Background

Quantitative motion analysis provides an objective description of joint kinematics and dynamics. It is recognised as a useful tool in clinics for functional assessment, diagnosis, planning of therapeutic and rehabilitative interventions, and outcome evaluation. In these applications, ensuring an accurate and reliable estimation of 3D joint moments is crucial. The most relevant sources of error affecting the estimation can be identified by reviewing how 3D joint dynamics is calculated. Two alternative methods are commonly applied (Fig. 1).

Fig. 1
figure 1

Schematic depiction of the workflow to estimate joint dynamics from measurements of kinematics and ground reaction forces (GRF), through kinematic and dynamic modelling of the body, and inertial parameters (inverse dynamics approach—IDA). The alternative estimation of external joint moments from kinematics and GRF is also reported

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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 [1,2,3,4]. 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 [5]. 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 [6].

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 [7], particularly for distal joints (ankle and knee) [1].

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 [12,13,14,15,16,17], geometric approaches [18, 19], data of living subjects obtained through medical imaging technologies [20,21,22,23], or estimates provided by the solution of a non-linear optimization problem [24,25,26].

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.

Methods

Articles selection

Inclusion and exclusion criteria

We included studies published in English as full papers, using stereophotogrammetry and force platforms as measurement systems, analysing gait and activities of daily living (Table 1). Subsequently, we excluded articles not analysing the impact on joint dynamics of kinematics measurements and processing, GRF measurements and processing, joint kinematic and dynamic modelling, and body segment inertial parameters.

Table 1 Inclusion criteria considered for the current systematic review
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Search strategy

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.

Review process

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

In the following sections, the terms ‘‘agreement’’, ‘‘reliability’’, ‘‘reproducibility’’, and ‘‘repeatability’’ will be routinely used. As previously highlighted by Bartlett and Frost [27], these terms have been frequently abused in the literature. We therefore decided to strictly adhere to the definitions reported in [27], which are summarized here for convenience:

  • 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’’ [27]. 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 [28];

  • 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.

Results

Review selection and identification

The initial search yielded 8251 (Web of Science), 4535 (Scopus) and 7630 (PubMed) results (Fig. 2). Over the three search engines, subsequent refinement yielded to a total of 1039 results for kinematics and processing, 291 for GRF measurements and processing, 2786 for joint models, and 1000 for BSIP, respectively. Selection performed separately for each area and based on title and abstract or full text, lead to 38, 5, 22, and 20 journal papers. Despite considering studies conducted on healthy subjects only, the search reported 6 studies including patients [5, 29,30,31,32,33] whose conclusions were valid independently from the population of interest and were retained for further analysis. After excluding duplicates, 67 papers were finally listed.

Fig. 2
figure 2

Search strategy flow chart. After running the general search, the three researched databases listed 8251, 4535, 7630 papers, respectively (including duplicates). Subsequent refinement yielded to a total of 1039 results for kinematics and processing, 291 for GRF measurements and processing, 2786 for joint models, and 1000 for BSIP, respectively. After examining the title, abstract or full text, only 38, 5, 22, and 20 remained. The overall total, without counting articles included in more than one area of analysis and duplicates, was 67 papers

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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.

Kinematics

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 [34]. 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) [9]. Another source of uncertainty is represented by the identification of anatomical landmarks which, being a subjective procedure, is prone to repeatability issues [8]. 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 [35].

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 [36]. Several methods were described for its compensation: digital filters, splines, spectrum analysis techniques [37], Kalman smoothing and multi-body kinematics optimization [38]. A sensitivity analysis was performed in [39] and it was found that filtering kinematic data with a cut-off value of 4.5 Hz improves gait dynamic estimates.

Soft-tissue artifact

Few studies quantified the effect of soft tissue artifacts of thigh and shank on the knee moments during walking [40, 41], stair ascent [42] and sit-to-stand [43] 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 [43]. This result was confirmed during the load transfer phase of stair ascent, but only for knee extension [42]. Similar trends in magnitude were measured for both moments during the single support phase of walking [40, 41]. Also, Buczek et al. [41] 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 [41]. 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 [46] 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 [38]. Finally, Langenderfer et al. applied a probabilistic method to quantify the effect of the uncertainty in locating anatomical landmarks and BSIPs on joint moments [47]. 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. [48] 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 [41]. 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 [49].

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, 52,53,54,55,56,57]. It can be argued that joint moments expressed in local CSs may allow interpreting the trajectories in terms of the moments that cause them [58]. 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 [55] or actual pathological gait (resulting in about 20% BW * H variability due to CS for key peak moments of hip, knee, and ankle) [56]. Similar results were obtained in [50]: 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 [33]. 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 [54]. 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 [33], although statistical techniques, such as principal component analysis, may help in highlighting pathological features that are independent of the coordinate system selection [32].

Gait protocols

Several stereophotogrammetric protocols have been proposed for clinical gait analysis [61]; the effect of their differences on joint moment estimation was analyzed during level walking [62,63,64]. 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. [64] 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 [65], 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 [64] 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 [66].

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 [67]. 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 [68].

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 [70] and reducing the errors in projecting the joint moment components in the sagittal and frontal planes [69]. Similarly, Petit and colleagues [71] 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 [72], 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 [73]. In both [73] and [72], 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 [74] 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 [75]. 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 [79,80,81,82,83,84,85]: during in situ testing errors superimposed to COP coordinates were found double than the reference ones [82,83,84]; accuracy decreases as the point of application of the force moves to the platform peripheries [82], although distributed loads seem to be less affected by this phenomenon than concentrated ones [81]; 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 [84]. Moreover, the performance of the force platform can differ in dynamic compared to static conditions [79]. 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 [80], 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 [89]. McCaw and DeVita [77] 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. [35], 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. [34] 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. [78] 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 [90] 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 [5].

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 [92,93,94], multi-body kinematics optimization techniques [95] or bio-imaging techniques [96].

Studies classification

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 [94]. 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 [5] or using force/moment sensors in prosthetic limb of amputees [97,98,99], 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.

In Table 2, a concise classification and description of the relevant literature is provided.

Table 2 Details of studies analyzed for the joint model parameters effect on the dynamics estimates
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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.

Hip joint

The simulation carried out by Stagni and colleagues indicated that errors in the hip joint centre (HJC) location greatly affect hip joint moment [11]. 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 [11]. Reinbolt and colleagues [100] 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 [11]. 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 [30]. 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%) [29]. 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 [101] and [102] can be explained by the different errors direction affecting the HJC estimates. In fact, whereas Lenaerts and colleagues [30] found that the estimated HJC was located about 30 mm anteriorly and 21 mm proximally, in the work of Bartels and co-workers [29], 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 [103] 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 [104] 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) [101]. Sinclair and colleagues [102] 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 [105] 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 [100] (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 [29] 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 [46] found in simulation a sensitivity of the knee moment similar to that observed for the application point of the external forces.

Multi-joint

Langenderfer and colleagues [47] 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 [100] 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 [94] 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.

Inertial parameters

The motor tasks evaluated were: level walking (17 studies), walking on treadmill (2 study), and stair ascending/descending (2 studies). All studies except one [108] assessed the entire stride of the cycle (stance and swing phases).

Two types of investigation were performed (Table 3): in the 13 experimental studies, different set of BSIPs were used while in the 11 simulation studies the values of the BSIPs were varied applying deterministic or probabilistic approaches (for details see Table 3). Joint moment estimated with different values of BSIPs were compared and in same case the percentage variation was reported.

Table 3 Details of studies analyzed for the body segment inertial parameters (BSIPs) effect on the dynamics estimates
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Statistically significant differences were observed in the estimated BSIPs not only using different approaches [23] but also using different data within the same approach [109]. 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 [110]. 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% [109]. 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% [112] and 20.11% [113], respectively. During stair ascending/descending, a maximum of 21.8% in the transverse plane at the hip moment was reported [114].

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 [116] and in a third study distal BSIPs showed little effect on proximal joint moment [110].

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 [47], not much greater than that of the inter-trial variability [110], smaller than that of marker placement and soft tissue artifact [117], lower than that caused by a 0.5 Hz adjustment in the cut-off frequency of the filter used to process the data [112], and produced no clinically meaningful difference in the GDI-kinetic scores [31].

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 [118] 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.

The literature highlights the importance of taking due care of:

  1. 1.

    Compensating for noise affecting marker trajectories especially when dynamics is estimated using kinematics only;

  2. 2.

    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).

  3. 3.

    Identifying in a consistent manner joint parameter when comparing joint moments;

  4. 4.

    Interpreting IDA results in the light of the protocol used to estimate them and of the coordinate system used for their expression;

  5. 5.

    Properly assessing in situ GRF measurement errors, and estimating their potential effect on the final clinical decision process;

  6. 6.

    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.

Therefore, the reader shall consider the potential benefits of using:

  1. 1.

    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°) [119]. 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 [120];

  2. 2.

    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;

  3. 3.

    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;

  4. 4.

    Customized BSIPs to better highlight the muscle role in decelerating lower limb during the swing phase only in special populations, such as amputee patients [121,122,123].

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].