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)     

Effects of hip joint centre mislocation on gait analysis results

Methods to determine the hip joint centre (HJC) location are necessary in gait analysis. It has been demonstrated that the methods proposed in the literature involve large mislocation errors. The choice should be made according to the extent by which HJC location errors distort the estimates of angles and resultant moments at the hip and knee joints. This study aimed at quantifying how mislocation errors propagate to these gait analysis results. Angles and moments at the hip and knee joint were calculated for five able-bodied subjects during level walking. The nominal position of the HJC was determined as the position of the pivot point of a 3D movement of the thigh relative to the pelvis. Angles and moments were then re-calculated after having added to HJC co-ordinates errors in the range of +/-30 mm. Angles and moments at both hip and knee joints were affected by HJC mislocation. The hip moments showed the largest propagation error: a 30 mm HJC anterior mislocation resulted in a propagated error into flexion/extension component of about -22%. The hip abduction/adduction moment was found the second largest affected quantity: a 30 mm lateral HJC mislocation produced a propagated error of about -15%. Finally, a 30 mm posterior HJC mislocation produced a delay of the flexion-to-extension timing in the order of 25% of the stride duration. HJC estimation methods with minimum antero-posterior error should therefore be preferred.     

Similarities in the Neural Control of the Shoulder and Elbow Joints Belie Their Structural Differences

Movement of the hand in three dimensional space is primarily controlled by the orientation of the shoulder and elbow complexes. Due to discrepancies in proprioceptive acuity, overlap in motor cortex representation and grossly different anatomies between these joints, we hypothesized that there would be differences in the accuracy of aimed movements between the two joints. Fifteen healthy young adults were tested under four conditions – shoulder motion with the elbow constrained and unconstrained, and elbow motion with the shoulder constrained and unconstrained. End point target locations for each joint were set to coincide with joint excursions of 10, 20 or 30 degrees of either the shoulder or elbow joint. Targets were presented in a virtual reality environment. For the constrained condition, there were no significant differences in angular errors between the two joints, suggesting that the central nervous system represents linked segment models of the limb in planning and controlling movements. For the unconstrained condition, although angle errors were higher, hand position errors remained the same as those of the constrained trials. These results support the idea that the CNS utilizes abundant degrees of freedom to compensate for the potentially different contributions to end-point errors introduced by each joint.     

Statistical shape modelling versus linear scaling: Effects on predictions of hip joint centre location and muscle moment arms in people with hip osteoarthritis

Marker-based dynamic functional or regression methods are used to compute joint centre locations that can be used to improve linear scaling of the pelvis in musculoskeletal models, although large errors have been reported using these methods. This study aimed to investigate if statistical shape models could improve prediction of the hip joint centre (HJC) location. The inclusion of complete pelvis imaging data from computed tomography (CT) was also explored to determine if free-form deformation techniques could further improve HJC estimates. Mean Euclidean distance errors were calculated between HJC from CT and estimates from shape modelling methods, and functional- and regression-based linear scaling approaches. The HJC of a generic musculoskeletal model was also perturbed to compute the root-mean squared error (RMSE) of the hip muscle moment arms between the reference HJC obtained from CT and the different scaling methods. Shape modelling without medical imaging data significantly reduced HJC location error estimates (11.4 ± 3.3 mm) compared to functional (36.9 ± 17.5 mm, p = <0.001) and regression (31.2 ± 15 mm, p = <0.001) methods. The addition of complete pelvis imaging data to the shape modelling workflow further reduced HJC error estimates compared to no imaging (6.6 ± 3.1 mm, p = 0.002). Average RMSE were greatest for the hip flexor and extensor muscle groups using the functional (16.71 mm and 8.87 mm respectively) and regression methods (16.15 mm and 9.97 mm respectively). The effects on moment-arms were less substantial for the shape modelling methods, ranging from 0.05 to 3.2 mm. Shape modelling methods improved HJC location and muscle moment-arm estimates compared to linear scaling of musculoskeletal models in patients with hip osteoarthritis.     

Subject-specific hip geometry and hip joint centre location affects calculated contact forces at the hip during gait

Hip loading affects the development of hip osteoarthritis, bone remodelling and osseointegration of implants. In this study, we analyzed the effect of subject-specific modelling of hip geometry and hip joint centre (HJC) location on the quantification of hip joint moments, muscle moments and hip contact forces during gait, using musculoskeletal modelling, inverse dynamic analysis and static optimization. For 10 subjects, hip joint moments, muscle moments and hip loading in terms of magnitude and orientation were quantified using three different model types, each including a different amount of subject-specific detail: (1) a generic scaled musculoskeletal model, (2) a generic scaled musculoskeletal model with subject-specific hip geometry (femoral anteversion, neck-length and neck-shaft angle) and (3) a generic scaled musculoskeletal model with subject-specific hip geometry including HJC location. Subject-specific geometry and HJC location were derived from CT. Significant differences were found between the three model types in HJC location, hip flexion–extension moment and inclination angle of the total contact force in the frontal plane. No model agreement was found between the three model types for the calculation of contact forces in terms of magnitude and orientations, and muscle moments. Therefore, we suggest that personalized models with individualized hip joint geometry and HJC location should be used for the quantification of hip loading. For biomechanical analyses aiming to understand modified hip joint loading, and planning hip surgery in patients with osteoarthritis, the amount of subject-specific detail, related to bone geometry and joint centre location in the musculoskeletal models used, needs to be considered.     

Effects of gleno-humeral joint centre mislocation on gleno-humeral kinematics and kinetics

The gleno-humeral (GH) rotation centre is typically estimated using predictive or functional methods, however these methods may lead to location errors. This study aimed at determining a location error threshold above which statistically significant changes in the values of kinematic and kinetic GH parameters occur. The secondary aims were to quantify the effects of the direction of mislocation (X, Y or Z axis) of the GH rotation centre on GH kinematic and kinetic parameters.

Shoulder flexion and abduction movements of 11 healthy volunteers were recorded using a standard motion capture system (Vicon, Oxford Metrics Ltd, Oxford, UK), then GH kinematic and kinetic parameters were computed. The true position of the GH rotation centre was determined using a low dose x-ray scanner (EOS? imaging, France) and this position was transferred to the motion data. GH angles and moments were re-computed for each position of the GH rotation centre after errors of up to ± 20?mm were added in increments of ± 5?mm to each axis. The three-dimensional error range was 5?mm to 34.65?mm.

GH joint angle and moment values were significantly altered from 10?mm of three-dimensional error, and from 5?mm of error on individual axes. However, errors on the longitudinal and antero-posterior axes only caused very small alterations of GH joint angle and moment values respectively. Future research should develop methods of GH rotation centre estimation that produce three-dimensional location errors of less than 10?mm to reduce error propagation on GH kinematics and kinetics.     

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.     

Hip joint centre location: An ex vivo study

The human hip joint is normally represented as a spherical hinge and its centre of rotation is used to construct femoral anatomical axes and to calculate hip joint moments. The estimate of the hip joint centre (HJC) position using a functional approach is affected by stereophotogrammetric errors and soft tissue artefacts. The aims of this study were (1) to assess the accuracy with which the HJC position can be located using stereophotogrammetry and (2) to investigate the effects of hip motion amplitude on this accuracy. Experiments were conducted on four adult cadavers. Cortical pins, each equipped with a marker cluster, were implanted in the pelvis and femur, and eight skin markers were attached to the thigh. Recordings were made while an operator rotated the hip joint exploiting the widest possible range of motion. For HJC determination, a proximal and a distal thigh skin marker cluster and two recent analytical methods, the quartic sphere fit (QFS) method and the symmetrical centre of rotation estimation (SCoRE) method, were used. Results showed that, when only stereophotogrammetric errors were taken into account, the analytical methods performed equally well. In presence of soft tissue artefacts, HJC errors highly varied among subjects, methods, and skin marker clusters (between 1.4 and 38.5 mm). As expected, larger errors were found in the subject with larger soft tissue artefacts. The QFS method and the distal cluster performed generally better and showed a mean HJC location accuracy better than 10 mm over all subjects. The analysis on the effect of hip movement amplitude revealed that a reduction of the amplitude does not improve the HJC location accuracy despite a decrease of the artefact amplitude.     

Acetabular morphology and resurfacing design

The bony surfaces of 18 archaeological hemipelves were scanned using a 3D laser surface scanner and CyDir™ software on a Silicon Graphics workstation. The acetabular area was selected and point data from the approximately spherical bone surface saved. These data were input to a MATLAB routine that calculated the radius and centre of the best-fit sphere. The goodness of fit was estimated using the mean and standard deviation of the distance of the bone surface points from the sphere surface. Eight points, at approximately equal distances around the acetabular rim, were selected with reference to bony landmarks. A plane containing three of these points served as an orientation reference plane. The vectors joining the eight rim points to the centre of the best-fit sphere were found. The angles between these vectors and the normal to the reference plane were calculated. Paired angles were summed to give the angle subtended by the acetabular rim in four directions. The overall mean angle was 158° (range of mean angles 145°–173°). The largest individual angles, some exceeding 180°, were in the superior–inferior direction, while the mean angle in the anterior–posterior direction, i.e. that controlling flexion-extension, was 152°. Males had larger subtended angles than females, although the difference was not statistically significant. Simulated reaming increased all angles by approximately 10°. The subtended angles are important parameters in the design of the acetabular component of a hip replacement and particularly important in resurfacing hip replacement when the volume available is tightly constrained.     

A practical solution to reduce soft tissue artifact error at the knee using adaptive kinematic constraints

Musculoskeletal modeling and simulations have vast potential in clinical and research fields, but face various challenges in representing the complexities of the human body. Soft tissue artifact from skin-mounted markers may lead to non-physiological representation of joint motions being used as inputs to models in simulations. To address this, we have developed adaptive joint constraints on five of the six degree of freedom of the knee joint based on in vivo tibiofemoral joint motions recorded during walking, hopping and cutting motions from subjects instrumented with intra-cortical pins inserted into their tibia and femur. The constraint boundaries vary as a function of knee flexion angle and were tested on four whole-body models including four to six knee degrees of freedom. A musculoskeletal model developed in OpenSim simulation software was constrained to these in vivo boundaries during level gait and inverse kinematics and dynamics were then resolved. Statistical parametric mapping indicated significant differences (p < 0.05) in kinematics between bone pin constrained and unconstrained model conditions, notably in knee translations, while hip and ankle flexion/extension angles were also affected, indicating the error at the knee propagates to surrounding joints. These changes to hip, knee, and ankle kinematics led to measurable changes in hip and knee transverse plane moments, and knee frontal plane moments and forces. Since knee flexion angle can be validly represented using skin mounted markers, our tool uses this reliable measure to guide the five other degrees of freedom at the knee and provide a more valid representation of the kinematics for these degrees of freedom.     

Determining the location of hip joint centre: application of a conchoid's shape to the acetabular cartilage surface of magnetic resonance images

Preoperative planning, or intraoperative navigation of hip surgery, including joint-preserving procedures such as osteotomy or joint-replacing procedures such as total arthroplasty, needs to be performed with a high degree of accuracy to ensure a successful outcome. The ability to precisely localise the hip joint rotation centre may prove to be very useful in this context. The human hip joint has been shown to be a conchoid shape, and therefore the accurate location of the hip joint centre (HJC) cannot be computed simply as the centre of a sphere. This study describes a method for determining the HJC by applying a conchoid shape to the acetabular cartilage surface of magnetic resonance images, in order to increase the accuracy of the HJC location which had previously been calculated by a functional method using reconstructed three-dimensional surface bony models. By approximating a conchoid shape to the acetabulum, it was possible to compensate for HJC calculation errors.     

Assessment of anatomical frame variation effect on joint angles: A linear perturbation approach

Although the interpretability and reliability of joint kinematics depends strongly on the accuracy and precision of determining the anatomical frame (AF) orientation, the exact dependency of joint angle error on AF misalignment is still not clear. To fully understand the behavior, this study uses linear perturbations to quantify joint angle error due to known modifications of the AFs, where the joint angles are calculated according to the Cardanic convention. The result is a functional representation of joint angle error with dependence on nominal joint angles and on the orientations of the alternative AFs relative to the nominal AFs. The results are validated using numerical analysis on knee joint angle data during walking. The derived relationship elucidates results from previous work studying this effect and allows AF differences to be inferred by joint angle curves when multiple sets of joint angle curves are collected simultaneously.     

In vivo estimation of the glenohumeral joint centre by functional methods: Accuracy and repeatability assessment

Several algorithms have been proposed for determining the centre of rotation of ball joints. These algorithms are used rather to locate the hip joint centre. Few studies have focused on the determination of the glenohumeral joint centre. However, no studies have assessed the accuracy and repeatability of functional methods for glenohumeral joint centre.This paper aims at evaluating the accuracy and the repeatability with which the glenohumeral joint rotation centre (GHRC) can be estimated in vivo by functional methods. The reference joint centre is the glenohumeral anatomical centre obtained by medical imaging. Five functional methods were tested: the algorithm of Gamage and Lasenby (2002), bias compensated (Halvorsen, 2003), symmetrical centre of rotation estimation (Ehrig et al., 2006), normalization method (Chang and Pollard, 2007), helical axis (Woltring et al., 1985). The glenohumeral anatomical centre (GHAC) was deduced from the fitting of the humeral head.Four subjects performed three cycles of three different movements (flexion/extension, abduction/adduction and circumduction). For each test, the location of the glenohumeral joint centre was estimated by the five methods. Analyses focused on the 3D location, on the repeatability of location and on the accuracy by computing the Euclidian distance between the estimated GHRC and the GHAC. For all the methods, the error repeatability was inferior to 8.25 mm. This study showed that there are significant differences between the five functional methods. The smallest distance between the estimated joint centre and the centre of the humeral head was obtained with the method of Gamage and Lasenby (2002).     

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.     

System and modelling errors in motion analysis: implications for the measurement of the elbow angle in cricket bowling

The system and modelling errors of two fundamentally different motion capture systems (opto-reflective vs. video-based) were tested under various conditions, to determine their ability to accurately measure flexion-extension of the elbow angle in cricket bowling. A mechanical arm was used for all testing, that enabled known elbow flexion-extension and abduction ("carry") angles to be manually set. The root mean squared (RMS) error of 0.6 degrees for the opto-reflective system (Vicon-612) was more accurate in reconstructing a known angle than the video-based system (Peak Motus) (RMS error 2.3 degrees ) in the laboratory, when the same mathematical procedure (model) was applied to calculate the elbow flexion-extension angle. When different models were applied to the raw marker trajectories collected using the video-based system, RMS was lowest for the external marker segmental cluster models (2.3 degrees ) compared with 9.4 degrees for the vector and 4.5 degrees for the projected vector approaches, where joint centres were visually approximated. Real world, field-based comparisons using the video-based system showed that occluding the arm and therefore the shoulder, elbow and wrist joint centre locations by placing a shirt on the arm, increased RMS error for both vector (7.8 degrees -9.0 degrees ) and projected vector (4.3 degrees -5.1 degrees ) modelling approaches.     

Validation of a functional method for the estimation of hip joint centre location

The present study assesses the accuracy with which the subject specific coordinates of the hip joint centre (HJC) in a pelvic anatomical frame can be estimated using different methods. The functional method was applied by calculating the centre of the best sphere described by the trajectory of markers placed on the thigh during several trials of hip rotations. Different prediction methods, proposed in the literature and in the present investigation, which estimate the HJC of adult subjects using regression equations and anthropometric measurements, were also assessed. The accuracy of each of the above-mentioned methods was investigated by comparing their predictions with measurements obtained on a sample of 11 male adult able-bodied volunteers using roentgen stereophotogrammetric analysis (RSA), assumed to provide the true HJC locations. Prediction methods estimated the HJC location at an average rms distance of 25-30 mm. The functional method performed significantly better and estimated HJCs within a rms distance of 13 mm on average. This result may be confidently generalised if the photogrammetric experiment is carefully conducted and an optimal analytical approach used. The method is therefore suggested for use in motion analysis when the subject's hip range of motion is not limited. In addition, the facts that it is not an invasive technique and that it has relatively small and un-biased errors, make it suitable for regression equations identification with no limit to sample size and population typology.     

Measurement of finger joint angles and maximum finger forces during cylinder grip activity

Finger joint angles and finger forces during maximal cylindrical grasping were measured using multi-camera photogrammetry and pressure-sensitive sheets, respectively. The experimental data were collected from four healthy subjects gripping cylinders of five different sizes. For joint angles, an image analysis system was used to digitize slides showing markers. During the calibration of the camera system, both the nonlinear least square and the direct linear transform methods were applied and compared, the former providing the fewer errors; it was used to determine joint angles. Data were collected from the pressure-sensitive grip films by using the same image analysis system as used in the collection of the joint angle data. The method of using pressure-sensitive sheets provided an estimation of the weighted centre of the phalangeal forces. Results indicate that finger flexion angles at the metacarpophalangeal and proximal interphalangeal joints gradually increase as cylinder diameter decreases, but that at the distal interphalangeal joint the angle remains constant throughout all cylinder sizes. It was also found that most of the radio-ulnar deviation and the axial rotation angles at the finger joints deviate from zero, but the deviations are small. For the force measurement, it was found that total finger force increases as cylinder size decreases, and the phalangeal force centres are not located at the mid-points of the phalanges. The data obtained in this experiment would be useful for muscle force predictions and for the design of handles.     

Comparison of hierarchical and six degrees-of-freedom marker sets in analyzing gait kinematics

The objective of this study was to determine how marker spacing, noise, and joint translations affect joint angle calculations using both a hierarchical and a six degrees-of-freedom (6DoF) marker set. A simple two-segment model demonstrates that a hierarchical marker set produces biased joint rotation estimates when sagittal joint translations occur whereas a 6DoF marker set mitigates these bias errors with precision improving with increased marker spacing. These effects were evident in gait simulations where the 6DoF marker set was shown to be more accurate at tracking axial rotation angles at the hip, knee, and ankle.