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.     

Use of dual Euler angles to quantify the three-dimensional joint motion and its application to the ankle joint complex

This paper presents a modified Euler angles method, dual Euler angles approach, to describe general spatial human joint motions. In dual Euler angles approach, the three-dimensional joint motion is considered as three successive screw motions with respect to the axes of the moving segment coordinate system; accordingly, the screw motion displacements are represented by dual Euler angles. The algorithm for calculating dual Euler angles from coordinates of markers on the moving segment is also provided in this study. As an example, the proposed method is applied to describe motions of ankle joint complex during dorsiflexion–plantarflexion. A Flock of Birds electromagnetic tracking device (FOB) was used to measure joint motion in vivo. Preliminary accuracy tests on a gimbal structure demonstrate that the mean errors of dual Euler angles evaluated by using source data from FOB are less than 1° for rotations and 1 mm for translations, respectively. Based on the pilot study, FOB is feasible for quantifying human joint motions using dual Euler angles approach.     

Validation of a new model-based tracking technique for measuring three-dimensional, in vivo glenohumeral joint kinematics

Shoulder motion is complex and significant research efforts have focused on measuring glenohumeral joint motion. Unfortunately, conventional motion measurement techniques are unable to measure glenohumeral joint kinematics during dynamic shoulder motion to clinically significant levels of accuracy. The purpose of this study was to validate the accuracy of a new model-based tracking technique for measuring three-dimensional, in vivo glenohumeral joint kinematics. We have developed a model-based tracking technique for accurately measuring in vivo joint motion from biplane radiographic images that tracks the position of bones based on their three-dimensional shape and texture. To validate this technique, we implanted tantalum beads into the humerus and scapula of both shoulders from three cadaver specimens and then recorded biplane radiographic images of the shoulder while manually moving each specimen's arm. The position of the humerus and scapula were measured using the model-based tracking system and with a previously validated dynamic radiostereometric analysis (RSA) technique. Accuracy was reported in terms of measurement bias, measurement precision, and overall dynamic accuracy by comparing the model-based tracking results to the dynamic RSA results. The model-based tracking technique produced results that were in excellent agreement with the RSA technique. Measurement bias ranged from -0.126 to 0.199 mm for the scapula and ranged from -0.022 to 0.079 mm for the humerus. Dynamic measurement precision was better than 0.130 mm for the scapula and 0.095 mm for the humerus. Overall dynamic accuracy indicated that rms errors in any one direction were less than 0.385 mm for the scapula and less than 0.374 mm for the humerus. These errors correspond to rotational inaccuracies of approximately 0.25 deg for the scapula and 0.47 deg for the humerus. This new model-based tracking approach represents a non-invasive technique for accurately measuring dynamic glenohumeral joint motion under in vivo conditions. The model-based technique achieves accuracy levels that far surpass all previously reported non-invasive techniques for measuring in vivo glenohumeral joint motion. This technique is supported by a rigorous validation study that provides a realistic simulation of in vivo conditions and we fully expect to achieve these levels of accuracy with in vivo human testing. Future research will use this technique to analyze shoulder motion under a variety of testing conditions and to investigate the effects of conservative and surgical treatment of rotator cuff tears on dynamic joint stability.     

Accuracy and precision of a method to study kinematics of the temporomandibular joint: combination of motion data and CT imaging

The purpose of the study was to test the precision and accuracy of a method used to track selected landmarks during motion of the temporomandibular joint (TMJ). A precision phantom device was constructed and relative motions between two rigid bodies on the phantom device were measured using optoelectronic (OE) and electromagnetic (EM) motion tracking devices. The motion recordings were also combined with a 3D CT image for each type of motion tracking system (EM+CT and OE+CT) to mimic methods used in previous studies. In the OE and EM data collections, specific landmarks on the rigid bodies were determined using digitization. In the EM+CT and OE+CT data sets, the landmark locations were obtained from the CT images. 3D linear distances and 3D curvilinear path distances were calculated for the points. The accuracy and precision for all 4 methods were evaluated (EM, OE, EM+CT and OE+CT). In addition, results were compared with and without the CT imaging (EM vs. EM+CT, OE vs. OE+CT). All systems overestimated the actual 3D curvilinear path lengths. All systems also underestimated the actual rotation values. The accuracy of all methods was within 0.5mm for 3D curvilinear path calculations, 0.05mm for 3D linear distance calculations and 0.2 degrees for rotation calculations. In addition, Bland-Altman plots for each configuration of the systems suggest that measurements obtained from either system are repeatable and comparable.     

Direct comparison of kinematic data collected using an electromagnetic tracking system versus a digital optical system

The purpose of this study was to quantify the dynamic accuracy of kinematics measured by a digital optical motion analysis system in a gait analysis laboratory (capture volume approximately 20m(3)) compared to a standard range direct-current electromagnetic (EM) tracking device (capture volume approximately 1m(3)). This is a subset of a larger effort to establish an appropriate marker set for the optical system to quantify upperlimb kinematics simultaneously with gait, in comparison to previous studies of isolated upperlimb movements that have employed EM tracking devices. Rigid clusters of spherical reflective markers and EM sensors were attached to a mechanical articulator that mimicked three-dimensional joint rotations, similar to the elbow. As the articulator was moved through known ranges of motion (i.e. gold standard), kinematic data were collected simultaneously using both tracking systems. Both systems were tended to underestimate the range of motion; however, the application of post hoc smoothing and least-squares correction algorithms reduced these effects. When smoothing and correction algorithms were used, the magnitude of the mean difference between the gold standard and either the EM or optical system did not exceed 2 degrees for any of the compound motions performed. This level of agreement suggests that the measurements obtained from either system are clinically comparable, provided appropriate smoothing and correction algorithms are employed.     

Evaluation and calibration of an electromagnetic tracking device for biomechanical analysis of lifting tasks.

Electromagnetic motion tracking devices are increasingly used as a kinematic measuring tool. The aim of this study was to evaluate a long-range transmitter in an environment with a conventional force plate present in order to assess its suitability for further biomechanical applications. Using a calibration apparatus developed in our lab and Optotrack measurements, the performances of the Motion Star were evaluated. Positions and orientations were measured in a 140 x 80 x 120 cm(3) space centered on the force plate. Using a mathematical model developed at Queen's University, these data were calibrated. Errors on position and orientation were less than 150 mm and 10 degrees before calibration of the Motion Star, and less than 20mm and 2 degrees after calibration, with no differences between data collected with the force plate switched on/off. These errors did not depend on sensor orientation. Variability of the signal was small indicating minimal noise. Field distortion was the largest source of measurement error, which increased with the distance between the transmitter and the sensor and the proximity of the sensor to the force plate. Before its use for biomechanical analysis of lifting tasks and validation of dynamic models using force plate data, the data from electromagnetic motion tracking devices must be calibrated to decrease the errors due to electromagnetic field distortion.     

Articulated external fixation of the ankle: minimizing motion resistance by accurate axis alignment

This study describes how an optimal single hinge axis position can be established for the application of articulated external fixation to the ankle joint. By deliberately introducing various amounts of relative mal-alignment between the optimal talocrural joint axis and the actual fixator hinge axis, it was possible to measure the corresponding amounts of additional resistance to joint motion. In a cadaveric study of six ankle specimens, we determined the instant axis of rotation of the talocrural joint from 3-D kinematic data. acquired by an electromagnetic motion tracking system. For each specimen, an optimal fixator hinge position was calculated from these motion data. Compared to the intact natural joint, aligning the fixator along the optimized axis position caused a moderate increase in energy (0.14 J) needed to rotate the ankle through a prescribed plantar/dorsiflexion range. However, malpositioning the hinge by 10 mm caused more than five times that amount of increase in motion resistance. While articulated external fixation with limited internal fixation can establish a favorable environment for the repair of severe injuries such as tibial pilon fractures, the large additional resistance to motion accompanying a malpositioned fixator axis suggests the development of untoward intra-articular forces that could act to disturb fragment alignment.     

A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement

A neuromusculoskeletal tracking (NMT) method was developed to estimate muscle forces from observed motion data. The NMT method combines skeletal motion tracking and optimal neuromuscular tracking to produce forward simulations of human movement quickly and accurately. The skeletal motion tracker calculates the joint torques needed to actuate a skeletal model and track observed segment angles and ground forces in a forward simulation of the motor task. The optimal neuromuscular tracker resolves the muscle redundancy problem dynamically and finds the muscle excitations (and muscle forces) needed to produce the joint torques calculated by the skeletal motion tracker. To evaluate the accuracy of the NMT method, kinematics and ground forces obtained from an optimal control (parameter optimization) solution for maximum-height jumping were contaminated with both random and systematic noise. These data served as input observations to the NMT method as well as an inverse dynamics analysis. The NMT solution was compared to the input observations, the original optimal solution, and a simulation driven by the inverse dynamics torques. The results show that, in contrast to inverse dynamics, the NMT method is able to produce an accurate forward simulation consistent with the optimal control solution. The NMT method also requires 3 orders-of-magnitude less CPU time than parameter optimization. The speed and accuracy of the NMT method make it a promising new tool for estimating muscle forces using experimentally obtained kinematics and ground force data.     

Accuracy of the functional method of hip joint center location: effects of limited motion and varied implementation.

Accurate location of the hip joint center is essential for computation of hip kinematics and kinetics as well as for determination of the moment arms of muscles crossing the hip. The functional method of hip joint center location involves fitting a pelvis-fixed sphere to the path traced by a thigh-fixed point while a subject performs hip motions; the center of this sphere is the hip joint center. The aim of the present study was to evaluate the potential accuracy of the functional method and the dependence of its accuracy on variations in its implementation and the amount of available hip motion. The motions of a mechanical linkage were studied to isolate the factors of interest, removing errors due to skin movement and the palpation of bony landmarks that are always present in human studies. It was found that reducing the range of hip motion from 30 degrees to 15 degrees did significantly increase hip joint center location errors, but that restricting motion to a single plane did not. The magnitudes of these errors, however, even in the least accurate cases, were smaller than those previously reported for either the functional method or other methods based on pelvis measurements of living subjects and cadaver specimens. Neither increasing the number of motion data observations nor analyzing the motion of a single thigh marker (rather than the centroid of multiple markers) was found to significantly increase error. The results of this study (1) imply that the limited range of motion that is often evident in subjects with hip pathology does not preclude accurate determination of the hip joint center when the functional method is used; and (2) provide guidelines for the use of the functional method in human subjects.     

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.     

Static and dynamic error of a biplanar videoradiography system using marker-based and markerless tracking techniques

The use of biplanar videoradiography technology has become increasingly popular for evaluating joint function in vivo. Two fundamentally different methods are currently employed to reconstruct 3D bone motions captured using this technology. Marker-based tracking requires at least three radio-opaque markers to be implanted in the bone of interest. Markerless tracking makes use of algorithms designed to match 3D bone shapes to biplanar videoradiography data. In order to reliably quantify in vivo bone motion, the systematic error of these tracking techniques should be evaluated. Herein, we present new markerless tracking software that makes use of modern GPU technology, describe a versatile method for quantifying the systematic error of a biplanar videoradiography motion capture system using independent gold standard instrumentation, and evaluate the systematic error of the W.M. Keck XROMM Facility's biplanar videoradiography system using both marker-based and markerless tracking algorithms under static and dynamic motion conditions. A polycarbonate flag embedded with 12 radio-opaque markers was used to evaluate the systematic error of the marker-based tracking algorithm. Three human cadaveric bones (distal femur, distal radius, and distal ulna) were used to evaluate the systematic error of the markerless tracking algorithm. The systematic error was evaluated by comparing motions to independent gold standard instrumentation. Static motions were compared to high accuracy linear and rotary stages while dynamic motions were compared to a high accuracy angular displacement transducer. Marker-based tracking was shown to effectively track motion to within 0.1?mm and 0.1 deg under static and dynamic conditions. Furthermore, the presented results indicate that markerless tracking can be used to effectively track rapid bone motions to within 0.15 deg for the distal aspects of the femur, radius, and ulna. Both marker-based and markerless tracking techniques were in excellent agreement with the gold standard instrumentation for both static and dynamic testing protocols. Future research will employ these techniques to quantify in vivo joint motion for high-speed upper and lower extremity impacts such as jumping, landing, and hammering.     

Minimizing errors associated with calculating the location of the helical axis for spinal motions

One of the more common comparative tools used to quantify the motion of the vertebral joint is the orientation and position of the (finite) helical axis of motion as well as the amount of translation along, and rotation about, this axis. A survey of recent studies that utilize the helical axis of motion to compare motion before and after total disc replacement reveals a lack of concern for the relative errors associated with this metric. Indeed, intrinsic algorithmic and experimental errors that arise when interpreting motion tracking data can easily lead to a misinterpretation of the changes caused by replacement disc devices. While previous studies examining these errors exist, most have overlooked the errors associated with the determination of the location of the helical axis and its intersection with a chosen plane. The purpose of the study presented in this paper was to evaluate the sensitivity and reliability of the helical axis of motion as a comparative tool for kinematically evaluating spinal prostheses devices. To this end, we simulated a typical spine biomechanics testing experiment to investigate the accuracy of calculating the helical axis and its associated parameters using several popular algorithms. The resultant data motivated the development of a new algorithm that is a hybrid of two existing algorithms. The improved accuracy of this hybrid method made it possible to quantify some of the changes to the kinematics of a spinal unit that are induced by distinct placements of a total disc replacement.     

Assessment of the functional method of hip joint center location subject to reduced range of hip motion

Motion analysis of the lower extremities usually requires determination of the location of the hip joint center. The results of several recent studies have suggested that kinematic and kinetic variables calculated from motion analysis data are highly sensitive to errors in hip joint center location. "Functional" methods in which the location of the hip joint center is determined from the relative motion of the thigh and pelvis, rather than from the locations of bony landmarks, are promising but may be ineffective when motion is limited. The aims of the present study were to determine whether the accuracy of the functional method is compromised in young and elderly subjects when limitations on hip motion are imposed and to investigate the possibility of locating the hip joint center using data collected during commonly studied motions (walking, sit-to-stand, stair ascent, stair descent) rather than using data from an ad hoc trial in which varied hip motions are performed. The results of the study suggested that functional methods would result in worst-case hip joint center location errors of 26mm (comparable to the average errors previously reported for joint center location based on bony landmarks) when available hip motion is substantially limited. Much larger errors ( approximately 70mm worst-case), however, resulted when hip joint centers were located from data collected during commonly performed motions, perhaps because these motions are, for the most part, restricted to the sagittal plane. It appears that the functional method can be successfully implemented when range of motion is limited but still requires collection of a special motion trial in which hip motion in both the sagittal and frontal planes is recorded.     

Three-dimensional motion of the upper extremity joints during various activities of daily living

Highly reliable information on the range of motion (ROM) required to perform activities of daily living (ADL) is important to allow rehabilitation professionals to make appropriate clinical judgments of patients with limited ROM of the upper extremity joints. There are, however, no data available that take full account of corrections for gimbal-lock and soft tissue artifacts, which affect estimation errors for joint angles. We used an electromagnetic three-dimensional tracking system (FASTRAK) to measure the three-dimensional ROM of the upper extremity joints of healthy adults (N=20, age range 18–34) during 16 ADL movement tasks. The ROM required for the performance of each movement was shown in terms of the joint angle at the completion of the task, using a new definition of joint angle and regression analysis to compensate for estimation errors. The results of this study may be useful in setting goals for the treatment of upper extremity joint function.     

Non-invasive determination of coupled motion of the scapula and humerus--an in-vitro validation

Measuring the motion of the scapula and humerus with sub-millimeter levels of accuracy in six-degrees-of-freedom (6-DOF) is a challenging problem. The current methods to measure shoulder joint motion via the skin do not produce clinically significant levels of accuracy. Thus, the purpose of this study was to validate a non-invasive markerless dual fluoroscopic imaging system (DFIS) model-based tracking technique for measuring dynamic in-vivo shoulder kinematics. Our DFIS tracks the positions of bones based on their projected silhouettes to contours on recorded pairs of fluoroscopic images. For this study, we compared markerlessly tracking the bones of the scapula and humerus to track them with implanted titanium spheres using a radiostereometric analysis (RSA) while manually manipulating a cadaver specimen's arms. Additionally, we report the repeatability of the DFIS to track the scapula and humerus during dynamic shoulder motion. The difference between the markerless model-based tracking technique and the RSA was ±0.3 mm in translation and ±0.5° in rotation. Furthermore, the repeatability of the markerless DFIS model-based tracking technique for the scapula and humerus was ±0.2 mm and ±0.4°, respectively. The model-based tracking technique achieves an accuracy that is similar to an invasive RSA tracking technique and is highly suited for non-invasively studying the in-vivo motion of the shoulder. This technique could be used to investigate the scapular and humeral biomechanics in both healthy individuals and in patients with various pathologies under a variety of dynamic shoulder motions encountered during the activities of daily living.     

The accuracy of joint surface models constructed from data obtained with an electromagnetic tracking device

Electromagnetic tracking devices are widely used in biomechanics. In this article a method is evaluated to construct models of articular surfaces using an electromagnetic tracking device. First, the accuracy of the space tracker was examined and optimised. Then, from several joint surfaces random points were measured and eighth degree polynomials were fitted to these measurements. To check if the fit converged well, plots of cross sections of the model with corresponding data points were examined. The accuracy of the models was determined by comparing them with computed tomography data and by reproducibility tests. All the fits converged well to the data. The root mean square (RMS) error of the models varied from 0.07 to 0. 18mm, and was proportional to the size and complexity of the surface. This was mainly due to systematic errors made by the space tracker, which were also proportional to the size and complexity of the surface.     

Determining dual Euler angles of the ankle complex in vivo using "flock of birds" electromagnetic tracking device

The dual Euler angles method has been proposed as an alternative approach to describe the general spatial human joint motion. In this study, the dual Euler angles method was applied to study the three-dimensional motion of the ankle complex. The methodology for obtaining dual Euler angles of the ankle complex was developed by using a "Flock of Birds" electromagnetic tracking device. The repeatability of the methodology was studied based on the intertester and intratester variability analysis. Finally kinematic coupling characteristics of the ankle complex during dorsiflexion-plantarflexion, eversion-inversion, and abduction-adduction were analyzed according to the parameters of the dual Euler angles.     

Fusion of radiostereometric analysis data into computed tomography space: application to the elbow joint

Improvement of joint prostheses is dependent upon information concerning the biomechanical properties of the joint. Radiostereometric analysis (RSA) and electromagnetic techniques have been applied in previous cadaver and in vivo studies on the elbow joint to provide valuable information concerning joint motion axes. However, such information is limited to mathematically calculated positions of the axes according to an orthogonal coordinate system and is difficult to relate to individual skeletal anatomy. The aim of this study was to evaluate the in vivo application of a new fusion method to provide three-dimensional (3D) visualization of flexion axes according to bony landmarks. In vivo RSA data of the elbow joint's flexion axes was combined with data obtained by 3D computed tomography (CT). Results were obtained from five healthy subjects after one was excluded due to an instable RSA marker. The median error between imported and transformed RSA marker coordinates and those obtained in the CT volume was 0.22 mm. Median maximal rotation error after transformation of the rigid RSA body to the CT volume was 0.003 degrees . Points of interception with a plane calculated in the RSA orthogonal coordinate system were imported into the CT volume, facilitating the 3D visualization of the flexion axes. This study demonstrates a successful fusion of RSA and CT data, without significant loss of RSA accuracy. The method could be used for relating individual motion axes to a 3D representation of relevant joint anatomy, thus providing important information for clinical applications such as the development of joint prostheses.