee joint consisting of two bony structures and their articular cartilage layers, menisci, and four principal ligaments was used to investigate the detailed response of the unconstrained joint under up to 100 N posterior femoral force at different flexion angles from 0 to 90 degrees. The analysis was repeated after the transection of the anterior cruciate ligament (ACL). The boundary conditions were selected to assure a stable and unconstrained response of the joint throughout the range of motion. The results indicated the ACL as the primary structure to resist the drawer load throughout the range of flexion considered and that the joint primary and coupled laxities substantially increased in its absence. At full extension under drawer, forces in collateral ligaments increased significantly resulting in larger overall contact forces as the ACL was transected. In the ACL-deficient joint, such large forces in collateral ligaments, however, diminished as flexion angle varied from 0 to 90 degrees. At full extension or flexion angles up to approximately 30 degrees, the medial meniscus and adjacent medial tibial and femoral cartilage layers were subjected to substantially larger loads and stresses following the transection of the ACL. Adequate consideration of such couplings is important in avoiding further damage to joint structures subsequent to an injury and restoring adequate function following injuries to primary components.

Preliminary comparison of the rupture of human and rabbit anterior cruciate ligaments

OBJECTIVE

This study was aimed at examining ruptures of the human anterior cruciate ligaments by scanning electron microscopy and video imaging and comparing the appearance of the rupture surfaces with those from rabbit anterior cruciate ligaments.

DESIGN

The specimens were tested to failure as femur-anterior cruciate ligament-tibia complexes using an Instron 8511 materials testing machine.

BACKGROUND

Rupture of the anterior cruciate ligament is a major clinical problem, leading to instability of the knee joint. Due to the frequency and potential severity of the injuries, a need still exists for information on the biomechanical properties of ligaments under loading conditions, which occur at the time of trauma.

METHODS

Four human femur-anterior cruciate ligament-tibia complexes were loaded to failure at a displacement rate of 0.008 m/s. Video recordings of the tests were used to study the progress of the ruptures and to compare the modes of failure of the ligaments. Scanning electron microscopy was employed to study the appearance of collagen fibres at the rupture surfaces.

RESULTS

The modes of failure of the rabbit anterior cruciate ligament and appearance of the rupture surfaces were similar to those of the human anterior cruciate ligaments.

CONCLUSION

The rabbit anterior cruciate ligament provides a model for investigating failure of the human ligament during trauma.

RELEVANCE

The results will be of significance since most studies on ligaments are carried out on animal models with the intention of applying the deductions from the results to human ligaments. Examining the appearance of collagen fibres at these surfaces may help us to understand more about what actually happens during and after ligament rupture.

Biomechanical response of the passive human knee joint under anterior-posterior forces

OBJECTIVE: To investigate the detailed biomechanics of the passive tibiofemoral knee joints in full extension under anterior/posterior drawer forces of up to 400 N. DESIGN: A nonlinear three-dimensional finite element model of the entire human tibiofemoral joint consisting of bony structures, their articular cartilage layers, menisci, and four principal ligaments was utilized. BACKGROUND: The mechanics of the knee joint, specially under drawer forces, have extensively been investigated. Despite all these works, the detailed joint biomechanics, specially the role of boundary conditions, load transmission through menisci/articular cartilage layers, and coupling between menisci and cruciate ligaments are not yet quantified. METHODS: Nonlinear elastostatic analyses were carried out considering the tibiofemoral joint at full extension under anterior and posterior loads of up to 400 N applied either to the tibial or the femoral shaft. Cases with various boundary conditions, cruciate ligament deficiency (anterior or posterior), and total unilateral meniscectomy (medial or lateral) were analysed. RESULTS: In addition to the total primary anterior-posterior motion of about 9 mm at +/-400 N, significant coupled external tibial rotations of about 9 degrees and 10 degrees were computed under 400 N femoral posterior and anterior forces, respectively. The response was influenced by the manner of loading and boundary conditions. The anterior cruciate ligament and posterior cruciate ligament were the primary restraints to femoral posterior and anterior drawer forces, respectively. Section of either of these ligaments drastically increased the joint anterior-posterior motion. In the absence of cruciates, the collaterals became the primary restraints in both anterior-posterior forces. In this case, the tibial plateaus, specially the medial one in the anterior cruciate ligament-deficient joint, experienced much larger compressive forces. In addition to causing an increase in joint primary anterior-posterior laxity and anterior cruciate ligament forces, medial meniscectomy substantially increased coupled tibial external rotation, forces on the lateral plateau, and stresses in the articular cartilage of the lateral plateau. RELEVANCE: Our results suggest an increased role for the medial meniscus in the anterior cruciate ligament-deficient joint. Lateral meniscectomy had much smaller effects on results than the medial one. The success of any anterior cruciate ligament replacement or meniscal transplantation in the restoration of the joint stability and the protection of the articular cartilage against excessive stresses depends on the coupling between the anterior cruciate ligament and medial meniscus. Absence of any of these components would drastically influence the joint response.

Quantitative assessment of anterior cruciate ligament deficiency: applied load versus applied displacement

The Salford static knee instrument (SSKI) was developed to determine the quantitative assessment of the human knee joint in vivo by utilizing the technique of applied displacement and measurement of resistive load as proposed by Butler et al. (1). The instrument was used in parallel with the device developed by Al-Turaiki (2) which utilized the opposite method of assessment. The objective of the research was to examine which of the two techniques provided the more reliable and accurate method of knee assessment. Fourteen patients with suspected isolated rupture of the anterior cruciate ligament (ACL) were subjected to anterior-posterior drawer testing on both devices. The results showed that each instrument produced results which confirmed the clinical diagnosis by indicating a significant decrease in anterior stiffness when comparing the injured and uninjured knees. [SSKI device (p = 0.000) and Al-Turaiki (2) device (p = 0.002) statistical significant difference testing with Bonferonni Alpha correction p = 0.0125]. The results showed the Salford static knee instrument indicated a 58 per cent decrease in anterior stiffness and the Al-Turaiki (2) device a 35 per cent decrease when comparing the injured and uninjured knees. In conclusion it is suggested that the application of displacement and measurement of load as proposed by Butler et al. (1) may be the most appropriate technique for precise clinical diagnosis of pathological human knee joint instability.

Finite element analysis of human knee joint in varus-valgus

OBJECTIVE: The overall response, load transmission, role of ligaments, and state of stress in various components under varus-valgus moments in the intact and collateral-deficient tibiofemoral joint are investigated. DESIGN: A non-linear finite element model consisting of bony structures (tibia and femur), their articular cartilage layers, medial and lateral menisci and four primary ligaments (cruciates and collaterals) is utilized. BACKGROUND: Valgus and varus stresses are among the primary mechanisms of injury to knee ligaments. Several in vitro studies have investigated the role of ligaments in resisting such loads and on the way deficiency in either collateral may affect the response. METHODS: Cartilage layers are isotropic while menisci are non-homogeneous composite. The articulation of cartilage layers with each other and with the intervening menisci and the wrapping of the medial collateral ligament around the tibial edge are treated as large displacement frictionless contact problems. The non-linear elastostatic response of the joint at full extension is computed under varus-valgus moments applied to the femur with the tibia fixed. Cases simulating deficiency in collaterals and constraint on femoral axial rotation are also studied. RESULTS: The response is non-linear with large coupled axial rotations, internal in varus and external in valgus. In intact and collateral-deficient states, the joint shows varus or valgus openings so that the articulation occurs at one plateau only, medial in varus and lateral in valgus. Large tensile forces in cruciates in collateral-cut models generate higher compression penalty on the loaded plateau. CONCLUSIONS: Collaterals are the primary load-bearing structures; their absence would substantially increase primary laxities, coupled axial rotations, forces in cruciates, and articular contact forces. Good agreement with measurements is found. RELEVANCE: Detailed knowledge of joint biomechanics is essential in the diagnosis, prevention and treatment of observed disorders. Absence of collateral ligaments increases the loads in cruciates and contact stresses transmitted through cartilage layers and menisci, and thus places the affected components at more risk, especially when varus-valgus is accompanied by other modes of loading as well.

Analysis of skiing accidents involving combined injuries to the medial collateral and anterior cruciate ligaments

Two types of ligament injuries common in skiing are the isolated ruptures of the anterior cruciate and ruptures of the medial collateral, either with or without rupture of the anterior cruciate. Based on research related to ligament injury mechanics and two-mode release binding function, the purpose of this paper was to critically assess the ability of two-mode release bindings to prevent combined medial collateral and anterior cruciate ligament injuries. Making this assessment entailed several steps. First, I determined the loads typically transmitted by the knee during falls in which combined injuries occurred. Because more than one load was transmitted, the next step was to discern which of the loads was more damaging. Finally, heel-toe type bindings were evaluated for their potential to release in response to damaging loads. I concluded that combined medial collateral and anterior cruciate ligament injuries typically occur in forward, twisting-type falls in which the primary loads are external axial and valgus moments. An external axial moment is more damaging than a valgus moment, both to the medial collateral ligament when the joint is intact and to the anterior cruciate ligament when the medial collateral ligament is damaged. Because heel-toe type bindings offer release sensitivity to this moment, the release level of the toepiece in twist is an important factor in the prevention of these injuries.

Parameter sensitivity of a mathematical model of the anterior cruciate ligament

This paper presents the results of an investigation into parameter sensitivity of a mathematical model of the human anterior cruciate ligament (ACL). The model ACL comprised a continuous array of fibres mapped between part-elliptical attachment areas on the femur and tibia. Relative motion of the two bones was controlled by a planar four-bar linkage. Parameter modifications were: (a) an alternative set of values for the coordinates of the four-bar linkage joints; (b) rotation of the attachment areas of the ligament by +/- 30 degrees; and (c) variation of some mechanical properties. The alternative four-bar linkage parameter set produced extremely large changes in ACL force values, up to 130 per cent. Rotating the tibial attachment changed forces by less than 20 per cent, whereas rotating the femoral attachment changed forces by up to 100 per cent. Altering the mechanical parameters produced the smallest differences in force, under 15 per cent. These results highlight the importance, when using a theoretical model, of establishing the values of the parameters defining the model as accurately as possible and of carrying out a parameter sensitivity study. From a clinical viewpoint, they also suggest that, when reconstructing a ruptured ACL, one of the most important considerations must be to position the femoral attachment of the graft as accurately as is feasible.

Accurate measurement of three-dimensional knee replacement kinematics using single-plane fluoroscopy

A simple extension of a previously reported object recognition technique has been used to implement a six-degree-of-freedom position/orientation estimator for the measurement of knee replacement motion from two-dimensional (2-D) fluoroscopic images. Computer modeling studies and controlled mechanical tests were performed to assess the accuracy of the technique. The results indicate that knee rotations can be measured with an accuracy of approximately one degree and that sagittal plane translations can be measured with an accuracy of approximately 0.5 mm. The measurement technique is uniquely well suited for performing dynamic kinematic measurements on individuals with knee replacements, and for performing comparative studies among subjects with different designs of knee replacements.

Role of the medial structures in the intact and anterior cruciate ligament-deficient knee. Limits of motion in the human knee

We measured motion limits in human cadaveric knees before and after sectioning the anterior cruciate ligament and the medial structures. Sectioning the medial collateral ligament in an anterior cruciate ligament-deficient knee increased the anterior translation limit at 90 degrees of flexion but not at 30 degrees of flexion. The tibia displaced straight anteriorly without exhibiting the coupled internal rotation that occurred in intact and anterior cruciate ligament-deficient knees. A lateral 15 N-m abduction moment produced a coupled external rotation in the medial collateral ligament-deficient knee. This was in marked contrast to intact, anterior cruciate ligament-deficient, or combined medial collateral ligament and anterior cruciate ligament-deficient knees, in which an abduction moment produced a coupled internal rotation. Sectioning only the medial collateral ligament caused a small but significant increase in the abduction rotation limit, whereas larger increases in the abduction rotation limit occurred when the posterior oblique ligament and posterior medial capsule were cut in addition to the medial collateral ligament. Cutting the medial collateral ligament increased the external rotation limit. The increase was independent of whether the anterior cruciate ligament was intact or sectioned. Subsequent cutting of the posterior oblique ligament and posterior medial capsule further increased the external rotation limit.

Biomechanical function of the human anterior cruciate ligament

Knowledge about the biomechanical function of the anterior cruciate ligament (ACL) is very important in the treatment of the ACL deficient knee. This article presents an overview of the biomechanical function of the ACL, including its structural and mechanical properties as well as its role in knee stabilization and normal kinematics. Tensile properties of the prospective biological grafts and future directions in ACL research are also discussed.

The anterior cruciate ligament in controlling axial rotation. An evaluation of its effect

Changes in axial tibial rotation after anterior cruciate ligament sectioning were evaluated in 14 fresh human knee joints. Simulation of vertical stance in a quadriceps-stabilized knee was performed. Internal and external rotational torques were applied before and after anterior cruciate ligament sectioning. Pivot shift tests were done in the intact and anterior cruciate ligament sectioned knee. Results of pivot shift tests were all negative before sectioning and positive after isolated sectioning. No significant change in axial rotation occurred between the intact and sectioned knee for external rotation (P = 0.24) or internal rotation (P = 0.12). Presence of a load at the femoral housing in both the intact and ligament-sectioned knees caused a significant change in external rotation (P < 0.0001). No significant change was noted in internal rotation between loaded and unloaded states (P = 0.70). Total tibial rotation in the intact knee was noted to vary between 31 degrees at 0 degree of flexion and 42 degrees at 60 degrees of flexion. These results suggest that the anterior cruciate ligament does not play a significant role in limiting axial rotation and that rotational instability is not a major factor after isolated anterior cruciate ligament rupture.

Loading and deformation of the cat posterior knee joint capsule in axial and extension rotations

Deformation and loading of the knee posterior joint capsule were studied in the cat, in extension rotations and in axial external (ER) and internal (IR) rotations at full extension. Loads were measured in the ligament along the upper edge of the capsule, using mechanically sensitive neurons that were calibrated as load cells. Strains were measured across the surface of the capsule, by tracking a set of markers attached to its surface. External rotations produced small loads in the cable: with applied moments of up to 0.25 Nm, cable tensions were less than 0.8 mPa. The cable was not loaded by internal rotations. Axial rotations produced predominantly shear strains in the capsule. Extension produced small loads in the ligament and the predominant capsule strain was tensile along the axis of the femur. These results show that the posterior capsule has a small role in resisting extension, a minimal role in providing axial stability in ER, and no such role in IR.

A technique for the evaluation of the contributions of knee structures to knee mechanics in the knee that has a reconstructed anterior cruciate ligament

A technique to quantify the restraining action of specific knee structures during anterior/posterior (A/P) tibial displacement tests in the goat knee that has a reconstructed anterior cruciate ligament (ACL) is described. Joint specimens were mounted in an instrumented test stand to measure both the forces on, and resulting translations of, the tibia in the A/P direction. The intact grafted knee was tested first, after which structures were sequentially cut or removed, or both, and the test was repeated. The ACL graft remained intact in the joint during this process; therefore, subsequent axial failure testing was possible. Analysis of the resulting force-displacement curves allowed the percentage contribution and anterior joint stiffness to be determined for each structure at a fixed anterior displacement in 12 goat knees 6 months after ACL allografting. The allografts were found to provide about 56% of the total restraining force, more than any other structure examined. Studies of this kind will be important in the documentation of the changing role of an autograft or allograft in a reconstructed knee over time.

A model of human knee ligaments in the sagittal plane. Part 2: Fibre recruitment under load

A mathematical model of the knee ligaments in the sagittal plane is used to study the forces in the cruciate and collateral ligaments produced by anterior/posterior tibial translation. The model is based on ligament fibre functional architecture. Geometric analysis of the deformed configurations of the model ligaments provides the additional compatibility conditions necessary for calculation of the statically indeterminate distributions of strain and stress within the ligaments and the sharing of load between ligaments. The investigation quantifies the process of ligament fibre recruitment, which occurs when fibres made slack by passive flexion/extension of the knee stretch and change their spatial positions in order to resist applied loads. The calculated ligament forces are in reasonable agreement with experimental results reported in the literature. The model explains some subtleties of ligament function not incorporated in models that represent the ligaments by a small number of lines.

Apparatus to obtain rotational flexibility of the human knee under moment loads in vivo

The contributions of this paper are twofold. One is the design and performance evaluation of new equipment to determine the rotational flexibility of the human knee in vivo. Since determining knee flexibility requires the application of external loads and the measurement of knee rotations, the new equipment consists of a load application stand and a triaxial goniometer. The triaxial goniometer noninvasively mounts to the leg and directly measures the relative three degrees-of-freedom rotations of the knee sequentially and independently. The goniometer incorporates several unique design features which enhance measurement accuracy. The load stand applies pure varus/valgus and external/internal axial moments either individually or in combination through the use of motors controlled by the test subject. Unique to this design are features which enable the application of moments to the knee which minimise shear forces. Other unique design features permit the stand to control hip and knee flexion angles, muscle contraction, and axial loading. To assess the accuracy with which rotations are measured during experiments, three tests were conducted with the equipment. One test evaluated the inherent accuracy of the goniometer, a second test assessed the potential for goniometer slippage during loading, and a third explored the effect of goniometer mounting on the repeatability of results. A special verification apparatus facilitated evaluation of goniometer inherent accuracy. A second contribution of the paper is an investigation of the effect of foot constraints (i.e. boundary conditions) on flexibility results. To make this investigation, three subjects were tested with the knee at 15 degrees of flexion. Results revealed large differences in flexibility between constraining the foot in both external/internal and varus/valgus rotations and permitting the foot to rotate freely in the direction not being loaded. Further, constraint moments as high as 23 Nm were also recorded. These results emphasise that in order to obtain accurate flexibility results for isolated loads, the foot must be unconstrained by the loading apparatus.

Rotational flexibility of the human knee due to varus/valgus and axial moments in vivo

Knee ligamentous injuries persist in the sport of Alpine skiing. To better understand the load mechanisms which lead to injury, pure varus/valgus and pure axial moments were applied both singly and in combination to the right knees of six human test subjects. The corresponding relative knee rotations in three degrees of freedom were measured. Knee flexion angles for each test subject were 15 and 60 degrees for the individual moments and 60 degrees for the combination moments. For both knee flexion angles the hip flexion angle was 0 degrees. Leg muscles were quiescent and axial force was minimal during all tests. Tables of data include sample statistics for each of four flexibility parameters in each loading direction. Data were analyzed statistically to test for significant differences in flexibility parameters between the test conditions. In flexing the knee from 15 to 60 degrees, the resulting knee rotations under single moments depended upon flexion angle with varus, valgus, and internal rotations increasing significantly. Also, rotations were different depending on load direction; varus rotation was significantly different and greater than valgus rotation at both flexion angles. Also external rotation was significantly different and greater than internal at 15 degrees flexion, but not at 60 degrees flexion. Coupled rotations under single moments were also observed. Applying pure varus/valgus moments resulted in coupled external/internal rotations which were inconsistent and hence not significant. Applying pure axial moments resulted in consistent and hence significant varus/valgus rotations; an external axial moment induced varus rotation and an internal axial moment induced valgus rotation. For combination moments, varus/valgus rotations decreased significantly from those rotations at similar load levels in the single moment studies. Also, a varus moment significantly increased external rotation and a valgus moment significantly decreased internal rotation. These differences indicate significant interaction between corresponding load combinations. These results suggest that load interaction is a potentially important phenomenon in knee injury mechanics.

Effects of surgical treatment and immobilization on the healing of the medial collateral ligament: a long-term multidisciplinary study

The long-term effects of surgical repair and immobilization on the healing of the transected medial collateral ligament (MCL) were studied biomechanically, biochemically and histologically in a canine model. Twelve adult canines were divided into two experimental groups and studied at 48 weeks postoperatively. For Group I, the transected MCL of the left knee was not repaired, and the joint was not immobilized. For Group II, the MCL was repaired and the joint was immobilized for six weeks. The right knee of each canine was sham-operated and served as the control. Histologically, the collagen fibers were less aligned in both of the experimental groups than in the controls. Furthermore, there were minimal differences in collagen and fibroblast alignment between the groups, although poorer alignment was observed for Group I at 12 weeks. Biochemically, the levels of types I and III collagen, reducible collagen cross-links and total collagen concentration for both groups returned to normal levels. Biomechanically, Group I achieved better results than Group II in terms of varus-valgus (V-V) knee rotation and ultimate load of the femur-MCL-tibia complex (FMTC), as these values returned to the level of controls. However, the mechanical properties of the healing MCLs did not compare well with the controls; the tensile strength was only 62% and 45% of controls for Groups I and II, respectively, at 48 weeks. These results suggest that conservative treatment (i.e., no surgical intervention) with early mobilization is better than surgical treatment with immobilization for an isolated Grade III MCL injury.

Measurement of joint capsule tissue loading in the cat knee using calibrated mechanoreceptors

The vertical loading in the posterior capsule of the cat knee has been measured while the knee is rotated into hyperextension. Tissue loading was determined using a previously verified model of the capsule that represents its upper edge as a catenary suspension cable. Tensile loads in the cable were measured using the discharge of mechanoreceptive sensory neurons that had been calibrated as load sensors. The results revealed that the capsule is very lightly loaded in extension rotations. Less than 4% of the applied moment is sustained by the capsule.

Calibrating joint capsule mechanoreceptors as in vivo soft tissue load cells

A method has been developed whereby the discharge of mechanically sensitive neurons from the cat knee joint capsule can be calibrated and used as load cells. The neurons are located in the upper edge of the capsule which has been previously modeled as a suspension cable and where the loading has been shown to be one dimensional. The calibration procedure relies upon applying known point loads to the cable and measuring its shape. The biomechanical model is then used to compute the cable tension at the neuron location. Results for 20 neurons showed a strong linear relationship between the tension and the frequency of neuronal discharge (r = 0.96, S.D. = 0.05). For 11 of these neurons the in vivo calibration was verified by subsequently excising the posterior capsule and recording from the same neuron while subjecting the cable to measured uniaxial loads. Results showed good agreement between the in vivo and in vitro calibrations. Once calibrated these neurons can be used as load sensors to study in vivo joint loading.

The envelope of passive knee joint motion

The purpose of this study is to create an accurate experimental database for the passive (in vitro) freedom-of-motion characteristics of the human knee joint on a subject to subject basis, suitable for the verification and enhancement of mathematical knee-joint models. Knee-joint specimens in a six degree-of-freedom motion rig are moved through flexion under several combinations of external loads, including tibial torques, axial forces and AP-forces. Euler rotation angles and translation vectors, describing the relative, spatial motions of the joint are measured using an accurate Roentgen Stereo Photogrammetric system. Conceptually the joint is considered as a two degrees-of-freedom of motion mechanism (flexion-tibial rotation), whereby the limits of internal and external tibial rotation are defined at torques of +/- 3 Nm. The motion pathways along these limits are defined as the envelopes of passive knee joint motion. It is found that these envelope pathways are consistent and hardly influenced by additional axial forces up to 300 N and AP-forces of 30 N. Within the envelope of motion, however, the motion patterns are highly susceptible to small changes in the external load configuration. It is shown that the external tibial rotation during extension ('screw-home mechanism') is not an obligatory effect of the passive joint characteristics, but a direct result of the external loads. Anatomical differences notwithstanding, the inter-individual discrepancies in the motion patterns of the four specimens tested, showed to be relatively small in a qualitative sense. Quantitative differences can be explained by small differences in the alignment of the coordinate systems relative to the joint anatomy and by differences in rotatory laxity.

Contribution of the musculature to rotatory laxity and torsional stiffness at the knee

The relationships between the mean rectified EMG from two muscle groups crossing the knee joint and the rotational stiffness and laxity about the longitudinal axis of the lower leg were investigated. The EMG signals from three of the quadricep muscle group and two of the hamstring muscle group were monitored using surface electrodes. Each subject sustained self-induced muscle activity from specific muscle combinations while the foot was twisted internally and externally by the researcher. Joint rotation was measured using an electrogoniometer. Analyses of the data showed increased joint stiffness with increased numbers of active muscles. The stiffness measurements ranged from 0.16 to 2.54 Nm degree-1 depending upon the combination of active muscles. The stiffness measured in different tests were very repeatable with standard deviations ranging from 0.02 to 0.25 Nm degree-1. Increases in joint stiffness of over 400% by activation of these muscles were measured.

Treatment of the medial collateral ligament injury. I: The importance of anterior cruciate ligament on the varus-valgus knee laxity

The purpose of this study was to explain the functional roles of the medial collateral ligament (MCL) and the ACL and how they affect the kinematics of the knee joint after isolated MCL injury. Varus-valgus joint laxity was quantitatively measured using a device which allowed various degrees of freedom (DOF) of joint motion during application of a varus-valgus bending moment to the canine knee joint. When the knee motion was limited to 3 DOF (varus-valgus rotation, proximal-distal, and medial-lateral translation), valgus laxity increased significantly (171%) after sectioning the MCL. Thus, the MCL was the primary restraint to the valgus bending moment in the 3 DOF mode. However, the effect of sectioning the MCL on valgus laxity became minimal (21% increase) when the DOF of knee motion was increased to 5 (by adding axial tibial rotation and anterior-posterior translation). In this situation, external and internal tibial axial rotation were coupled with the varus and valgus rotation of the knee joint, respectively, and the ACL also functioned to restrain the varus-valgus rotation. The results of this study suggest that under normal knee joint motion, the functional deficit of the MCL in valgus rotation was compensated for by the remaining structures, especially by the ACL.

Treatment of the medial collateral ligament injury. II: Structure and function of canine knees in response to differing treatment regimens

In order to assess the healing of the medial collateral ligament (MCL) and to detect the various effects of treatment regimens, in vivo animal experiments using a canine model were performed. Thirty-five canine MCLs were surgically transected and treated using three clinically popular regimens, e.g., no repair with cage and farm activities (Group 1), repair with 3 weeks immobilization (Group 2), and repair with 6 weeks immobilization (Group 3). The varus-valgus laxity of the knee joint, structural properties of the femur-MCL-tibia (FMT) complex and the mechanical properties of the MCL substance (healing site) were quantitatively measured at 6, 12, and 48 weeks postoperatively. It was found that Group 1 animals had the best results. The varus-valgus laxity of the knee joint and the structural properties of the FMT complex returned to values comparable with the contralateral control by 12 weeks. The recovery of the mechanical properties of the MCL substance was slower and not complete, even at 48 weeks. In confirmation with previous studies, prolonged immobilization was shown to have deleterious effects on MCL healing. The results of this study indicated that early mobilization is the treatment of choice in cases of isolated MCL injury. Also, this study emphasized the importance and effectiveness of using various biomechanical parameters in addition to the conventional ultimate values at failure to evaluate the progress of soft tissue repair.

A microcomputer controlled snow ski binding system--II. Release decision theories

A hierarchy of release decision theories for both tibia fracture and knee ligamentous injury are defined and simulated on a computer. Moment loading data, recorded during actual skiing by the microcomputer-based ski binding system described in Part I, are processed by the various release decision theories. At the bottom of the hierarchy is the simplest theory which treats boot loading as quasi-static and compares moment components to threshold levels. Another stage of the hierarchy defines an analytic expression for a combined loading failure locus. Note that this is the first formulation of a combined loading release decision theory. Yet another stage of the hierarchy computes bone moments via dynamic system leg models. The various release decision theories are evaluated by comparing processed results to both pain and bone failure limits. For the data generated by the field tests conducted to date, the simplest release decision theory satisfied the retention requirement for pain limits in the presence of muscle activity for both torsion and forward bending. For pain limits in the absence of muscle activity the retention requirement was not satisfied however. Another result is that leg dynamics are significant. A final result is that combined loading considerations lead to a more conservative theory.

Control exerted by ligaments

The function of the ligaments as local controllers, independent of the central nervous system, in maintaining the integrity of the joint is demonstrated by modelling the human knee in the sagittal plane, and studying its anterior-posterior motion. In addition to the ligaments, the model includes the characteristic geometry of the joint surface and some muscle groups. The connecting reaction forces at the point of contact between the tibia and the femur are considered to be constraint forces due to three different surface motions--gliding, rolling and combined gliding and rolling. It is demonstrated that the ligamentous structure maintains these holonomic and nonholonomic constraints that describe the joint motion, and that stability of the knee joint is provided mainly by ligaments. Muscular structures further stabilize and contribute to joint movement. Computer simulation of rolling movement of the knee is presented to illustrate the importance of the ligaments for joint integrity and stability.