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

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

Computational modeling of a dynamic knee simulator for reproduction of knee loading

As a first step towards reproducing desired three-dimensional joint loading and motion on a dynamic knee simulator, the goal of this study was to develop and verify a three-dimensional computational model that generated control profiles for the simulator using desired knee loading and motion as model inputs. The developed model was verified by predicting tibio-femoral loading on an instrumented analog knee for given actuator forces and the ability to generate simulator control profiles was demonstrated using a three-dimensional walking profile. The model predicted axial tibia loading for a sagittal-plane dual-limb squat within 1% of measured peak loading. Adding out-of-sagittal-plane forces decreased the accuracy of load prediction. The model generated control profiles to the simulator that produced axial tibia loading within 16% of desired for walking. Discrepancies in predicted and measured quadriceps forces influenced the accuracy of the generated control profiles. Future work will replace the analog knee in both the model and machine with a prosthetic knee.     

Prediction of antagonistic muscle forces using inverse dynamic optimization during flexion/extension of the knee.

This paper examined the feasibility of using different optimization criteria in inverse dynamic optimization to predict antagonistic muscle forces and joint reaction forces during isokinetic flexion/extension and isometric extension exercises of the knee. Both quadriceps and hamstrings muscle groups were included in this study. The knee joint motion included flexion/extension, varus/valgus, and internal/external rotations. Four linear, nonlinear, and physiological optimization criteria were utilized in the optimization procedure. All optimization criteria adopted in this paper were shown to be able to predict antagonistic muscle contraction during flexion and extension of the knee. The predicted muscle forces were compared in temporal patterns with EMG activities (averaged data measured from five subjects). Joint reaction forces were predicted to be similar using all optimization criteria. In comparison with previous studies, these results suggested that the kinematic information involved in the inverse dynamic optimization plays an important role in prediction of the recruitment of antagonistic muscles rather than the selection of a particular optimization criterion. Therefore, it might be concluded that a properly formulated inverse dynamic optimization procedure should describe the knee joint rotation in three orthogonal planes.     

Knee joint secondary motion accuracy improved by quaternion-based optimizer with bony landmark constraints

Skin marker-based motion analysis has been widely used in biomechanical studies and clinical applications. Unfortunately, the accuracy of knee joint secondary motions is largely limited by the nonrigidity nature of human body segments. Numerous studies have investigated the characteristics of soft tissue movement. Utilizing these characteristics, we may improve the accuracy of knee joint motion measurement. An optimizer was developed by incorporating the soft tissue movement patterns at special bony landmarks into constraint functions. Bony landmark constraints were assigned to the skin markers at femur epicondyles, tibial plateau edges, and tibial tuberosity in a motion analysis algorithm by limiting their allowed position space relative to the underlying bone. The rotation matrix was represented by quaternion, and the constrained optimization problem was solved by Fletcher's version of the Levenberg-Marquardt optimization technique. The algorithm was validated by using motion data from both skin-based markers and bone-mounted markers attached to fresh cadavers. By comparing the results with the ground truth bone motion generated from the bone-mounted markers, the new algorithm had a significantly higher accuracy (root-mean-square (RMS) error: 0.7 ± 0.1 deg in axial rotation and 0.4 ± 0.1 deg in varus-valgus) in estimating the knee joint secondary rotations than algorithms without bony landmark constraints (RMS error: 1.7 ± 0.4 deg in axial rotation and 0.7 ± 0.1 deg in varus-valgus). Also, it predicts a more accurate medial-lateral translation (RMS error: 0.4 ± 0.1 mm) than the conventional techniques (RMS error: 1.2 ± 0.2 mm). The new algorithm, using bony landmark constrains, estimates more accurate secondary rotations and medial-lateral translation of the underlying bone.     

Simulation of Codman's paradox reveals a general law of motion

Codman's paradox refers to a specific pattern of motion at the shoulder joint. It asked how a mysterious axial rotation about the longitudinal axis of the arm occurred during two or three sequential arm rotations that did not involve rotation about the long-axis. The objective of this paper was to find how the mysterious axial rotation occurred in the Codman's paradox. First, Codman's paradox and Codman's rotation were defined in general situations that involved arm rotations about orthogonal axes starting from the neutral attitude as well as rotations about non-orthogonal axes and starting from non-neutral attitudes. Then a general law of motion was proposed to answer the question of the Codman's paradox, which is stated as when the long-axis of the arm performs a closed-loop motion by three sequential rotations defined as Codman's rotation, it produces an equivalent axial rotation angle about the long-axis. The equivalent axial rotation angle equals the angle of swing-the second rotation in the three sequential long-axis rotations. Validity of the proposed law of motion is demonstrated by computer simulation of various Codman's rotations. Clinical relevance of the proposed law of motion is also discussed in the paper.     

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

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

Effect of a pedicle-screw-based motion preservation system on lumbar spine biomechanics: A probabilistic finite element study with subsequent sensitivity analysis

Pedicle-screw-based motion preservation systems are often used to support a slightly degenerated disc. Such implants are intended to reduce intradiscal pressure and facet joints forces, while having a minimal effect on the motion patterns.In a probabilistic finite element study with subsequent sensitivity analysis, the effects of 10 input parameters, such as elastic modulus and diameter of the elastic rod, distraction of the segment, level of bridged segments, etc. on the output parameters intervertebral rotations, intradiscal pressures, and facet joint forces were determined. A validated finite element model of the lumbar spine was employed. Probabilistic studies were performed for seven loading cases: upright standing, flexion, extension, left and right lateral bending and left and right axial rotation.The simulations show that intervertebral rotation angles, intradiscal pressures and facet joint forces are in most cases reduced by a motion preservation system. The influence on intradiscal pressure is small, except in extension. For many input parameter combinations, the values for intervertebral rotations and facet joint forces are very low, which indicates that the implant is too stiff in these cases. The output parameters are affected most by the following input parameters: loading case, elastic modulus and diameter of the elastic rod, distraction of the segment, and angular rigidity of the connection between screws and rod.The designated functions of a motion preservation system can best be achieved when the longitudinal rod has a low stiffness, and when the connection between rod and pedicle screws is rigid.     

Lower extremity coupling parameters during locomotion and landings

During ballistic locomotion and landing activities, the lower extremity joints must function synchronously to dissipate the impact. The coupling of subtalar motion to tibial and knee rotation has been hypothesized to depend on the dynamic requirements of the task. This study was undertaken to look for differences in the coupling of 3-D foot and knee motions during walking, jogging, and landing from a jump. Twenty recreationally active young women with normal foot alignment (as assessed by a licensed physical therapist) were videotaped with high-speed cameras (250 Hz) during walking, jogging, hopping, and jumping trials. Coupling coefficients were compared among the four activities. The ratio of eversion to tibial rotation increased from the locomotion to the landing trials, indicating that with the increased loading demands of the activity, the requirements of foot motion increased. However, this increased motion was not proportionately translated into rotation of the tibia through the subtalar joint. Furthermore, the ratio of knee flexion to knee internal rotation increased significantly from the walking to landing trials. Together these findings suggest that femoral rotation may compensate for the increase in tibial rotation as the force-dissipating demands of the task increase. The relative unbalance among the magnitude of foot, tibial, and knee rotations observed with increasing task demands may have direct implications on clinical treatments aimed at reducing knee motion via controlling motion at the foot during landing tasks.     

The envelope of passive knee joint motion

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

Search for critical loading condition of the spine--a meta analysis of a nonlinear viscoelastic finite element model

The relative vulnerability of spinal motion segments to different loading combinations remains unknown. The meta-analysis described here using the results of a validated L2-L3 nonlinear viscoelastic finite element model was designed to investigate the critical loading and its effect on the internal mechanics of the human lumbar spine. A Box-Behnken experimental design was used to design the magnitude of seven independent variables associated with loads, rotations and velocity of motion. Subsequently, an optimization method was used to find the primary and secondary variables that influence spine mechanical output related to facet forces, disc pressure, ligament forces, annulus matrix compressive/shear stresses and anulus fibers strain. The mechanical responses with respect to the two most-relevant variables were then regressed linearly using the response surface quadratic model. Axial force and sagittal rotation were identified as the most-relevant variables for mechanical responses. The procedure developed can be used to find the critical loading for finite element models with multi input variables. The derived meta-models can be used to predict the risk associated with various loading parameters and in setting safer load limits.     

Search for critical loading condition of the spine–A meta analysis of a nonlinear viscoelastic finite element model

The relative vulnerability of spinal motion segments to different loading combinations remains unknown. The meta-analysis described here using the results of a validated L2–L3 nonlinear viscoelastic finite element model was designed to investigate the critical loading and its effect on the internal mechanics of the human lumbar spine. A Box-Behnken experimental design was used to design the magnitude of seven independent variables associated with loads, rotations and velocity of motion. Subsequently, an optimization method was used to find the primary and secondary variables that influence spine mechanical output related to facet forces, disc pressure, ligament forces, annulus matrix compressive/shear stresses and anulus fibers strain. The mechanical responses with respect to the two most-relevant variables were then regressed linearly using the response surface quadratic model. Axial force and sagittal rotation were identified as the most-relevant variables for mechanical responses. The procedure developed can be used to find the critical loading for finite element models with multi input variables. The derived meta-models can be used to predict the risk associated with various loading parameters and in setting safer load limits.     

Comparative role of disc degeneration and ligament failure on functional mechanics of the lumbar spine

Understanding spinal kinematics is essential for distinguishing between pathological conditions of spine disorders, which ultimately lead to low back pain. It is of high importance to understand how changes in mechanical properties affect the response of the lumbar spine, specifically in an effort to differentiate those associated with disc degeneration from ligamentous changes, allowing for more precise treatment strategies. To do this, the goals of this study were twofold: (1) develop and validate a finite element (FE) model of the lumbar spine and (2) systematically alter the properties of the intervertebral disc and ligaments to define respective roles in functional mechanics. A three-dimensional non-linear FE model of the lumbar spine (L3-sacrum) was developed and validated for pure moment bending. Disc degeneration and sequential ligament failure were modelled. Intersegmental range of motion (ROM) and bending stiffness were measured. The prediction of the FE model to moment loading in all three planes of bending showed very good agreement, where global and intersegmental ROM and bending stiffness of the model fell within one standard deviation of the in vitro results. Degeneration decreased ROM for all directions. Stiffness increased for all directions except axial rotation, where it initially increased then decreased for moderate and severe degeneration, respectively. Incremental ligament failure produced increased ROM and decreased stiffness. This effect was much more pronounced for all directions except lateral bending, which is minimally impacted by ligaments. These results indicate that lateral bending may be more apt to detect the subtle changes associated with degeneration, without being masked by associated changes of surrounding stabilizing structures.     

Optimised loads for the simulation of axial rotation in the lumbar spine

Simplified loading modes (pure moment, compressive force) are usually applied in the in vitro studies to simulate flexion-extension, lateral bending and axial rotation of the spine. The load magnitudes for axial rotation vary strongly in the literature. Therefore, the results of current investigations, e.g. intervertebral rotations, are hardly comparable and may involve unrealistic values. Thus, the question 'which in vitro applicable loading mode is the most realistic' remains open. A validated finite element model of the lumbar spine was employed in two sensitivity studies to estimate the ranges of results due to published load assumptions and to determine the input parameters (e.g. torsional moment), which mostly affect the spinal load and kinematics during axial rotation. In a subsequent optimisation study, the in vitro applicable loading mode was determined, which delivers results that fit best with available in vivo measurements. The calculated results varied widely for loads used in the literature with potential high deviations from in vivo measured values. The intradiscal pressure is mainly affected by the magnitude of the compressive force, while the torsional moment influences mainly the intervertebral rotations and facet joint forces. The best agreement with results measured in vivo were found for a compressive follower force of 720N and a pure moment of 5.5Nm applied to the unconstrained vertebra L1. The results reveal that in many studies the assumed loads do not realistically simulate axial rotation. The in vitro applicable simplified loads cannot perfectly mimic the in vivo situation. However, the optimised values lead to the best agreement with in vivo measured values. Their consequent application would lead to a better comparability of different investigations.     

Ligaments and articular contact guide passive knee flexion

The aim of this study was to test the hypothesis that the coupled features of passive knee flexion are guided by articular contact and by the isometric fascicles of the ACL, PCL and MCL. A three-dimensional mathematical model of the knee was developed, in which the articular surfaces in the lateral and medial compartments and the isometric fascicles in the ACL, PCL and MCL were represented as five constraints in a one degree-of-freedom parallel spatial mechanism. Mechanism analysis techniques were used to predict the path of motion of the tibia relative to the femur. Using a set of anatomical parameters obtained from a cadaver specimen, the model predicts coupled internal rotation and ab/adduction with flexion. These predictions correspond well to measurements of the cadaver specimen’s motion. The model also predicts posterior translation of contact on the tibia with flexion. Although this is a well-known feature of passive knee flexion, the model predicts more translation than has been reported from experiments in the literature. Modelling of uncertainty in the anatomical parameters demonstrated that the discrepancy between theoretical predictions and experimental measurement can be attributed to parameter sensitivity of the model. This study shows that the ligaments and articular surfaces work together to guide passive knee motion. A principal implication of the work is that both articular surface geometry and ligament geometry must be preserved or replicated by surgical reconstruction and replacement procedures to ensure normal knee kinematics and by extension, mechanics.     

Dynamic finite element knee simulation for evaluation of knee replacement mechanics

In vitro pre-clinical testing of total knee replacement (TKR) devices is a necessary step in the evaluation of new implant designs. Whole joint knee simulators, like the Kansas knee simulator (KKS), provide a controlled and repeatable loading environment for comparative evaluation of component designs or surgical alignment under dynamic conditions. Experimental testing, however, is time and cost prohibitive for design-phase evaluation of tens or hundreds of design variations. Experimentally-verified computational models provide an efficient platform for analysis of multiple components, sizes, and alignment conditions. The purpose of the current study was to develop and verify a computational model of a dynamic, whole joint knee simulator. Experimental internal-external and valgus-varus laxity tests, followed by dynamic deep knee bend and gait simulations in the KKS were performed on three cadaveric specimens. Specimen-specific finite element (FE) models of posterior-stabilized TKR were created from magnetic resonance images and CAD geometry. The laxity data was used to optimize mechanical properties of tibiofemoral soft-tissue structures on a specimen-specific basis. Each specimen was subsequently analyzed in a computational model of the experimental KKS, simulating both dynamic activities. The computational model represented all joints and actuators in the experimental setup, including a proportional-integral-derivative (PID) controller to drive quadriceps actuation. The computational model was verified against six degree-of-freedom patellofemoral (PF) and tibiofemoral (TF) kinematics and actuator loading during both deep knee bend and gait activities, with good agreement in trends and magnitudes between model predictions and experimental kinematics; differences were less than 1.8 mm and 2.2° for PF and TF translations and rotations. The whole joint FE simulator described in this study can be applied to investigate a wide range of clinical and research questions.     

On the estimate of the two dominant axes of the knee using an instrumented spatial linkage

This article presents the validation of a technique to assess the appropriateness of a 2 degree-of-freedom model for the human knee, and, in which case, the dominant axes of flexion/extension and internal/external longitudinal rotation are estimated. The technique relies on the use of an instrumented spatial linkage for the accurate detection of passive knee kinematics, and it is based on the assumption that points on the longitudinal rotation axis describe nearly circular and planar trajectories, whereas the flexion/extension axis is perpendicular to those trajectories through their centers of rotation. By manually enforcing a tibia rotation while bending the knee in flexion, a standard optimization algorithm is used to estimate the approximate axis of longitudinal rotation, and the axis of flexion is estimated consequently. The proposed technique is validated through simulated data and experimentally applied on a 2 degree-of-freedom mechanical joint. A procedure is proposed to verify the fixed axes assumption for the knee model. The suggested methodology could be possibly valuable in understanding knee kinematics, and in particular for the design and implant of customized hinged external fixators, which have shown to be effective in knee dislocation treatment and rehabilitation.     

Quantifying in vivo laxity in the anterior cruciate ligament and individual knee joint structures

A custom knee loading apparatus (KLA), when used in conjunction with magnetic resonance imaging, enables in vivo measurement of the gross anterior laxity of the knee joint. A numerical model was applied to the KLA to understand the contribution of the individual joint structures and to estimate the stiffness of the anterior-cruciate ligament (ACL). The model was evaluated with a cadaveric study using an in situ knee loading apparatus and an ElectroForce test system. A constrained optimization solution technique was able to predict the restraining forces within the soft-tissue structures and joint contact. The numerical model presented here allowed in vivo prediction of the material stiffness parameters of the ACL in response to applied anterior loading. Promising results were obtained for in vivo load sharing within the structures. The numerical model overestimated the ACL forces by 27.61–92.71%. This study presents a novel approach to estimate ligament stiffness and provides the basis to develop a robust and accurate measure of in vivo knee joint laxity.     

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.     

Knee model sensitivity to cruciate ligaments parameters: a stability simulation study for a living subject

If the biomechanic function of the different anatomical sub-structures of the knee joint was needed in physiological conditions, the only possible way is a modelling approach. Subject-specific geometries and kinematic data, acquired from the same living subject, were the foundations of the 3D quasi-static knee model developed. Each cruciate ligament was modelled by means of 25 elastic springs, paying attention to the anatomical twisting of the fibres. The sensitivity of the model to the cross-sectional area was performed during the anterior/posterior tibial translations, the sensitivity to all the cruciate ligaments parameters was performed during the internal/external rotations. The model reproduced very well the mechanical behaviour reported in literature during anterior/posterior translations, in particular considering 30% of the mean insertional area. During the internal/external tibial rotations, similar behaviour of the axial torques was obtained in the three sensitivity analyses. The overlapping of the ligaments was assessed at about 25 degrees of internal axial rotation. The presented model featured a good level of accuracy in combination with a low computational weight, and it could provide an in vivo estimation of the role of the cruciate ligaments during the execution of daily living activities.