Evaluation of a 3D object registration method for analysis of humeral kinematics

In 3D image-based studies of joint kinematics, 3D registration methods should be automatic, insensitive to segmentation inconsistencies and use coordinate systems that have clinically relevant orientations and locations because this is important for analyzing rotation angles and translation directions. We developed and evaluated a registration method, which is based on the cylindrical geometry of the humerus shaft and an analysis of the inertia moments of the humerus head, in order to consistently and automatically orient the humerus coordinate system according to its anatomy. Registration techniques must be thoroughly evaluated. In this study we used a well-detectable marker as reference, from which coordinate system determination errors of a 3D object could be measured. This allowed us to quantify by means of unique error analysis the translational and rotational errors in terms of how much and about/along which humeral axis errors occurred. The evaluation experiments were performed using virtual rotations of 3D humeral binary image, a humerus model and a 3D image of a volunteer's shoulder. They indicated that the humeral coordinate system determination errors primarily originated from segmentation inconsistencies, which influenced mostly the humeral transverse axes orientation. The error analysis revealed that the developed registration method reduced the effect of manual segmentation inconsistencies on the orientation of the humeral transverse axes up to 37%, in comparison to the commonly used inertia registration.     

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.     

In vivo determination of the anatomical axes of the ankle joint complex: An optimization approach

This study investigates the feasibility of a subject-specific three-dimensional model of the ankle joint complex for kinematic and dynamic analysis of movement. The ankle joint complex was modelled as a three-segment system, connected by two ideal highe joints: the talocrural and the subtalar joint. A mathematical formulation was developed to express the three-dimensional translation and rotation between the foot and shank segments as a function of the two joint angles, and 12 model parameters describing the locations of the joint axes. An optimization method was used to fit the model parameters to three-dimensional kinematic data of foot and shank markers, obtained during test movements throughout the entire physiological range of motion of the ankle joint. The movement of the talus segment, which cannot be measured non-invasively, is not necessary for the analysis.

This optimization method was used to determine the position and orientation of the joint axes in 14 normal subjects. After optimization, the discrepancy between the best fitting model and actual marker kinematics was between 1 and 3 mm for all subjects. The predicted inclination of the subtalar joint axis from the horizontal plane was 37.4±2.7°, and the medial deviation was 18.0±16.2°. The lateral side of the talucrural axis was directed slightly posteriorly (6.8±8.1°), and inclined downward by 7.0±5.4°. These results are similar to previously reported typical results from anatomical, in vitro, studies. Reproducibility was evaluated by repeated testing of one subject, which resulted in variations of about one-fifth of the standard deviation within the group, the inclination of the subtalar joint axis was significantly correlated to the arch height and a radiographic ‘tarsal index’. It is concluded that this optimization method provides the opportunity to incorporate inter-individual anatomical differences into kinematic and dynamic analysis of the ankle joint complex. This allows a more functional interpretation of kinematic data, and more realistic estimates of internal forces.     

Functionally interpretable local coordinate systems for the upper extremity using inertial & magnetic measurement systems

BackgroundInertial Magnetic Measurement Systems (IMMS) are becoming increasingly popular by allowing for measurements outside the motion laboratory. The latest models enable long term, accurate measurement of segment motion in terms of joint angles, if initial segment orientations can accurately be determined. The standard procedure for definition of segmental orientation is based on the measurement of positions of bony landmarks (BLM). However, IMMS do not deliver position information, so an alternative method to establish IMMS based, anatomically understandable segment orientations is proposed.MethodsFor five subjects, IMMS recordings were collected in a standard anatomical position for definition of static axes, and during a series of standardized motions for the estimation of kinematic axes of rotation. For all axes, the intra- and inter-individual dispersion was estimated. Subsequently, local coordinate systems (LCS) were constructed on the basis of the combination of IMMS axes with the lowest dispersion and compared with BLM based LCS.FindingsThe repeatability of the method appeared to be high; for every segment at least two axes could be determined with a dispersion of at most 3.8°. Comparison of IMMS based with BLM based LCS yielded compatible results for the thorax, but less compatible results for the humerus, forearm and hand, where differences in orientation rose to 17.2°.InterpretationAlthough different from the ‘gold standard’ BLM based LCS, IMMS based LCS can be constructed repeatable, enabling the estimation of segment orientations outside the laboratory.ConclusionsA procedure for the definition of local reference frames using IMMS is proposed.     

A three-dimensional musculoskeletal model for gait analysis. Anatomical variability estimates

Three-dimensional coordinates defining the origin and insertion of 40 muscle units, and bony landmarks for osteometric scaling were identified on dry bone specimens. Interspecimen coordinate differences along the anterior-posterior axis of the pelvis and the long bone axes of the pelvis, femur and leg were reduced by scaling but landmark differences along the other axes were not. The coordinates were mapped to living subjects using close-range photogrammetry to locate superficial reference markers. The error of predicting the positions of internal coordinates was assessed by comparing joint centre locations calculated from local axes defining the orientation of segments superior and inferior to a joint. A difference was attributed to: anatomical variability not accounted for by scaling; errors in identifying and placing reference landmarks; the accuracy of locating markers using photogrammetry and error introduced by marker oscillation during movement. Anatomical differences between specimens are one source of error in defining a musculoskeletal model but larger errors are introduced when such models are mapped to living subjects.     

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.     

Evaluation of alternative technical markers for the pelvic coordinate system

In this study, we evaluated alternative technical markers for the motion analysis of the pelvic segment. Thirteen subjects walked eight times while tri-dimensional kinematics were recorded for one stride of each trial. Five marker sets were evaluated, and we compared the tilt, obliquity, and rotation angles of the pelvis segment: (1) standard: markers at the anterior and posterior superior iliac spines (ASIS and PSIS); (2) markers at the PSIS and at the hip joint centers, HJCs (estimated by a functional method and described with clusters of markers at the thighs); (3) markers at the PSIS and HJCs (estimated by a predictive method and described with clusters of markers at the thighs); (4) markers at the PSIS and HJCs (estimated by a predictive method and described with skin-mounted markers at the thighs based on the Helen-Hayes marker set); (5) markers at the PSIS and at the iliac spines. Concerning the pelvic angles, evaluation of the alternative technical marker sets evinced that all marker sets demonstrated similar precision across trials (about 1°) but different accuracies (ranging from 1° to 3°) in comparison to the standard marker set. We suggest that all the investigated marker sets are reliable alternatives to the standard pelvic marker set.     

A comparison of two non-invasive methods for measuring scapular orientation in functional positions

Identification of scapular dyskinesis and evaluation of interventions depend on the ability to properly measure scapulothoracic (ST) motion. The most widely used measurement approach is the acromion marker cluster (AMC), which can yield large errors in extreme humeral elevation and can be inaccurate in children and patient populations. Recently, an individualized regression approach has been proposed as an alternative to the AMC. This technique utilizes the relationship between ST orientation, humerothoracic orientation and acromion process position derived from calibration positions to predict dynamic ST orientations from humerothoracic and acromion process measures during motion. These individualized regressions demonstrated promising results for healthy adults; however, this method had not yet been compared to the more conventional AMC. This study compared ST orientation estimates by the AMC and regression approaches to static ST angles determined by surface markers placed on palpated landmarks in typically developing adolescents performing functional tasks. Both approaches produced errors within the range reported in the literature for skin-based scapular measurement techniques. The performance of the regression approach suffered when applied to positions outside of the range of motion in the set of calibration positions. The AMC significantly underestimated ST internal rotation across all positions and overestimated posterior tilt in some positions. Overall, root mean square errors for the regression approach were smaller than the AMC for every position across all axes of ST motion. Accordingly, we recommend the regression approach as a suitable technique for measuring ST kinematics in functional motion.     

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.     

Comparison of different calculations of three-dimensional joint kinematics from video-based system data

When skin-fixed marker trajectories are used to calculate 3D joint kinematics, the measurement errors (i.e. the difference between the trajectories of the external markers and those of the skeleton) influence to some extent the accuracy of the results, depending both on the calculation method and on the axes about which the rotations are expressed. The purpose of this paper is to compare several expressions of joint angular variations. Two kinematic concepts are used to calculate the changes in the orientation of the distal segment versus the proximal one: the first method consists of computing the components of the spatial attitude vector, the second one deals with the determination of elementary rotations about successive axes. For each of these methods, two sets of three axes are tested to express the results: the axes forming the reference frame affixed to the body segment adjacent to the joint (named fixed axes), and a set consisting of a first axis belonging to the proximal segment, a third axis belonging to the distal segment and a second (floating) axis defined as the cross-product between the two other ones (named mobile axes). To compare these four distinct expressions on the knee joint, numerical simulations of perturbed skin marker trajectories are performed, based on experimental data recorded by a Motion Analysis system during a normal gait cycle. A significant difference is pointed out only for the internal–external rotation angle, for which the best expression — from the viewpoint of sensitivity to experimental errors — is obtained using the components of the attitude vector in a segment-embedded reference frame.     

Can one angle be simply subtracted from another to determine range of motion in three-dimensional motion analysis?

To determine the range of motion of a joint between an initial orientation and a final orientation, it is convenient to subtract initial joint angles from final joint angles, a method referred to as the vectorial approach. However, for three-dimensional movements, the vectorial approach is not mathematically correct. To determine the joint range of motion, the rotation matrix between the two orientations should be calculated, and angles describing the range of motion should be extracted from this matrix, a method referred to as the matrical approach. As the matrical approach is less straightforward to implement, it is of interest to identify situations in which the vectorial approach leads to insubstantial errors. In this study, the vectorial approach was compared to the matrical approach, and theoretical justification was given for situations in which the vectorial approach can reasonably be used. The main findings are that the vectorial approach can be used if (1) the motion is planar (Woltring HJ. 1994. 3-D attitude representation of human joints: a standardization proposal. J Biomech 27(12): 1399–1414), (2) the angles between the final and the initial orientation are small (Woltring HJ. 1991. Representation and calculation of 3-D joint movement. Hum Mov Sci 10(5): 603–616), (3) the angles between the initial orientation of the distal segment and the proximal segment are small and finally (4) when only one large angle occurs between the initial orientation of the distal segment and the proximal segment and the angle sequence is chosen in such a way that this large angle occurs on the first axis of rotation. These findings provide specific criteria to consider when choosing the angle sequence to use for movement analysis.     

Proposal of a thorax segment coordinate system for the 3D kinematical analysis of the cervical spine

The International Society of Biomechanics detailed the recommendations for 3D kinematics of intervertebral movements (Wu, et al. 2002. J Biomech. 35:543–548), but does not specify how to adapt this proposal to describe the kinematics of the cervical spine, between the head and the thorax. The analysis of the literature shows that no consensus exists at the present time on this subject. The objective of our study was to identify the reference points that formed the most rigid triplet allowing building an optimal thorax segment coordinate system (SCS). We thus measured the variations of distances between markers placed on various anatomical landmarks, and then the deformations of the combinations of three markers on different cervical movements of a sample of 10 asymptomatic subjects. The results show that the triplet formed by the sternum and both acromions undergoes less deformation on the flexion–extension movement. For all the other movements (lateral bending, axial rotation and complex movements), the triplet formed by sternum, T3 and TH (positioned on the thoracic spinal column, in a horizontal plane containing the sternal marker), undergoes less deformation. As a conclusion, the optimal triplet to define the thorax SCS for 3D kinematical analysis of the cervical spine is that formed by the markers: sternum, T3 and TH. This triplet makes it possible to define an orthonormal SCS, the axes of which coincide with anatomical directions, i.e. with the functional axes of the movement.     

Proposal of a thorax segment coordinate system for the 3D kinematical analysis of the cervical spine

The International Society of Biomechanics detailed the recommendations for 3D kinematics of intervertebral movements (Wu, et al. 2002. J Biomech. 35:543-548), but does not specify how to adapt this proposal to describe the kinematics of the cervical spine, between the head and the thorax. The analysis of the literature shows that no consensus exists at the present time on this subject. The objective of our study was to identify the reference points that formed the most rigid triplet allowing building an optimal thorax segment coordinate system (SCS). We thus measured the variations of distances between markers placed on various anatomical landmarks, and then the deformations of the combinations of three markers on different cervical movements of a sample of 10 asymptomatic subjects. The results show that the triplet formed by the sternum and both acromions undergoes less deformation on the flexion-extension movement. For all the other movements (lateral bending, axial rotation and complex movements), the triplet formed by sternum, T3 and TH (positioned on the thoracic spinal column, in a horizontal plane containing the sternal marker), undergoes less deformation. As a conclusion, the optimal triplet to define the thorax SCS for 3D kinematical analysis of the cervical spine is that formed by the markers: sternum, T3 and TH. This triplet makes it possible to define an orthonormal SCS, the axes of which coincide with anatomical directions, i.e. with the functional axes of the movement.     

A kinematic model for calculating cup alignment error during total hip arthroplasty

Reduced range of motion, prosthetic impingement, and joint dislocation can all result from misalignment of the acetabular component (i.e. cup alignment) in patients undergoing total hip arthroplasty. Most methods for acetabular component alignment are designed to provide 45-50 degrees abduction and 15-25 degrees of operative anteversion (also known as flexion) with respect to the anterior pelvic plane coordinate system. Yet in most cases, this coordinate system is not assigned properly, due to differences in patient anatomy and improper positioning in the operating room. This misalignment can result in an error in the cup alignment, which can cause the above-mentioned consequences. This work presents a complete mathematical formulation for the analysis of the inaccuracies related to the anterior pelvic plane axes (APPA) definition and their effect on final cup orientation. We do this by introducing a method taken from Kinematics of Mechanisms, and by representing the errors in the APPA as three concurrent axes of rotation, followed by the version and abduction rotations which are defined relative to the previous rotations. We also present a sensitivity analysis of the results by introducing differential changes between sequential coordinate frames, which simulates the errors in the APPA and their effect on cup orientation. Finally, we demonstrate a computational method which provides corrected version and abduction angles to achieve the desired cup orientation, given that the actual measurement errors are known.     

Difference between palpation and optoelectronics recording of scapular motion

The aim of this study is to determine the errors of scapular localisation due to skin relative to bone motion with an optoelectronic tracking system. We compared three-dimensional (3D) scapular positions obtained with skin markers to those obtained through palpation of three scapular anatomical landmarks. The scapular kinematics of nine subjects were collected. Static positions of the scapula were recorded with the right arm elevated at 0°, 40°, 80°, 120° and 160° in the sagittal plane. Palpation and subsequent digitisation of anatomical landmarks on scapula and thorax were done at the same positions. Scapular 3D orientation was also computed during 10 repeated movements of arm elevation between 0° and 180°. Significant differences in scapular kinematics were seen between static positions and palpation when considering anterior/posterior tilt and upward/downward rotation at angles over 120° of humeral elevation and only at 120° for internal/external rotation. There was no significant difference between positions computed during static positions and during the movement for the three scapular orientations. A rotation correction model is presented in order to reduce the errors between static position and palpation measurement.     

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)     

New mathematical definition and calculation of axial rotation of anatomical joints

In the field of joint kinematics, clinical terms such as internal-external, or medical-lateral, rotations are commonly used to express the rotation of a body segment about its own long axis. However, these terms are not defined in a strict mathematical sense. In this paper, a new mathematical definition of axial rotation is proposed and methods to calculate it from the measured Euler angles are given. The definition and methods to calculate it from the measured Euler angles are given. The definition is based on the integration of the component of the angular velocity vector projected onto the long axis of the body segment. First, the absolute axial rotation of a body segment with respect to the stationary coordinate system is defined. This definition is then generalized to give the relative axial rotation of one body segment with respect to the other body segment where the two segments are moving in the three-dimensional space. The well-known Codman's paradox is cited as an example to make clear the difference between the definition so far proposed by other researchers and the new one.     

Registration of 6-DOFs electrogoniometry and CT medical imaging for 3D joint modeling

The paper describes a method in which two data-collecting systems, medical imaging and electrogoniometry, are combined to allow the accurate and simultaneous modeling of both the spatial kinematics and the morphological surface of a particular joint. The joint of interest (JOI) is attached to a Plexiglas jig that includes four metallic markers defining a local reference system (R(GONIO)) for the kinematics data. Volumetric data of the JOI and the R(GONIO) markers are collected from medical imaging. The spatial location and orientation of the markers in the global reference system (R(CT)) of the medical-imaging environment are obtained by applying object-recognition and classification methods on the image dataset. Segmentation and 3D isosurfacing of the JOI are performed to produce a 3D model including two anatomical objects-the proximal and distal JOI segments. After imaging, one end of a custom-made 3D electrogoniometer is attached to the distal segment of the JOI, and the other end is placed at the R(GONIO) origin; the JOI is displaced and the spatial kinematics data is recorded by the goniometer. After recording, data registration from R(GONIO) to R(CT) occurred prior to simulation. Data analysis was performed using both joint coordinate system (JCS) and instantaneous helical axis (IHA).Finally, the 3D joint model is simulated in real time using the experimental kinematics data. The system is integrated into a computer graphics interface, allowing free manipulation of the 3D scene.The overall accuracy of the method has been validated with two other kinematics data collection methods including a 3D digitizer and interpolation of the kinematics data from discrete positions obtained from medical imaging. Validation has been performed on both superior and inferior radio-ulna joints (i.e. prono-supination motion). Maximal RMS error was 1 degrees and 1.2mm on the helical axis rotation and translation, respectively. Prono-supination of the forearm showed a total rotation of 132 degrees for 0.8mm of translation. The method reproducibility using JCS parameters was in average 1 degrees (maximal deviation=2 degrees ) for rotation, and 1mm (maximal deviation=2mm) for translation. In vitro experiments have been performed on both knee joint and ankle joint. Averaged JCS parameters for the knee were 109 degrees, 17 degrees and 4 degrees for flexion, internal rotation and abduction, respectively. Averaged maximal translation values for the knee were 12, 3 and 4mm posteriorly, medially and proximally, respectively. Averaged JCS parameters for the ankle were 43 degrees, 9 degrees and 3 degrees for plantarflexion, adduction and internal rotation, respectively. Averaged maximal translation values for the ankle were 4, 2 and 1mm anteriorly, medially and proximally, respectively.     

Novel approach to ambulatory assessment of human segmental orientation on a wearable sensor system

A new method using a double-sensor difference based algorithm for analyzing human segment rotational angles in two directions for segmental orientation analysis in the three-dimensional (3D) space was presented. A wearable sensor system based only on triaxial accelerometers was developed to obtain the pitch and yaw angles of thigh segment with an accelerometer approximating translational acceleration of the hip joint and two accelerometers measuring the actual accelerations on the thigh. To evaluate the method, the system was first tested on a 2° of freedom mechanical arm assembled out of rigid segments and encoders. Then, to estimate the human segmental orientation, the wearable sensor system was tested on the thighs of eight volunteer subjects, who walked in a straight forward line in the work space of an optical motion analysis system at three self-selected speeds: slow, normal and fast. In the experiment, the subject was assumed to walk in a straight forward way with very little trunk sway, skin artifacts and no significant internal/external rotation of the leg. The root mean square (RMS) errors of the thigh segment orientation measurement were between 2.4° and 4.9° during normal gait that had a 45° flexion/extension range of motion. Measurement error was observed to increase with increasing walking speed probably because of the result of increased trunk sway, axial rotation and skin artifacts. The results show that, without integration and switching between different sensors, using only one kind of sensor, the wearable sensor system is suitable for ambulatory analysis of normal gait orientation of thigh and shank in two directions of the segment-fixed local coordinate system in 3D space. It can then be applied to assess spatio-temporal gait parameters and monitoring the gait function of patients in clinical settings.