In vivo knee moments and shear after total knee arthroplasty

Tibiofemoral loading is very important in cartilage degeneration as well as in component survivorship after total knee arthroplasty. We have previously reported the axial knee forces in vivo. In this study, a second-generation force-sensing device that measured all six components of tibial forces was implanted in a 74-kg, 83-year-old male. Video motion analysis, ground reaction forces, and knee forces were measured during walking, stair climbing, chair-rise, and squat activities. Peak total force was 2.3 times body weight (BW) during walking, 2.5 x BW during chair rise, 3.0 x BW during stair climbing, and 2.1 x BW during squatting. Peak anterior shear force at the tibial tray was 0.30 x BW during walking, 0.17 x BW during chair rise, 0.26 x BW during stair climbing, and 0.15 x BW during squatting. Peak flexion moment at the tray was 1.9% BW x Ht (percentage of body weight multiplied by height) for chair-rise activity and 1.7% BW x Ht for squat activity. Peak adduction moment at the tray was -1.1% BW x Ht during chair-rise, -1.3% BW x Ht during squatting. External knee flexion and adduction moments were substantially greater than flexion and adduction moments at the tray. The axial component of forces predominated especially during the stance phase of walking. Shear forces and moments at the tray were very modest compared to total knee forces. These findings indicate that the soft tissues around the knee absorbed most of the external shear forces. Our results highlight the importance of direct measurements of knee forces.     

Subject-specific knee joint geometry improves predictions of medial tibiofemoral contact forces

Estimating tibiofemoral joint contact forces is important for understanding the initiation and progression of knee osteoarthritis. However, tibiofemoral contact force predictions are influenced by many factors including muscle forces and anatomical representations of the knee joint. This study aimed to investigate the influence of subject-specific geometry and knee joint kinematics on the prediction of tibiofemoral contact forces using a calibrated EMG-driven neuromusculoskeletal model of the knee. One participant fitted with an instrumented total knee replacement walked at a self-selected speed while medial and lateral tibiofemoral contact forces, ground reaction forces, whole-body kinematics, and lower-limb muscle activity were simultaneously measured. The combination of generic and subject-specific knee joint geometry and kinematics resulted in four different OpenSim models used to estimate muscle–tendon lengths and moment arms. The subject-specific geometric model was created from CT scans and the subject-specific knee joint kinematics representing the translation of the tibia relative to the femur was obtained from fluoroscopy. The EMG-driven model was calibrated using one walking trial, but with three different cost functions that tracked the knee flexion/extension moments with and without constraint over the estimated joint contact forces. The calibrated models then predicted the medial and lateral tibiofemoral contact forces for five other different walking trials. The use of subject-specific models with minimization of the peak tibiofemoral contact forces improved the accuracy of medial contact forces by 47% and lateral contact forces by 7%, respectively compared with the use of generic musculoskeletal model.     

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.     

Individual muscle contributions to the axial knee joint contact force during normal walking

Muscles are significant contributors to the high joint forces developed in the knee during human walking. Not only do muscles contribute to the knee joint forces by acting to compress the joint, but they also develop joint forces indirectly through their contributions to the ground reaction forces via dynamic coupling. Thus, muscles can have significant contributions to forces at joints they do not span. However, few studies have investigated how the major lower-limb muscles contribute to the knee joint contact forces during walking. The goal of this study was to use a muscle-actuated forward dynamics simulation of walking to identify how individual muscles contribute to the axial tibio-femoral joint force. The simulation results showed that the vastii muscles are the primary contributors to the axial joint force in early stance while the gastrocnemius is the primary contributor in late stance. The tibio-femoral joint force generated by these muscles was at times greater than the muscle forces themselves. Muscles that do not cross the knee joint (e.g., the gluteus maximus and soleus) also have significant contributions to the tibio-femoral joint force through their contributions to the ground reaction forces. Further, small changes in walking kinematics (e.g., knee flexion angle) can have a significant effect on the magnitude of the knee joint forces. Thus, altering walking mechanics and muscle coordination patterns to utilize muscle groups that perform the same biomechanical function, yet contribute less to the knee joint forces may be an effective way to reduce knee joint loading during walking.     

In vivo contact kinematics and contact forces of the knee after total knee arthroplasty during dynamic weight-bearing activities

Analysis of polyethylene component wear and implant loosening in total knee arthroplasty (TKA) requires precise knowledge of in vivo articular motion and loading conditions. This study presents a simultaneous in vivo measurement of tibiofemoral articular contact forces and contact kinematics in three TKA patients. These measurements were accomplished via a dual fluoroscopic imaging system and instrumented tibial implants, during dynamic single leg lunge and chair rising-sitting. The measured forces and contact locations were also used to determine mediolateral distribution of axial contact forces. Contact kinematics data showed a medial pivot during flexion of the knee, for all patients in the study. Average axial forces were higher for lunge compared to chair rising-sitting (224% vs. 187% body weight). In this study, we measured peak anteroposterior and mediolateral forces averaging 13.3% BW during lunge and 18.5% BW during chair rising-sitting. Mediolateral distributions of axial contact force were both patient and activity specific. All patients showed equitable medial-lateral loading during lunge but greater loads at the lateral compartment during chair rising-sitting. The results of this study may enable more accurate reproduction of in vivo loads and articular motion patterns in wear simulators and finite element models. This in turn may help advance our understanding of factors limiting longevity of TKA implants, such as aseptic loosening and polyethylene component wear, and enable improved TKA designs.     

Two-dimensional dynamic modelling of human knee joint

A mathematical dynamic model of the two-dimensional representation of the knee joint is presented. The profiles of the joint surfaces are determined from X-ray films and they are represented by polynomials. The joint ligaments are modelled as nonlinear elastic springs of realistic stiffness properties. Nonlinear equations of motion coupled with nonlinear constraint conditions are solved numerically. Time derivatives are approximated by Newmark difference formulae and the resulting nonlinear algebraic equations are solved employing the Newton-Raphson iteration scheme. Several dynamic loads are applied to the center of mass of the tibia and the ensuing motion is investigated. Numerical results on ligament forces, contact point locations between femur and tibia, and the orientation of tibia relative to femur are presented. The results are shown to be consistent with the anatomy of the knee joint.     

A multibody knee model with discrete cartilage prediction of tibio-femoral contact mechanics

Combining musculoskeletal simulations with anatomical joint models capable of predicting cartilage contact mechanics would provide a valuable tool for studying the relationships between muscle force and cartilage loading. As a step towards producing multibody musculoskeletal models that include representation of cartilage tissue mechanics, this research developed a subject-specific multibody knee model that represented the tibia plateau cartilage as discrete rigid bodies that interacted with the femur through deformable contacts. Parameters for the compliant contact law were derived using three methods: (1) simplified Hertzian contact theory, (2) simplified elastic foundation contact theory and (3) parameter optimisation from a finite element (FE) solution. The contact parameters and contact friction were evaluated during a simulated walk in a virtual dynamic knee simulator, and the resulting kinematics were compared with measured in vitro kinematics. The effects on predicted contact pressures and cartilage–bone interface shear forces during the simulated walk were also evaluated. The compliant contact stiffness parameters had a statistically significant effect on predicted contact pressures as well as all tibio-femoral motions except flexion–extension. The contact friction was not statistically significant to contact pressures, but was statistically significant to medial–lateral translation and all rotations except flexion–extension. The magnitude of kinematic differences between model formulations was relatively small, but contact pressure predictions were sensitive to model formulation. The developed multibody knee model was computationally efficient and had a computation time 283 times faster than a FE simulation using the same geometries and boundary conditions.     

Three-dimensional dynamic simulation of total knee replacement motion during a step-up task.

A three-dimensional dynamic model of the tibiofemoral and patellofemoral articulations was developed to predict the motions of knee implants during a step-up activity. Patterns of muscle activity, initial joint angles and velocities, and kinematics of the hip and tinkle were measured experimentally and used as inputs to the simulation. Prosthetic knee kinematics were determined by integration of dynamic equations of motion subject to forces generated by muscles, ligaments, and contact at both the tibiofemoral and patellofemoral articulations. The modeling of contacts between implants did not rely upon explicit constraint equations; thus, changes in the number of contact points were allowed without modification to the model formulation. The simulation reproduced experimentally measured flexion-extension angle of the knee (within one standard deviation), but translations at the tibiofemoral articulations were larger during the simulated step-up task than those reported for patients with total knee replacements.     

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.     

Computational modeling of bone density profiles in response to gait: a subject-specific approach

The goal of this study is to explore the potential of computational growth models to predict bone density profiles in the proximal tibia in response to gait-induced loading. From a modeling point of view, we design a finite element-based computational algorithm using the theory of open system thermodynamics. In this algorithm, the biological problem, the balance of mass, is solved locally on the integration point level, while the mechanical problem, the balance of linear momentum, is solved globally on the node point level. Specifically, the local bone mineral density is treated as an internal variable, which is allowed to change in response to mechanical loading. From an experimental point of view, we perform a subject-specific gait analysis to identify the relevant forces during walking using an inverse dynamics approach. These forces are directly applied as loads in the finite element simulation. To validate the model, we take a Dual-Energy X-ray Absorptiometry scan of the subject’s right knee from which we create a geometric model of the proximal tibia. For qualitative validation, we compare the computationally predicted density profiles to the bone mineral density extracted from this scan. For quantitative validation, we adopt the region of interest method and determine the density values at fourteen discrete locations using standard and custom-designed image analysis tools. Qualitatively, our two- and three-dimensional density predictions are in excellent agreement with the experimental measurements. Quantitatively, errors are less than 3% for the two-dimensional analysis and less than 10% for the three-dimensional analysis. The proposed approach has the potential to ultimately improve the long-term success of possible treatment options for chronic diseases such as osteoarthritis on a patient-specific basis by accurately addressing the complex interactions between ambulatory loads and tissue changes.     

A comparison of the influence of global functional loads vs. local contact anatomy on articular cartilage thickness at the knee

Cartilage contact geometry, along with joint loading, can play an important role in determining local articular cartilage tissue stress. Thus individual variations in cartilage thickness can be associated with both individual variations in joint loading associated with activities of daily living as well as individual differences in the anatomy of the contacting surfaces of the joint. The purpose of this study was to isolate the relationship between cartilage thickness predicted by individual variations in contact surface geometry based on the radii of the femur and tibia vs. cartilage thickness predicted by individual variations in joint loading. Knee magnetic resonance (MR) images and the peak knee adduction moments during walking were obtained from 11 young healthy male subjects (age 30.5+/-5.1 years). The cartilage thicknesses and surface radii of the femoral and tibial cartilage were measured in the weight-bearing regions of the medial and lateral compartments of three-dimensional models from the MR images. The ratio of contact pressure between the medial and lateral compartments was calculated from the radii of tibiofemoral contact surface geometries. The results showed that the medial to lateral pressure ratios were not correlated with the medial to lateral cartilage thickness ratios. However, in general, pressure was higher in the lateral than medial compartments and cartilage was thicker in the lateral than medial compartments. The peak knee adduction moment showed a significant positive linear correlation with medial to lateral thickness ratio in both femur (R(2)=0.43,P<0.01) and tibia (R(2)=0.32,P<0.01). The results of this study suggest that the dynamics of walking is an important factor to describe individual differences in cartilage thickness for normal subjects.     

Muscular coordination of knee motion during the terminal-swing phase of normal gait

Children with cerebral palsy often walk with diminished knee extension during the terminal-swing phase, resulting in a troublesome "crouched" posture at initial contact and a shortened stride. Treatment of this gait abnormality is challenging because the factors that extend the knee during normal walking are not well understood, and because the potential of individual muscles to limit terminal-swing knee extension is unknown. This study analyzed a series of three-dimensional, muscle-driven dynamic simulations to quantify the angular accelerations of the knee induced by muscles and other factors during swing. Simulations were generated that reproduced the measured gait dynamics and muscle excitation patterns of six typically developing children walking at self-selected speeds. The knee was accelerated toward extension in the simulations by velocity-related forces (i.e., Coriolis and centrifugal forces) and by a number of muscles, notably the vasti in mid-swing (passive), the hip extensors in terminal swing, and the stance-limb hip abductors, which accelerated the pelvis upward. Knee extension was slowed in terminal swing by the stance-limb hip flexors, which accelerated the pelvis backward. The hamstrings decelerated the forward motion of the swing-limb shank, but did not contribute substantially to angular motions of the knee. Based on these data, we hypothesize that the diminished knee extension in terminal swing exhibited by children with cerebral palsy may, in part, be caused by weak hip extensors or by impaired hip muscles on the stance limb that result in abnormal accelerations of the pelvis.     

Three-dimensional kinematics of the human knee during walking.

Three-dimensional kinematics of the tibiofemoral joint were studied during normal walking. Target markers were fixed to tibia and femur by means of intra-cortical traction pins. Radiographs of the lower limb were obtained to compute the position of the target markers relative to internal anatomical structures. High-speed cine cameras were used to measure three-dimensional coordinates of the target markers in five subjects walking at a speed of 1.2 m s-1. Relative motion between tibia and femur was resolved according to a joint coordinate system (JCS). The measurements have identified that substantial angular and linear motions occur about and along each of the JCS axes during walking. The results do not, however, support the traditional view that the so-called 'screw home' mechanism of the knee joint operates during gait.     

Simulating dynamic activities using a five-axis knee simulator

This work describes the design and capabilities of the Purdue Knee Simulator: Mark II and a sagittal-plane model of the machine. This five-axis simulator was designed and constructed to simulate dynamic loading activities on either cadaveric knee specimens or total knee prostheses mounted on fixtures. The purpose of the machine was to provide a consistent, realistic loading of the knee joint, allowing the kinematics and specific loading of the structures of the knee to be determined based on condition, articular geometry, and simulated activity. The sagittal-plane model of the knee simulator was developed both to predict the loading at the knee from arbitrary inputs and to generate the necessary inputs required to duplicate specified joint loading. Measured tibio-femoral compressive force and quadriceps tension were shown to be in good agreement with the predicted loads from the model. A controlled moment about the ankle-flexion axis was also shown to change the loading on the quadriceps.     

The effect of valgus/varus malalignment on load distribution in total knee replacements

Valgus or varus malpositioning of the tibial component of a total knee implant may cause increased propensity for loosening or implant wear and eventually may lead to revision surgery. The aim of this study was to determine the effect of valgus/varus malalignment on tibio-femoral mechanics during surgical trial reduction and simulated gait loading. In seven cadaver legs, posterior cruciate sparing total knee replacements were implanted and tibial inserts representing a neutral alignment and 3 degrees and 5 degrees varus and valgus alignments were sequentially inserted. Each knee with each insert was loaded in a manner representative of a trial reduction performed during knee surgery and loaded in a physiological knee simulator. Simulated gait performed on the simulator demonstrated that internal/external and adduction/abduction rotations showed statistical changes with some of the angled inserts at different points in the walking cycle. Neither medial/lateral nor anterior/posterior translations changed statistically during simulated walking. The pressure distribution and total load in the medial and lateral compartments of the tibial component changed significantly with as little as a 3 degrees variation in angulation when loaded in a manner representative of a trial reduction or with a knee simulator. These results support the need for precise surgical reconstruction of the mechanical axis of the knee and proper alignment of the tibial component. These results further demonstrate that tibial contact pressures measured during a trial reduction method may be predictive of contact mechanics at the higher loading seen in the knee simulator.     

Experimental validation of a finite element model of a human cadaveric tibia

Finite element (FE) models of long bones are widely used to analyze implant designs. Experimental validation has been used to examine the accuracy of FE models of cadaveric femurs; however, although convergence tests have been carried out, no FE models of an intact and implanted human cadaveric tibia have been validated using a range of experimental loading conditions. The aim of the current study was to create FE models of a human cadaveric tibia, both intact and implanted with a unicompartmental knee replacement, and to validate the models against results obtained from a comprehensive set of experiments. Seventeen strain rosettes were attached to a human cadaveric tibia. Surface strains and displacements were measured under 17 loading conditions, which consisted of axial, torsional, and bending loads. The tibia was tested both before and after implantation of the knee replacement. FE models were created based on computed tomography (CT) scans of the cadaveric tibia. The models consisted of ten-node tetrahedral elements and used 600 material properties derived from the CT scans. The experiments were simulated on the models and the results compared to experimental results. Experimental strain measurements were highly repeatable and the measured stiffnesses compared well to published results. For the intact tibia under axial loading, the regression line through a plot of strains predicted by the FE model versus experimentally measured strains had a slope of 1.15, an intercept of 5.5 microstrain, and an R(2) value of 0.98. For the implanted tibia, the comparable regression line had a slope of 1.25, an intercept of 12.3 microstrain, and an R(2) value of 0.97. The root mean square errors were 6.0% and 8.8% for the intact and implanted models under axial loads, respectively. The model produced by the current study provides a tool for simulating mechanical test conditions on a human tibia. This has considerable value in reducing the costs of physical testing by pre-selecting the most appropriate test conditions or most favorable prosthetic designs for final mechanical testing. It can also be used to gain insight into the results of physical testing, by allowing the prediction of those variables difficult or impossible to measure directly.     

Three-dimensional knee joint contact forces during walking in unilateral transtibial amputees

Individuals with unilateral transtibial amputations have greater prevalence of osteoarthritis in the intact knee joint relative to the residual leg and non-amputees, but the cause of this greater prevalence is unclear. The purpose of this study was to compare knee joint contact forces and the muscles contributing to these forces between amputees and non-amputees during walking using forward dynamics simulations. We predicted that the intact knee contact forces would be higher than those of the residual leg and non-amputees. In the axial and mediolateral directions, the intact and non-amputee legs had greater peak tibio-femoral contact forces and impulses relative to the residual leg. The peak axial contact force was greater in the intact leg relative to the non-amputee leg, but the stance phase impulse was greater in the non-amputee leg. The vasti and hamstrings muscles in early stance and gastrocnemius in late stance were the largest contributors to the joint contact forces in the non-amputee and intact legs. Through dynamic coupling, the soleus and gluteus medius also had large contributions, even though they do not span the knee joint. In the residual leg, the prosthesis had large contributions to the joint forces, similar to the soleus in the intact and non-amputee legs. These results identify the muscles that contribute to knee joint contact forces during transtibial amputee walking and suggest that the peak knee contact forces may be more important than the knee contact impulses in explaining the high prevalence of intact leg osteoarthritis.