Influence of kinematic analysis methods on detecting ankle and subtalar joint instability

Patients with subtalar joint instability may be misdiagnosed with ankle instability, which may lead to chronic instability at the subtalar joint. Therefore, it is important to understand the difference in kinematics after ligament sectioning and differentiate the changes in kinematics between ankle and subtalar instability. Three methods may be used to determine the joint kinematics; the Euler angles, the Joint Coordinate System (JCS) and the helical axis (HA). The purpose of this study was to investigate the influence of using either method to detect subtalar and ankle joints instability. 3D kinematics at the ankle and subtalar joint were analyzed on 8 cadaveric specimens while the foot was intact and after sequentially sectioning the anterior talofibular ligament (ATFL), the calcaneofibular ligament (CFL), the cervical ligament and the interosseous talocalcaneal ligament (ITCL). Comparison in kinematics calculated from sensor and anatomical landmarks was conducted as well as the influence of Euler angles and JCS rotation sequence (between ISB recommendation and previous research) on the subtalar joint. All data showed a significant increase in inversion when the ITCL was sectioned. There were differences in the data calculated using sensors coordinate systems vs. anatomic coordinate systems. Anatomic coordinate systems were recommended for these calculations. The Euler angle and JCS gave similar results. Differences in Euler angles and JCS sequence lead to the same conclusion in detecting instability at the ankle and subtalar joint. As expected, the HA detected instability in plantarflexion at the ankle joint and in inversion at the subtalar joint.     

A new in vivo technique for determination of 3D kinematics and contact areas of the patello-femoral and tibio-femoral joint

Patello-femoral disorders are often caused by changes of patello-femoral and/or tibio-femoral kinematics. However, until now there has been no quantitative in vivo technique, that is able to obtain 3D kinematics and contact areas of all knee compartments simultaneously on a non-invasive basis. The aim of this study was therefore to develop and apply a technique which allows for determination of 3D kinematics and contact areas of the patello-femoral and tibio-femoral joint during different knee flexion angles and under neuromuscular activation patterns. One knee of each of the 10 healthy volunteers was examined in an open MR system under flexing isometric muscle activity at 30 degrees and 90 degrees. Three-dimensional kinematics and contact areas of the patello-femoral and tibio-femoral joints were analyzed by 3D image postprocessing. The reproducibility of the imaging technique yielded a coefficient of variation of 4.6% for patello-femoral, 4.7% for femoro-tibial displacement and 8.6% for contact areas. During knee flexion (30-90 degrees ), patella tilt (opened to medial) decreased (8.8+/-3.4 degrees vs. 4.6+/-3.1 degrees, p<0.05), while lateral patellar shift increased significantly (1.6+/-2.3mm vs. 3.4+/-3.0mm, p<0.05). Furthermore, a significant posterior translation and external rotation of the femur relative to the tibia was observed. Patello-femoral contact areas increased significantly in size (134+/-60mm(2) vs. 205+/-96 mm(2)) during knee flexion. This technique shows a high reproducibility and provides physiologic in vivo data of 3D kinematics and contact areas of the patello-femoral and the tibio-femoral joint during knee flexion. This allows for advanced in vivo diagnostics, and may help to improve therapy of patello-femoral disorders in the future.     

An automatic 2D–3D image matching method for reproducing spatial knee joint positions using single or dual fluoroscopic images

Fluoroscopic image technique, using either a single image or dual images, has been widely applied to measure in vivo human knee joint kinematics. However, few studies have compared the advantages of using single and dual fluoroscopic images. Furthermore, due to the size limitation of the image intensifiers, it is possible that only a portion of the knee joint could be captured by the fluoroscopy during dynamic knee joint motion. In this paper, we presented a systematic evaluation of an automatic 2D–3D image matching method in reproducing spatial knee joint positions using either single or dual fluoroscopic image techniques. The data indicated that for the femur and tibia, their spatial positions could be determined with an accuracy and precision less than 0.2 mm in translation and less than 0.4° in orientation when dual fluoroscopic images were used. Using single fluoroscopic images, the method could produce satisfactory accuracy in joint positions in the imaging plane (in average up to 0.5 mm in translation and 1.3° in rotation), but large variations along the out-plane direction (in average up to 4.0 mm in translation and 2.2° in rotation). The precision of using single fluoroscopic images to determine the actual knee positions was worse than its accuracy obtained. The data also indicated that when using dual fluoroscopic image technique, if the knee joint outlines in one image were incomplete by 80%, the algorithm could still reproduce the joint positions with high precisions.     

An automatic 2D-3D image matching method for reproducing spatial knee joint positions using single or dual fluoroscopic images

Fluoroscopic image technique, using either a single image or dual images, has been widely applied to measure in vivo human knee joint kinematics. However, few studies have compared the advantages of using single and dual fluoroscopic images. Furthermore, due to the size limitation of the image intensifiers, it is possible that only a portion of the knee joint could be captured by the fluoroscopy during dynamic knee joint motion. In this paper, we presented a systematic evaluation of an automatic 2D-3D image matching method in reproducing spatial knee joint positions using either single or dual fluoroscopic image techniques. The data indicated that for the femur and tibia, their spatial positions could be determined with an accuracy and precision less than 0.2?mm in translation and less than 0.4° in orientation when dual fluoroscopic images were used. Using single fluoroscopic images, the method could produce satisfactory accuracy in joint positions in the imaging plane (in average up to 0.5?mm in translation and 1.3° in rotation), but large variations along the out-plane direction (in average up to 4.0?mm in translation and 2.2° in rotation). The precision of using single fluoroscopic images to determine the actual knee positions was worse than its accuracy obtained. The data also indicated that when using dual fluoroscopic image technique, if the knee joint outlines in one image were incomplete by 80%, the algorithm could still reproduce the joint positions with high precisions.     

A reproducible method for studying three-dimensional knee kinematics

The methods used in movement analysis often rely on the definition of joint coordinate systems permitting three-dimensional (3D) kinematics. The first aim of this research project was to present a functional and postural method (FP method) to define a bone-embedded anatomical frame (BAF) on the femur and tibia, and, subsequently, a knee joint coordinate system. The repeatability of the proposed method was also assessed. Using FP method to define the BAFs, 4 kinematic parameters (flexion/extension, abduction/adduction, tibial internal/external rotation, and antero-posterior translation) were computed for 15 subjects walking on a treadmill. The repeatability for all four kinematic parameters was then assessed, using intra- and inter-observer settings. After pooling the results for all observers, the mean repeatability value ranged between 0.4 degrees and 0.8 degrees for rotation angles and between 0.8 and 2.2 mm for translation.     

In vivo kinematics of two-component total ankle arthroplasty during non-weightbearing and weightbearing dorsiflexion/plantarflexion

Relatively high rates of loosening and implant failure have been reported after total ankle arthroplasty, especially in first and second generation implants. Abnormal kinematics and incongruency of the articular surface may cause increased loads applied to the implant with concomitant polyethylene wear, resulting in loosening and implant failure. The purpose of this study was to measure three-dimensional kinematics of two-component total ankle arthroplasty during non-weightbearing and weightbearing activities, and to investigate incongruency of the articular surfaces during these activities. Forty-seven patients with a mean age of 71 years were enrolled. Radiographs were taken at non-weightbearing maximal dorsiflexion and plantarflexion, and weightbearing maximal dorsiflexion, plantarflexion, and neutral position. 3D-2D model-image registration was performed using the radiographs and the three-dimensional implant models, and three-dimensional joint angles were determined. The implanted ankles showed 18.1±8.6° (mean±standard deviation) of plantarflexion, 0.1±0.7° of inversion, 1.2±2.0° of internal rotation, and 0.8±0.6mm of posterior translation of the talar component in the non-weightbearing activity, and 17.8±7.5° of plantarflexion, 0.4±0.5° of inversion, 1.8±2.0° of internal rotation, and 0.7±0.5mm of posterior translation in the weightbearing activity. There were no significant differences between the non-weightbearing and weightbearing kinematics except for the plantarflexion angle. Incongruency of the articular surface occurred in more than 75% of the ankles. Our observations will provide useful data against which kinematics of other implant designs, such as three-component total ankle arthroplasty, can be compared.     

The coupled motion of the femur and patella during in vivo weightbearing knee flexion

The movement of the knee joint consists of a coupled motion between the tibiofemoral and patellofemoral articulations. This study measured the six degrees-of-freedom kinematics of the tibia, femur, and patella using dual-orthogonal fluoroscopy and magnetic resonance imaging. Ten normal knees from ten living subjects were investigated during weightbearing flexion from full extension to maximum flexion. The femoral and the patellar motions were measured relative to the tibia. The femur externally rotated by 12.9 deg and the patella tilted laterally by 16.3 deg during the full range of knee flexion. Knee flexion was strongly correlated with patellar flexion (R(2)=0.91), posterior femoral translation was strongly correlated to the posterior patellar translation (R(2)=0.87), and internal-external rotation of the femur was correlated to patellar tilt (R(2)=0.73) and medial-lateral patellar translation (R(2)=0.63). These data quantitatively indicate a kinematic coupling between the tibia, femur, and patella, and provide base line information on normal knee joint kinematics throughout the full range of weightbearing flexion. The data also suggest that the kinematic coupling of tibia, femur, and patella should be considered when investigating patellar pathologies and when developing surgical techniques to treat knee joint diseases.     

Mandibular kinematics represented by a non-orthogonal floating axis joint coordinate system

There are many methods used to represent joint kinematics (e.g., roll, pitch, and yaw angles; instantaneous center of rotation; kinematic center; helical axis). Often in biomechanics internal landmarks are inferred from external landmarks. This study represents mandibular kinematics using a non-orthogonal floating axis joint coordinate system based on 3-D geometric models with parameters that are "clinician friendly" and mathematically rigorous. Kinematics data for two controls were acquired from passive fiducial markers attached to a custom dental clutch. The geometric models were constructed from MRI data. The superior point along the arc of the long axis of the condyle was used to define the coordinate axes. The kinematic data and geometric models were registered through fiducial markers visible during both protocols. The mean absolute maxima across the subjects for sagittal rotation, coronal rotation, axial rotation, medial-lateral translation, anterior-posterior translation, and inferior-superior translation were 34.10 degrees, 1.82 degrees, 1.14 degrees, 2.31, 21.07, and 6.95 mm, respectively. All the parameters, except for one subject's axial rotation, were reproducible across two motion recording sessions. There was a linear correlation between sagittal rotation and translation, the dominant motion plane, with approximately 1.5 degrees of rotation per millimeter of translation. The novel approach of combining the floating axis system with geometric models succinctly described mandibular kinematics with reproducible and clinician friendly parameters.     

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.     

Influence of patellar position on tibial rotation after total knee arthroplasty]

AIM: Common total knee arthroplasty leads to resection of the anterior cruciate ligament. Lacking the ligamentous guidance, tibial rotation depends on different factors, i.e., muscle vectors. The present study measured the influence of the knee extensor mechanism determined by the mediolateral patella position on tibial rotation after implantation of two different knee prostheses. MATERIALS AND METHODS: Physiologic tibial rotation and mediolateral patella translation were measured in ten fresh-frozen knee specimens. After implantation of the Interax- and Genesis II-prosthesis in each five of the ten specimens, kinematic measurements were made again with a determination of significant alterations. RESULTS: The maximal medial patella position relative to the centre of the tibia was -6.6 mm (representing lateralisation); the maximal external tibial rotation was 4.1 degrees. After implantation of the Genesis II-prosthesis the external tibial rotation was reduced (p=0.03) with a relatively medialised patella (p=0.01), whereas after implantation of the Interax-prosthesis the external tibial rotation was increased (p=0.01) while the patella was measured to be lateralised similar to physiologic conditions. CONCLUSION: The results of the current study revealed a potential influence of mediolateral patella position on tibial rotation following total knee arthroplasty, while both prosthesis systems were not able to reproduce physiologic joint kinematics.     

Double-step registration of in vivo stereophotogrammetry with both in vitro 6-DOFs electrogoniometry and CT medical imaging

Standard registration techniques of bone morphology to motion analysis data often lead to unsatisfactory motion simulation because of discrepancies during the location of anatomical landmarks in the datasets. This paper describes an iterative registration method of a three-dimensional (3D) skeletal model with both 6 degrees-of-freedom joint kinematics and standard motion analysis data. The method is demonstrated in this paper on the lower limb. The method includes two steps. A primary registration allowed synchronization of in vitro kinematics of the knee and ankle joints using flexion/extension angles from in vivo gait analysis. Results from primary registration were then improved by a so-called advanced registration, which integrated external constraints obtained from experimental gait pre-knowledge. One cadaver specimen was analyzed to obtain both joint kinematics of knee and ankle joints using 3D electrogoniometry, and 3D bone morphology from medical imaging data. These data were registered with motion analysis data from a volunteer during the execution of locomotor tasks. Computer graphics output was implemented to visualize the results for a motion of sitting on a chair. Final registration results allowed the observation of both in vivo motion data and joint kinematics from the synchronized specimen data. The method improved interpretation of gait analysis data, thanks to the combination of realistic 3D bone models and joint mechanism. This method should be of interest both for research in gait analysis and medical education. Validation of the overall method was performed using RMS of the differences between bone poses estimated after registration and original data from motion analysis.     

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.     

In vivo determination of normal and anterior cruciate ligament-deficient knee kinematics

The objective of the current study was to use fluoroscopy to accurately determine the three-dimensional (3D), in vivo, weight-bearing kinematics of 10 normal and five anterior cruciate ligament deficient (ACLD) knees. Patient-specific bone models were derived from computed tomography (CT) data. 3D computer bone models of each subject's femur, tibia, and fibula were recreated from the CT 3D bone density data. Using a model-based 3D-to-2D imaging technique registered CT images were precisely fit onto fluoroscopic images, the full six degrees of freedom motion of the bones was measured from the images. The computer-generated 3D models of each subject's femur and tibia were precisely registered to the 2D digital fluoroscopic images using an optimization algorithm that automatically adjusts the pose of the model at various flexion/extension angles. Each subject performed a weight-bearing deep knee bend while under dynamic fluoroscopic surveillance. All 10 normal knees experienced posterior femoral translation of the lateral condyle and minimal change in position of the medial condyle with progressive knee flexion. The average amount of posterior femoral translation of the lateral condyle was 21.07 mm, whereas the average medial condyle translation was 1.94 mm, in the posterior direction. In contrast, all five ACLD knees experienced considerable change in the position of the medial condyle. The average amount of posterior femoral translation of the lateral condyle was 17.00 mm, while the medial condyle translation was 4.65 mm, in the posterior direction. In addition, the helical axis of motion was determined between maximum flexion and extension. A considerable difference was found between the center of rotation locations of the normal and ACLD subjects, with ACLD subjects exhibiting substantially higher variance in kinematic patterns.     

ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion--part I: ankle, hip, and spine. International Society of Biomechanics

The Standardization and Terminology Committee (STC) of the International Society of Biomechanics (ISB) proposes a general reporting standard for joint kinematics based on the Joint Coordinate System (JCS), first proposed by Grood and Suntay for the knee joint in 1983 (J. Biomech. Eng. 105 (1983) 136). There is currently a lack of standard for reporting joint motion in the field of biomechanics for human movement, and the JCS as proposed by Grood and Suntay has the advantage of reporting joint motions in clinically relevant terms. In this communication, the STC proposes definitions of JCS for the ankle, hip, and spine. Definitions for other joints (such as shoulder, elbow, hand and wrist, temporomandibular joint (TMJ), and whole body) will be reported in later parts of the series. The STC is publishing these recommendations so as to encourage their use, to stimulate feedback and discussion, and to facilitate further revisions. For each joint, a standard for the local axis system in each articulating bone is generated. These axes then standardize the JCS. Adopting these standards will lead to better communication among researchers and clinicians.     

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.     

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

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

Validation of a non-invasive fluoroscopic imaging technique for the measurement of dynamic knee joint motion

The accurate measurement of the in vivo knee joint kinematics in six degrees-of-freedom (6DOF) remains a challenge in biomedical engineering. We have adapted a dual fluoroscopic imaging system (DFIS) to investigate the various in vivo dynamic knee joint motions. This paper presents a thorough validation of the accuracy and repeatability of the DFIS system when used to measure 6DOF dynamic knee kinematics. First, the validation utilized standard geometric spheres made from different materials to demonstrate the capability of the DFIS technique to determine the object positions under changing speeds. The translational pose of the spheres could be recreated to less than 0.15±0.09 mm for velocities below 300 mm/s. Next, tantalum beads were inserted into the femur and tibia of two fresh frozen cadaver knees to compare the dynamic kinematics measured by matching knee models to the kinematics from the tantalum bead matching—a technique similar to Roentgen stereophotogrammetric analysis (RSA). Each cadaveric knee was attached to the crosshead of a tensile testing machine and vertically translated at a rate of 16.66 mm/s while images were captured with the DFIS. Subsequently, the tibia was held fixed and the femur manually flexed from full extension to 90° of flexion, as the DFIS acquired images. In vitro translation of the cadaver knee using the tensile testing machine deviated from predicted values by 0.08±0.14 mm for the matched knee models. The difference between matching the knee and tantalum bead models during the dynamic flexion–extension motion of the knee was 0.1±0.65°/s in flexion speed; 0.24±0.16 mm in posterior femoral translation; and 0.16±0.61° in internal–external tibial rotation. Finally, we applied the method to investigate the knee kinematics of a living subject during a step ascent and treadmill gait. High repeatability was demonstrated for the in vivo application. Thus, the DFIS provides an easy and powerful tool for accurately determining 6DOF positions of the knee when performing daily functional activities.     

Comparative assessment of knee joint models used in multi-body kinematics optimisation for soft tissue artefact compensation

Estimating joint kinematics from skin-marker trajectories recorded using stereophotogrammetry is complicated by soft tissue artefact (STA), an inexorable source of error. One solution is to use a bone pose estimator based on multi-body kinematics optimisation (MKO) embedding joint constraints to compensate for STA. However, there is some debate over the effectiveness of this method. The present study aimed to quantitatively assess the degree of agreement between reference (i.e., artefact-free) knee joint kinematics and the same kinematics estimated using MKO embedding six different knee joint models. The following motor tasks were assessed: level walking, hopping, cutting, running, sit-to-stand, and step-up. Reference knee kinematics was taken from pin-marker or biplane fluoroscopic data acquired concurrently with skin-marker data, made available by the respective authors. For each motor task, Bland-Altman analysis revealed that the performance of MKO varied according to the joint model used, with a wide discrepancy in results across degrees of freedom (DoFs), models and motor tasks (with a bias between −10.2° and 13.2° and between −10.2 mm and 7.2 mm, and with a confidence interval up to ±14.8° and ±11.1 mm, for rotation and displacement, respectively). It can be concluded that, while MKO might occasionally improve kinematics estimation, as implemented to date it does not represent a reliable solution to the STA issue.     

Measuring three-dimensional knee kinematics under torsional loading

Excessive knee joint laxity is often used as an indicator of joint disease or injury. Clinical assessment devices are currently limited to anterior–posterior drawer measurements, while tools used to measure movement in the remaining degrees of freedom are either invasive or prone to soft tissue artefact. The objective of this work was, therefore, to develop a methodology whereby in vivo knee joint kinematics could be measured in three dimensions under torsional loading while still maintaining a non-invasive procedure. A device designed to administer a subject-normalized torque in the transverse plane of the knee was securely fastened to the outer frame of an open magnetic resonance imaging (MRI) magnet. Low resolution 3D T1-weighted images (6.25 mm slice thickness) were generated by the 0.2 Tesla MRI scanner in less than 3 min while the joint was under load. The 3D image volume was then shape-matched to a high resolution image volume (1.56 mm slice thickness) scanned in a no-load position. Three-dimensional rotations and translations of the tibia with respect to the femur were calculated by comparing the transformation matrices before and after torque was applied. Results from six subjects showed that this technique was repeatable over five trials with the knee in extended and flexed positions. Differences in range of rotation were shown between subjects and between knee positions, suggesting that this methodology has sufficient utility for further application in clinical studies.     

Expression of joint moment in the joint coordinate system

The question of using the nonorthogonal joint coordinate system (JCS) to report joint moments has risen in the literature. However, the expression of joint moments in a nonorthogonal system is still confusing. The purpose of this paper is to present a method to express any 3D vector in a nonorthogonal coordinate system. The interpretation of these expressions in the JCS is clarified and an example for the 3D joint moment vector at the shoulder and the knee is given. A nonorthogonal projection method is proposed based on the mixed product. These nonorthogonal projections represent, for a 3D joint moment vector, the net mechanical action on the JCS axes. Considering the net mechanical action on each axis seems important in order to assess joint resistance in the JCS. The orthogonal projections of the same 3D joint moment vector on the JCS axes can be characterized as "motor torque." However, this interpretation is dependent on the chosen kinematic model. The nonorthogonal and orthogonal projections of shoulder joint moment during wheelchair propulsion and knee joint moment during walking were compared using root mean squares (rmss). rmss showed differences ranging from 6 N?m to 22.3 N?m between both projections at the shoulder, while differences ranged from 0.8 N?m to 3.0 N?m at the knee. Generally, orthogonal projections were of lower amplitudes than nonorthogonal projections at both joints. The orthogonal projection on the proximal or distal coordinates systems represents the net mechanical actions on each axis, which is not the case for the orthogonal projection (i.e., motor torque) on JCS axes. In order to represent the net action at the joint in a JCS, the nonorthogonal projection should be used.