Joint kinematics estimation using a multi-body kinematics optimisation and an extended Kalman filter,and embedding a soft tissue artefact model

To reduce the impact of the soft tissue artefact (STA) on the estimate of skeletal movement using stereophotogrammetric and skin-marker data, multi-body kinematics optimisation (MKO) and extended Kalman filters (EKF) have been proposed. This paper assessed the feasibility and efficiency of these methods when they embed a mathematical model of the STA and simultaneously estimate the ankle, knee and hip joint kinematics and the model parameters. A STA model was used that provides an estimate of the STA affecting the marker-cluster located on a body segment as a function of the kinematics of the adjacent joints. The MKO and the EKF were implemented with and without the STA model. To assess these methods, intra-cortical pin and skin markers located on the thigh, shank, and foot of three subjects and tracked during the stance phase of running were used. Embedding the STA model in MKO and EKF reduced the average RMS of marker tracking from 12.6 to 1.6 mm and from 4.3 to 1.9 mm, respectively, showing that a STA model trial-specific calibration is feasible. Nevertheless, with the STA model embedded in MKO, the RMS difference between the estimated and the reference joint kinematics determined from the pin markers slightly increased (from 2.0 to 2.1 deg) On the contrary, when the STA model was embedded in the EKF, this RMS difference was slightly reduced (from 2.0 to 1.7 deg) thus showing a better potentiality of this method to attenuate STA effects and improve the accuracy of joint kinematics estimate.     

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.     

A constrained extended Kalman filter for the optimal estimate of kinematics and kinetics of a sagittal symmetric exercise

This paper presents a method for real-time estimation of the kinematics and kinetics of a human body performing a sagittal symmetric motor task, which would minimize the impact of the stereophotogrammetric soft tissue artefacts (STA). The method is based on a bi-dimensional mechanical model of the locomotor apparatus the state variables of which (joint angles, velocities and accelerations, and the segments lengths and inertial parameters) are estimated by a constrained extended Kalman filter (CEKF) that fuses input information made of both stereophotogrammetric and dynamometric measurement data. Filter gains are made to saturate in order to obtain plausible state variables and the measurement covariance matrix of the filter accounts for the expected STA maximal amplitudes. We hypothesised that the ensemble of constraints and input redundant information would allow the method to attenuate the STA propagation to the end results. The method was evaluated in ten human subjects performing a squat exercise. The CEKF estimated and measured skin marker trajectories exhibited a RMS difference lower than 4 mm, thus in the range of STAs. The RMS differences between the measured ground reaction force and moment and those estimated using the proposed method (9 N and 10 N m) were much lower than obtained using a classical inverse dynamics approach (22 N and 30 N m). From the latter results it may be inferred that the presented method allows for a significant improvement of the accuracy with which kinematic variables and relevant time derivatives, model parameters and, therefore, intersegmental moments are estimated.     

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.     

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).     

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.     

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.     

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.     

Soft tissue displacement over pelvic anatomical landmarks during 3-D hip movements

The position, in a pelvis-embedded anatomical coordinate system, of skin points located over the following anatomical landmarks (AL) was determined while the hip assumed different spatial postures: right and left anterior superior and posterior superior iliac spines, and the sacrum. Postures were selected as occurring during walking and during a flexion–extension and circumduction movement, as used to determine the hip joint centre position (star-arc movement). Five volunteers, characterised by a wide range of body mass indices (22–37), were investigated. Subject-specific MRI pelvis digital bone models were obtained. For each posture, the pose of the pelvis-embedded anatomical coordinate system was determined by registering this bone model with points digitised over bony prominences of the pelvis, using a wand carrying a marker-cluster and stereophotogrammetry. The knowledge of how the position of the skin points varies as a function of the hip posture provided information regarding the soft tissue artefact (STA) that would affect skin markers located over those points during stereophotogrammetric movement analysis. The STA was described in terms of amplitude (relative to the position of the AL during an orthostatic posture), diameter (distance between the positions of the AL which were farthest away from each other), and pelvis orientation. The STA amplitude, exhibited, over all postures, a median [inter-quartile] value of 9[6] and 16[11] mm, for normal and overweight volunteers, respectively. STA diameters were larger for the star-arc than for the walking postures, and the direction was predominantly upwards. Consequent errors in pelvic orientation were in the range 1–9 and 4–11 degrees, for the two groups respectively.     

Propagation of the hip joint centre location error to the estimate of femur vs pelvis orientation using a constrained or an unconstrained approach

To estimate hip joint angles during selected motor tasks using stereophotogrammetric data, it is necessary to determine the hip joint centre position. The question is whether the errors affecting that determination propagate less to the angles estimates when a three degrees of freedom (DOFs) constraint (spherical hinge) is used between femur and pelvis, rather than when the two bones are assumed to be unconstrained (six DOFs). An analytical relationship between the hip joint centre location error and the joint angle error was obtained limited to the planar case. In the 3-D case, a similar relationship was obtained using a simulation approach based on experimental data. The joint angle patterns resulted in a larger distortion using a constrained approach, especially when wider rotations occur. The range of motion of the hip flexion-extension, obtained simulating different location errors and without taking into account soft tissue artefacts, varied approximately 7 deg using a constrained approach and up to 1 deg when calculated with an unconstrained approach. Thus, the unconstrained approach should be preferred even though its estimated three linear DOFs most unlikely carry meaningful information.     

Soft tissue artefacts of skin markers on the lower limb during cycling: Effects of joint angles and pedal resistance

Soft tissue artefacts (STA) are a major error source in skin marker-based measurement of human movement, and are difficult to eliminate non-invasively. The current study quantified in vivo the STA of skin markers on the thigh and shank during cycling, and studied the effects of knee angles and pedal resistance by using integrated 3D fluoroscopy and stereophotogrammetry. Fifteen young healthy adults performed stationary cycling with and without pedal resistance, while the marker data were measured using a motion capture system, and the motions of the femur and tibia/fibula were recorded using a bi-plane fluoroscopy-to-CT registration method. The STAs with respect to crank and knee angles over the pedaling cycle, as well as the within-cycle variations, were obtained and compared between resistance conditions. The thigh markers showed greater STA than the shank ones, the latter varying linearly with adjacent joint angles, the former non-linearly with greater within-cycle variability. Both STA magnitudes and within-cycle variability were significantly affected by pedal resistance (p < 0.05). The STAs appeared to be composed of one component providing the stable and consistent STA patterns and another causing their variations. Mid-segment markers experienced smaller STA ranges than those closer to a joint, but tended to have greater variations primarily associated with pedal resistance and muscle contractions. The current data will be helpful for a better choice of marker positions for data collection, and for developing methods to compensate for both stable and variation components of the STA.     

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.     

Bone orientation and position estimation errors using Cosserat point elements and least squares methods: Application to gait

The aim of this study was to analyze the accuracy of bone pose estimation based on sub-clusters of three skin-markers characterized by triangular Cosserat point elements (TCPEs) and to evaluate the capability of four instantaneous physical parameters, which can be measured non-invasively in vivo, to identify the most accurate TCPEs. Moreover, TCPE pose estimations were compared with the estimations of two least squares minimization methods applied to the cluster of all markers, using rigid body (RBLS) and homogeneous deformation (HDLS) assumptions. Analysis was performed on previously collected in vivo treadmill gait data composed of simultaneous measurements of the gold-standard bone pose by bi-plane fluoroscopy tracking the subjects' knee prosthesis and a stereophotogrammetric system tracking skin-markers affected by soft tissue artifact. Femur orientation and position errors estimated from skin-marker clusters were computed for 18 subjects using clusters of up to 35 markers. Results based on gold-standard data revealed that instantaneous subsets of TCPEs exist which estimate the femur pose with reasonable accuracy (median root mean square error during stance/swing: 1.4/2.8 deg for orientation, 1.5/4.2 mm for position). A non-invasive and instantaneous criteria to select accurate TCPEs for pose estimation (4.8/7.3 deg, 5.8/12.3 mm), was compared with RBLS (4.3/6.6 deg, 6.9/16.6 mm) and HDLS (4.6/7.6 deg, 6.7/12.5 mm). Accounting for homogeneous deformation, using HDLS or selected TCPEs, yielded more accurate position estimations than RBLS method, which, conversely, yielded more accurate orientation estimations. Further investigation is required to devise effective criteria for cluster selection that could represent a significant improvement in bone pose estimation accuracy.     

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.     

Kinematics and kinetics of unanticipated misstep conditions: Femoral fracture implications in the elderly

Most hip fractures are thought to occur after falling during everyday activities. We speculated that hip fractures might also occur because of excessive loading of the hip joint during an unexpected misstep consequently leading to a fall. The aims of this study were to explore the kinematics and kinetics of the lower extremity joints during missteps as compared with regular stepping, as well as to compare the magnitude of forces acting upon the hip joint with the threshold forces expected to fracture the hip. Fourteen healthy adults performed two forward steps on a 17.8 cm high platform under the following four conditions: forward with and without vision, as well as a misstep (the box for the final step unexpectedly removed without participant awareness), and regular stepping down with eyes open. The results revealed no differences between stepping forward with and without vision. When compared with both stepping forward and regular stepping down, the misstep revealed altered joint positions accompanied by increased forces and moments acting upon the hip joint. For example, the peak vertical proximal thigh segment force was 3.05±0.55 BW vs. 1.23±0.14 BW and 0.91±0.09 BW (p<.001; misstep vs. regular stepping down and stepping forward, respectively), while the proximal thigh segment moment in frontal plane was 1.39±0.70 Nm/kg vs. 0.18±0.32 Nm/kg of adduction and 0.16±0.19 Nm/kg of abduction (p<.001). When compared with the literature data, the forces during misstep were within the range of those forces that could result in hip fractures in the elderly. Therefore, it may be possible for the elderly to experience hip/proximal femur fractures during missteps prior to falling.     

Effect of various upper limb multibody models on soft tissue artefact correction: A case study

Soft tissue artefacts (STA) introduce errors in joint kinematics when using cutaneous markers, especially on the scapula. Both segmental optimisation and multibody kinematics optimisation (MKO) algorithms have been developed to improve kinematics estimates. MKO based on a chain model with joint constraints avoids apparent joint dislocation but is sensitive to the biofidelity of chosen joint constraints. Since no recommendation exists for the scapula, our objective was to determine the best models to accurately estimate its kinematics. One participant was equipped with skin markers and with an intracortical pin screwed in the scapula. Segmental optimisation and MKO for 24-chain models (including four variations of the scapulothoracic joint) were compared against the pin-derived kinematics using root mean square error (RMSE) on Cardan angles. Segmental optimisation led to an accurate scapula kinematics (1.1° ≤ RMSE ≤ 3.3°) even for high arm elevation angles. When MKO was applied, no clinically significant difference was found between the different scapulothoracic models (0.9° ≤ RMSE ≤ 4.1°) except when a free scapulothoracic joint was modelled (1.9° ≤ RMSE ≤ 9.6°). To conclude, using MKO as a STA correction method was not more accurate than segmental optimisation for estimating scapula kinematics.     

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.     

Accuracy map of an optical motion capture system with 42 or 21 cameras in a large measurement volume

Optical motion capture is commonly used in biomechanics to measure human kinematics. However, no studies have yet examined the accuracy of optical motion capture in a large capture volume (>100 m³), or how accuracy varies from the center to the extreme edges of the capture volume. This study measured the dynamic 3D errors of an optical motion capture system composed of 42 OptiTrack Prime 41 cameras (capture volume of 135 m³) by comparing the motion of a single marker to the motion reported by a ThorLabs linear motion stage. After spline interpolating the data, it was found that 97% of the capture area had error below 200 μm. When the same analysis was performed using only half (21) of the cameras, 91% of the capture area was below 200 μm of error. The only locations that exceeded this threshold were at the extreme edges of the capture area, and no location had a mean error exceeding 1 mm. When measuring human kinematics with skin-mounted markers, uncertainty of marker placement relative to underlying skeletal features and soft tissue artifact produce errors that are orders of magnitude larger than the errors attributed to the camera system itself. Therefore, the accuracy of this OptiTrack optical motion capture system was found to be more than sufficient for measuring full-body human kinematics with skin-mounted markers in a large capture volume (>100 m³).     

An innovative application of a small-scale motion analysis technique to quantify human skin deformation in vivo

This study highlights a new experimental method developed to measure full-field deformation of human skin in vivo. The technique uses a small-scale Qualisys (Sweden) 3D motion capture system and an array of reflective markers placed on the forearm of five healthy volunteers. A load of up to 1.5 N was applied to induce skin deformation by pulling a fine wire attached to the centre of the marker configuration. Loading and marker displacements were recorded simultaneously. 3D marker trajectory data was generated for three different load directions. Tests were repeated to investigate accuracy and repeatability. Calibration results indicate the accuracy of the motion capture system with an average residual of 0.05 mm. The procedure was found to be repeatable and accurate for five repeated tests of measured displacements with a maximum variance of 5%. Experimental data are presented to demonstrate robustness and the ability to produce significant outputs. For all five subjects, at 1 N load, the mean and standard deviations of skin axial and lateral displacements were found to be 11.7±1.6 mm and 12.3±3.3 mm, respectively. The axial displacements ratio (u₉₀/u₀) ranges from 0.63 to 1.45 with mean±standard deviation of 0.982±0.34 and 0.982±0.32 for left and right arms, respectively. The experiments generated useful and accurate data that can be used to study the viscoelastic, hyperelastic or anisotropic behaviour of human skin. The measured displacements will be analysed further to determine the mechanical properties of skin using inverse Finite Element Analysis and Ogden model.     

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).