On the estimation of joint kinematics during gait.

In gait analysis, the concepts of Euler and helical (screw) angles are used to define the three-dimensional relative joint angular motion of lower extremities. Reliable estimation of joint angular motion depends on the accurate definition and construction of embedded axes within each body segment. In this paper, using sensitivity analysis, we quantify the effects of uncertainties in the definition and construction of embedded axes on the estimation of joint angular motion during gait. Using representative hip and knee motion data from normal subjects and cerebral palsy patients, the flexion-extension axis is analytically perturbed +/- 15 degrees in 5 degrees steps from a reference position, and the joint angles are recomputed for both Euler and helical angle definitions. For the Euler model, hip and knee flexion angles are relatively unaffected while the ab/adduction and rotation angles are significantly affected throughout the gait cycle. An error of 15 degrees in the definition of flexion-extension axis gives rise to maximum errors of 8 and 12 degrees for the ab/adduction angle, and 10-15 degrees for the rotation angles at the hip and knee, respectively. Furthermore, the magnitude of errors in ab/adduction and rotation angles are a function of the flexion angle. The errors for the ab/adduction angles increase with increasing flexion angle and for the rotation angle, decrease with increasing flexion angle. In cerebral palsy patients with flexed knee pattern of gait, this will result in distorted estimation of ab/adduction and rotation. For the helical model, similar results are obtained for the helical angle and associated direction cosines.(ABSTRACT TRUNCATED AT 250 WORDS)     

Sensitivity of the knee joint kinematics calculation to selection of flexion axes

Various flexion axes have been used in the literature to describe knee joint kinematics. This study measured the passive knee kinematics of six cadaveric human knee specimens using two widely accepted flexion axes; transepicondylar axis and the geometric center axis. These two axes were found to form an angle of 4.0 degrees +/- 0.8 degrees. The tibial rotation calculated using the transepicondylar axis was significantly different than the rotation obtained using the geometric center axis for the same knee motion. At 90 degrees of flexion, the tibial rotation obtained using the transepicondylar axis was 4.8 degrees +/- 9.4 degrees whereas the rotation recorded using the geometric center axis at the same flexion angle was 13.8 degrees +/- 10.2 degrees. At 150 degrees of knee flexion, the rotations obtained from the transepicondylar and the geometric center axes were 7.2 degrees +/- 5.7 degrees and 19.9 degrees +/- 6.9 degrees, respectively. The data suggest that a clear definition of the flexion axis is necessary when reporting knee joint kinematics.     

Cruciate coupling and screw-home mechanism in passive knee joint during extension--flexion

The screw-home mechanism and coupling between forces in cruciate ligaments during passive knee joint flexion were investigated for various boundary conditions, flexion axis alignments and posterior cruciate ligaments (PCL)/anterior cruciate ligament (ACL) conditions. A developed non-linear 3D finite element model was used to perform detailed elasto-static response analyses of the human tibiofemoral joint as a function of flexion angle varying from 10 degrees hyper-extension to 90 degrees flexion. The tibia rotated internally as the femur flexed and externally as the femur extended. The re-alignment of the flexion axis by +/-5 degrees rotation about the axial (distal-proximal) axis, transection of the ACL and changes in cruciate ligament initial strains substantially influenced the 'screw-home' motion. On the other hand, restraint on this coupled rotation diminished ACL forces in flexion. A remarkable coupling was predicted between ACL and PCL forces in flexion; forces in both cruciate ligaments increased as the initial strain or pretension in one of them increased whereas they both diminished as one of them was cut or became slack. This has important consequences in joint functional biomechanics following a ligament injury or replacement surgery and, hence, in the proper management of joint disorders.     

The use of sequential MR image sets for determining tibiofemoral motion: reliability of coordinate systems and accuracy of motion tracking algorithm

The use of magnetic resonance imaging has been proposed by many investigators for establishment of joint reference systems and kinematic tracking of musculoskeletal joints. In this study, the intraobserver and interobserver reliability of a strategy to establish anatomic reference systems using manually selected fiducial points were quantified for seven sets of MR images of the human knee joint. The standard error of the measurement of the intraobserver and interobserver errors were less than 2.6 degrees, and 1.2 mm for relative tibiofemoral orientation and displacement, respectively. An automated motion tracking algorithm was also validated with a controlled motion experiment in a cadaveric knee joint. The controlled displacements and rotations prescribed in our motion tracking validation were highly correlated to those predicted (Pearson's correlation = 0.99, RMS errors = 0.39 mm, 0.38 degree). Finally, the system for anatomic reference system definition and motion tracking was demonstrated with a set of MR images of in vivo passive flexion in the human knee.     

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.     

The effect of the point of application of anterior tibial loads on human knee kinematics

Coupled axial tibial rotation in response to an anterior tibial load has been used as a common diagnostic measurement and as a means to load the ligamentous structures during laboratory tests. However, the exact location of the point of application of these loads as well as the corresponding sensitivity of the coupled tibial rotation to this point can have an effect on the function of the soft tissues at the joint. Therefore, the purpose of this study was to determine the effects of four different points of application of the anterior tibial load on the anterior tibial translation and coupled axial tibial rotation. The four points include: (1) geometric point - midway between the collateral ligament insertion sites on the tibia, (2) clinical point - a position that attempts to simulate clinical diagnostic tests, (3) medial point - a position medial to the geometric point and (4) lateral point - a position lateral to the clinical point. A robotic/universal force-moment sensor testing system was used to apply the anterior tibial load at the four points of application and to record the resulting joint motion. Anterior tibial translation in response to an anterior tibial load of 100N was found not to vary between the four points of application of the anterior tibial load at all flexion angles examined. However, internal tibial rotation was found for the lateral point (13+/-10 degrees at 30 degrees of knee flexion) in all specimens and clinical point (8+/-10 degrees at 30 degrees of knee flexion) while external rotation resulted when the load was applied at the medial point (-8+/-7 degrees at 30 degrees of knee flexion). Both internal and external tibial rotations occurred throughout the range of flexion when the tibial load was applied at the geometric point. The results suggest that the clinical point should be used as the point of application of the anterior tibial load whenever clinical examinations are simulated and multi-degree-of-freedom joint and soft tissue function are examined.     

A new model to predict in vivo human knee kinematics under physiological-like muscle activation

Although a number of approaches have attempted to model knee kinematics, rarely have they been validated against in vivo data in a larger subject cohort. Here, we assess the feasibility of four-bar linkage mechanisms in addressing knee kinematics and propose a new approach that is capable of accounting for lengthening characteristics of the ligaments, including possible laxity, as well as the internal/external rotation of the joint. MR scans of the knee joints of 12 healthy volunteers were taken at flexion angles of 0 degrees , 30 degrees and 90 degrees under both passive and active muscle conditions. By reconstructing the surfaces at each position, the accuracy of the four-bar linkage mechanism was assessed for every possible combination of points within each cruciate ligament attachment area. The specific set of parameters that minimized the deviation between the predictions and the in vivo pose was derived, producing a mean error of 1.8 and 2.5 on the medial and 1.7 and 2.4mm on the lateral side at 30 degrees and 90 degrees flexion, respectively, for passive motion, significantly improving on the models that did not consider internal/external rotation. For active flexion, mean medial errors were 3.3 and 4.7 mm and lateral errors 3.4 and 4.8 mm. Using this best parameter set, a generic predictive model was created and assessed against the known in vivo positions, producing a maximum average error of 4.9 mm at 90 degrees flexion. The accuracy achieved shows that kinematics may be accurately reconstructed for subject specific musculoskeletal models to allow a better understanding of the load distribution within the knee.     

Ambulatory measurement of 3D knee joint angle

Three-dimensional measurement of joint motion is a promising tool for clinical evaluation and therapeutic treatment comparisons. Although many devices exist for joints kinematics assessment, there is a need for a system that could be used in routine practice. Such a system should be accurate, ambulatory, and easy to use. The combination of gyroscopes and accelerometers (i.e., inertial measurement unit) has proven to be suitable for unrestrained measurement of orientation during a short period of time (i.e., few minutes). However, due to their inability to detect horizontal reference, inertial-based systems generally fail to measure differential orientation, a prerequisite for computing the three-dimentional knee joint angle recommended by the Internal Society of Biomechanics (ISB). A simple method based on a leg movement is proposed here to align two inertial measurement units fixed on the thigh and shank segments. Based on the combination of the former alignment and a fusion algorithm, the three-dimensional knee joint angle is measured and compared with a magnetic motion capture system during walking. The proposed system is suitable to measure the absolute knee flexion/extension and abduction/adduction angles with mean (SD) offset errors of -1 degree (1 degree ) and 0 degrees (0.6 degrees ) and mean (SD) root mean square (RMS) errors of 1.5 degrees (0.4 degrees ) and 1.7 degrees (0.5 degrees ). The system is also suitable for the relative measurement of knee internal/external rotation (mean (SD) offset error of 3.4 degrees (2.7 degrees )) with a mean (SD) RMS error of 1.6 degrees (0.5 degrees ). The method described in this paper can be easily adapted in order to measure other joint angular displacements such as elbow or ankle.     

Non-invasive assessment of soft-tissue artifact and its effect on knee joint kinematics during functional activity

The soft-tissue interface between skin-mounted markers and the underlying bones poses a major limitation to accurate, non-invasive measurement of joint kinematics. The aim of this study was twofold: first, to quantify lower limb soft-tissue artifact in young healthy subjects during functional activity; and second, to determine the effect of soft-tissue artifact on the calculation of knee joint kinematics. Subject-specific bone models generated from magnetic resonance imaging (MRI) were used in conjunction with X-ray images obtained from single-plane fluoroscopy to determine three-dimensional knee joint kinematics for four separate tasks: open-chain knee flexion, hip axial rotation, level walking, and a step-up. Knee joint kinematics was derived using the anatomical frames from the MRI-based, 3D bone models together with the data from video motion capture and X-ray fluoroscopy. Soft-tissue artifact was defined as the degree of movement of each marker in the anteroposterior, proximodistal and mediolateral directions of the corresponding anatomical frame. A number of different skin-marker clusters (total of 180) were used to calculate knee joint rotations, and the results were compared against those obtained from fluoroscopy. Although a consistent pattern of soft-tissue artifact was found for each task across all subjects, the magnitudes of soft-tissue artifact were subject-, task- and location-dependent. Soft-tissue artifact for the thigh markers was substantially greater than that for the shank markers. Markers positioned in the vicinity of the knee joint showed considerable movement, with root mean square errors as high as 29.3 mm. The maximum root mean square errors for calculating knee joint rotations occurred for the open-chain knee flexion task and were 24.3°, 17.8° and 14.5° for flexion, internal–external rotation and abduction–adduction, respectively. The present results on soft-tissue artifact, based on fluoroscopic measurements in healthy adult subjects, may be helpful in developing location- and direction-specific weighting factors for use in global optimization algorithms aimed at minimizing the effects of soft-tissue artifact on calculations of knee joint rotations.     

Effects of femoral component placement on the balancing of a total knee at surgery

Misalignment and soft-tissue imbalance in total knee arthroplasty (TKA) can cause discomfort, pain, inadequate motion and instability that may require revision surgery. Balancing can be defined as equal collateral ligament tensions or equal medial and lateral compartmental forces during the flexion range. Our goal was to study the effects on balancing of linear femoral component misplacements (proximal, distal, anterior, posterior); and different component rotations in mechanical alignment compared to kinematic alignment throughout the flexion path. A test rig was constructed such that the position of a standard femoral component could be adjusted to simulate the linear and rotational positions. With the knee in neutral reference values of the collateral tensions were adjusted to give anatomic contact force patterns, measured with an instrumented tibial trial. The deviations in the forces for each femoral component position were then determined. Compartmental forces were significantly influenced by 2 mm linear errors in the femoral component placement. However, the errors were least for a distal error, equivalent to undercutting the distal femur. The largest errors mainly increase the lateral condyle force, occurred for proximal and posterior component errors. There were only small contact force differences between kinematic and mechanical alignment. Based on these results, surgeons should avoid overcutting the distal femur and undercutting the posterior femur. However, the 2–3 degrees varus slope of the joint line as in kinematic alignment did not have much effect on balancing, so mechanical or kinematic alignment were equivalent.     

Multi-body optimization with subject-specific knee models: performance at high knee flexion angles

When estimating knee kinematics from skin markers and stereophotogrammetry, multi-body optimization (MBO) has provided promising results for reducing soft tissue artefacts (STA), but can still be improved. The goal of this study was to assess the performance of MBO with subject-specific knee models at high knee flexion angles (up to 110°) against knee joint kinematics measured by magnetic resonance imaging. Eight subjects were recruited. MBO with subject-specific knee models was more effective in compensating STA compared to no kinematic and spherical constraints, in particular for joint displacements. Moreover, it seems to be more reliable over large ranges of knee flexion angle. The ranges of root mean square errors for knee rotations/displacements were 3.0°–9.2°/1.3–3.5 mm for subject-specific knee models, 6.8°–8.7°/6.0–12.4 mm without kinematic constraint and 7.1°–9.8°/4.9–12.5 mm for spherical constraints.     

Helical axes of skeletal knee joint motion during running

The purpose of this study was to determine the changes in the axis of rotation of the knee that occur during the stance phase of running. Using intracortical pins, the three-dimensional skeletal kinematics of three subjects were measured during the stance phase of five running trials. The stance phase was divided into equal motion increments for which the position and orientation of the finite helical axes (FHA) were calculated relative to a tibial reference frame. Results were consistent within and between subjects. At the beginning of stance, the FHA was located at the midepicondylar point and during the flexion phase moved 20mm posteriorly and 10mm distally. At the time of peak flexion, the FHA shifted rapidly by about 10-20mm in proximal and posterior direction. The angle between the FHA and the tibial transverse plane increased gradually during flexion, to about 15 degrees of medial inclination, and then returned to zero at the start of the extension phase. These changes in position and orientation of FHA in the knee should be considered in analyses of muscle function during human movement, which require moment arms to be defined relative to a functional rotation axis. The finding that substantial changes in axis of rotation occurred independent of flexion angle suggests that musculoskeletal models must have more than one kinematic degree-of-freedom at the knee. The same applies to the design of knee prostheses, if the goal is to restore normal muscle function.     

In-vivo measurement of dynamic joint motion using high speed biplane radiography and CT: application to canine ACL deficiency

Dynamic assessment of three-dimensional (3D) skeletal kinematics is essential for understanding normal joint function as well as the effects of injury or disease. This paper presents a novel technique for measuring in-vivo skeletal kinematics that combines data collected from high-speed biplane radiography and static computed tomography (CT). The goals of the present study were to demonstrate that highly precise measurements can be obtained during dynamic movement studies employing high frame-rate biplane video-radiography, to develop a method for expressing joint kinematics in an anatomically relevant coordinate system and to demonstrate the application of this technique by calculating canine tibio-femoral kinematics during dynamic motion. The method consists of four components: the generation and acquisition of high frame rate biplane radiographs, identification and 3D tracking of implanted bone markers, CT-based coordinate system determination, and kinematic analysis routines for determining joint motion in anatomically based coordinates. Results from dynamic tracking of markers inserted in a phantom object showed the system bias was insignificant (-0.02 mm). The average precision in tracking implanted markers in-vivo was 0.064 mm for the distance between markers and 0.31 degree for the angles between markers. Across-trial standard deviations for tibio-femoral translations were similar for all three motion directions, averaging 0.14 mm (range 0.08 to 0.20 mm). Variability in tibio-femoral rotations was more dependent on rotation axis, with across-trial standard deviations averaging 1.71 degrees for flexion/extension, 0.90 degree for internal/external rotation, and 0.40 degree for varus/valgus rotation. Advantages of this technique over traditional motion analysis methods include the elimination of skin motion artifacts, improved tracking precision and the ability to present results in a consistent anatomical reference frame.     

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.     

Cross-Talk Correction Method for Knee Kinematics in Gait Analysis Using Principal Component Analysis (PCA): A New Proposal

Background

In 3D gait analysis, the knee joint is usually described by the Eulerian way. It consists in breaking down the motion between the articulating bones of the knee into three rotations around three axes: flexion/extension, abduction/adduction and internal/external rotation. However, the definition of these axes is prone to error, such as the “cross-talk” effect, due to difficult positioning of anatomical landmarks. This paper proposes a correction method, principal component analysis (PCA), based on an objective kinematic criterion for standardization, in order to improve knee joint kinematic analysis.

Methods

The method was applied to the 3D gait data of two different groups (twenty healthy subjects and four with knee osteoarthritis). Then, this method was evaluated with respect to three main criteria: (1) the deletion of knee joint angle cross-talk (2) the reduction of variance in the varus/valgus kinematic profile (3) the posture trial varus/valgus deformation matching the X-ray value for patients with knee osteoarthritis. The effect of the correction method was tested statistically on variabilities and cross-talk during gait.

Results

Cross-talk was lower (p<0.05) after correction (the correlation between the flexion-extension and varus-valgus kinematic profiles being annihilated). Additionally, the variance in the kinematic profile for knee varus/valgus and knee flexion/extension was found to be lower and higher (p<0.05), respectively, after correction for both the left and right side. Moreover, after correction, the posture trial varus/valgus angles were much closer to x-ray grading.

Conclusion

The results show that the PCA correction applied to the knee joint eliminates the cross-talk effect, and does not alter the radiological varus/valgus deformation for patients with knee osteoarthritis. These findings suggest that the proposed correction method produces new rotational axes that better fit true knee motion.     

The movement of the normal tibio-femoral joint

This review describes the anatomy of the articular surfaces and their movement in the normal tibio-femoral joint, together with methods of measurement in volunteers. Forces and soft tissues are excluded. To measure movement, the articular surfaces and natural or inserted movement markers must be imaged by some combination of MRI, CT, RSA or fluoroscopy. With the aid of computer-imaging, the movements can then be related to an anatomy-based co-ordinate system to avoid kinematic cross-talk. Methods of depicting these movements which are understandable to engineers and clinicians are discussed. The shapes of the articular surfaces are reported. They are relevant to landmarks and co-ordinate systems and form a basis for inferring the nature of the movements which take place in the knee. The movements of the condyles are described from hyperextension to full passive flexion. Medially the condyle hardly moves antero-posteriorly from 0 degrees to 120 degrees but the contact area transfers from an anterior pair of tibio-femoral surfaces at 10 degrees to a posterior pair at about 30 degrees . Thus because of the shapes of the bones, the medial contact area moves backwards with flexion to 30 degrees but the condyle does not. Laterally the femoral condyle and the contact area move posteriorly but to a variable extent in the mid-range causing tibial internal rotation to occur with flexion around a medial axis. From 120 degrees to full flexion both condyles roll back onto the posterior horn so that the tibio-femoral joint subluxes.     

Physical sensor difference-based method and virtual sensor difference-based method for visual and quantitative estimation of lower limb 3D gait posture using accelerometers and magnetometers

An approach using a physical sensor difference-based algorithm and a virtual sensor difference-based algorithm to visually and quantitatively confirm lower limb posture was proposed. Three accelerometers and two MAG(3)s (inertial sensor module) were used to measure the accelerations and magnetic field data for the calculation of flexion/extension (FE) and abduction/adduction (AA) angles of hip joint and FE, AA and internal/external rotation (IE) angles of knee joint; then, the trajectories of knee and ankle joints were obtained with the joint angles and segment lengths. There was no integration of acceleration or angular velocity for the joint rotations and positions, which is an improvement on the previous method in recent literature. Compared with the camera motion capture system, the correlation coefficients in five trials were above 0.91 and 0.92 for the hip FE and AA, respectively, and higher than 0.94, 0.93 and 0.93 for the knee joint FE, AA and IE, respectively.     

Comparison of three formal methods used to estimate the functional axis of rotation: an extensive in-vivo analysis performed on the knee joint

Estimating the main axis of rotation (AoR) of a human joint represents an important issue in biomechanics. This study compared three formal methods used to estimate functional AoR, namely a cylindrical fitting method, a mean helical axis transformation, and a symmetrical axis approach. These methods were tested on 106 subjects undergoing navigated total knee arthroplasty. AoR orientation in 3D and in the frontal and coronal planes provided by each method was compared to the transepicondylar axis direction. Although all the methods resulted effective, significant differences were identified among them, relatively to the orientation in 3D and in the frontal plane projection. This was probably due to the presence of secondary rotations during the first degrees of knee flexion.     

Assessment of screw displacement axis accuracy and repeatability for joint kinematic description using an electromagnetic tracking device

Screw displacement axes (SDAs) have been employed to describe joint kinematics in biomechanical studies. Previous reports have investigated the accuracy of SDAs combining various motion analysis techniques and smoothing procedures. To our knowledge, no study has assessed SDA accuracy describing the relative movement between adjacent bodies with an electromagnetic tracking system. This is important, since in relative motion, neither body is fixed and consequently sensitivity to potential measurement errors from both bodies may be significant. Therefore, this study assessed the accuracy of SDAs for describing relative motion between two moving bodies. We analyzed numerical simulated data, and physical experimental data recorded using a precision jig and electromagnetic tracking device. The numerical simulations demonstrated SDA position accuracy (p=0.04) was superior for single compared to relative body motion, whereas orientation accuracy (p=0.2) was similar. Experimental data showed data-filtering (Butterworth filter) improved SDA position and orientation accuracies for rotation magnitudes smaller or equal to 5.0 degrees, with no effect at larger rotation magnitudes (p<0.05). This suggests that in absence of a filter, SDAs should only be calculated at rotations of greater than 5.0 degrees. For rotation magnitudes of 0.5 degrees (5.0 degrees ) about the SDA, SDA position and orientation error measurements determined from filtered experimental data were 3.75+/-0.30 mm (3.31+/-0.21 mm), and 1.10+/-0.04 degrees (1.04+/-0.03 degrees ), respectively. Experimental accuracy values describing the translation along and rotation about the SDA, were 0.06+/-0.00 mm and 0.09+/-0.01 degrees, respectively. These small errors establish the capability of SDAs to detect small translations, and rotations. In conclusion, application of SDAs should be a useful tool for describing relative motion in joint kinematic studies.