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).     

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

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

Elastic properties of an intact and ACL-ruptured knee joint: measurement, mathematical modelling, and haptic rendering

An analytical, dynamic model of the human knee joint has been developed to simulate the unloaded knee joint behaviour in 6 degrees of freedom. It is based on extensive robot-based measurements of the elastic properties of a human cadaver knee joint. The measured data are compared with data from the literature to ensure that a proper database for modelling is used. The analytical modelling of the passive elastic joint properties is done with Local Linear Model Trees. The deduced knee joint model incorporates passive elastic properties of the internal knee joint structures, passive elastic muscle forces, damping forces, gravitational forces, and external forces. There are two sets of parameters, one simulating the movement of the intact knee joint, and a second simulating the knee joint with ruptured anterior cruciate ligament. The dynamic model can be easily processed in real-time. It is implemented in the haptic display of the Munich Knee Joint Simulator (MKS), which enables a person to move a plastic leg driven by a robot manipulator and feel the simulated knee joint force. Orthopaedic physicians judged the performance of the dynamic knee joint model by executing physical knee joint tests at the MKS.     

Knee joint motion and ligament forces before and after ACL reconstruction

The goal of this in vitro study was to investigate the initial postoperative mechanical state of the knee with various types of anterior cruciate ligament (ACL) reconstructions. An experimental knee testing system was developed for the in vitro measurement of ligament forces and three-dimensional joint motion as external loads were applied to fresh knee specimens. Two groups of knee specimens were tested. In test series #1, two intraarticular reconstructions were performed in each of five specimens using semifree and free patellar tendon grafts with bone blocks. In test series #2, a more carefully controlled intraarticular reconstruction was performed in five specimens using a semifree composite graft consisting of the semitendinosus and gracilis tendons augmented with the Ligament Augmentation Device. Ligament force and joint motion data were collected as anteriorly directed tibial loads were applied to the normal joint, the joint with a cut ACL and the reconstructed joint. These knee joint states were compared on the basis of ACL or graft forces, joint motion and load sharing by the collateral ligaments. The dominate result of the study was that the forces and motions defining the mechanical state of the knee after the ACL reconstructions in both test series were highly variable and abnormal when compared to the normal knee state. The higher level of surgical control series #2 did not decrease this variability. There was a poor correlation between motion of the reconstructed knee relative to normal, and the ACL graft force. There was little consistent difference in force and motion results between the surgical procedures tested.     

Material and functional properties of articular cartilage and patellofemoral contact mechanics in an experimental model of osteoarthritis

The purposes of this study were to determine the in situ functional and material properties of articular cartilage in an experimental model of joint injury, and to quantify the corresponding in situ joint contact mechanics. Experiments were performed in the anterior cruciate ligament (ACL) transected knee of the cat and the corresponding, intact contralateral knee, 16 weeks following intervention. Cartilage thickness, stiffness, effective Young’s modulus, and permeability were measured and derived from six locations of the knee. The total contact area and peak pressures in the patellofemoral joint were obtained in situ using Fuji Pressensor film, and comparisons between experimental and contralateral joint were made for corresponding loading conditions. Total joint contact area and peak pressure were increased and decreased significantly (=0.01), respectively, in the experimental compared to the contralateral joint. Articular cartilage thickness and stiffness were increased and decreased significantly (=0.01), respectively, in the experimental compared to the contralateral joint in the four femoral and patellar test locations. Articular cartilage material properties (effective Young’s modulus and permeability) were the same in the ACL-transected and intact joints. These results demonstrate for the first time the effect of changes in articular cartilage properties on the load transmission across a joint. They further demonstrate a substantial change in the joint contact mechanics within 16 weeks of ACL transection. The results were corroborated by theoretical analysis of the contact mechanics in the intact and ACL-transected knee using biphasic contact analysis and direct input of cartilage properties and joint surface geometry from the experimental animals. We conclude that the joint contact mechanics in the ACL-transected cat change within 16 weeks of experimental intervention.     

The effect of hamstring muscle compensation for anterior laxity in the ACL-deficient knee during gait

The hamstring muscles have been recognized as an important element in compensating for the loss of stability in the ACL-deficient knee, but it is still not clear whether the hamstring muscle force can completely compensate for the loss of ACL, and the consequences of increased hamstring muscle force. A two-dimensional anatomical knee model in the sagittal plane was developed to examine the effect of various levels of hamstring muscle activation on restraining anterior tibial translation in the ACL-deficient knee during level walking. The model included the tibiofemoral and patellofemoral joints, four major ligaments, the medial capsule, and five muscle units surrounding the knee. Simulations were conducted to determine anterior tibial translation and internal joint loading at a single selected position when the knee was under a peak external flexion moment during early stance phase of gait. Incremental hamstring muscle forces were applied to the modeled normal and the ACL-deficient knees. Results of simulations showed that the ACL injury increased the anterior tibial translation by 11.8mm, while 56% of the maximal hamstring muscle force could reduce the anterior translation of the tibia to a normal level during the stance phase of gait. The consequences of increased hamstring muscle force included increased quadriceps muscle force and joint contact force.     

Stresses and strains in the medial meniscus of an ACL deficient knee under anterior loading: a finite element analysis with image-based experimental validation

The menisci are believed to play a stabilizing role in the ACL-deficient knee, and are known to be at risk for degradation in the chronically unstable knee. Much of our understanding of this behavior is based on ex vivo experiments or clinical studies in which we must infer the function of the menisci from external measures of knee motion. More recently, studies using magnetic resonance (MR) imaging have provided more clear visualization of the motion and deformation of the menisci within the tibio-femoral articulation. In this study, we used such images to generate a finite element model of the medial compartment of an ACL-deficient knee to reproduce the meniscal position under anterior loads of 45, 76, and 107 N. Comparisons of the model predictions to boundaries digitized from images acquired in the loaded states demonstrated general agreement, with errors localized to the anterior and posterior regions of the meniscus, areas in which large shear stresses were present. Our model results suggest that further attention is needed to characterize material properties of the peripheral and horn attachments. Although overall translation of the meniscus was predicted well, the changes in curvature and distortion of the meniscus in the posterior region were not captured by the model, suggesting the need for refinement of meniscal tissue properties.     

Kinematic motion of the anterior cruciate ligament deficient knee during functionally high and low demanding tasks

The purpose of this study was to determine whether mechanical adaptations were present in patients with anterior cruciate ligament (ACL)-deficient knees during high-demand activities. Twenty-two subjects with unilateral ACL deficiency (11 males and 11 females, 19.6 months after injury) performed five different activities at a comfortable speed (level walking, ascending and descending steps, jogging, jogging to a 90-degree side cutting toward the opposite direction of the tested side). Three-dimensional knee kinematics for the ACL-deficient knees and uninjured contralateral knees were evaluated using the Point Cluster Technique. There was no significant difference in knee flexion angle, but an offset toward the knee in less valgus and more external tibial rotation was observed in the ACL-deficient knee. The tendency was more obvious in high demand motions, and a significant difference was clearly observed in the side cutting motions. These motion patterns, with the knee in less valgus and more external tibial rotation, are proposed to be an adaptive movement to avoid pivot shift dynamically, and reveal evidence in support of a dynamic adaptive motion occurring in ACL-deficient knees.     

Suture augmentation following ACL injury to restore the function of the ACL, MCL, and medial meniscus in the goat stifle joint

Functional tissue engineering (FTE) approaches have shown promise in healing an injured anterior cruciate ligament (ACL) of the knee. Nevertheless, additional mechanical augmentation is needed to maintain joint stability and appropriate loading of the joint while the ACL heals. The objective of this study was to quantitatively evaluate how mechanical augmentation using sutures restores the joint kinematics as well as the distribution of loading among the ACL, medial collateral ligament, and medial meniscus (MM) in response to externally applied loads. Eight goat stifle joints were tested on a robotic/universal force-moment sensor testing system under two loading conditions: (1) a 67N anterior tibial load (ATL) and (2) a 67N ATL with 100N axial compression. For each joint, four experimental conditions were tested at 30°, 60°, and 90° of flexion: the (1) intact and (2) ACL-deficient joint, as well as following (3) suture repair of the transected ACL, and (4) augmentation using sutures passed from the femur to the tibia. Under the 67N ATL, suture augmentation could restore the anterior tibial translation (ATT) to within 3mm of the intact joint (p>0.05), representing a 54-76% improvement over suture repair (p<0.05). With the additional axial compression, the ATT and in-situ forces of the sutures following suture augmentation remained 2-3 times closer to normal (p<0.05). Also, the in-situ forces in the MM were 58-73% lower (p<0.05). Thus, suture augmentation may be helpful in combination with FTE approaches for ACL healing by providing the needed initial joint stability while lowering the loads on the MM.     

Comparison of shear forces and ligament loading in the healthy and ACL-deficient knee during gait

The purpose of this study was to predict and explain the pattern of shear force and ligament loading in the ACL-deficient knee during walking, and to compare these results to similar calculations for the healthy knee. Musculoskeletal modeling and computer simulation were combined to calculate ligament forces in the ACL-deficient knee during walking. Joint angles, ground-reaction forces, and the corresponding lower-extremity muscle forces obtained from a whole-body dynamic optimization simulation of walking were input into a second three-dimensional model of the lower extremity that represented the knee as a six degree-of-freedom spatial joint. Anterior tibial translation (ATT) increased throughout the stance phase of gait when the model ACL was removed. The medial collateral ligament (MCL) was the primary restraint to ATT in the ACL-deficient knee. Peak force in the MCL was three times greater in the ACL-deficient knee than in the ACL-intact knee; however, peak force sustained by the MCL in the ACL-deficient knee was limited by the magnitude of the total anterior shear force applied to the tibia. A decrease in anterior tibial shear force was brought about by a decrease in the patellar tendon angle resulting from the increase in ATT. These results suggest that while the MCL acts as the primary restraint to ATT in the ACL-deficient knee, changes in patellar tendon angle reduce total anterior shear force at the knee.     

A new method to investigate in vivo knee behavior using a finite element model of the lower limb

Several finite element models have been developed for estimating the mechanical response of joint internal structures, where direct or indirect in vivo measurement is difficult or impossible. The quality of the predictions made by those models is largely dependent on the quality of the experimental data (e.g. load/displacement) used to drive them. Also numerical problems have been described in the literature when using implicit finite element techniques to simulate problems that involve contacts and large displacements. In this study, a unique strategy was developed combining high accuracy in vivo three-dimensional kinematics and a lower limb finite element model based on explicit finite element techniques. The method presents an analytical technique applied to a dynamic loading condition (impact during hopping on one leg). The validation of the lower limb model focused on the response of the whole model and the knee joint in particular to the imposed 3D femoral in vivo kinematics and ground reaction forces. The approach outlined in this study introduces a generic tool for the study of in vivo knee joint behavior.     

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.     

Modeling of constrained articular cartilage growth in an intact knee with focal knee resurfacing metal implant

The purpose of the present study was to develop a model to simulate the articular cartilage growth in an intact knee model with a metal implant replacing a degenerated portion of the femoral cartilage. The human knee joint was approximated with a simplified axisymmetric shape of the femoral condyle along with the cartilage, meniscus and bones. Two individually growing constituents (proteoglycans and collagen) bound to solid matrix were considered in the solid phase of the cartilage. The cartilage behavior was modeled with a nonlinear biphasic porohyperelastic material model, and meniscus with a transversely isotropic linear biphasic poroelastic material model. Two criteria (permeation and shear), both driven by mechanical loading, were considered to trigger the growth in the solid constituents. Mechanical loading with sixty heavy cycles was considered to represent daily walking activity. The growth algorithm was implemented for 90 days after implantation. The results from simulations show that both cartilage layers were more stimulated near the implant which lead to more growth of the cartilage near the defect. The method developed in the present work could be a powerful technique if more accurate material data and growth laws were available.     

'Equivalent geometry' of the knee and the prediction of tensions along the cruciates: an experimental study

In this paper we introduce the concept of the functional (or equivalent) geometry of the knee, which is an attempt to reduce the natural knee with its complex geometry, frictional resistance and deformable cartilage into a two-dimensional joint comprising rigid femur and tibia in frictionless contact. An apparatus and method are described to measure the slope of the tangent to the surfaces of the 'equivalent' bones at their 'point' of contact. An antero posterior force of +/-300-500 N and axial compressive load of twice body weight were applied on cadaveric knee joints. The corresponding displacement of the tibia in the saggital plane was measured firstly with both cruciates intact and then when each was severed in turn. From the data obtained both the slope of the tangent mentioned above and the tensions developed along the cruciates under the influence of the forces applied were calculated. The results showed that the functional geometry of the knee in the saggital plane can be represented by a convex femur and a concave tibia. The tensions along the cruciates calculated on the basis of the experimental measurements were nearly always lower than the antero posterior force applied, and although this corroborated the trend demonstrated in a previous theoretical analysis, they were lower still. The reason for this may be the deformation of the cartilage under load, thus modifying the geometry of contact resulting in a more concave tibia of the 'equivalent' knee joint, than that of the rigid model used in the theoretical analysis.     

Modeling and optimal control of an energy-storing prosthetic knee

Advanced prosthetic knees for transfemoral amputees are currently based on controlled damper mechanisms. Such devices require little energy to operate, but can only produce negative or zero joint power, while normal knee joint function requires alternative phases of positive and negative work. The inability to generate positive work may limit the user's functional capabilities, may cause undesirable adaptive behavior, and may contribute to excessive metabolic energy cost for locomotion. In order to overcome these problems, we present a novel concept for an energy-storing prosthetic knee, consisting of a rotary hydraulic actuator, two valves, and a spring-loaded hydraulic accumulator. In this paper, performance of the proposed device will be assessed by computational modeling and by simulation of functional activities. A computational model of the hydraulic system was developed, with methods to obtain optimal valve control patterns for any given activity. The objective function for optimal control was based on tracking of joint angles, tracking of joint moments, and the energy cost of operating the valves. Optimal control solutions were obtained, based on data collected from three subjects during walking, running, and a sit-stand-sit cycle. Optimal control simulations showed that the proposed device allows near-normal knee function during all three activities, provided that the accumulator stiffness was tuned to each activity. When the energy storage mechanism was turned off in the simulations, the system functioned as a controlled damper device and optimal control results were similar to literature data on human performance with such devices. When the accumulator stiffness was tuned to walking, simulated performance for the other activities was sub-optimal but still better than with a controlled damper. We conclude that the energy-storing knee concept is valid for the three activities studied, that modeling and optimal control can assist the design process, and that further studies using human subjects are justified.     

Steeper posterior tibial slope markedly increases ACL force in both active gait and passive knee joint under compression

The role of the posterior tibial slope (PTS) in anterior cruciate ligament (ACL) risk of injury has been supported by many imaging studies but refuted by some in vitro works. The current investigation was carried out to compute the effect of ±5^o change in PTS on knee joint biomechanics in general and ACL force/strain in particular. Two validated finite element (FE) models of the knee joint were employed; one active lower extremity musculoskeletal model including a complex FE model of the knee joint driven by in vivo kinematics/kinetics collected in gait of asymptomatic subjects, and the other its isolated unconstrained passive tibiofemoral (TF) joint considered under 1400 N compression at four different knee flexion angles (0°–45°). In the TF model, the compression force was applied at the joint mechanical balance point causing no rotations in sagittal and frontal planes.     

Evaluation of the mechanical efficiency of knee braces based on computational modeling

Knee orthotic devices are commonly prescribed by physicians and medical practitioners for preventive or therapeutic purposes on account of their claimed effect: joint stabilisation and proprioceptive input. However, the force transfer mechanisms of these devices and their level of action remain controversial. The objectives of this work are to characterise the mechanical performance of conventional knee braces regarding their anti-drawer effect using a finite element model of a braced lower limb. A design of experiment approach was used to quantify meaningful mechanical parameters related to the efficiency and discomfort tolerance of braces. Results show that the best tradeoff between efficiency and discomfort tolerance is obtained by adjusting the brace length or the strap tightening. Thanks to this computational analysis, novel brace designs can be evaluated for an optimal mechanical efficiency and a better compliance of the patient with the treatment.     

Computer-assisted evaluation of kinematics of the two bundles of the anterior cruciate ligament.

The aim of this cadaveric study was to describe the kinematics of the anterior cruciate ligament (ACL)-intact, posterolateral (PL) bundle-deficient and ACL-deficient knee by applying a protocol for computer-assisted evaluation of knee kinematics. The hypothesis that the PL bundle functions mainly at low knee flexion angles was tested. An optical tracking system was used to acquire knee joint motion on 10 knees during clinical evaluations by tracking markers rigidly attached to the bones. The protocol included acquisition of anterior-posterior (AP) translations and internal-external (IE) rotations, and evaluation of three clinical knee laxity tests (anterior drawer, manual and instrumented Lachman). The data demonstrated no significant contribution to AP translation and IE laxity from the PL bundle over the entire range of motion. The clinical knee laxity tests showed no significant differences between the ACL-intact and PL bundle-deficient states. The hypothesis could not be proven. Current clinical knee laxity measurements may not be suited for detecting subtle changes such as PL bundle deficiency in the ACL anatomy. The computation of knee laxity might be a step towards a more precise kinematic test of knee stability not only in the native and torn ACL state of the knee but also in the reconstructed knee.     

Partial meniscectomy changes fluid pressurization in articular cartilage in human knees

Partial meniscectomy is believed to change the biomechanics of the knee joint through alterations in the contact of articular cartilages and menisci. Although fluid pressure plays an important role in the load support mechanism of the knee, the fluid pressurization in the cartilages and menisci has been ignored in the finite element studies of the mechanics of meniscectomy. In the present study, a 3D fibril-reinforced poromechanical model of the knee joint was used to explore the fluid flow dependent changes in articular cartilage following partial medial and lateral meniscectomies. Six partial longitudinal meniscectomies were considered under relaxation, simple creep, and combined creep loading conditions. In comparison to the intact knee, partial meniscectomy not only caused a substantial increase in the maximum fluid pressure but also shifted the location of this pressure in the femoral cartilage. Furthermore, these changes were positively correlated to the size of meniscal resection. While in the intact joint, the location of the maximum fluid pressure was dependent on the loading conditions, in the meniscectomized joint the location was predominantly determined by the site of meniscal resection. The partial meniscectomy also reduced the rate of the pressure dissipation, resulting in even larger difference between creep and relaxation times as compared to the case of the intact knee. The knee joint became stiffer after meniscectomy because of higher fluid pressure at knee compression followed by slower pressure dissipation. The present study indicated the role of fluid pressurization in the altered mechanics of meniscectomized knees.     

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.