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

Hip joint

 Mathematical simulation

Sensitivity analysis

[11]

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

[100]

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

 Experimental

Method comparison with gold standard

[29]

Both studies compared the joint moment obtained using generic scaled musculoskeletal model [16] with the HJC location determined using a regressive method [3] and with subject-specific HJC location derived from CT scan

[30]

[103]

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

[104]

This study investigated the clinical agreement of four commonly used regression equation sets on 18 healthy pediatric subjects during gait

[102]

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

Knee joint

 Experimental

Sensitivity analysis

[105]

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

[29]

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

 Mathematical simulation

[100]

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

[46]

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”

Ankle joint

 Mathematical simulation

Sensitivity analysis

[100]

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

 Experimental

Method comparison with gold standard

[29]

Ankle joint moment obtained using generic scaled musculoskeletal model [16] and with subject-specific ankle joint centre location derived from CT scan. No information about ankle joint and axes determination were provided

Multi-joint

 Mathematical simulation

Perturbation of markers/ALs positions

[47]

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 [25]

[106]

Both studies performed a sensitivity analysis using a highly subject-specific muscolo-skeletal model defined from computer tomography [27] and magnetic resonance [28]. 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

[107]

 Experimental

Inter-session repeatability

[94]

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

[51]

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

[69]

The study compared the inter-sessions variability of joint moments obtained with the Plug-in-Gait protocol [5] 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

[126]

The study implemented four different body estimators methods: Davis model [127], a kinematic constrained method [76], a single-body optimal method and a multi-body kinematics optimization method [128]. 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