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.     

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.     

An optimized protocol for hip joint centre determination using the functional method

The functional method identifies the hip joint centre (HJC) as the centre of rotation of the femur relative to the pelvis during an ad hoc movement normally recorded using stereophotogrammetry. This method may be used for the direct determination of subject-specific HJC coordinates or for creating a database from which regression equations may be derived that allow for the prediction of those coordinates. In order to contribute to the optimization of the functional method, the effects of the following factors were investigated: the algorithm used to estimate the HJC coordinates from marker coordinates, the type and amplitude of the movement of the femur relative to the pelvis, marker cluster location and dimensions, and the number of data samples. This was done using a simulation approach which, in turn, was validated using experiments made on a physical analogue of the pelvis and femur system. The algorithms used in the present context were classified and, in some instances, modified in order to optimize both accuracy and computation time, and submitted to a comparative evaluation. The type of movement that allowed for the most accurate results consisted of several flexion-extension/abduction-adduction movements performed on vertical planes of different orientations, followed by a circumduction movement. The accuracy of the HJC estimate improved, with an increasing rate, as a function of the amplitude of these movements. A sharp improvement was found as the number of the photogrammetric data samples used to describe the movement increased up to 500. For optimal performance with the recommended algorithms, markers were best located as far as possible from each other and with their centroid as close as possible to the HJC. By optimizing the analytical and experimental protocol, HJC location error not caused by soft tissue artefacts may be reduced by a factor of ten with a maximal expected value for such error of approximately 1mm.     

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.     

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.     

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.     

Computed tomography-based joint locations affect calculation of joint moments during gait when compared to scaling approaches

Hip joint moments are an important parameter in the biomechanical evaluation of orthopaedic surgery. Joint moments are generally calculated using scaled generic musculoskeletal models. However, due to anatomical variability or pathology, such models may differ from the patient's anatomy, calling into question the accuracy of the resulting joint moments. This study aimed to quantify the potential joint moment errors caused by geometrical inaccuracies in scaled models, during gait, for eight test subjects. For comparison, a semi-automatic computed tomography (CT)-based workflow was introduced to create models with subject-specific joint locations and inertial parameters. 3D surface models of the femora and hemipelves were created by segmentation and the hip joint centres and knee axes were located in these models. The scaled models systematically located the hip joint centre (HJC) up to 33.6 mm too inferiorly. As a consequence, significant and substantial peak hip extension and abduction moment differences were recorded, with, respectively, up to 23.1% and 15.8% higher values in the image-based models. These findings reaffirm the importance of accurate HJC estimation, which may be achieved using CT- or radiography-based subject-specific modelling. However, obesity-related gait analysis marker placement errors may have influenced these results and more research is needed to overcome these artefacts.     

An approach for hip joint center calculation for use in seated postures

In seated postures, such as those in office or automotive seats, locating the hip joint center (HJC) using three markers on the pelvis has been difficult if not impossible. A two-target approach by Bell et al. (J. Biomech. 23 (1990) 617) has been used, however, this method was shown to have inaccuracies when compared to the three-target method developed by Seidel et al. (J. Biomech. 28 (1995) 995). A new two-target method that is specific to the seated environment, has better accuracy than the Bell et al. approach, and is based on the Seidel et al. approach was developed and tested on 13 seated subjects. This new method used three targets and an initial reference file to estimate the HJC location. Once the HJC was located, assumptions were made that the magnitudes between the HJC and the respective anterior superior iliac spine, and the HJC and the respective lateral epicondyle remained constant. The primary concern when evaluating this new method was the affect of seated posture movement, in particular leg splay and spinal flexion on the assumptions. The results obtained with the new approach were compared to Seidel et al. and provided HJC locations with average differences of 3.8, 1.2 and 2.8mm for spinal flexion in the anterior/posterior, medial/lateral and superior/inferior directions, respectively, and 2.3, 1.0 and 1.4mm for knee splay. The proposed method provided better HJC estimation than the Bell et al. approach particularly in the superior/inferior dimensions.     

Hip joint centre localisation with an unscented Kalman filter

The accurate estimation of the hip joint centre (HJC) in gait analysis and in computer assisted orthopaedic procedures is a basic requirement. Functional methods, based on rigid body localisation, assessing the kinematics of the femur during circumduction movements (pivoting) have been used for estimating the HJC. Localising the femoral segment only, as it is usually done in total knee replacement procedure, can give rise to estimation errors, since the pelvis, during the passive pivoting manoeuvre, might undergo spatial displacements. This paper presents the design and test of an unscented Kalman filter that allows the estimation of the HJC by observing the pose of the femur and the 3D coordinates of a single marker attached to the pelvis. This new approach was validated using a hip joint mechanical simulator, mimicking both hard and soft tissues. The algorithm performances were compared with the literature standards and proved to have better performances in case of pelvis translation greater than 8 mm, thus satisfying the clinical requirements of the application.     

Prediction of the hip joint centre in adults, children, and patients with cerebral palsy based on magnetic resonance imaging

The location of the hip joint centre (HJC) is required for calculations of hip moments, the location and orientation of the femur, and muscle lengths and lever arms. In clinical gait analysis, the HJC is normally estimated using regression equations based on normative data obtained from adult populations. There is limited relevant anthropometric data available for children, despite the fact that clinical gait analysis is predominantly used for the assessment of children with cerebral palsy. In this study, pelvic MRI scans were taken of eight adults (ages 23-40), 14 healthy children (ages 5-13) and 10 children with spastic diplegic cerebral palsy (ages 6-13). Relevant anatomical landmarks were located in the scans, and the HJC location in pelvic coordinates was found by fitting a sphere to points identified on the femoral head. The predictions of three common regression equations for HJC location were compared to those found directly from MRI. Maximum absolute errors of 31 mm were found in adults, 26 mm in children, and 31 mm in the cerebral palsy group. Results from regression analysis and leave-one-out cross-validation techniques on the MRI data suggested that the best predictors of HJC location were: pelvic depth for the antero-posterior direction; pelvic width and leg length for the supero-inferior direction; and pelvic depth and pelvic width for the medio-lateral direction. For single-variable regression, the exclusion of leg length and pelvic depth from the latter two regression equations is proposed. Regression equations could be generalised across adults, children and the cerebral palsy group.     

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).     

Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip

Computational models may have the ability to quantify the relationship between hip morphology, cartilage mechanics and osteoarthritis. Most models have assumed the hip joint to be a perfect ball and socket joint and have neglected deformation at the bone-cartilage interface. The objective of this study was to analyze finite element (FE) models of hip cartilage mechanics with varying degrees of simplified geometry and a model with a rigid bone material assumption to elucidate the effects on predictions of cartilage stress. A previously validated subject-specific FE model of a cadaveric hip joint was used as the basis for the models. Geometry for the bone-cartilage interface was either: (1) subject-specific (i.e. irregular), (2) spherical, or (3) a rotational conchoid. Cartilage was assigned either a varying (irregular) or constant thickness (smoothed). Loading conditions simulated walking, stair-climbing and descending stairs. FE predictions of contact stress for the simplified models were compared with predictions from the subject-specific model. Both spheres and conchoids provided a good approximation of native hip joint geometry (average fitting error ～0.5 mm). However, models with spherical/conchoid bone geometry and smoothed articulating cartilage surfaces grossly underestimated peak and average contact pressures (50% and 25% lower, respectively) and overestimated contact area when compared to the subject-specific FE model. Models incorporating subject-specific bone geometry with smoothed articulating cartilage also underestimated pressures and predicted evenly distributed patterns of contact. The model with rigid bones predicted much higher pressures than the subject-specific model with deformable bones. The results demonstrate that simplifications to the geometry of the bone-cartilage interface, cartilage surface and bone material properties can have a dramatic effect on the predicted magnitude and distribution of cartilage contact pressures in the hip joint.     

Sensitivity analysis of hip joint centre estimation based on three-dimensional CT scans

In morphological analysis of the femur, the hip joint centre (HJC) is generally determined using a 3D model of the femoral head based on medical images. However, the portion of the image selected to represent the femoral head may influence the HJC. We determined if this influence invalidates the results of three HJC calculation methods, one of which we introduce here.

To isolate femoral heads in cadaver CT images, thresholds were applied to the distance between femur and acetabulum models. The sensitivity of the HJC to these thresholds and the differences between methods were quantified.

For thresholds between 6 and 9 mm and healthy hips, differences between methods were below 1 mm and all methods were insensitive to threshold changes. For higher thresholds, the fovea capitis femoris disturbed the HJC. In two deformed hips, the new method performed superiorly. We conclude that for normal hips all methods produce valid results.     

Sensitivity analysis of hip joint centre estimation based on three-dimensional CT scans

In morphological analysis of the femur, the hip joint centre (HJC) is generally determined using a 3D model of the femoral head based on medical images. However, the portion of the image selected to represent the femoral head may influence the HJC. We determined if this influence invalidates the results of three HJC calculation methods, one of which we introduce here. To isolate femoral heads in cadaver CT images, thresholds were applied to the distance between femur and acetabulum models. The sensitivity of the HJC to these thresholds and the differences between methods were quantified. For thresholds between 6 and 9?mm and healthy hips, differences between methods were below 1?mm and all methods were insensitive to threshold changes. For higher thresholds, the fovea capitis femoris disturbed the HJC. In two deformed hips, the new method performed superiorly. We conclude that for normal hips all methods produce valid results.     

MRI-based assessment of hip joint translations

To better understand movement limitations and, to some extent, the pathogenesis of osteoarthritis, it is important to quantitatively measure femoroacetabular translations to assess if any joint subluxation occurs. In this paper, we aim at measuring hip joint displacements from magnetic resonance images (MRI) based on a surface registration technique. Because this measurement is related to the location of the hip joint center (HJC), we investigate and compare different HJC estimation approaches based on patient-specific 3D bone models. We estimate the HJC based on a simulated circumduction while minimizing inter-articular distance changes. Measurements of femoroacetabular translations during low amplitude abductions ($80$ samples) and extreme flexions ($60$ samples) in female professional dancers, which is a population potentially exposed to femoroactebaluar impingements, do not show any significant subluxation.     

Patient-specific acetabular shape modelling: comparison among sphere,ellipsoid and conchoid parameterisations

The shape of the human acetabular cup was commonly represented as a hemisphere, but different geometries and patient-specific shapes have been recently proposed in the literature. Our aim was to test the limits of the sphericity assumption by comparing three different parameterisations, namely the sphere, the ellipsoid and the rotational conchoid. Models of hip surfaces, reconstructed from CT scans taken from Caucasian race cadavers and patients, were automatically processed to extract the acetabular surface. Two separate analyses were carried out on the overall acetabular shape, including both the acetabular fossa and the lunate surface (case A) and acetabular cup represented by the lunate surface only (case B). Nonlinear gradient-based and evolutionary computation approaches were implemented for the fitting process. Minor differences from the three idealised geometries were detected (median values of the fitting errors < 1 mm). Nonetheless, the sphere fitting was found to be statistically different from both the ellipsoid (p < 2.50e ? 10) and the conchoid (p < 1.07e ? 09), whereas no statistical difference was detected between the ellipsoid and the conchoid for case A. Significance of the difference between ellipsoid and sphere (p < 4.55e ? 12) and between conchoid and sphere (p < 1.93e ? 11) was found for case B as well. Interestingly, for case B statistical difference was detected between the ellipsoid and the conchoid. In conclusion, we synthesise that the morphology of the overall acetabular cup can be parameterised both with an ellipsoid shape and with a conchoid shape as well with superior quality than the simple sphere. Differently, if one considers just the lunate surface, better fitting results are expected when using the ellipsoid.     

Assessment of a greater trochanter-based method of locating the hip joint center

An alternative, yet unverified, predictive method that places the hip joint center (HJC) at one-quarter of the distance from the ipsolateral to the contralateral greater trochanter (GT method) is currently widely used in the biomechanics community. Therefore, the objective of this study was to confirm that this method is a viable option for estimating HJC coordinates. To accomplish this, HJC coordinates in the pelvic anatomical coordinate system were estimated via the GT method, a functional method, and the regression equations proposed by Bell et al. (1990). The HJC coordinated estimated by the functional method served as a baseline measurement. The results of this study demonstrate that all three methods evaluated offer repeatable estimates of HJC location. In comparison to the functional method, the GT method yielded a HJC estimate that was 7.6 mm medial, 12.2 mm posterior, and 4.8 mm proximal. On the other hand, the Bell regression equations estimated the HJC to be 2.6 mm medial, 7.2 mm posterior, and 21.7 mm proximal relative to the functional method. Additionally, the total 3D difference between the GT and functional methods was 23.5 mm compared to the 30.8 mm difference between the Bell and functional methods. These results suggest that the GT method is a viable option for estimating HJC coordinates.     

In-vitro experimental assessment of a new robust algorithm for hip joint centre estimation

Hip joint centre (HJC) localization is used in several biomedical applications, such as movement analysis and computer-assisted orthopaedic surgery.The purpose of this study was to validate in vitro a new algorithm (MC-pivoting) for HJC computation and to compare its performances with the state-of-the-art (least square approach–LSA). The MC-pivoting algorithm iteratively searches for the 3D coordinates of the point belonging to the femoral bone that, during the circumduction of the femur around the hip joint (pivoting), runs the minimum length trajectory. The algorithm was initialized with a point distribution that can be considered close to a Monte Carlo simulation sampling all around the LSA estimate.The performances of the MC-pivoting algorithm, compared with LSA, were evaluated with tests on cadavers. Dynamic reference frames were applied on both the femur and the pelvis and were tracked by an optical localizer.Results proved the algorithm accuracy (1.7 mm±1.6, 2.3—median value±quartiles), reliability (smaller upper quartiles of the errors distribution with respect to LSA) and robustness (reduction of the errors also in case of large pelvis displacements).     

The effect on conventional gait model kinematics and kinetics of hip joint centre equations in adult healthy gait

The Conventional Gait Model (CGM) needs to benefit from large investigations on localization of the hip joint centre (HJC). Incorrect positions from the native equations were demonstrated (Sangeux et al., 2014; Harrington et al., 2007). More accurate equations were proposed but their impact on kinematics and kinetic CGM outputs was never evaluated. This short communication aims at examining if adoption of new HJC equations would alter standard CGM outputs. Sixteen able bodied participants underwent a full 3-D optoelectronic gait analysis followed by a 3-D ultrasound localization of their hips. Data were processed through the open source python package pyCGM2 replicating kinematic and kinetic processing of the native CGM. Compared with 3D ultrasound location, Hara equations improved the accuracy of sagittal plane kinematics (0.6°) and kinetics (0.02 N m kg⁻¹) for the hip. The worst case participant exhibited Harrington’s equations reached a deviation of 3° for the sagittal kinematics. In the coronal plane, Hara and Harrington equations presented similar differences (1°) for the hip whilst Davis equations had the largest deviation for hip abduction (2.7°) and hip abductor moment (0.10 N m kg⁻¹).Both Harrington and Hara equations improved the CGM location of the HJC. Hara equations improved results in the sagittal plane, plus utilise a single anthropometrics measurement, leg length, that may be more robust. However, neither set of equations had significant effect on kinematics. We reported some effects on kinetics, particularly in the coronal plane, which warrant caution in interpreting outputs using different sets of equations.     

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.