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.     

Description and error evaluation of an in vitro knee joint testing system

An experimental system for the analysis of knee joint biomechanics is presented. The system provides for the simultaneous recording of ligament forces using buckle transducers and three-dimensional joint motion using an instrumented spatial linkage, as in vitro specimens are subjected to a variety of external loads by a pneumatic loading apparatus with associated force transducers. The system components are described, and results of an evaluation of system errors and accuracy are presented. The experimental setup has been successfully used in the analysis of normal knee ligament mechanics, as well as surgical reconstructions of the anterior cruciate ligament. The system can also be adapted to test other human or animal in vitro joints.     

Ligament balancing in TKA: evaluation of a force-sensing device and the influence of patellar eversion and ligament release

Ligament balancing in total knee arthroplasty may have an important influence on joint stability and prosthesis lifetime. In order to provide quantitative information and assistance during ligament balancing, a device that intraoperatively measures knee joint forces and moments was developed. Its performance and surgical advantages were evaluated on six cadaver specimens mounted on a knee joint loading apparatus allowing unconstrained knee motion as well as compression and varus-valgus loading. Four different experiments were performed on each specimen. (1) Knee joints were axially loaded. Comparison between applied and measured compressive forces demonstrated the accuracy and reliability of in situ measurements (1.8N). (2) Assessment of knee stability based on condyle contact forces or varus-valgus moments were compared to the current surgical method (difference of varus-valgus loads causing condyle lift-off). The force-based approach was equivalent to the surgical method while the moment-based, which is considered optimal, showed a tendency of lateral imbalance. (3) To estimate the importance of keeping the patella in its anatomical position during imbalance assessment, the effect of patellar eversion on the mediolateral distribution of tibiofemoral contact forces was measured. One fourth of the contact force induced by the patellar load was shifted to the lateral compartment. (4) The effect of minor and major medial collateral ligament releases was biomechanically quantified. On average, the medial contact force was reduced by 20% and 46%, respectively. Large variation among specimens reflected the difficulty of ligament release and the need for intraoperative force monitoring. This series of experiments thus demonstrated the device's potential to improve ligament balancing and survivorship of total knee arthroplasty.     

A novel device to apply controlled flexion and extension to the rat knee following anterior cruciate ligament reconstruction

We designed and validated a novel device for applying flexion-extension cycles to a rat knee in an in vivo model of anterior cruciate ligament reconstruction (ACL-R). Our device is intended to simulate rehabilitation motion and exercise post ACL-R to optimize physical rehabilitation treatments for the improved healing of tendon graft ligament reconstructions. The device was validated for repeatability of the knee kinematic motion by measuring the force versus angular rotation response from repeated trials using cadaver rats. The average maximum force required for rotating an ACL reconstructed rat knee through 100 degrees of flexion-extension was 0.4 N with 95% variability for all trials within ±0.1 N.     

Combined measurement and modeling of specimen-specific knee mechanics for healthy and ACL-deficient conditions

Quantifying the mechanical environment at the knee is crucial for developing successful rehabilitation and surgical protocols. Computational models have been developed to complement in vitro studies, but are typically created to represent healthy conditions, and may not be useful in modeling pathology and repair. Thus, the objective of this study was to create finite element (FE) models of the natural knee, including specimen-specific tibiofemoral (TF) and patellofemoral (PF) soft tissue structures, and to evaluate joint mechanics in intact and ACL-deficient conditions. Simulated gait in a whole joint knee simulator was performed on two cadaveric specimens in an intact state and subsequently repeated following ACL resection. Simulated gait was performed using motor-actuated quadriceps, and loads at the hip and ankle. Specimen-specific FE models of these experiments were developed in both intact and ACL-deficient states. Model simulations compared kinematics and loading of the experimental TF and PF joints, with average RMS differences [max] of 3.0° [8.2°] and 2.1° [8.4°] in rotations, and 1.7 [3.0] and 2.5 [5.1] mm in translations, for intact and ACL-deficient states, respectively. The timing of peak quadriceps force during stance and swing phase of gait was accurately replicated within 2° of knee flexion and with an average error of 16.7% across specimens and pathology. Ligament recruitment patterns were unique in each specimen; recruitment variability was likely influenced by variations in ligament attachment locations. ACL resections demonstrated contrasting joint mechanics in the two specimens with altered knee motion shown in one specimen (up to 5 mm anterior tibial translation) while increased TF joint loading was shown in the other (up to 400 N).     

Forces in anterior cruciate ligament during simulated weight-bearing flexion with anterior and internal rotational tibial load

This study determined in-vitro anterior cruciate ligament (ACL) force patterns and investigated the effect of external tibial loads on the ACL force patterns during simulated weight-bearing knee flexions. Nine human cadaveric knee specimens were mounted on a dynamic knee simulator, and weight-bearing knee flexions with a 100N of ground reaction force were simulated; while a robotic/universal force sensor (UFS) system was used to provide external tibial loads during the movement. Three external tibial loading conditions were simulated, including no external tibial load (termed BW only), a 50N anterior tibial force (ATF), and a 5Nm internal rotation tibial torque (ITT). The tibial and femoral kinematics was measured with an ultrasonic motion capture system. These movement paths were then accurately reproduced on a robotic testing system, and the in-situ force in the ACL was determined via the principle of superposition. The results showed that the ATF significantly increased the in-situ ACL force by up to 60% during 0-55 degrees of flexion, while the ITT did not. The magnitude of ACL forces decreased with increasing flexion angle for all loading conditions. The tibial anterior translation was not affected by the application of ATF, whereas the tibial internal rotation was significantly increased by the application of ITT. These data indicate that, in a weight-bearing knee flexion, ACL provides substantial resistance to the externally applied ATF but not to the ITT.     

The importance of quadriceps and hamstring muscle loading on knee kinematics and in-situ forces in the ACL

This study investigated the effect of hamstring co-contraction with quadriceps on the kinematics of the human knee joint and the in-situ forces in the anterior cruciate ligament (ACL) during a simulated isometric extension motion of the knee. Cadaveric human knee specimens (n = 10) were tested using the robotic universal force moment sensor (UFS) system and measurements of knee kinematics and in-situ forces in the ACL were based on reference positions on the path of passive flexion/extension motion of the knee. With an isolated 200 N quadriceps load, the knee underwent anterior and lateral tibial translation as well as internal tibial rotation with respect to the femur. Both translation and rotation increased when the knee was flexed from full extension to 30 of flexion; with further flexion, these motion decreased. The addition of 80 N antagonistic hamstrings load significantly reduced both anterior and lateral tibial translation as well as internal tibial rotation at knee flexion angles tested except at full extension. At 30 of flexion, the anterior tibial translation, lateral tibial translation, and internal tibial rotation were significantly reduced by 18, 46, and 30%, respectively (p<0.05). The in-situ forces in the ACL under the quadriceps load were found to increase from 27.8+/-9.3 N at full extension to a maximum of 44.9+/-13.8 N at 15 of flexion and then decrease to 10 N beyond 60 of flexion. The in-situ force at 15 was significantly higher than that at other flexion angles (p<0.05). The addition of the hamstring load of 80 N significantly reduced the in-situ forces in the ACL at 15, 30 and 60 of flexion by 30, 43, and 44%, respectively (p<0.05). These data demonstrate that maximum knee motion may not necessarily correspond to the highest in-situ forces in the ACL. The data also suggest that hamstring co-contraction with quadriceps is effective in reducing excessive forces in the ACL particularly between 15 and 60 of knee flexion.     

The effect of weightbearing and external loading on anterior cruciate ligament strain

A force balance between the ligaments, articular contact, muscles and body weight maintains knee joint stability. Thus, it is important to study anterior cruciate ligament (ACL) biomechanics, in vivo, under weightbearing conditions. Our objective was to compare the ACL strain response under weightbearing and non-weightbearing conditions and in combination with three externally applied loadings: (1) anterior-posterior shear forces, (2) internal-external torques, and (3) varus-valgus moments. A strain transducer was implanted on the ACL of 11 subjects. All joint loadings were performed with the knee at 20 degrees of flexion. A significant increase in ACL strain was observed as the knee made the transition from non-weightbearing to weightbearing. During anterior shear loading, the strain values produced during weightbearing were greater than those of the non-weightbearing knee (shear loads <40N). At higher shear loads, the strain values became equal. During axial torsion, an internal torque of 10Nm strained the ACL when the knee was non-weightbearing while an equivalent external torque did not. Weightbearing significantly increased ACL strain values in comparison to non-weightbearing with the application of external torques and low internal torques (<3Nm). The strains became equal for higher internal torques. For V-V loading, the ACL was not strained in the non-weightbearing knee. However, weightbearing increased the ACL strain values over the range of moments tested. These data have important clinical ramifications in the development of rehabilitation protocols following ACL reconstruction since weightbearing has been previously thought to provide a protective mechanism to the healing graft.     

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.     

Calibration and application of an intra-articular force transducer for the measurement of patellar tendon graft forces: an in situ evaluation.

The objective of this study was to evaluate two calibration methods for the "Arthroscopically Implantable Force Probe" (AIFP) that are potentially suitable for in vivo use: (1) a direct, experimentally based method performed by applying a tensile load directly to the graft after it is harvested but prior to implantation (the "pre-implantation" technique), and (2) an indirect method that utilizes cadaver-based analytical expressions to transform the AIFP output versus anterior shear load relationship, which may be established in vivo, to resultant graft load (the "post-implantation" technique). The AIFP outputs during anterior shear loading of the knee joint using these two calibration methods were compared directly to graft force measurements using a ligament cutting protocol and a 6 DOF load cell. The mean percent error (actual-measured)/(actual)* 100) associated with the pre-implantation calibration ranged between 85 and 175 percent, and was dependent on the knee flexion angle tested. The percent error associated with the post-implantation technique was evaluated in two load ranges: loads less than 40 N, and loads greater than 40 N. For graft force values greater than 40 N, the mean percent errors inherent to the post-implantation calibration method ranged between 20 and 29 percent, depending on the knee flexion angle tested. Below 40 N, these errors were substantially greater. Of the two calibration methods evaluated, the post-implantation approach provided a better estimate of the ACL graft force than the pre-implantation technique. However, the errors for the post-implantation approach were still high and suggested that caution should be employed when using implantable force probes for in vivo measurement of ACL graft forces.     

New parameters describing how knee ligaments carry force in situ predict interspecimen variations in laxity during simulated clinical exams

Knee laxity, defined as the net translation or rotation of the tibia relative to the femur in a given direction in response to an applied load, is highly variable from person to person. High levels of knee laxity as assessed during routine clinical exams are associated with first-time ligament injury and graft reinjury following reconstruction. During laxity exams, ligaments carry force to resist the applied load; however, relationships between intersubject variations in knee laxity and variations in how ligaments carry force as the knee moves through its passive envelope of motion, which we refer to as ligament engagement, are not well established. Thus, the objectives of this study were, first, to define parameters describing ligament engagement and, then, to link variations in ligament engagement and variations in laxity across a group of knees. We used a robotic manipulator in a cadaveric knee model (n = 20) to quantify how important knee stabilizers, namely the anterior and posterior cruciate ligaments (ACL and PCL, respectively), as well as the medial collateral ligament (MCL) engage during respective tests of anterior, posterior, and valgus laxity. Ligament engagement was quantified using three parameters: (1) in situ slack, defined as the relative tibiofemoral motion from the neutral position of the joint to the position where the ligament began to carry force; (2) in situ stiffness, defined as the slope of the linear portion of the ligament force–tibial motion response; and (3) ligament force at the peak applied load. Knee laxity was related to parameters of ligament engagement using univariate and multivariate regression models. Variations in the in situ slack of the ACL and PCL predicted anterior and posterior laxity, while variations in both in situ slack and in situ stiffness of the MCL predicted valgus laxity. Parameters of ligament engagement may be useful to further characterize the in situ biomechanical function of ligaments and ligament grafts.     

Inter-insertional distance is a poor correlate for ligament load: Analysis from in vivo gait kinetics data

In many analytic models of the knee joint, inter-insertional distance is used as the measure to define the load in a ligament. In addition, the direction of the load is taken to be the direction between the two insertions. Our in vivo data on the ovine ligament loads during gait, however, indicate that a wide range of forces is possible in the ligament for any specified inter-insertional distance. To understand the complex relationship between the bone orientations and ligament load better, an artificial neural network (ANN) model was developed. The six degree-of-freedom (6-DOF) in vivo kinematics of femur relative to tibia (joint kinematics) was used as input, and the magnitude of the anterior cruciate ligament (ACL) load was used as output/target. While the trained network was able to predict peak ligament loads with remarkable accuracy (R-square=0.98), an explicit relationship between joint kinematics and ACL load could not be determined. To examine the experimental and ANN observations further, a finite element (FE) model of the ACL was created. The geometry of the FE model was reconstructed from magnetic resonance images (MRI) of an ACL, and an isotropic, hyperelastic, nearly incompressible constitutive model was implemented for the ACL. The FE simulation results also indicate that a range of loads is possible in the ACL for a given inter-insertional distance, in concordance with the experimental/ANN observations. This study provides new insights for models of the knee joint; a simple force–length relationship for the ligament is not exact, nor is a single point to single point direction. More detailed microstructure-function data is required.     

The effects of femoral graft placement on in vivo knee kinematics after anterior cruciate ligament reconstruction

Achieving anatomical graft placement remains a concern in Anterior Cruciate Ligament (ACL) reconstruction. The purpose of this study was to quantify the effect of femoral graft placement on the ability of ACL reconstruction to restore normal knee kinematics under in vivo loading conditions. Two different groups of patients were studied: one in which the femoral tunnel was placed near the anterior and proximal border of the ACL (anteroproximal group, n=12) and another where the femoral tunnel was placed near the center of the ACL (anatomic group, n=10) MR imaging and biplanar fluoroscopy were used to measure in vivo kinematics in these patients during a quasi-static lunge. Patients with anteroproximal graft placement had up to 3.4mm more anterior tibial translation, 1.1mm more medial tibial translation and 3.7° more internal tibial rotation compared to the contralateral side. Patients with anatomic graft placement had motion that more closely replicated that of the intact knee, with anterior tibial translation within 0.8mm, medial tibial translation within 0.5mm, and internal tibial rotation within 1°. Grafts placed anteroproximally on the femur likely provide insufficient restraint to these motions due to a more vertical orientation. Anatomical femoral placement of the graft is more likely to reproduce normal ACL orientation, resulting in a more stable knee. Therefore, achieving anatomical graft placement on the femur is crucial to restoring normal knee function and may decrease the rates of joint degeneration after ACL reconstruction.     

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

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

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.     

Analysis of forces of ACL reconstructions at the tunnel entrance: is tunnel enlargement a biomechanical problem?

Bone tunnel enlargement is a common phenomenon following reconstruction of the anterior cruciate ligament (ACL). Biomechanical and biological factors have been reported as potential causes of this problem. However, there is no analysis of forces between the graft and bone, as the graft changes direction at the bone tunnel entrance. The purpose of this study was to study these 'redirecting forces'. Magnetic resonance images of 10 patients with an ACL reconstruction (age: 26+/-6.8 years) were used to determine the angle between graft and drill holes. Vector analysis was used to calculate the direction and magnitude of the perpendicular component of the force between the bone tunnel and the graft at the entrance of the bone tunnel. Force components were projected into the radiographically important sagittal and coronal planes. Tension of ACL reconstructions was recorded during passive knee motion in 10 cadaveric knee experiments (age: 28.9+/-10.6 years) and the tension multiplied with the force component for each plane. Results are reported for the coronal and sagittal planes, respectively: For -10 degrees of extension, the percentages of graft tension were determined to be 17+/-7 (max: 26; min: 7%) and 26+/-9 (max: 39; min: 16%) for the tibia. They were 59+/-6 (max: 66; min: 48%) and 99+/-1 (max: 1.00; min: 99%) for the femur. Force components were 14.68+/-6.54 and 25.73+/-12.96 N for the tibial tunnel. For the femoral tunnel, they were 52.48+/-19.03 and 90.77+/-32.06 N. Percentages of graft tension and force components were significantly higher for the femoral tunnel compared with the tibial tunnel. Moreover, in the sagittal direction, force components for the femoral tunnel were significantly higher compared with the coronal plane (Wilcoxon test, p < 0.01). The differences in force components calculated in this study corresponds with the amount of tunnel enlargement in the radiographic planes in the literature providing evidence that biomechanical forces play a key role in postoperative tunnel expansion.     

Computational stability of human knee joint at early stance in Gait: Effects of muscle coactivity and anterior cruciate ligament deficiency

As one of the most complex and vulnerable structures of body, the human knee joint should maintain dynamic equilibrium and stability in occupational and recreational activities. The evaluation of its stability and factors affecting it is vital in performance evaluation/enhancement, injury prevention and treatment managements. Knee stability often manifests itself by pain, hypermobility and giving-way sensations and is usually assessed by the passive joint laxity tests. Mechanical stability of both the human knee joint and the lower extremity at early stance periods of gait (0% and 5%) were quantified here for the first time using a hybrid musculoskeletal model of the lower extremity. The roles of muscle coactivity, simulated by setting minimum muscle activation at 0–10% levels and ACL deficiency, simulated by reducing ACL resistance by up to 85%, on the stability margin as well as joint biomechanics (contact/muscle/ligament forces) were investigated. Dynamic stability was analyzed using both linear buckling and perturbation approaches at the final deformed configurations in gait. The knee joint was much more stable at 0% stance than at 5% due to smaller ground reaction and contact forces. Muscle coactivity, when at lower intensities (<3% of its maximum active force), increased dynamic stability margin. Greater minimum activation levels, however, acted as an ineffective strategy to enhance stability. Coactivation also substantially increased muscle forces, joint loads and ACL force and hence the risk of further injury and degeneration. A deficiency in ACL decreases total ACL force (by 31% at 85% reduced stiffness) and the stability margin of the knee joint at the heel strike. It also markedly diminishes forces in lateral hamstrings (by up to 39%) and contact forces on the lateral plateau (by up to 17%). Current work emphasizes the need for quantification of the lower extremity stability margin in gait.     

Effect of knee musculature on anterior cruciate ligament strain in vivo

Squatting is a commonly prescribed exercise following reconstruction of the anterior cruciate ligament (ACL). The objective of this paper was to measure the in vivo strain patterns of the normal ACL and the load at the knee for the simple squat and for squatting with a “sport cord”. A sport cord is a large elastic rubber tube used for added resistance. Strain patterns were deduced using displacement data from a Hall Effect Strain Transducer (HEST), while joint loads were determined by a mathematical model with inputs from a force plate and electrogoniometers. ACL strain for the free squat in one subject had a maximum of 2% at a knee angle of 10° and was slack for knee angles >17°. In squatting with a sport cord, peak strain was 1% at 10° and was slack at knee angles >14°. Since these peak strains are low, squatting appears to be a safe exercise for conservative rehabilitation of ACL reconstruction patients. In addition, the sport cord is a recommended augmentation to the activity. We believe that the decrease in strain with the sport cord results from added joint stiffness due to greater compressive forces at the tibiofemoral joint. This greater compressive force results from the approximately 10% increase in quadriceps activity. From shear force data predicted by the mathematical model, the maximum anterior drawer force for free squatting (50 N) was considerably less than for sport cord squatting (430 N). Therefore, the value of shear force at the tibiofemoral joint only partially determines the load placed on the ACL.     

A quasi-static three-dimensional, mathematical, three-body segment model of the canine knee

A mathematical, three-dimensional, anatomically accurate model of the canine knee was created to determine the forces in the knee ligaments and the knee joint reaction forces during the stance phase of a slow walk. This quasi-static model considered both the tibio-femoral and patello-femoral articulations. The geometric and morphometric data of the hind limb were obtained from cadaver data. Muscle forces acting on the femur and the hip joint reaction force were determined by numerical optimization. Ligaments were modeled as non-linear-springs. Ligament material properties were obtained from the literature pertaining to the human knee. The model consists of-28 non-linear algebraic equations describing equilibrium of the femur and the patella, and geometric constraints. This system of equations was solved by a non-linear least-squares method. Results are presented for a knee with an intact cranial cruciate ligament (CCL) and for a knee with a ruptured CCL. Forces predicted to occur in the CCL by analysis of the model were found to be very similar to reported results of CCL forces measured in vivo in goats.