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.     

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.     

Determination of patient-specific multi-joint kinematic models through two-level optimization

Dynamic patient-specific musculoskeletal models have great potential for addressing clinical problems in orthopedics and rehabilitation. However, their predictive capability is limited by how well the underlying kinematic model matches the patient's structure. This study presents a general two-level optimization procedure for tuning any multi-joint kinematic model to a patient's experimental movement data. An outer level optimization modifies the model's parameters (joint position and orientations) while repeated inner level optimizations modify the model's degrees of freedom given the current parameters, with the goal of minimizing errors between model and experimental marker trajectories. The approach is demonstrated by fitting a 27 parameter, three-dimensional, 12 degree-of-freedom lower-extremity kinematic model to synthetic and experimental movement data for isolated joint (hip, knee, and ankle) and gait (full leg) motions. For noiseless synthetic data, the approach successfully recovered the known joint parameters to within an arbitrarily tight tolerance. When noise was added to the synthetic data, root-mean-square (RMS) errors between known and recovered joint parameters were within 10.4 degrees and 10 mm. For experimental data, RMS marker distance errors were reduced by up to 62% compared to methods that estimate joint parameters from anatomical landmarks. Optimized joint parameters found using a loaded full-leg gait motion differed significantly from those found using unloaded individual joint motions. In the future, this approach may facilitate the creation of dynamic patient-specific musculoskeletal models for predictive clinical applications.     

Evaluation of a new algorithm to determine the hip joint center

Accurately locating the hip joint center is a challenging and important step in many biomechanical investigations. The purpose of this study was to test the accuracy and robustness of a "pivoting" algorithm used to locate the hip center. We tested the performance of this algorithm with data acquired by manipulating a ball and socket model of the hip through several motion patterns. The smallest mean errors of 2.2+/-0.2 mm occurred with a circumduction motion pattern, while the largest errors of 4.2+/-1.3 mm occurred with single-plane motion (e.g., flexion/extension). Introducing random noise with an amplitude of 30 mm increased the errors by only 1.3+/-0.5 mm with a circumduction motion pattern. The pivoting algorithm performs well in the laboratory, and further work is warranted to evaluate its performance in a clinical setting.     

Frontal joint dynamics when initiating stair ascent from a walk versus a stand

Ascending stairs is a challenging activity of daily living for many populations. Frontal plane joint dynamics are critical to understand the mechanisms involved in stair ascension as they contribute to both propulsion and medio-lateral stability. However, previous research is limited to understanding these dynamics while initiating stair ascent from a stand. We investigated if initiating stair ascent from a walk with a comfortable self-selected speed could affect the frontal plane lower-extremity joint moments and powers as compared to initiating stair ascent from a stand and if this difference would exist at consecutive ipsilateral steps on the stairs. Kinematics data using a 3-D motion capture system and kinetics data using two force platforms on the first and third stair treads were recorded simultaneously as ten healthy young adults ascended a custom-built staircase. Data were collected from two starting conditions of stair ascent, from a walk (speed: 1.42 ± 0.21 m/s) and from a stand. Results showed that subjects generated greater peak knee abductor moment and greater peak hip abductor moment when initiating stair ascent from a walk. Greater peak joint moments and powers at all joints were also seen while ascending the second ipsilateral step. Particularly, greater peak hip abductor moment was needed to avoid contact of the contralateral limb with the intermediate step by counteracting the pelvic drop on the contralateral side. This could be important for therapists using stair climbing as a testing/training tool to evaluate hip strength in individuals with documented frontal plane abnormalities (i.e. knee and hip osteoarthritis, ACL injury).     

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.     

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.     

Introducing a new staircase design to quantify healthy knee function during stair ascent and descent

The design, manufacture and validation of a new free standing staircase for motion analysis measurements are described in this paper. The errors in vertical force measurements introduced when the stairs interface with a force plate (FP) are less than 0.6%. The centre of pressure error introduced is less than 0.7 mm compared to the error from the FP. The challenges of introducing stair gait into a clinical trial with a limited number of FPs and time limitations for assessment sessions are addressed by introducing this cost effective solution.

The staircase was used in a study to measure non-pathological knee function of 10 subjects performing stair ascent and descent. The resulting knee kinematics and knee joint moments are in agreement with previous studies. The kinematic and joint moment profiles provide a normative range, which will be useful in future studies for identifying alterations in joint function associated with pathology and intervention.     

Predicting the influence of hip and lumbar flexibility on lifting motions using optimal control

Computational models of the human body coupled with optimization can be used to predict the influence of variables that cannot be experimentally manipulated. Here, we present a study that predicts the motion of the human body while lifting a box, as a function of flexibility of the hip and lumbar joints in the sagittal plane. We modeled the human body in the sagittal plane with joints actuated by pairs of agonist-antagonist muscle torque generators, and a passive hamstring muscle. The characteristics of a stiff, average and flexible person were represented by co-varying the lumbar range-of-motion, lumbar passive extensor-torque and the hamstring passive muscle-force. We used optimal control to solve for motions that simulated lifting a 10 kg box from a 0.3 m height. The solution minimized the total sum of the normalized squared active and passive muscle torques and the normalized passive hamstring muscle forces, over the duration of the motion. The predicted motion of the average lifter agreed well with experimental data in the literature. The change in model flexibility affected the predicted joint angles, with the stiffer models flexing more at the hip and knee, and less at the lumbar joint, to complete the lift. Stiffer models produced similar passive lumbar torque and higher hamstring muscle force components than the more flexible models. The variation between the motion characteristics of the models suggest that flexibility may play an important role in determining lifting technique.     

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.     

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.     

Detection of the hip center in computer-assisted surgery: An in vitro assessment study

The HKA i.e. the angle between the hip, knee and ankle centers is a clinical parameter widely used in orthopedic surgery. It can be intraoperatively assessed with computer-assisted surgery navigation systems by computing the 3D location of these joint centers. The hip center is computed using functional methods but is defined by the experts as the anatomical center of the femoral head. The aim of this in vitro study is therefore to assess, first, the accuracy of these functional methods for the determination of the HKA and, second, their reproducibility. We have analyzed on six cadaveric lower limbs the accuracy and the reproducibility of functional methods and their impact on the HKA values. The anatomical hip center has been used as the reference value. The reproducibility is 5.2 mm for the determination of the functional hip centers. The average impact on the HKA is 1.2° (4° max). Despite a lack of reproducibility of the functional methods, the impact on the HKA is limited. The accuracy of the functional methods on the HKA can therefore be enough for some clinical applications.     

Sensitivity of a subject-specific musculoskeletal model to the uncertainties on the joint axes location

Subject-specific musculoskeletal models have become key tools in the clinical decision-making process. However, the sensitivity of the calculated solution to the unavoidable errors committed while deriving the model parameters from the available information is not fully understood. The aim of this study was to calculate the sensitivity of all the kinematics and kinetics variables to the inter-examiner uncertainty in the identification of the lower limb joint models. The study was based on the computer tomography of the entire lower-limb from a single donor and the motion capture from a body-matched volunteer. The hip, the knee and the ankle joint models were defined following the International Society of Biomechanics recommendations. Using a software interface, five expert anatomists identified on the donor's images the necessary bony locations five times with a three-day time interval. A detailed subject-specific musculoskeletal model was taken from an earlier study, and re-formulated to define the joint axes by inputting the necessary bony locations. Gait simulations were run using OpenSim within a Monte Carlo stochastic scheme, where the locations of the bony landmarks were varied randomly according to the estimated distributions. Trends for the joint angles, moments, and the muscle and joint forces did not substantially change after parameter perturbations. The highest variations were as follows: (a) 11° calculated for the hip rotation angle, (b) 1% BW × H calculated for the knee moment and (c) 0.33 BW calculated for the ankle plantarflexor muscles and the ankle joint forces. In conclusion, the identification of the joint axes from clinical images is a robust procedure for human movement modelling and simulation.     

Repeatability of gait data using a functional hip joint centre and a mean helical knee axis

Repeatability of traditional kinematic and kinetic models is affected by the ability to accurately locate anatomical landmarks (ALs) to define joint centres and anatomical coordinate systems. Numerical methods that define joint centres and axes of rotation independent of ALs may also improve the repeatability of kinematic and kinetic data. The purpose of this paper was to compare the repeatability of gait data obtained from two models, one based on ALs (AL model), and the other incorporating a functional method to define hip joint centres and a mean helical axis to define knee joint flexion/extension axes (FUN model). A foot calibration rig was also developed to define the foot segment independent of ALs. The FUN model produced slightly more repeatable hip and knee joint kinematic and kinetic data than the AL model, with the advantage of not having to accurately locate ALs. Repeatability of the models was similar comparing within-tester sessions to between-tester sessions. The FUN model may also produce more repeatable data than the AL model in subject populations where location of ALs is difficult. The foot calibration rig employed in both the AL and FUN model provided an easy alternative to define the foot segment and obtain repeatable data, without accurately locating ALs on the foot.     

Compensation for inertial and gravity effects in a moving force platform

Force plates for human movement analysis provide accurate measurements when mounted rigidly on an inertial reference frame. Large measurement errors occur, however, when the force plate is accelerated, or tilted relative to gravity. This prohibits the use of force plates in human perturbation studies with controlled surface movements, or in conditions where the foundation is moving or not sufficiently rigid. Here we present a linear model to predict the inertial and gravitational artifacts using accelerometer signals. The model is first calibrated with data collected from random movements of the unloaded system and then used to compensate for the errors in another trial. The method was tested experimentally on an instrumented force treadmill capable of dynamic mediolateral translation and sagittal pitch. The compensation was evaluated in five experimental conditions, including platform motions induced by actuators, by motor vibration, and by human ground reaction forces. In the test that included all sources of platform motion, the root-mean-square (RMS) errors were 39.0 N and 15.3 N m in force and moment, before compensation, and 1.6 N and 1.1 N m, after compensation. A sensitivity analysis was performed to determine the effect on estimating joint moments during human gait. Joint moment errors in hip, knee, and ankle were initially 53.80 N m, 32.69 N m, and 19.10 N m, and reduced to 1.67 N m, 1.37 N m, and 1.13 N m with our method. It was concluded that the compensation method can reduce the inertial and gravitational artifacts to an acceptable level for human gait analysis.     

The efficacy of a video-based marker-less tracking system for gait analysis

Most clinical gait analyses are conducted using motion capture systems which track retro-reflective markers that are placed on key landmarks of the participants. An alternative to a three-dimensional (3D) motion capture, marker-based, optical camera system may be a marker-less video-based tracking system. The aim of our study was to investigate the efficacy of the use of a marker-less tracking system in the calculation of 3D joint angles for possible use in clinical gait analysis. Ten participants walked and jogged on a treadmill and their kinematic data were captured with a marker and marker-less tracking system simultaneously. The hip, knee and ankle angles in the frontal, sagittal and transverse planes were computed. Root Mean Square differences (RMS_diff) between corresponding angles for each participant’s support phase were calculated and averaged to derive the mean within-subject RMS_diff. These within-subject means were averaged to obtain the mean between-subject RMS_diff for the relevant joint angles in the two gait conditions (walking and jogging). The RMS_diff between the two tracking systems was less than 1° for all rotations of the three joint angles of the hip and knee. However, there were slightly larger differences in the ankle joint angles. The results of this study suggest a potential application in gait analysis in clinical settings where observations of anatomical motions may provide meaningful feedback.     

Mandibular kinematics represented by a non-orthogonal floating axis joint coordinate system

There are many methods used to represent joint kinematics (e.g., roll, pitch, and yaw angles; instantaneous center of rotation; kinematic center; helical axis). Often in biomechanics internal landmarks are inferred from external landmarks. This study represents mandibular kinematics using a non-orthogonal floating axis joint coordinate system based on 3-D geometric models with parameters that are "clinician friendly" and mathematically rigorous. Kinematics data for two controls were acquired from passive fiducial markers attached to a custom dental clutch. The geometric models were constructed from MRI data. The superior point along the arc of the long axis of the condyle was used to define the coordinate axes. The kinematic data and geometric models were registered through fiducial markers visible during both protocols. The mean absolute maxima across the subjects for sagittal rotation, coronal rotation, axial rotation, medial-lateral translation, anterior-posterior translation, and inferior-superior translation were 34.10 degrees, 1.82 degrees, 1.14 degrees, 2.31, 21.07, and 6.95 mm, respectively. All the parameters, except for one subject's axial rotation, were reproducible across two motion recording sessions. There was a linear correlation between sagittal rotation and translation, the dominant motion plane, with approximately 1.5 degrees of rotation per millimeter of translation. The novel approach of combining the floating axis system with geometric models succinctly described mandibular kinematics with reproducible and clinician friendly parameters.     

Justification of triaxial goniometer for the measurement of joint rotation

The modified triaxial goniometer was designed based on the gyroscopic concept. This device is capable of measuring the joint three-dimensional angular motion corresponding to a specific set of Eulerian angles. Since the angular measurement by this device is not sequence dependent, it is convenient to provide unique motion patterns of the joint from one position to another. The joint rotational axes are oriented based on identifiable bony landmarks which provide a convenient visualization of the anatomical motion involved. The error caused by the exoskeletal attachment of the instrument can be theoretically corrected. Considering all factors in joint functional evaluation, the triaxial goniometer is a useful and effective method to provide simple real time three-dimensional angular motion measurements.     

Determination of muscle loading at the hip joint for use in pre-clinical testing

The stability of joint endoprostheses depends on the loading conditions to which the implant-bone complex is exposed. Due to a lack of appropriate muscle force data, less complex loading conditions tend to be considered in vitro. The goal of this study was to develop a load profile that better simulates the in vivo loading conditions of a "typical" total hip replacement patient and considers the interdependence of muscle and joint forces. The development of the load profile was based on a computer model of the lower extremities that has been validated against in vivo data. This model was simplified by grouping functionally similar hip muscles. Muscle and joint contact forces were computed for an average data set of up to four patients throughout walking and stair climbing. The calculated hip contact forces were compared to the average of the in vivo measured forces. The final derived load profile included the forces of up to four muscles at the instances of maximum in vivo hip joint loading during both walking and stair climbing. The hip contact forces differed by less than 10% from the peak in vivo value for a "typical" patient. The derived load profile presented here is the first that is based on validated musculoskeletal analyses and seems achievable in an in vitro test set-up. It should therefore form the basis for further standardisation of pre-clinical testing by providing a more realistic approximation of physiological loading conditions.