Methodological factors affecting joint moments estimation in clinical gait analysis: a systematic review
© The Author(s) 2017
Received: 2 March 2017
Accepted: 8 August 2017
Published: 18 August 2017
Quantitative gait analysis can provide a description of joint kinematics and dynamics, and it is recognized as a clinically useful tool for functional assessment, diagnosis and intervention planning. Clinically interpretable parameters are estimated from quantitative measures (i.e. ground reaction forces, skin marker trajectories, etc.) through biomechanical modelling. In particular, the estimation of joint moments during motion is grounded on several modelling assumptions: (1) body segmental and joint kinematics is derived from the trajectories of markers and by modelling the human body as a kinematic chain; (2) joint resultant (net) loads are, usually, derived from force plate measurements through a model of segmental dynamics. Therefore, both measurement errors and modelling assumptions can affect the results, to an extent that also depends on the characteristics of the motor task analysed (i.e. gait speed). Errors affecting the trajectories of joint centres, the orientation of joint functional axes, the joint angular velocities, the accuracy of inertial parameters and force measurements (concurring to the definition of the dynamic model), can weigh differently in the estimation of clinically interpretable joint moments. Numerous studies addressed all these methodological aspects separately, but a critical analysis of how these aspects may affect the clinical interpretation of joint dynamics is still missing. This article aims at filling this gap through a systematic review of the literature, conducted on Web of Science, Scopus and PubMed. The final objective is hence to provide clear take-home messages to guide laboratories in the estimation of joint moments for the clinical practice.
KeywordsInverse dynamics approach Kinematics Dynamics Joint moments Stereophotogrammetry Gait analysis methodology Reproducibility Reliability Sensitivity Error propagation
The first is the so-called inverse dynamics approach (IDA): the human body is represented as a multi-body chain of rigid segments, and Newton–Euler mechanics is applied iteratively to each segment to calculate net internal joint moments and forces [1–4]. Marker trajectories from stereophotogrammetry and ground reaction forces (GRF) from dynamometric platforms (“force platform” in short), are the input to the kinematic and dynamic models of the human body.
In general, the resultant joint moments acting at a joint are generated by a combination of muscle, ligament, and joint contact forces . However, in almost all clinical gait analysis protocols, human joints are represented by either ideal spherical or hinge joint whose centre/axis approximates the joint centre/axis of rotation. Within this modelling assumption and in the hypothesis that friction is negligible, the resultant of the bone-to-bone contact forces passes very close to the geometrical centre/axis of the joint and therefore its contribution to the net moment is commonly neglected. Therefore, as first approximation, it can be assumed that the resultant moment of the intersegmental forces represents an estimate of the overall muscular moment plus the contribution of the ligaments. Following this description, the specificity of bi-articular muscles is disregarded .
IDA also requires the estimation of the body segment inertial parameters (BSIP) (i.e. mass, position of the centre of mass in the segment coordinate system, moments of inertia), usually obtained for a specific subject from generalised anthropometric tables.
A second simplified method requires only segmental/joint kinematics and GRF to estimate external moments. This approach neglects the contribution of the segment inertial and gravitational forces, assuming all the mass concentrated in the body centre of mass, and provides an estimate of joint moments only during the stance phase of gait (when GRF is measured) with minimal computational effort. Despite of its extreme simplicity, this approach has been applied in clinical gait analysis studies, and provided reasonable estimations of joint loadings during the stance phase, when the inertial contribution is minor , particularly for distal joints (ankle and knee) .
It follows that the sources of error can be summarized in four groups: (1) kinematic measures and processing, (2) measure of the GRF and processing, (3) determination of joint model parameters, and (4) estimation of the inertial parameters.
Kinematic errors include, for instance, the errors intrinsic in the measurement system, the soft tissue artefact and the inaccurate localization of anatomical landmarks, with the latter two recognized the most critical [8, 9].
GRF is measured by force platforms as the resultant mechanical interaction between the foot and the ground, described in the form of a 3D force vector applied in the centre of pressure (COP), represented in the platform coordinate system. Force platforms are prone to measurement errors per-se, but their calibration in the stereophotogrammetric coordinate system should also be regarded as a potential source of inaccuracy.
Errors comprised in joint parameters include the position of the joint centres, and the position and direction of the joint axes of rotations. The latter errors have an effect on both joint kinematics and dynamics [10, 11].
Finally, BSIPs can be estimated using several methods, namely predictive equations based on measurements of cadavers or living subjects [12–17], geometric approaches [18, 19], data of living subjects obtained through medical imaging technologies [20–23], or estimates provided by the solution of a non-linear optimization problem [24–26].
Numerous studies analysed, separately or in conjunction, the influence of these sources of error on the estimation of joint moments, but a systematic review of their impact on the clinical interpretability of results is missing. The present systematic review aims at filling this gap by investigating which of the aforementioned factors influence the estimation of joint moments to a greater extent. Whenever possible, implications on sensitivity, reliability and reproducibility of data for clinical use were also addressed.
Inclusion and exclusion criteria
Inclusion criteria considered for the current systematic review
Stereophotogrammetry and force platforms
Gait and selected activities of daily living (stair, chair, squat)
Areas of interest
Kinematics measurements and processing
Force measurements and processing
Joint model parameters
Body segment inertial parameters
Journal papers in English
Cohort under investigation
Healthy and able-bodied human subjects
Articles were searched in Web of Science, PubMed, and Scopus (until February 9, 2017). Keyword search was performed to match words in the title, abstract, or keywords fields. A first general search was performed selecting keywords to define subjects, general topics of interest and motor tasks. Four subsequent refinement searches were performed for kinematics (V.C. and G.V.) and force (R.S.) measurements and processing, joint parameters (A.Ce.), and body segment inertial parameters (S.F.). All Boolean researches are reported in Appendix.
Each reviewer first removed conference proceedings, theses, and duplicate journal references. Secondly, title and abstracts of the remaining papers were evaluated for inclusion based on the relevance to the four areas of search. A full text evaluation was performed if the title and abstract failed to provide adequate information. Finally, a manual screening of the reference lists of all included studies was undertaken to include further eligible studies not retrieved during the systematic database search.
Reliability, reproducibility and sensitivity analyses
Repeatability refers to the variation in repeated measurements made on the same subject under identical conditions, e.g., same method and same rater;
Reproducibility refers to variation in measurements made on a subject under changing conditions, e.g., using different methods. When the changing condition refers to two different methods, this specific type of reproducibility study is commonly referred to as ‘‘method comparison study’’;
Reliability relates the ‘‘magnitude of the measurement error in observed measurements to the inherent variability in the underlying level of the quantity between subjects’’ . Therefore, reliability depends upon the heterogeneity of the population in which the measurements are made. The typical parameters used in reliability analysis are the intra-class correlation coefficients (ICC) or the coefficient of multiple correlation (CMC) widely adopted in human movement analysis ;
Agreement ‘‘quantifies how close two measurements made on the same subject are, and is measured on the same scale as the measurements themselves.’’ Agreement is an intrinsic characteristic of the method(s) and does not depend on the population in which measurements are made, unless bias or measurement precision varies with the true value being measured. Therefore, the measured agreement does not typically need to be recomputed when considering pathological groups, if the distribution of measurement errors is uniform across the range of true values.
To compare the results provided by the different studies, joint moment values were also expressed in % BW * H thus obtaining dimensionless quantities whenever possible. When no information about the subject/s height was reported in the original articles, a reference height of 1.7 m was considered. The results obtained after conversion were reported within brackets and were rounded to the nearest decimal place.
Review selection and identification
Of the 67 papers, 11 were included in more than one area and were analysed multiple times according to the focus of the analysis, but were included only once in Additional file 1: Appendix S1 (on-line material), where the studies identified for inclusion in the systematic review are listed.
The reviewed articles suggest that interactions exist between joint kinematics and the resultant joint moments, the measured/estimated kinematics being indeed one of the principal causes of uncertainty in dynamics estimations . Kinematic errors typically include: apparent marker movements (due to errors in marker reconstruction performed by the optical systems), and real marker movements (due to the interposition of soft tissues between markers and the underlying bone, the so-named soft tissue artifact—STA) . Another source of uncertainty is represented by the identification of anatomical landmarks which, being a subjective procedure, is prone to repeatability issues . Overall, this source of error introduces uncertainties that can assume a considerable importance (6–232% of the estimated torque magnitude: 0.005–0.03% BW * H), these magnitudes being smaller for more distal joints .
In this section, we analyze the influence on IDA results of these three factors, as well as the role of the bone pose estimation and the definition of the coordinate systems, and of the gait protocol adopted.
Measure of marker trajectories
The literature remarks that noise affecting marker trajectories represents the first source of error to be compensated, due to its amplification/propagation during differentiation to calculate velocities and accelerations. This issue is particularly important when dynamics is estimated using kinematics only, without GRF measures . Several methods were described for its compensation: digital filters, splines, spectrum analysis techniques , Kalman smoothing and multi-body kinematics optimization . A sensitivity analysis was performed in  and it was found that filtering kinematic data with a cut-off value of 4.5 Hz improves gait dynamic estimates.
Few studies quantified the effect of soft tissue artifacts of thigh and shank on the knee moments during walking [40, 41], stair ascent  and sit-to-stand  against gold standard measurements. Knee extensor and abduction moments were significantly underestimated in the middle of the stance phase of sit to stand, in correspondence to load increase . This result was confirmed during the load transfer phase of stair ascent, but only for knee extension . Similar trends in magnitude were measured for both moments during the single support phase of walking [40, 41]. Also, Buczek et al.  suggested a similar role for the artifact in underestimating the knee extension moment in the same phase, but only inferring it from the comparison of two marker protocols, including and not including a marker on the lateral epicondyle. It was concluded that the magnitude of the observed differences would not likely affect the clinical interpretation of the data . It must be kept in mind, however, that the soft tissue artifact does not only affect pose estimation, but also the determination of the hip joint centre, when estimated through a functional approach [44, 45]. Errors in this determination, as mentioned in the Joint Model Parameter section, may well influence the clinical interpretation.
Identification of palpable anatomical features
Three studies focused on errors of palpable anatomical landmark positions and, consequently, of anatomical coordinate systems [38, 46, 47]. Silva and Ambrósio  reported that the sensitivity of IDA results to a perturbation in the digitized knee coordinates was associated to errors in the net knee moments of 200-1500 Nm/m on the three axes (corresponding to 0.2–1.2% BW * H). De Groote et al., proved that the uncertainty in locating anatomical landmarks affects joint moments to a larger extent than the uncertainty in BSIPs . Finally, Langenderfer et al. applied a probabilistic method to quantify the effect of the uncertainty in locating anatomical landmarks and BSIPs on joint moments . They concluded that awareness of this uncertainty is crucial in the evaluation of healthy normal and pathologic gait and can improve clinical diagnoses.
Bone-pose estimation and coordinate systems definitions
The articles reviewed highlight that the selection of the coordinate systems (CS), despite arbitrary and not an error per-se, influences IDA results and, possibly, their interpretation. This influence can arise both from the definition of the CS used to describe body segment anatomy and the choice of the CS in which joint moments are expressed. If a multi-body (or single-body) kinematics optimization is used, the segment accelerations are also modified. Moniz-Pereira et al.  proved that lower limb joint dynamics is sensitive to different pose estimation algorithms, although to a lesser extent than joint kinematics, especially for the frontal and transverse planes (max. RMS difference between algorithms: 0.12 Nm/kg corresponding to 0.07% BW * H (35.4%) vs 11.7° (64%), respectively).
The definition of the shank anatomical CS was proved to influence knee extension and abduction moments: knee extension moments had greater peaks when expressed about an anatomical axis following the line of the malleoli than when the moment was reported about the same axis rotated around the shank longitudinal axis to become parallel to the frontal plane of the subject; conversely, this last choice entails significantly greater first peak abduction moment . Similarly, the choice of different anatomical landmarks (ALs) of the distal femur to define the femoral anatomical CS had an impact up to 25% on the knee flexion–extension moment .
For clinical gait analysis, the simple analysis of the sagittal plane moments (2D approach) was often considered appropriate, showing little differences in the overall joint moment patterns when compared to 3D models [50, 51]. Nevertheless, the sagittal view provides only part of the information, especially at the hip level, where abductor moment plays an important role in maintaining trunk balance in the frontal plane.
When a 3D analysis is performed (although all possible CSs for the expression of the net moment vector are mathematically valid), differences in joint moment profiles can be expected depending on the components of this vector being expressed in the global CS or in the proximal, distal or joint CSs [50, 52–57]. It can be argued that joint moments expressed in local CSs may allow interpreting the trajectories in terms of the moments that cause them . Indeed, for able-bodied adult gait, joint moments represented in the global CS and in different anatomical CSs (being it either proximal or distal or a non-orthogonal joint CS), presented significant differences primarily for the transverse and frontal plane joint moments (resulting in about 5% BW * H variability due to CS for key peak moments of hip, knee, and ankle) [56, 57]. Further differences in the transverse and frontal plane joint moments may arise for simulated  or actual pathological gait (resulting in about 20% BW * H variability due to CS for key peak moments of hip, knee, and ankle) . Similar results were obtained in : based on a larger adult sample, differences arose also in the frontal plane, with global CSs generally underestimating adductor muscle moment. Frontal plane moments are also influenced at joint CS level by whether the adduction moment axis follows or does not follow the internal/external rotation of the lower limb . At the ankle level, only for frontal plane the global CS proved to overestimate the invertor moment at midstance and underestimate the late stance evertor moment . Using non-orthogonal CS, either based on the axes used to describe joint kinematics [52, 53], or on generalized coordinates [46, 59], may yield better anatomical insight on the joint structures involved with the joint dynamics. In both cases, the final results depend on whether an orthogonal and non-orthogonal projection of the joint moment on the axes of joint CS are used [13, 52, 53, 60].
Care should, therefore, be taken whenever comparisons between studies are made in which the anatomical CS axes used to define the bone pose or to represent the joint moments are not the same. These differences may influence the clinical interpretation according to the parameter under analysis , although statistical techniques, such as principal component analysis, may help in highlighting pathological features that are independent of the coordinate system selection .
Several stereophotogrammetric protocols have been proposed for clinical gait analysis ; the effect of their differences on joint moment estimation was analyzed during level walking [62–64]. Specifically, excellent intra-session repeatability was obtained for the analyzed protocols, with an excellent reliability in the sagittal plane (CMC > 0.95) and a good reliability in the other two anatomical planes (CMC > 0.67). Kadaba et al.  also found a lower repeatability of knee moments with respect to hip and ankle moments. Similar considerations were also extended to stair climbing using the Kadaba’s protocol , with joint dynamics more reproducible than kinematics, especially for abduction–adduction and internal–external rotation at all joints. A comparison between the Kadaba’s protocol  and a six degrees of freedom model showed that most differences were subtle and unlikely to affect clinical interpretations for normal children, but few substantial differences may deserve further investigation, especially for pathological movements or morphology that may exacerbate model differences .
Inter-laboratory consistency of gait analysis measurements using the same protocol is also an investigated issue. Comparison of normative data, as collected using the same protocol in two clinical gait analysis services, highlighted only slight differences in hip and knee extensor moments and all powers, with RMS differences for the inter-laboratory means of less than 0.1 Nm/kg for joint moments (corresponding to 0.006% BW * H), and 0.21 W/kg for powers . Inter-laboratory consistency was also assessed by testing one subject with five different protocols: higher differences were found for kinematics than for kinetics, the latter circumstance being noticeable due to inter-protocol differences, such as the use of standard IDA instead of using GRF for joint moments calculation [35, 68]. In general, differences of 0.5 Nm/kg were pointed out (corresponding to 0.03% BW * H), which are lower than the established minimum detectable change for gait kinematics and dynamics for healthy adults .
Changes in the protocols have been proposed to improve IDA calculations, either addressing anatomical calibration or soft tissue artifact. For instance, modified versions of the Davis protocol were proposed using additional markers [69, 70], improving the between-day repeatability  and reducing the errors in projecting the joint moment components in the sagittal and frontal planes . Similarly, Petit and colleagues  added three proximal shank markers, improving the definition of the proximal shank which, in turn, reduced the knee moment lever arm and lowered the sagittal knee moment. The same reduction was not observed for the knee ab-adduction moment.
Further modifications to gait protocols were adopted for the foot, increasing the number of segments used for its modeling, with the effect of reducing overestimation of ankle joint powers, typical of single-segment models , or producing a better description of ankle kinematics in the frontal plane during stance. Improvements in kinematics significantly influenced joint dynamics at the upper levels, in particular the peak hip adductor moment . In both  and , additional tracking markers for both forefoot and rearfoot were added to the typical cluster tracking calcaneal–tibial motion.
Optimized IDA estimates and their implications in clinical gait analysis
Discrepancies in joint dynamics due to different IDA computational approaches has been studied in  and knee moment profiles across methods were shown to be different, even though with comparable magnitudes. To overcome this issue, procedures to increase IDA quality were proposed, such as static optimization using a least-square approach, which provided a reduction of about 30% on joint torque errors with respect to the conventional Newton–Euler method . Dynamic optimization models are also used to reconstruct the pose of the body segments under analysis, reducing the consequences of soft tissue artifacts (multi-body kinematics optimization) [38, 76]. This approach, adopting body segment chains with kinematic constraints to model the joints, may be considered adequate for the description of physiological gait. Its adoption is questionable for pathological gait because it alters the joint behavior, that does not follow anymore the kinematic model assumed in the multi-body kinematics optimization.
Ground reaction force
The number of published papers analysing the propagation of uncertainties in the measurement of GRF is small. Only four papers were found investigating this specific problem [34, 35, 77, 78], of which only two specifically addressed the effect of errors superimposed to GRF measurements [77, 78]. None of them took into account the potential additional measurement errors introduced by the calibration of the force platform in the stereophotogrammetric coordinate system.
When dealing with the estimation of joint dynamics, the majority of the literature considers GRF measurements virtually error-free. Little attention is paid to errors that intrinsically characterize any measurement procedure, and even less attention to the potential effect on the biomechanical variables analysed and the resulting clinical interpretation.
Just like any measurement device, force platforms are characterised by a certain measurement accuracy, declared by the producer in the device data-sheet. According to the data-sheet of common commercial force plates, the expected measurement errors can be bounded between 0.2 and 2% of their Full-Scale Output (FSO). Typical values of FSO in gait analysis are 500 N for force components in the platform plane and 2500 N for the orthogonal component. Although not constant throughout the acquisition, errors in the order of 1–10 N and 5–50 N can reasonably occur in the horizontal and vertical components, respectively, accompanied with errors up to 0.01 m in COP coordinates [34, 35, 77, 78].
When GRF is measured in a gait analysis session, other sources of errors can superimpose to those characteristics of a properly functioning device. Platform calibration errors or inaccuracies, inappropriate setting of the platform (e.g. low threshold, sampling frequency), modifications in the behaviour of the electronic components (e.g. cable interference, contacts, electrical inductance resulting from chances in temperature, humidity or simply aging of the device components) can significantly affect the performance of any force platform integrated in a gait analysis laboratory [79–85]: during in situ testing errors superimposed to COP coordinates were found double than the reference ones [82–84]; accuracy decreases as the point of application of the force moves to the platform peripheries , although distributed loads seem to be less affected by this phenomenon than concentrated ones ; the minimum vertical force threshold might be up to 113 N in order to estimate the COP within a distance with the declared SD of 0.003 m . Moreover, the performance of the force platform can differ in dynamic compared to static conditions . Due to the relevance of these measurement uncertainties, a number of methods for the in situ assessment of the performance of force platform have been proposed in the literature [79, 84, 85], as well as possible compensation methods [82, 86].
Therefore, the lack of attention paid to the likelihood of errors in force measurement is somewhat surprising , particularly in the field of gait analysis, where force measurement data are often proposed as a reference for the gait laboratory quality check [87, 88].
It could be argued that the impact of these measurement errors can be negligible when compared to other sources of error and in terms of their propagation to joint moments. This does not seem to be the case, despite the limited amount of available literature . McCaw and DeVita  analysed the effect of errors up to 0.01 m superimposed to COP coordinates in a sagittal model of gait, observing average changes 14% in maximum angular torques (approximately 0.8% BW * H), and up to 13% in the estimation of the flexion–extension transitions time. In their comprehensive analysis of the uncertainties in inverse dynamics solutions, Riemer et al. , pointed out that the values of the maximum estimated uncertainties relative to peak joint torque for the ankle, knee and hip are 6–12% (approximately), 50–105% and 114–232%, respectively, depending on the set of perturbations; these uncertainties result from errors superimposed on kinematics, body inertial parameters and force plate measurements, but for the lower body model, the uncertainties in the distance from the COP to the ankle centre of rotation is one of the major contributors. Pàmies-Vilà et al.  implemented a similar comprehensive analysis on a 2D model of gait, taking into account uncertainties in the measured force components compatible with those declared in the device data-sheet; the error in the ground reaction torque highly affects the results, up to a normalised root mean square error of 52% in the hip torque; this analysis shows that GRF errors produce higher root mean square errors and normalised root mean square errors than those introduced by inaccuracies in BSIP, but similar to those produced by inadequate kinematic processing. Finally, Camargo et al.  analysed the influence of uncertainties in the COP localization on gait dynamics at different velocities, showing that resulting uncertainties on joint moments increase with increasing velocities.
Joint model parameters
Commonly, human joints are modelled either as spherical or hinge joints. Whereas for the hip joint, the functional consistency between the actual joint and the spherical joint model is almost perfect  and therefore a unique centre of rotation exists, this is not true for other human joints. For instance, it was demonstrated that in the knee joint during normal gait the tibiofemoral contact loads contribute substantially to both net extension and adduction moments .
Once a convenient joint model is chosen, this has to be tailored for the specific subject under analysis (joint model calibration). Joint calibration procedure is crucial since errors in the parameter determination (joint centre position and axis position and direction) heavily affect the estimated muscular moment arms and consequently the joint moments and their interpretation. Joint parameters are commonly defined by using regressive equations from palpated external anatomical landmarks [64, 91], functional approaches [92–94], multi-body kinematics optimization techniques  or bio-imaging techniques .
The literature introduced the potential benefits of using functional joint centres and axes instead of palpable anatomical landmarks or regressive joint centres to estimate joint dynamics, producing slightly more repeatable hip and knee joint moments . Several studies have dealt with the effects of errors in the joint parameters identification on the estimation of the lower limb joint moments. Since joint moments cannot be directly measured unless implanting instrumented prostheses  or using force/moment sensors in prosthetic limb of amputees [97–99], a ground truth is rarely available for evaluation. Therefore, the most common solution is to assess changes in the joint moments patterns due to any changes in possible input data and parameter values. This was accomplished either by directly or indirectly perturbing the joint parameters through mathematical simulations or experimentally by determining the joint parameters using different methods.
Details of studies analyzed for the joint model parameters effect on the dynamics estimates
Type of analysis
The effects of HJC perturbation in the range ±30 mm on the resultant moments at the knee and hip was investigated via a mathematical simulation during level walking
The model parameters of the lower limb were perturbed via a Monte Carlo simulation (joint centres ±10 mm; joint axes ±10°) to evaluate the influence on joint torques
Method comparison with gold standard
Both studies compared the joint moment obtained using generic scaled musculoskeletal model  with the HJC location determined using a regressive method  and with subject-specific HJC location derived from CT scan
This study compared hip joint moments as obtained using standardized X-rays and four non-invasive regressive methods in ten healthy adults during gait
Method comparison without gold standard
This study investigated the clinical agreement of four commonly used regression equation sets on 18 healthy pediatric subjects during gait
The study tested the influence of different HJC locations, determined according to three regressive methods and a functional method, on hip and knee joint kinetics during a squat exercise on 15 healthy subjects
The effects of KJC perturbation in the range ±10 mm in the anteroposterior direction was investigated via a mathematical simulation at different walking speed on 18 healthy subjects
Method comparison with gold standard
The knee was described by the planar model and its rotation axis was determined both from skin markers using generic-scaled models and from CT-images of the knee condyles. Eight subjects were analyzed
The effects of different knee axis inclination on knee joint moment estimation were then investigated. The knee was modelled as a hinge joint and both knee joint centre (±10 mm) and axis (±10°) were perturbed via a MonteCarlo simulation
A biomechanical model based on natural coordinates was developed by modelling the knee joint as a revolute joint. Authors conducted a sensitivity analysis by directly perturbing the coordinates of the “knee anatomical point”
The ankle joint was model as a universal joint (two non-intersecting axes) and the effect of errors on the joint parameters estimation were investigated via Monte Carlo simulation
Method comparison with gold standard
Ankle joint moment obtained using generic scaled musculoskeletal model  and with subject-specific ankle joint centre location derived from CT scan. No information about ankle joint and axes determination were provided
Perturbation of markers/ALs positions
A 3D inverse dynamic model of the lower limbs was used to investigate the effect of intra-rater variability in ALs identification. The amount of variability in the ALs identification was described as normal distribution according to experimental observations available in the literature 
Both studies performed a sensitivity analysis using a highly subject-specific muscolo-skeletal model defined from computer tomography  and magnetic resonance . Thanks to the use of high resolution bio-imaging, the uncertainties in the ALs identifications were very small (<2 mm) and therefore errors in joint centres and axes parameters were of one order of magnitude smaller than those observed by using skin markers for ALs locations
This study compared the repeatability of joint moments obtained from two different gait models (inter- and intra-examiner) on ten healthy subjects. The two gait models differed for the identification of the hip joint centre and the knee flexion–extension axis which in the first case were identified from the skin markers position whereas in the second case using a functional approach
The agreement between the joint moments calculated by a 2D and a 3D inverse dynamics models was assessed on 15 healthy subjects during gait recordings. However, since the two models did not share the same joint centres locations differences were expected
The study compared the inter-sessions variability of joint moments obtained with the Plug-in-Gait protocol  with those obtained using a modified version of it including three extra markers on the medial sides to facilitate the identification of the knee and ankle centres and the calculation of the geometrical prediction of the HJC. Twenty-five subjects were analyzed including 14 healthy and 11 with pathological knee varus alignment
Method comparison without gold standard
The study implemented four different body estimators methods: Davis model , a kinematic constrained method , a single-body optimal method and a multi-body kinematics optimization method . Experimental data were collected on a single healthy adult subject. The effects of kinematic constraints on the estimation of both joint kinematics and moments were analysed in terms of marker trajectories residual, joint dislocation and dynamic residuals. No information on the joint centres or axes as determined by each methods are provided
Results and findings of the relevant studies are critically reviewed following the scheme proposed in Table 2 according to their relevance to the specific joint.
The simulation carried out by Stagni and colleagues indicated that errors in the hip joint centre (HJC) location greatly affect hip joint moment . They found that a 30 mm HJC anterior and lateral mislocation caused a mean error of about −22 and −15% in the flexion–extension and abduction–adduction moment components of the corresponding range, respectively (the corresponding values in units of per cent bodyweight (BW) times height (H) are −1.43 and −1.38% BW * H). These errors also produced a delay of about 25% of the stride duration in the flexion–extension moment timing . Reinbolt and colleagues  found, based on the Monte Carlo analyses, errors on the hip flexion–extension and hip abduction–adduction moments consistent with those reported by Stagni and co-workers . Similar conclusions, (i.e. overestimation of the peak hip flexion moment and altered timing of the transition from flexion–extension moment) were reached by Lenaerts and colleagues . Following a similar computational approach, Bartels and colleagues found a systematic HJC location error of 30 mm in the inferior direction and consequently, significant and substantial underestimation of the peak hip extension and abduction moment with respect to the image-based models (up to 23.1 and 15.8%) . Significant differences in knee extension moment were also observed, but these were limited (4.9%). For hip rotation and ankle plantar flexion, differences in joint moments were negligible. The contradictory results between  and  can be explained by the different errors direction affecting the HJC estimates. In fact, whereas Lenaerts and colleagues  found that the estimated HJC was located about 30 mm anteriorly and 21 mm proximally, in the work of Bartels and co-workers , the errors in the HJC location were found mainly inferiorly (median value 18.7 mm) and posteriorly (median value 5.6 mm) and evenly spread along the medio-lateral axis.
Kirkwood and colleagues  considered four regressive methods, and found average maximum errors between 0.02 and −0.21 Nm/kg in the sagittal plane (0.12 to −1.26% BW * H), −0.05 to 0.27 Nm/kg in the frontal plane (−0.30 to 1.62% BW * H) and −0.05 to −0.07 Nm/kg in the transverse plane (−0.30 to −0.42% BW * H). Unfortunately, since the HJC location errors associated to the four regressive methods were not explicitly reported, a direct comparison among regressive methods is difficult. Similarly, Kiernan and colleagues  found, among the regressive methods analysed, maximum differences of approximately 0.1 Nm/kg (0.7% BW * H) in the hip extensor moment and hip abduction moment and no differences in the hip rotation moments. However, clinical statistically significant differences were found when computing the Gait Deviation Index Kinetic (maximum differences equal to 4.36 points with a threshold of clinical significance equal to 3.6 points) . Sinclair and colleagues  found, during a squat exercise, statistically significant differences in both peak hip adduction moment and peak of knee external moment by comparing the HJC estimate as provided by a functional approach with those obtained from regression methods. Unfortunately, HJC locations were not reported.
Knee and ankle joints
Holden and Stanhope  found that an anterior knee joint centre (KJC) errors of ±10 mm caused, at fast gait speed, a maximum variation of the knee flexion–extension moment up to 0.71% BW * H. Furthermore, since knee joint moment decreases by decreasing the gait speed, at low speed KJC error can change the sign of the moment and thus impede the interpretation as flexor or extensor. Similar results were found by Reinbolt and colleagues  (errors on the knee flexion–extension peak equal to 0.92% %BW * H). Similar percentage errors were found for the abduction–adduction knee moment. Ankle joint moment errors were slightly larger for abduction–adduction than for dorsiflexion–plantarflexion. Bartels and colleagues  found small knee extension moment percentage differences between models (<5%) for a median deviation of the knee axis of 2.3°. For the ankle plantar flexion, differences in joint moments were negligible. Silva and Ambrosio  found in simulation a sensitivity of the knee moment similar to that observed for the application point of the external forces.
Langenderfer and colleagues  found that joint moments were also most sensitive to an uncertain localisation of ALs near the joint, because it translates into variability in the joint centres identification (i.e. ankle moments were sensitive to location of the lateral malleolus, knee moments to the femoral epicondyle location, etc.). Reinbolt and colleagues  showed that the variability in the magnitude of the moments increased when moving from the ankle to the knee and hip joints. Largest RMS errors were observed for the hip flexion–extension and abduction–adduction moments (4.14 and 1.06% BW * H), followed by the knee flexion–extension moment mean (RMS error about 0.92% BW * H). Interestingly, when high-resolution bio-imaging techniques were employed for the personalization of the kinematic model, uncertainty in the joint parameters identification were greatly reduced [106, 107].
Besier and co-workers  found, over the ten subjects analysed, highly repeatable joint moment patterns for hip, knee, and ankle in both sagittal and frontal plane (R2 > 0.75). When joint parameters are functionally determined, slight improvements in the hip and ankle joint moments were observed. The statistical significant differences observed in the magnitude of the moments were explained by differences in the joint centre location and joint axes used in 2D and 3D.
The motor tasks evaluated were: level walking (17 studies), walking on treadmill (2 study), and stair ascending/descending (2 studies). All studies except one  assessed the entire stride of the cycle (stance and swing phases).
Details of studies analyzed for the body segment inertial parameters (BSIPs) effect on the dynamics estimates
Affect the dynamics (joint moments and powers)
1 RE  and 1 MI (MR)
BSIPs were significantly different (exception: shank centre of mass, transverse—axis of radius of gyration about the knee)
Statistically significant differences in sagittal-plane of hip and knee moments and powers. Maximum of 0.3 and 0.7% BW * H/s for moment and power at the hip
2 RE (linear multivariate and non-linear) 
Variations up to 8%.
Influence generally small. Propagation error at the hip joint due to errors at the knee and ankle
BSIPs were significantly different (for the mass of the thigh Cheng closer to OM, for centre of mass Cheng and Dempster closer to OM, the moment of inertia no general results among body segment)
Differences in the sagittal plane of hip, knee and ankle moments. Differences smaller in the stance phase with respect to the swing phase
Appreciable differences on the sagittal plane of the hip moment. Some differences on frontal and coronal plane of the hip and knee moments (maximum 21.8% BW * H during stair descending). Larger during the swing phase
Small differences between ex vivo and in vivo data, between data from different populations and among different modality of inertial parameters acquisition. The root mean square value was negligible at the ankle and increased as moving proximally among the joints (maximum 21.8% BW * H in the transverse plane at the hip moment)
1MI (DXA-derived), 1 RE cadaver based 
BSIPs were significantly different (maximum differences were found for the foot: mass 36% lower, centre of mass 15% more proximally, moment of inertia 47% lower)
Small effect during the stance phase, and more of an effect during the swing phase on joint moment on sagittal plane. Root mean square error increased moving proximally (at the hip 0.065 ± 0.043 Nm/kg body weight, corresponding approximatively to 0.4 ± 0.3% BW * H)
1MI (DXA-derived), 1 RE cadaver based 
BSIPs were significantly different (maximum differences were found for moments of inertia 13–70%)
Negligible effect on joint moments of three children (sagittal plane), higher at the hip during swing phase (ranging from 0.03 Nm/kg body weight in the 10 year-old to 0.06 Nm/kg body weight in the 7 year-old, corresponding approximatively to 0.2% BW * H in the 10 year-old and 0.5% BW * H in the 7 year-old)
BSIPs were significantly different (mass, centre of mass, radius and moment of inertis) for each segment for both the cerebral palsy and control groups
Negligible effect on joint moment for both groups (sagittal plane).
Mean absolute variability between BSIP sets was low at the all three levels of the hip, knee and ankle (0.07, 0.04 and 0.01 Nm/kg respectively for the Control group and 0.04, 0.02 and 0.01 Nm/kg respectively for the CP group, corresponding approximatively to 0.5, 0.3 and 0.1% BW * H respectively for the control group and 0.3, 0.2 and 0.1% BW * H respectively for the CP group)
No clinically meaningful difference between GDI-kinetic scores for the different BSIP protocols (maximum difference between BSIP sets was 2.4 and 2.8 points for Control and CP groups, respectively)
Probabilistic analysis (advanced mean value, coefficients of variation: 0.12 for mass, 0.20 for moment of inertia, and 0.08 for centre-of-mass location ratio)
Negligible effect of BSIPs on lower limb joint moments (stance phase, 3D), lower than the effect of anatomical landmarks definition. Variability in the magnitude of moments increased when moving from the ankle to the knee and hip
BSIPs were significantly different: mass of the foot (up to 48.1%), centre of mass of thigh (8.3%), shank (9.7%) and foot, moment of inertia of shank and foot
Negligible effect of BSIPs on lower limb joint moments (3D), higher in swing phase and for hip joint (absolute difference less than 0.09Nm/kg (0.5% BW * H)
BSIPs were significantly different (mass and longitudinal moment of inertia of the thigh)
Negligible effect of BSIPs on lower limb joint moments (root mean square difference 0.7 and 4.3% for the knee and hip, respectively. Difference lower than that caused by a 0.5 Hz adjustment in the cut-off frequency of the filter used to process the data
Monte Carlo simulation (3000 iterations)
BSIPs had a relatively small impact on lower limb joint moments compared to the impact of marker error (marker placement and soft tissue artifact). The only exception was hip flex/ext during the swing period
24 RE studies classified as: cadaveric, living (Caucasian), male living (Caucasian), female living (Caucasian), living (non-Caucasian)
Monte Carlo simulation 2000 iterations (Latin Hypercube, Sampling method)
BSIPs were significantly different between living subjects and cadaver studies (thigh, calf and foot masses up to 15.44%, centre of mass of the foot, and moment of inertia of thigh 36.65%), between Caucasian females and males (calf and foot masses, centre of mass of thigh and foot up to 15.05%, and moment of inertia of thigh 30.86%), and between Caucasian and non-Caucasian subjects (mass and moment of inertia of thigh 21.97%)
Simulation results showed effect limited to the swing phase of the knee and hip. Experimental results showed little effect on joint moments, except for the swing phase. The magnitude of difference in the swing phase due to variability in BSIPs is not much greater than the inter-trial variability. Distal BSIPs have little effect on proximal joint moment
Statistical analysis (sample of errors from a normal distribution, three different maximum errors: 5, 10 and 15%)
The refinement of the BSIPs has little effect in gait analysis results (compared to kinematic data and ground reaction force). Higher effect during the swing phase
BSIPs varied in steps over nine levels by a defined percentage (−40 to 40%) of the baseline value 
Significant differences were found for the mass, centre of mass and moment of inertia for both the leg and thigh segments (more than 40%)
BSIPS variations significantly affect most of the dynamic estimates (particularly the swing phase). The magnitude of these effects was generally less than 1% of body weight
BSIPs were significantly different (from at least 9.73% up to 60%)
BSIPs variation has no effect on knee and ankle joint moments. For the hip joint moments, the effect is significant at slow, preferred and fast cadence (deviations reaching 17.91% and 20.11%, during the swing phase)
Two sets of Monte Carlo analyses with and without noise (variations of BSIP values, together or separately, within 25, 50, 75, and 100% of their allowable bounds obtained from OM)
BSIPs variation had no significant effect on calculated lower-extremity inverse dynamics joint torques (worst average 0.25% BW * H)
BSIPs varied ±30% of the baseline values 
Top-down approach: segment mass has effect on the calculated GRF. No report on lower limb joint moment
Regarding the BSIPs, the only main contributor of the uncertainty in the joint torques was the foot mass, the remaining secondary contributors were the other BSIPs
Perturbation of BSIP from 60 to 140% in steps of 10%
Limited effect of an individual parameter perturbation on the calculated moments (largest effect is found for shank centre of mass, with a ratio of absolute difference in torque and relative parameter perturbation maximally 7.81 Nm for hip flexion moment, corresponding approximatively to 0.6% BW * H). The additional influence of perturbing two parameters simultaneously is small
Perturbation of mass and moment of inertia considering the uncertainty reported by Dempster . Perturbation was performed considering the three segments (foot, shank, thigh) simultaneously and considering each segment independently
Segment mass uncertainty has limited effect on the net joint moment. However, in case of adopted recursive method there is error propagation in proximal direction
Statistically significant differences were observed in the estimated BSIPs not only using different approaches  but also using different data within the same approach . In a comprehensive analysis of 24 regression equation studies, BSIPs were found to be significantly different between living subjects and cadaver studies, between Caucasian females and males, and between Caucasian and non-Caucasian subjects, with highest differences for the moment of inertia of the thigh . Comparing BSIPs values obtained with regression equations and geometric models, the estimated mass and the moment of inertia of the leg and the thigh can vary up to more than 40% . Comparing BSIPs values calculated with dual energy X-ray absorptiometry and regression equation, the maximum difference was found for the foot segment and specifically for the moment of inertia [20, 111].
Analysing how these differences affect the lower limb joint moment estimations during activities of daily life, all studies reported smaller differences in stance compared to the swing phase, both during walking and stair ascending/descending (Table 3). Furthermore, all studies reported smaller effect moving distally from the hip to the ankle joint (Table 3). During walking, the maximum root mean square difference reported at the hip joint moment in the sagittal plane was for self-selected speed and fast-cadence 4.3%  and 20.11% , respectively. During stair ascending/descending, a maximum of 21.8% in the transverse plane at the hip moment was reported .
When the effect of the variation of a specific BSIP was investigated, no common result was found: in two cases the foot mass was the only main contributor of the uncertainty in the joint torques [35, 115], in another study the shank centre of mass has the largest effect  and in a third study distal BSIPs showed little effect on proximal joint moment .
Comparing the results with respect to other sources of error, the effect of BSIPs to the joint moment estimation was lower than that of anatomical landmarks definition , not much greater than that of the inter-trial variability , smaller than that of marker placement and soft tissue artifact , lower than that caused by a 0.5 Hz adjustment in the cut-off frequency of the filter used to process the data , and produced no clinically meaningful difference in the GDI-kinetic scores .
Reliability, reproducibility and sensitivity analyses
A detailed report about reliability, reproducibility and sensitivity of joint moments is reported as additional material. While the single studies have been analysed in the previous sections, it is impossible at present to formulate a global or overall summary, because of a noticeable lack of standardisation in data analysis among Authors. This is unfortunate and calls for initiatives promoting recommended statistical indexes in the field.
Discussion and conclusions
Uncertainty in the measured/estimated kinematics, anatomical calibration, and selection of appropriate joint model parameters, were confirmed as the main causes of errors in IDA results, with a potential serious impact in the clinical context. In addition, according to the limited available literature, the uncertainties in GRF measurement can have a comparable influence on the estimation of joint dynamics during gait. Looking at the role of BSIPs, results showed that, even if the effect of different BSIPs on joint moments was significantly different, it was not clinically meaningful for motor tasks of daily living such as walking, stair ascending/descending in healthy subjects.
The influence of the different mathematical approaches that can be adopted for the implementation of IDA was not analysed in the present review and this is a possible limitation. However, this aspect was deliberately excluded considering that differences in the computational implementations are meant to represent the same underlying mechanical system and are likely to have minor impact on clinical implementation of IDA results. Differences in estimated joint moments during gait  can produce maximal errors up to 25% of the range in flexion extension moment at the hip (negligible on other components), and this error can be regarded as minor for clinical use, when compared to other sources error that can result one order of magnitude higher, and when analysed considering how gait analysis data are interpreted in the clinics, which is comparing curves with coherent (in terms of calculation) reference bands, including inter- and intra-subject dispersion of data. In addition, the majority of IDA implementation for the calculation of joint moments for clinical use is made using the same commercial software, thus nullifying implementation differences.
The systematic analysis of the literature highlighted 67 papers discussing the sources of error affecting joint moments. The quality of the revised papers was evaluated, but no table was reported in the present work because quality is similar among studies: in all papers, the hypotheses were properly outlined and the overall design of the study was appropriate. However, a limited number of subjects was generally included, with effects on the grounding of the final conclusions. Most of these studies were indeed preliminary and/or explorative. The general criterion, followed by the authors of the present review, was only to exclude the works whose quality was considered insufficient and which did not add novel evidence.
The analysis of repeatability, reproducibility and sensitivity of moments across studies was also initiated and a comprehensive list of papers addressing each topic can be found in Additional file 1: Appendix S1 (on-line materials). However, the variety of parameters adopted in the literature is outstanding and preclude the formulation of a consistent overview, other than the analyses reported in the previous sections for kinematics, GRF, inertial parameters and joint model parameters.
Finally, further research is clearly needed to fully evaluate the uncertainties in GRF measurement, eventually analysing the problem in 3D, considering realistic in situ GRF errors, and evaluating the effect on external joint moments.
Compensating for noise affecting marker trajectories especially when dynamics is estimated using kinematics only;
Performing the anatomical calibration, especially for the HJC, since the related uncertainty affects joint moments to a larger extent than other concurring factors. Uncertainties on HJC location between 10 and 30 mm have a great impact on both hip flexion–extension and hip abduction–adduction moments (maximum moment variation between −1.43 and 1.62% BW * H).
Identifying in a consistent manner joint parameter when comparing joint moments;
Interpreting IDA results in the light of the protocol used to estimate them and of the coordinate system used for their expression;
Properly assessing in situ GRF measurement errors, and estimating their potential effect on the final clinical decision process;
not extending the results found for walking and stair ascending/descending motor tasks in case of activities involving higher accelerations and when no ground reaction force is available (e.g. sprinting, kicking…) due to the larger effect on swing phase and proximal joints.
Functional joint centres, when hip calibration movements are not too difficult to perform for the subject and sufficiently large hip joint ranges of motion can be acquired (>30°) . Care should be taken in limiting soft tissue artefacts during the functional tasks required for their estimate. The use of predictive equations is suggested otherwise ;
Modified protocols that include additional markers or, for the foot, additional body segments that were proved to improve repeatability and\or the accuracy of joint moments and powers;
High-resolution bioimaging techniques can be successfully employed to produce personalized musculoskeletal models thus improving joint moment estimation and loading, provided that an adequate model is created;
It may be hoped that the large body of knowledge revised in this review can constitute further momentum to the standardization of the procedures to obtain and report joint moments, as already done by the International Society of Biomechanics in 2002 for the reporting of the joint kinematics [124, 125].
VC, AC, SF and RS contributed in study design, articles review and writing the manuscript. AGC contributed in study design and writing the manuscript. All authors read and approved the final manuscript.
Submitted to Biomedical Engineering online invited Review in agreement with SIAMOC August 2nd, 2017.
Authors are listed in alphabetical order.
The authors declare that they have no competing interests.
Availability of data and materials
All data generated or analysed during this study are included in this published article and its additional information files.
All the authors agree to both proceed with the submission and have Dr. Andrea Giovanni Cutti act as an agent on their behalf in matters pertaining to the publication of the manuscript.
Consent for publication
Ethics approval and consent to participate
No ethical approval was needed for this study.
The authors gratefully acknowledge the contribution of SIAMOC, Italian Society of Motion Analysis in Clinics.
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- Fantozzi S, Garofalo P, Cuti AG, Stagni R. 3D joint moments in transfemoral and transtibial amputees: when is the “ground reaction vector technique” an alternative to inverse dynamics? J Mech Med Biol. 2012;12:1250061.View ArticleGoogle Scholar
- Winter DA. Three dimensional kinematics and kinetics. Biomech. Mot. Control Hum. Mov. 2009. p. 176–99.Google Scholar
- Zatsiorsky VM. Joint torques and forces: the inverse problem of dynamics. Kinet Hum Motion. 2002;2:365–454.Google Scholar
- Vaughan CL. Are joint torques the Holy Grail of human gait analysis? Hum Mov Sci. 1996;15:423–43.View ArticleGoogle Scholar
- Walter JP, Korkmaz N, Fregly BJ, Pandy MG. Contribution of tibiofemoral joint contact to net loads at the knee in gait. J Orthop Res. 2015;33:1054–60.View ArticleGoogle Scholar
- Zatsiorsky VM, Latash ML. What is a joint torque for joints spanned by multiarticular muscles? J Appl Biomech. 1993;9:333–6.View ArticleGoogle Scholar
- Krabbe B, Farkas R, Baumann W. Influence of inertia on intersegment moments of the lower extremity joints. J Biomech. 1997;30:517–9.View ArticleGoogle Scholar
- Della Croce U, Leardini A, Chiari L, Cappozzo A. Human movement analysis using stereophotogrammetry part 4: assessment of anatomical landmark misplacement and its effects on joint kinematics. Gait Posture. 2005;21:226–37.View ArticleGoogle Scholar
- Leardini A, Chiari L, Della U, Cappozzo A. Human movement analysis using stereophotogrammetry part 3. Soft tissue artifact assessment and compensation. Gait Posture. 2005;21:212–25.View ArticleGoogle Scholar
- Cereatti A, Camomilla V, Vannozzi G, Cappozzo A. Propagation of the hip joint centre location error to the estimate of femur vs pelvis orientation using a constrained or an unconstrained approach. J Biomech. 2007;40:1228–34.View ArticleGoogle Scholar
- Stagni R, Leardini A, Cappozzo A, Benedetti MG, Cappello A. Effects of hip joint centre mislocation on gait analysis results. J Biomech. 2000;33:1479–87.View ArticleGoogle Scholar
- de Leva P. Adjustments to Zatsiorsky–Seluyanov’s segment inertia parameters. J Biomech. 1996;29:1223–30.View ArticleGoogle Scholar
- Dumas R, Chèze L, Verriest JP. Adjustments to McConville et al. and Young et al. body segment inertial parameters. J Biomech. 2007;40:543–53.View ArticleGoogle Scholar
- Dempster WT. Space Requirements of the Seated Operator (Technical Report WADC-TR-55-159). Wright-Patterson Air Force Base, OH Aerosp. Med. Res. Lab. 1955.Google Scholar
- Clauser C, McConville J, Young J. Weight, volume and AMRL, center of mass of segments of the human body (Technical Report AMRL-TR-69-70). 1969.Google Scholar
- Winter DA. Antrhopometry. Biomechanics and motor control of human movement. 2nd ed. New York: Wiley; 1990. p. 51–74.Google Scholar
- Zatsiorsky V, Seluyanov V. The mass and inertia characteristics of the main segments of the human body. In: Matsui H, Kobayashi K, editors. Biomechanics, VIII-B. Champaign: Human Kinetics; 1983. p. 1152–9.Google Scholar
- Hatze H. A mathematical model for the computational determination of parameter values of anthropomorphic segments. J Biomech. 1980;13:833–43.View ArticleGoogle Scholar
- Yeadon MR. The simulation of aerial movement—II. A mathematical inertia model of the human body. J Biomech. 1990;23:67–74.View ArticleGoogle Scholar
- Ganley KJ, Powers CM. Determination of lower extremity anthropometric parameters using dual energy X-ray absorptiometry: the influence on net joint moments during gait. Clin Biomech. 2004;19:50–6.View ArticleGoogle Scholar
- Ganley KJ, Powers CM. Anthropometric parameters in children: a comparison of values obtained from dual energy x-ray absorptiometry and cadaver-based estimates. Gait Posture. 2004;19:133–40.View ArticleGoogle Scholar
- Cheng C-K, Chen H-H, Chen C-S, Lee C-L, Chen C-Y. Segment inertial properties of Chinese adults determined from magnetic resonance imaging. Clin Biomech. 2000;15:559–66.View ArticleGoogle Scholar
- Mungiole M, Martin PE. Estimating segment inertial properties: comparison of magnetic resonance imaging with existing methods. J Biomech. 1990;23:1039–46.View ArticleGoogle Scholar
- Vaughan CL, Andrews JG, Hay JG. Selection of body segment parameters by optimization methods. J Biomech Eng. 1982;104:38.View ArticleGoogle Scholar
- Riemer R, Hsiao-Wecksler ET. Improving net joint torque calculations through a two-step optimization method for estimating body segment parameters. J Biomech Eng. 2009;131:11007.Google Scholar
- Chen S-C, Hsieh H-J, Lu T-W, Tseng C-H. A method for estimating subject-specific body segment inertial parameters in human movement analysis. Gait Posture. 2011;33:695–700.View ArticleGoogle Scholar
- Bartlett JW, Frost C. Reliability, repeatability and reproducibility: analysis of measurement errors in continuous variables. Ultrasound Obstet Gynecol. 2008;31:466–75.View ArticleGoogle Scholar
- Ferrari A, Cutti AG, Cappello A. A new formulation of the coefficient of multiple correlation to assess the similarity of waveforms measured synchronously by different motion analysis protocols. Gait Posture. 2010;31:540–2.View ArticleGoogle Scholar
- Bartels W, Demol J, Gelaude F, Jonkers I, Vander Sloten J. Computed tomography-based joint locations affect calculation of joint moments during gait when compared to scaling approaches. Comput Methods Biomech Biomed Eng. 2015;18:1238–51.View ArticleGoogle Scholar
- Lenaerts G, Bartels W, Gelaude F, Mulier M, Spaepen A, Van der Perre G, et al. Subject-specific hip geometry and hip joint centre location affects calculated contact forces at the hip during gait. J Biomech. 2009;42:1246–51.View ArticleGoogle Scholar
- Kiernan D, Walsh M, O’Sullivan R, O’Brien T, Simms CK. The influence of estimated body segment parameters on predicted joint kinetics during diplegic cerebral palsy gait. J Biomech. 2014;47:284–8.View ArticleGoogle Scholar
- Brandon SCE, Deluzio KJ. Robust features of knee osteoarthritis in joint moments are independent of reference frame selection. Clin Biomech. 2011;26:65–70.View ArticleGoogle Scholar
- Newell RS, Hubley-Kozey CL, Stanish WD, Deluzio KJ. Detecting differences between asymptomatic and osteoarthritic gait is influenced by changing the knee adduction moment model. Gait Posture. 2008;27:485–92.View ArticleGoogle Scholar
- Pàmies-Vilà R, Font-Llagunes JM, Cuadrado J, Alonso FJ. Analysis of different uncertainties in the inverse dynamic analysis of human gait. Mech Mach Theory. 2012;58:153–64.View ArticleGoogle Scholar
- Riemer R, Hsiao-Wecksler ET, Zhang X. Uncertainties in inverse dynamics solutions: a comprehensive analysis and an application to gait. Gait Posture. 2008;27:578–88.View ArticleGoogle Scholar
- Lugrís U, Carlín J, Pàmies-Vilà R, Font-Llagunes JM, Cuadrado J. Solution methods for the double-support indeterminacy in human gait. Multibody Syst Dyn. 2013;30:247–63.MathSciNetView ArticleGoogle Scholar
- Alonso FJ, Del Castillo JM, Pintado P. Application of singular spectrum analysis to the smoothing of raw kinematic signals. J Biomech. 2005;38:1085–92.View ArticleGoogle Scholar
- De Groote F, De Laet T, Jonkers I, De Schutter J. Kalman smoothing improves the estimation of joint kinematics and kinetics in marker-based human gait analysis. J Biomech. 2008;41:3390–8.View ArticleGoogle Scholar
- Ren L, Jones RK, Howard D. Whole body inverse dynamics over a complete gait cycle based only on measured kinematics. J Biomech. 2008;41:2750–9.View ArticleGoogle Scholar
- Holden JP, Orsini JA, Siegel KL, Kepple TM, Gerber LH, Stanhope SJ. Surface movement errors in shank kinematics and knee kinetics during gait. Gait Posture. 1997;5:217–27.View ArticleGoogle Scholar
- Manal K, Mcclay I, Richards J, Galinat B, Stanhope S. Knee moment profiles during walking: errors due to soft tissue movement of the shank and the influence of the reference coordinate system. Gait Posture. 2002;15:10–7.View ArticleGoogle Scholar
- Tsai T, Lu T, Kuo M, Lin C. Effects of soft tissue artifacts on the calculated kinematics and kinetics of the knee during stair-ascent. J Biomech. 2011;44:1182–8.View ArticleGoogle Scholar
- Kuo MY, Tsai TY, Lin CC, Lu TW, Hsu HC, Shen WC. Influence of soft tissue artifacts on the calculated kinematics and kinetics of total knee replacements during sit-to-stand. Gait Posture. 2011;33:379–84.View ArticleGoogle Scholar
- De Rosario H, Page Á, Besa A, Valera Á. Propagation of soft tissue artifacts to the center of rotation: a model for the correction of functional calibration techniques. J Biomech. 2013;46:2619–25.View ArticleGoogle Scholar
- Kainz H, Carty CP, Modenese L, Boyd RN, Lloyd DG. Estimation of the hip joint centre in human motion analysis: a systematic review. Clin Biomech. 2015;30:319–29.View ArticleGoogle Scholar
- Silva MPT, Ambrósio JAC. Sensitivity of the results produced by the inverse dynamic analysis of a human stride to perturbed input data. Gait Posture. 2004;19:35–49.View ArticleGoogle Scholar
- Langenderfer JE, Laz PJ, Petrella AJ, Rullkoetter PJ. An efficient probabilistic methodology for incorporating uncertainty in body segment parameters and anatomical landmarks in joint loadings estimated from inverse dynamics. J Biomech Eng. 2008;130:014502/1–7.View ArticleGoogle Scholar
- Moniz-Pereira V, Cabral S, Carnide F, Veloso AP. Sensitivity of joint kinematics and kinetics to different pose estimation algorithms and joint constraints in the elderly. J Appl Biomech. 2014;30:446–60.View ArticleGoogle Scholar
- Thewlis D, Richards J, Bower J. Article discrepancies in knee joint moments using common anatomical frames defined by different palpable landmarks discrepancies in knee joint moments using common anatomical frames defined by different palpable landmarks. J Appl Biomech. 2008;24:185–90.View ArticleGoogle Scholar
- Liu J, Lockhart TE. Comparison of 3D joint moments using local and global inverse dynamics approaches among three different age groups. Gait Posture. 2006;23:480–5.View ArticleGoogle Scholar
- Alkjaer T, Simonsen EB, Dyhre P. Comparison of inverse dynamics calculated by two- and three-dimensional models during walking. Gait Posture. 2001;13:73–7.View ArticleGoogle Scholar
- O’Reilly OM, Sena MP, Feeley BT, Lots JC. On representations for joint moments using a joint coordinate system. J Biomech Eng. 2013;135:114504.View ArticleGoogle Scholar
- Desroches G, Chèze L, Dumas R. Expression of joint moment in the joint coordinate system. J Biomech Eng. 2010;132:1–4.View ArticleGoogle Scholar
- Hunt AE, Smith RM. Interpretation of ankle joint moments during the stance phase of walking: a comparison of two orthogonal axes systems. J Appl Biomech. 2001;17:173–80.View ArticleGoogle Scholar
- Schache AG, Fregly BJ, Crossley KM, Hinman RS, Pandy MG. The effect of gait modification on the external knee adduction moment is reference frame dependent. Clin Biomech. 2008;23:601–8.View ArticleGoogle Scholar
- Schache AG, Baker R. On the expression of joint moments during gait. Gait Posture. 2007;25:440–52.View ArticleGoogle Scholar
- Schache AG, Baker R, Vaughan CL. Differences in lower limb transverse plane joint moments during gait when expressed in two alternative reference frames. J Biomech. 2007;40:9–19.View ArticleGoogle Scholar
- Winter DA, Eng JJ, Ishac MG. A review of kinematic parameters in human walking. In: Craik RLB, Otais CA, editors. Gait analysis: theory and application. St. Louis: Mosby Publisher; 1995. p. 252–70.Google Scholar
- Dumas R, Chèze L. 3D inverse dynamics in non-orthonormal segment coordinate system. Med Biol Eng Comput. 2007;45:315–22.View ArticleGoogle Scholar
- Dumas R, Chèze L. Letter to the editor: joint moments in the joint coordinate system, Euler or dual Euler basis. J Biomech Eng. 2014;136:4–5.View ArticleGoogle Scholar
- Benedetti MG, Catani F, Leardini A, Pignotti E, Giannini S. Data management in gait analysis for clinical applications. Clin Biomech. 1998;13:204–15.View ArticleGoogle Scholar
- Ferrari A, Benedetti MG, Pavan E, Frigo C, Bettinelli D, Rabuffetti M, et al. Quantitative comparison of five current protocols in gait analysis. Gait Posture. 2008;28:207–16.View ArticleGoogle Scholar
- Duffell LD, Hope N, McGregor AH. Comparison of kinematic and kinetic parameters calculated using a cluster-based model and Vicon’s plug-in gait. Proc Inst Mech Eng H J Eng Med. 2014;228:206–10.View ArticleGoogle Scholar
- Kadaba MP, Ramakrishnan HK, Wooten ME, Gainey J, Gorton G, Cochran GVB. Repeatability of kinematic, kinetic, and EMG data in normal adult gait. J Orthop Res. 1989;7:849–60.View ArticleGoogle Scholar
- Yu B, Kienbacher T, Growney ES, Johnson ME, An KN. Reproducibility of the kinematics and kinetics of the lower extremity during normal stair-climbing. J Orthop Res. 1997;15:348–52.View ArticleGoogle Scholar
- Buczek FL, Rainbow MJ, Cooney KM, Walker MR, Sanders JO. Implications of using hierarchical and six degree-of-freedom models for normal gait analyses. Gait Posture. 2010;31:57–63.View ArticleGoogle Scholar
- Pinzone O, Schwartz MH, Thomason P, Baker R. The comparison of normative reference data from different gait analysis services. Gait Posture. 2014;40:286–90.View ArticleGoogle Scholar
- Benedetti MG, Merlo A, Leardini A. Inter-laboratory consistency of gait analysis measurements. Gait Posture. 2013;38:934–9.View ArticleGoogle Scholar
- Stief F, Böhm H, Michel K, Schwirtz A, Döderlein L. Reliability and accuracy in three dimensional gait analysis: a comparison of two lower body protocols. J Appl Biomech. 2013;29:105–11.View ArticleGoogle Scholar
- Yu B, Queen RM, Schrodt LA. Effect of external marker sets on between-day reproducibility of knee kinematics and kinetics in stair climbing and level walking. Res Sport Med. 2003;11:209–18.View ArticleGoogle Scholar
- Petit DJ, Willson JD, Barrios JA. Comparison of stance phase knee joint angles and moments using two different surface marker representations of the proximal shank in walkers and runners. J Appl Biomech. 2014;30:173–8.View ArticleGoogle Scholar
- Bruening DA, Cooney KM, Buczek FL. Gait & posture analysis of a kinetic multi-segment foot model part II : kinetics and clinical implications. Gait Posture. 2012;35:535–40.View ArticleGoogle Scholar
- Hashish R, Samarawickrame SD, Salem GJ. Short communication: a comparison of dorsal and heel plate foot tracking methods on lower extremity dynamics. J Biomech. 2014;47:1211–4.View ArticleGoogle Scholar
- Whatling GM, Evans SL, Holt CA. Comparing different data collection and analysis techniques for quantifying healthy knee joint function during stair ascent and descent. Proc Inst Mech Eng Part H J Eng Med. 2009;223:981–90.View ArticleGoogle Scholar
- Kuo AD. A least-squares estimation approach to improving the precision of inverse dynamics computations. J Biomech Eng. 1998;120:148–59.View ArticleGoogle Scholar
- Silva MPT, Ambrósio JAC. Kinematic data consistency in the inverse dynamic analysis of biomechanical systems. Multibody Syst. Dyn. 2002;8:219–39.MATHView ArticleGoogle Scholar
- McCaw ST, DeVita P. Errors in alignment of center of pressure and foot coordinates affect predicted lower extremity torques. J Biomech. 1995;28:985–8.View ArticleGoogle Scholar
- Camargo JF, Ackermann M, Loss JF, Sacco ICN. Influence of center of pressure estimation errors on 3D inverse dynamics solutions during gait at different velocities. J Appl Biomech. 2013;29:790–7.View ArticleGoogle Scholar
- Fairburn PS, Palmer R, Whybrow J, Fielden S, Jones S. A prototype system for testing force platform dynamic performance. Gait Posture. 2000;12:25–33.View ArticleGoogle Scholar
- Psycharakis SG, Miller S. Estimation of errors in force platform data. Res Q Exerc Sport. 2006;77:514–8.View ArticleGoogle Scholar
- Middleton J, Sinclair P, Patton R. Accuracy of centre of pressure measurement using a piezoelectric force platform. Clin Biomech. 1999;14:357–60.View ArticleGoogle Scholar
- Chockalingam N, Giakas G, Iossifidou A. Do strain gauge force platforms need in situ correction? Gait Posture. 2002;16:233–7.View ArticleGoogle Scholar
- Bobbert MF, Schamhardt HC. Accuracy of determining the point of force application with piezoelectric force plates. J Biomech. 1990;23:705–10.View ArticleGoogle Scholar
- Miyazaki S. A simple and practical method for evaluating overall measurement error of joint moments obtained by a force plate and a position sensing device. Front Med Biol Eng. 1992;4:257–70.Google Scholar
- Browne J, O’Hare N. A quality control procedure for force platform. Physiol Meas. 2000;21:515–24.View ArticleGoogle Scholar
- Cappello A, Bagalà F, Cedraro A, Chiari L. Non-linear re-calibration of force platforms. Gait Posture. 2011;33:724–6.View ArticleGoogle Scholar
- Holden JP, Selbie WS, Stanhope J. A proposed test to support the clinical movement analysis laboratory accreditation process. Gait Posture. 2003;17:205–13.View ArticleGoogle Scholar
- Lewis A, Stewart C, Postans N, Trevelyan J. Development of an instrumented pole test for use as a gait laboratory quality check. Gait Posture. 2007;26:317–22.View ArticleGoogle Scholar
- Kim H, Sakurai S, Ahn J. Errors in the measurement of center of pressure (CoP) computed with force plate affect on 3D lower limb joint moment during gait. Int J Sport Heal Sci. 2007;5:71–82.View ArticleGoogle Scholar
- Cereatti A, Margheritini F, Donati M, Cappozzo A. Is the human acetabulofemoral joint spherical? J Bone Joint Surg Br. 2010;92:311–4.View ArticleGoogle Scholar
- Bell AL, Pedersen DR, Brand RA. A comparison of the accuracy of several hip center location prediction methods. J Biomech. 1990;23:617–21.View ArticleGoogle Scholar
- Cappozzo A. Gait analysis methodology. Hum Mov Sci. 1984;3:27–50.View ArticleGoogle Scholar
- Churchill DL, Incavo SJ, Johnson CC, Beynnon BD. The transepicondylar axis approximates the optimal flexion axis of the knee. Clin Orthop Relat Res. 1998;356:111–8.View ArticleGoogle Scholar
- Besier TF, Sturnieks DL, Alderson JA, Lloyd DG. Repeatability of gait data using a functional hip joint centre and a mean helical knee axis. J Biomech. 2003;36:1159–68.View ArticleGoogle Scholar
- Charlton IW, Tate P, Smyth P, Roren L. Repeatability of an optimised lower body model. Gait Posture. 2004;20:213–21.View ArticleGoogle Scholar
- Taddei F, Ansaloni M, Testi D, Viceconti M. Virtual palpation of skeletal landmarks with multimodal display interfaces. Med Inform Internet Med. 2007;32:191–8.View ArticleGoogle Scholar
- Dumas R, Cheze L, Frossard L. Loading applied on prosthetic knee of transfemoral amputee: comparison of inverse dynamics and direct measurements. Gait Posture. 2009;30:560–2.View ArticleGoogle Scholar
- Schwarze M, Hurschler C, Seehaus F, Oehler S, Welke B. Loads on the prosthesis—socket interface of above-knee amputees during normal gait: validation of a multi-body simulation. J Biomech. 2013;46:1201–6.View ArticleGoogle Scholar
- Fiedler G, Slavens B, Smith RO, Briggs D, Hafner BJ. Criterion and construct validity of prosthesis-integrated measurement of joint moment data in persons with transtibial amputation. J Appl Biomech. 2014;30:431–8.View ArticleGoogle Scholar
- Reinbolt JA, Haftka RT, Chmielewski TL, Fregly BJ. Are patient-specific joint and inertial parameters necessary for accurate inverse dynamics analyses of gait? IEEE Trans Biomed Eng. 2007;54:782–93.View ArticleGoogle Scholar
- Rozumalski A, Schwartz MH. The GDI-kinetic: a new index for quantifying kinetic deviations from normal gait. Gait Posture. 2011;33:730–2.View ArticleGoogle Scholar
- Sinclair J, Atkins S, Vincent H. Influence of different hip joint centre locations on hip and knee joint kinetics and kinematics during the squat. J Hum Kinet. 2014;44:5–17.View ArticleGoogle Scholar
- Kirkwood RN, Culham EG, Costigan PA. Radiographic and non-invasive determination of the hip joint center location: effect on hip joint moments. Clin Biomech. 1999;14:227–35.View ArticleGoogle Scholar
- Kiernan D, Malone A, O’Brien T, Simms CK. The clinical impact of hip joint centre regression equation error on kinematics and kinetics during paediatric gait. Gait Posture. 2015;41:175–9.View ArticleGoogle Scholar
- Holden JP, Stanhope SJ. The effect of variation in knee center location estimates on net knee joint moments. Gait Posture. 1998;7:1–6.View ArticleGoogle Scholar
- Martelli S, Valente G, Viceconti M, Taddei F. Sensitivity of a subject-specific musculoskeletal model to the uncertainties on the joint axes location. Comput Methods Biomech Biomed Eng. 2015;18:1555–63.View ArticleGoogle Scholar
- Valente G, Pitto L, Testi D, Seth A, Delp SL, Stagni R, et al. Are subject-specific musculoskeletal models robust to the uncertainties in parameter identification? PLoS ONE. 2014;9:1–10.Google Scholar
- Bauer JJ, Pavol MJ, Snow CM, Hayes WC. MRI-derived body segment parameters of children differ from age-based estimates derived using photogrammetry. J Biomech. 2007;40:2904–10.View ArticleGoogle Scholar
- Pearsall DJ, Costigan PA. The effect of segment parameter error on gait analysis results. Gait Posture. 1999;9:173–83.View ArticleGoogle Scholar
- Nguyen TC, Reynolds KJ. The effect of variability in body segment parameters on joint moment using Monte Carlo simulations. Gait Posture. 2014;39:346–53.View ArticleGoogle Scholar
- Lee MK, Le NS, Fang AC, Koh MTH. Measurement of body segment parameters using dual energy X-ray absorptiometry and three-dimensional geometry: an application in gait analysis. J Biomech. 2009;42:217–22.View ArticleGoogle Scholar
- Muri J, Winter SL, Challis JH. Changes in segmental inertial properties with age. J Biomech. 2008;41:1809–12.View ArticleGoogle Scholar
- Rao G, Amarantini D, Berton E, Favier D. Influence of body segments’ parameters estimation models on inverse dynamics solutions during gait. J Biomech. 2006;39:1531–6.View ArticleGoogle Scholar
- Fantozzi S, Stagni R, Cappello A, Leardini A. Effect of different inertial parameter sets on joint moment calculation during stair ascending and descending. Med Eng Phys. 2005;27:537–41.View ArticleGoogle Scholar
- Zuk M, Pezowicz C. The influence of uncertainty in body segment mass on calculated joint moments and muscle forces. Inf Technol Med. 2016;472:349–59.Google Scholar
- Wesseling M, de Groote F, Jonkers I. The effect of perturbing body segment parameters on calculated joint moments and muscle forces during gait. J Biomech. 2014;47:596–601.View ArticleGoogle Scholar
- Myers CA, Laz PJ, Shelburne KB, Davidson BS. A probabilistic approach to quantify the impact of uncertainty propagation in musculoskeletal simulations. Ann Biomed Eng. 2015;43:1098–111.View ArticleGoogle Scholar
- Dumas R, Nicol E, Chèze L. Influence of the 3D inverse dynamic method on the joint forces and moments during gait. J Biomech Eng. 2007;129:786–90.View ArticleGoogle Scholar
- Cereatti A, Donati M, Camomilla V, Margheritini F, Cappozzo A. Hip joint centre location: an ex vivo study. J Biomech. 2009;42:818–23.View ArticleGoogle Scholar
- Sangeux M, Pillet H, Skalli W. Which method of hip joint centre localisation should be used in gait analysis? Gait Posture. 2014;40:20–5.View ArticleGoogle Scholar
- Dillon MP, Barker TM, Pettet G. Effect of inaccuracies in anthropometric data and linked-segment inverse dynamic modeling on kinetics of gait in persons with partial foot amputation. J Rehabil Res Dev. 2008;45:1303–16.View ArticleGoogle Scholar
- Goldberg EJ, Requejo PS, Fowler EG. The effect of direct measurement versus cadaver estimates of anthropometry in the calculation of joint moments during above-knee prosthetic gait in pediatrics. J Biomech. 2008;41:695–700.View ArticleGoogle Scholar
- Dumas R, Branemark R, Frossard L. Gait analysis of transfemoral amputees: errors in inverse dynamics are substantial and depend on prosthetic design. IEEE Trans Neural Syst Rehabil Eng. 2016;4320:1.Google Scholar
- Wu G, Siegler S, Allard P, Kirtley C, Leardini A, Rosenbaum D, et al. ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion—part I: ankle, hip, and spine. J Biomech. 2002;35:543–8.View ArticleGoogle Scholar
- Wu G, Van Der Helm FCT, Veeger HEJ, Makhsous M, Van Roy P, Anglin C, et al. ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion—part II: shoulder, elbow, wrist and hand. J Biomech. 2005;38:981–92.View ArticleGoogle Scholar
- Ojeda J, Martìnez-Reina J, Mayo J. The effect of kinematic constraints in the inverse dynamics problem in biomechanics. Multibody Syst Dyn. 2016;37:291–309.View ArticleGoogle Scholar
- Davis RB, Õunpuu S, Tyburski D, Gage JR. A gait analysis data collection and reduction technique. Hum Mov Sci. 1991;10:575–87.View ArticleGoogle Scholar
- Lu TW, O’Connor J. One position estimation from skin marker co-ordinates using global optimisation with joint constraints. J Biomech. 1999;32:129–34.View ArticleGoogle Scholar
- Jensen RK. Body segment mass, radius and radius of gyration proportions of children. J Biomech. 1986;19:359–68.View ArticleGoogle Scholar
- Challis JH. Accuracy of human limb moment of inertia estimations and their influence on resultant joint moments. J Appl Biomech. 1996;12:517–30.View ArticleGoogle Scholar
- Chandler, RF, Clauser CE, McConville, JT, Reynolds, HM YJ. Investigation of inertial properties of the human body (Technical Report AMRL-TR-74-137). 1975.Google Scholar
- Davinelli M, Stagni R, Fantozzi S, Cappello A. Inverse dynamics modeling in gait analysis. J Mech Med Biol. 2005;5:531–7.View ArticleGoogle Scholar
- Jensen RK. Changes in segment inertia proportions between 4 and 20 years. J Biomech. 1989;22:529–36.View ArticleGoogle Scholar
- Zatsiorsky VM, Seluyanov VN, Chugunova LG. In vivo body segment inertial parameters determination using a gamma-scanner method. In: Berme N, Cappozzo A, editors. Biomech. Hum. Mov. Appl. Rehabil. Sport. Ergon. 1990. p. 86–202.Google Scholar
- Hanavan E. A Mathematical Model of the Human Body (Technical Report AMRL-64-102). 1964.Google Scholar
- Kingma I, Toussaint H, De Looze M, Van Dieen J. Segmental inertial parameter evaluation in two anthropometric models by application of a dynamic linked segment model. J Biomech. 1996;29:693–704.View ArticleGoogle Scholar
- McConville JT, Churchill TD, Kaleps I, Clauser CE, Cuzzi J. Anthropometric relationships of body and body segments of inertia. 1980.Google Scholar