Computational and Experimental Study of Performance of an Artificial Ligament: DacronTM yarn

Abstract

The success rate of reconstructing the Anterior Cruciate Ligament (ACL) with prosthetic ligaments is currently low both in humans and animals. The stress distribution in prosthetic ligaments that causes failure is very complex and not yet understood. Therefore, we have begun to develop a Finite Element Model of a prosthetic ACL. Here we describe the normal and contact stresses in Dacron^TM yarn (a multi-fibrillar structure) using input data based on experimental measurements of the load and strain of six designed yarns.

The results show that the normal and contact stresses in the fibres of the ACL yarn are directly proportional to the yam strains. Increasing the twisting length (transverse deformation) of the yarn increases the normal stress in the fibres and the yarn modulus, but decreases the contact stresses between the fibres. The structural properties of a yarn are dependent on the specific arrangement of various filament types. Increasing the distance between the longitudinal (symmetry) axes of the filaments and the axis of symmetry of the yarn decreases the stresses.     

Loss of ACL function leads to alterations in tibial plateau common dynamic contact stress profiles

It has been suggested that the repetitive nature of altered joint tissue loading which occurs after anterior cruciate ligament (ACL) rupture can contribute to the development of osteoarthritis (OA). However, changes in dynamic knee joint contact stresses after ACL rupture have not been quantified for activities of daily living. Our objective was to characterize changes in dynamic contact stress profiles that occur across the tibial plateau immediately after ACL transection. By subjecting sensor-augmented cadaveric knees to simulated gait, and analyzing the resulting contact stress profiles using a normalized cross-correlation algorithm, we tested the hypothesis that common changes in dynamic contact stress profiles exist after ACL injury. Three common profiles were identified in intact knees, occurring on the: (I) posterior lateral plateau, (II) posterior medial plateau, and (III) central region of the medial plateau. In ACL-transected knees, the magnitude and shape of the common dynamic stress profiles did not change, but their locations on the tibial plateau and the number of knees identified for each profile changed. Furthermore, in the ACL transected knees, a unique common contact stress profile was identified in the posterior region of the lateral plateau near the tibial spine. This framework can be used to understand the regional and temporal changes in joint mechanics after injury.     

Finite element estimates of interface stress in the trans-tibial prosthesis using gap elements are different from those using automated contact

When compared with automated contact methods of finite element (FE) analyses, gap elements have certain inherent disadvantages in simulating large slip of compliant materials on stiff surfaces. However, automated contact has found limited use in the biomechanical literature. A non-linear, three-dimensional, geometrically accurate, FE analysis of the trans-tibial limb-socket prosthetic system was used to compare an automated contact interface model with a gap element model, and to evaluate the sensitivity of automated contact to interfacial coefficient of friction (COF). Peak normal stresses and resultant shear stresses were higher in the gap element model than in the automated contact model, while the maximum axial slip was less. Under proximally directed load, compared with automated contact, gap elements predicted larger areas of stress concentration that were located more distally. Gap elements did not predict any relative slip at the distal end, and also transmitted a larger proportion of axial load as shear stress. Both models demonstrated non -linear sensitivity to COF, with larger variation at lower magnitudes of COF. By imposing physical connections between interface surfaces, gap elements distort the interface stress distributions under large slip. Automated contact methods offer an attractive alternative in applications such as prosthetic FE modeling, where the initial position of the limb in the socket is not known, where local geometric features have high design significance, and where large slip occurs under load.     

A dynamic multibody model of the physiological knee to predict internal loads during movement in gravitational field

Obtaining tibio-femoral (TF) contact forces, ligament deformations and loads during daily life motor tasks would be useful to better understand the aetiopathogenesis of knee joint diseases or the effects of ligament reconstruction and knee arthroplasty. However, methods to obtain this information are either too simplified or too computationally demanding to be used for clinical application. A multibody dynamic model of the lower limb reproducing knee joint contact surfaces and ligaments was developed on the basis of magnetic resonance imaging. Several clinically relevant conditions were simulated, including resistance to hyperextension, varus–valgus stability, anterior–posterior drawer, loaded squat movement. Quadriceps force, ligament deformations and loads, and TF contact forces were computed. During anterior drawer test the anterior cruciate ligament (ACL) was maximally loaded when the knee was extended (392 N) while the posterior cruciate ligament (PCL) was much more stressed during posterior drawer when the knee was flexed (319 N). The simulated loaded squat revealed that the anterior fibres of ACL become inactive after 60° of flexion in conjunction with PCL anterior bundle activation, while most components of the collateral ligaments exhibit limited length changes. Maximum quadriceps and TF forces achieved 3.2 and 4.2 body weight, respectively. The possibility to easily manage model parameters and the low computational cost of each simulation represent key points of the present project. The obtained results are consistent with in vivo measurements, suggesting that the model can be used to simulate complex and clinically relevant exercises.     

A theoretical model of the knee and ACL: theory and experimental verification.

A three-dimensional mathematical model of the human knee joint was developed to examine the role of single ligaments, such as an anterior cruciate ligament (ACL) graft in ACL reconstruction, on joint motion and tissue forces. The model is linear and valid for small motions about an equilibrium position. The knee joint is modeled as two rigid bodies (the femur and the tibia) interconnected by deformable structures, including the ACL or ACL graft, the cartilage layer, and the remainder of the knee tissues (modeled as a single element). The model was demonstrated for the equilibrium condition of the knee in extension with an anterior tibial force, causing anterior drawer and hyperextension. The knee stiffness matrix for this condition was measured for a human right knee in vitro. Predicted model response was compared with experimental observations. Qualitative agreement was found between model and experiment, validating the model and its assumptions. The model was then used to predict the change in graft and cartilage forces and joint motion of the knee due to an increment of load in the normal joint both after ACL removal and with various altered states simulating ACL reconstructions. Results illustrate the interdependence between loads in the ACL graft, other knee structures, and contact force. Stiffer grafts and smaller maximum unloaded length of the ligament lead to higher graft and contact forces. Changes in cartilage stiffness alter load sharing between ACL graft and other joint tissues.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 2: Analysis of Ligament Function

A three-dimensional model of the knee is used to study ligament function during anterior-posterior (a-p) draw, axial rotation, and isometric contractions of the extensor and flexor muscles. The geometry of the model bones is based on cadaver data. The contacting surfaces of the femur and tibia are modeled as deformable; those of the femur and patella are assumed to be rigid. Twelve elastic elements are used to describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit represented as a three-element muscle in series with tendon. The calculations show that the forces applied during a-p draw are substantially different from those applied by the muscles during activity. Principles of knee-ligament function based on the results of in vitro experiments may therefore be overstated. Knee-ligament forces during straight a-p draw are determined solely by the changing geometry of the ligaments relative to the bones: ACL force decreases with increasing flexion during anterior draw because the angle between the ACL and the tibial plateau decreases as knee flexion increases; PCL force increases with increasing flexion during posterior draw because the angle between the PCL and the tibial plateau increases. The pattern of ligament loading during activity is governed by the geometry of the muscles spanning the knee: the resultant force in the ACL during isometric knee extension is determined mainly by the changing orientation of the patellar tendon relative to the tibia in the sagittal plane; the resultant force in the PCL during isometric knee flexion is dominated by the angle at which the hamstrings meet the tibia in the sagittal plane.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 2: Analysis of Ligament Function

A three-dimensional model of the knee is used to study ligament function during anterior-posterior (a-p) draw, axial rotation, and isometric contractions of the extensor and flexor muscles. The geometry of the model bones is based on cadaver data. The contacting surfaces of the femur and tibia are modeled as deformable; those of the femur and patella are assumed to be rigid. Twelve elastic elements are used to describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit represented as a three-element muscle in series with tendon. The calculations show that the forces applied during a-p draw are substantially different from those applied by the muscles during activity. Principles of knee-ligament function based on the results of in vitro experiments may therefore be overstated. Knee-ligament forces during straight a-p draw are determined solely by the changing geometry of the ligaments relative to the bones: ACL force decreases with increasing flexion during anterior draw because the angle between the ACL and the tibial plateau decreases as knee flexion increases; PCL force increases with increasing flexion during posterior draw because the angle between the PCL and the tibial plateau increases. The pattern of ligament loading during activity is governed by the geometry of the muscles spanning the knee: the resultant force in the ACL during isometric knee extension is determined mainly by the changing orientation of the patellar tendon relative to the tibia in the sagittal plane; the resultant force in the PCL during isometric knee flexion is dominated by the angle at which the hamstrings meet the tibia in the sagittal plane.     

Biomechanics of changes in ACL and PCL material properties or prestrains in flexion under muscle force-implications in ligament reconstruction

The effects of changes in cruciate ligament material and prestrain on knee joint biomechanics following ligament reconstruction surgery by a tendon are not adequately known. A 3D nonlinear finite element model of the entire knee joint was used to investigate the joint response at different flexion angles under a quadriceps force while varying ACL and PCL initial strains or material properties. The ACL and PCL forces as well as tibiofemoral contact forces/areas substantially increased with greater ACL or PCL initial strains or stiffness. The patellofemoral contact force slightly increased whereas the tibial extensor moment slightly decreased with tenser or stiffer ACL. Reverse trends were predicted with slacker ACL. Results confirm the hypotheses that changes in the prestrain of one cruciate ligament substantially influence the force in the other cruciate ligament and the entire joint and that the use of the patellar tendon (PT) as a replacement for cruciate ligaments markedly alters the joint biomechanics with trends similar to those predicted when increasing prestrains. Forces in both ACL and PCL ligaments increased as one of them became tenser or stiffer and diminished as it became slacker. These results have important consequences in joint biomechanics following ligament injuries or replacement and tend to recommend the use of grafts with smaller prestrains (i.e. slacker than intact) when using the PT as the replacement material with stiffness greater than that of replaced ligament itself.     

Biomechanics of changes in ACL and PCL material properties or prestrains in flexion under muscle force-implications in ligament reconstruction

The effects of changes in cruciate ligament material and prestrain on knee joint biomechanics following ligament reconstruction surgery by a tendon are not adequately known. A 3D nonlinear finite element model of the entire knee joint was used to investigate the joint response at different flexion angles under a quadriceps force while varying ACL and PCL initial strains or material properties. The ACL and PCL forces as well as tibiofemoral contact forces/areas substantially increased with greater ACL or PCL initial strains or stiffness. The patellofemoral contact force slightly increased whereas the tibial extensor moment slightly decreased with tenser or stiffer ACL. Reverse trends were predicted with slacker ACL. Results confirm the hypotheses that changes in the prestrain of one cruciate ligament substantially influence the force in the other cruciate ligament and the entire joint and that the use of the patellar tendon (PT) as a replacement for cruciate ligaments markedly alters the joint biomechanics with trends similar to those predicted when increasing prestrains. Forces in both ACL and PCL ligaments increased as one of them became tenser or stiffer and diminished as it became slacker. These results have important consequences in joint biomechanics following ligament injuries or replacement and tend to recommend the use of grafts with smaller prestrains (i.e. slacker than intact) when using the PT as the replacement material with stiffness greater than that of replaced ligament itself.     

Comparison of elastic,viscoelastic and failure tensile material properties of knee ligaments and patellar tendon

The knee ligaments and patellar tendon function in concert with each other and other joint tissues, and are adapted to their specific physiological function via geometry and material properties. However, it is not well known how the viscoelastic and quasi-static material properties compare between the ligaments. The purpose of this study was to characterize and compare these material properties between the knee ligaments and patellar tendon.Dumbbell-shaped tensile test samples were cut from bovine knee ligaments (ACL, LCL, MCL, PCL) and patellar tendon (PT) and subjected to tensile testing (n = 10 per ligament type). A sinusoidal loading test was performed at 8% strain with 0.5% strain amplitude using 0.1, 0.5 and 1 Hz frequencies. Subsequently, an ultimate tensile test was performed to investigate the stress-strain characteristics.At 0.1 Hz, the phase difference between stress and strain was higher in LCL compared with ACL, PCL and PT (p < 0.05), and at 0.5 Hz that was higher in LCL compared with all other ligaments and PT (p < 0.05). PT had the longest toe-region strain (p < 0.05 compared with PCL and MCL) and MCL had the highest linear and strain-dependent modulus, and toughness (p < 0.05 compared with ACL, LCL and PT).The results indicate that LCL is more viscous than other ligaments at low-frequency loads. MCL was the stiffest and toughest, and its modulus increased most steeply at the toe-region, possibly implying a greater amount of collagen. This study improves the knowledge about elastic, viscoelastic and failure properties of the knee ligaments and PT.     

Structure and function of matrix components in the cruciate ligaments. An immunohistochemical, electron-microscopic, and immunoelectron-microscopic study.

In the present study, the matrix components of 100 cruciate ligaments were analyzed by conventional electron microscopy, immunohistology, morphometry, and immunoelectron microscopy. The anterior (ACL) and the posterior (PCL) cruciate ligaments contained collagen types III, IV, and VI. Several structural glycoproteins, like fibronectin, laminin, entactin, tenascin, and undulin were detected using monoclonal antibodies. Whereas laminin and entactin were higher concentrated in the PCL, type VI collagen was more frequently found in the ACL. The ACL had a critical nourishment in its distal and middle thirds. In all ligament parts the PCL revealed a better vascular supply with strong correlation to type IV collagen expression. The normal matrix of the cruciate ligaments represented a complicated regulatory network of proteins, glycoproteins, elastic systems, and glycosaminoglycans with multiple functional interactions.     

An analytical model of joint contact

The stress distribution in the region of contact between a layered elastic sphere and a layered elastic cavity is determined using an analytical model to stimulate contact of articulating joints. The purpose is to use the solution to analyze the effects of cartilage thickness and stiffness, bone stiffness and joint curvature on the resulting stress field, and investigate the possibility of cracking of the material due to tensile and shear stresses. Vertical cracking of cartilage as well as horizontal splitting at the cartilage-calcified cartilage interface has been observed in osteoarthritic joints. The current results indicate that for a given system (material properties mu and nu constant), the stress distribution is a function of the ratio of contact radius to layer thickness (a/h), and while tensile stresses are seen to occur only when a/h is small, tensile strain is observed for all a/h values. Significant shear stresses are observed at the cartilage-bone interface. Softening of cartilage results in an increase in a/h, and a decrease in maximum normal stress. Cartilage thinning increases a/h and the maximum contact stress, while thickening has the opposite effect. A reduction in the indenting radius reduces a/h and increases the maximum normal stress. Bone softening is seen to have negligible effect on the resulting contact parameters and stress distribution.     

A three-dimensional finite element model of the human anterior cruciate ligament: a computational analysis with experimental validation

In this study, the force and stress distribution within the anteromedial (AM) and posterolateral (PL) bundles of the anterior cruciate ligament (ACL) in response to an anterior tibial load with the knee at full extension was calculated using a validated three-dimensional finite element model (FEM) of a human ACL. The interaction between the AM and PL bundles, as well as the contact and friction caused by the ACL wrapping around the bone during knee motion, were included in the model. The AM and PL bundles of the ACL were simulated as incompressible homogeneous and isotropic hyperelastic materials. The multiple-degrees-of-freedom (DOF) knee kinematics of a cadaveric knee were first obtained using a robotic/universal force-moment sensor testing system. These data were used as the boundary conditions for the FEM of the ACL to calculate the forces in the ACL. The calculated forces were compared to the in situ force in the ACL, determined experimentally, to validate the model. The validated FEM was then used to calculate the force and stress distribution within the ACL under an anterior tibial load at full extension. The AM and PL bundles shared the force, and the stress distribution was non-uniform within both bundles with the highest stress localized near the femoral insertion site. The contact and friction caused by the ACL wrapping around the bone during knee motion played the role of transferring the force from the ACL to the bone, and had a direct effect on the force and stress distribution of the ACL. This validated model will enable the analysis of force and stress distribution in the ACL in response to more complex loading conditions and has the potential to help design improved surgical procedures following ACL injuries.     

Effect of meniscus replacement fixation technique on restoration of knee contact mechanics and stability

The menisci are important biomechanical components of the knee. We developed and validated a finite element model of meniscal replacement to assess the effect of surgical fixation technique on contact behavior and knee stability. The geometry of femoral and tibial articular cartilage and menisci was segmented from magnetic resonance images of a normal cadaver knee using MIMICS (Materialise, Leuven, Belgium). A finite element mesh was generated using HyperWorks (Altair Inc, Santa Ana, CA). A finite element solver (Abaqus v6.9, Simulia, Providence, RI) was used to compute contact area and stresses under axial loading and to assess stability (reaction force generated during anteroposterior translation of the femur). The natural and surgical attachments of the meniscal horns and peripheral rim were simulated using springs. After total meniscectomy, femoral contact area decreased by 26% with a concomitant increase in average contact stresses (36%) and peak contact stresses (33%). Replacing the meniscus without suturing the horns did little to restore femoral contact area. Suturing the horns increased contact area and reduced peak contact stresses. Increasing suture stiffness correlated with increased meniscal contact stresses as a greater proportion of tibiofemoral load was transferred to the meniscus. A small incremental benefit was seen of simulated bone plug fixation over the suture construct with the highest stiffness (50 N/mm). Suturing the rim did little to change contact conditions. The nominal anteroposterior stiffness reduced by 3.1 N/mm after meniscectomy. In contrast to contact area and stress, stiffness of the horn fixation sutures had a smaller effect on anteroposterior stability. On the other hand suturing the rim of the meniscus affected anteroposterior stability to a much larger degree. This model emphasizes the importance of the meniscus in knee biomechanics. Appropriate meniscal replacement fixation techniques are likely to be critical to the clinical success of meniscal replacement. While contact conditions are mainly sensitive to meniscus horn fixation, the stability of the knee under anteroposterior shear loads appeared to be more sensitive to meniscal rim fixation. This model may also be useful in predicting the effect of biomaterial mechanical properties and meniscal replacement shape on knee contact conditions.     

Pattern of anterior cruciate ligament force in normal walking

The goal of this study was to calculate and explain the pattern of anterior cruciate ligament (ACL) loading during normal level walking. Knee-ligament forces were obtained by a two-step procedure. First, a three-dimensional (3D) model of the whole body was used together with dynamic optimization theory to calculate body-segmental motions, ground reaction forces, and leg-muscle forces for one cycle of gait. Joint angles, ground reaction forces, and muscle forces obtained from the gait simulation were then input into a musculoskeletal model of the lower limb that incorporated a 3D model of the knee. The relative positions of the femur, tibia, and patella and the forces induced in the knee ligaments were found by solving a static equilibrium problem at each instant during the simulated gait cycle. The model simulation predicted that the ACL bears load throughout stance. Peak force in the ACL (303 N) occurred at the beginning of single-leg stance (i.e., contralateral toe off). The pattern of ACL force was explained by the shear forces acting at the knee. The balance of muscle forces, ground reaction forces, and joint contact forces applied to the leg determined the magnitude and direction of the total shear force acting at the knee. The ACL was loaded whenever the total shear force pointed anteriorly. In early stance, the anterior shear force from the patellar tendon dominated the total shear force applied to the leg, and so maximum force was transmitted to the ACL at this time. ACL force was small in late stance because the anterior shear forces supplied by the patellar tendon, gastrocnemius, and tibiofemoral contact were nearly balanced by the posterior component of the ground reaction.     

Critical stresses for cancer cell detachment in microchannels

We present experiments involving cancer cells adhering to microchannels, subjected to increasing shear stresses (0.1–30 Pa). Morphological studies were carried out at different shear stresses. Cells exhibit spreading patterns similar to those observed under static conditions, as long as the shear stress is not too high. At critical wall shear stresses (around 2−5 Pa), cell-substrate contact area decreases until detachment at the larger stresses. Critical shear stresses are found to be lower for higher confinements (i.e. smaller cell height to channel height ratio). Fluorescent techniques were used to locate focal adhesions (typically 1 μm² in size) under various shearing conditions, showing that cells increase the number of focal contacts in the region facing the flow. To analyze such data, we propose a model to determine the critical stress, resulting from the competition between hydrodynamic forces and the adhesive cell resistance. With this model, typical adhesive stresses exerted at each focal contact can be determined and are in agreement with previous works.     

Spatial Change of Cruciate Ligaments in Rat Embryo Knee Joint by Three-Dimensional Reconstruction

This study aimed to analyze the spatial developmental changes of rat cruciate ligaments by three-dimensional (3D) reconstruction using episcopic fluorescence image capture (EFIC). Cruciate ligaments of Wister rat embryos between embryonic day (E) 16 and E20 were analyzed. Samples were sectioned and visualized using EFIC. 3D reconstructions were generated using Amira software. The length of the cruciate ligaments, distances between attachment points to femur and tibia, angles of the cruciate ligaments and the cross angle of the cruciate ligaments were measured. The shape of cruciate ligaments was clearly visible at E17. The lengths of the anterior cruciate ligament (ACL) and posterior cruciate ligament (PCL) increased gradually from E17 to E19 and drastically at E20. Distances between attachment points to the femur and tibia gradually increased. The ACL angle and PCL angle gradually decreased. The cross angle of the cruciate ligaments changed in three planes. The primordium of the 3D structure of rat cruciate ligaments was constructed from the early stage, with the completion of the development of the structures occurring just before birth.     

Actin stress fibres and cell-cell adhesion molecules in tendons: organisation in vivo and response to mechanical loading of tendon cells in vitro.

Tendons consist of parallel longitudinal rows of cells separated by collagen fibres. The cells are in intimate contact longitudinally within rows, and laterally via sheet-like lateral cell processes between rows. At points of contact, they are linked by gap junctions. Since tendons stretch under load, such cell contacts require protection. Here we describe the organisation of the actin cytoskeleton and actin-based cell-cell interactions in vivo and examine the effect of cyclic tensile loading on tendon cells in vitro. Cells within longitudinal rows contained short longitudinally running actin stress fibres. Each fibre was aligned with similar fibres in the cells longitudinally on either side, and fibres appeared to be linked via adherens junctions. Overall, these formed long oriented rows of stress fibres running along the rows of tendon cells. In culture, junctional components n-cadherin and vinculin and the stress fibre component tropomyosin increased in strained cultures, whereas actin levels remained constant. These results suggest that: (1) cells are linked via actin-associated adherens junctions along the line of principal strain; and (2) under load, cells appear to attach themselves more strongly together, and assemble more of their cytoplasmic actin into stress fibres with tropomyosin. Taken together, this suggests that cell-cell contacts are protected during stretch, and also that the stress fibres, which are contractile, may provide an active mechanism for recovery from stretch. In addition, stress fibres are ideally oriented to monitor tensile load and thus may be important in mechanotransduction and the generation of signals passed via the gap junction network.     

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.     

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.