Double calibration vs. global optimisation: performance and effectiveness for clinical application

A simulation study to investigate an extension to the point cluster technique

Joint kinematics are an important and widely utilized metric in quantitative human movement analysis. Typically, trajectory data for skin-mounted markers are collected using stereophotogrammetry, sometimes referred to as optical motion capture, and processed using various mathematical models to estimate joint kinematics (e.g., angles). Among the various sources of noise in optical motion capture data, soft tissue artifacts (STAs) remain a critical source of error. This study investigates the performance of the point cluster technique (PCT), an extension of the PCT using perturbation theory (PCT-PT), and singular value decomposition least squares (SVD-LS) method (as a reference) for 100 different marker configurations on the thigh and shank during treadmill walking. This study provides additional evidence that the PCT method is significantly limited by the underlying mathematical constraints governing its optimization process. Furthermore, the results suggest the PCT-PT method outperforms the PCT method across all performance metrics for both body segments during the entire gait cycle. For position-based metrics, the PCT-PT method provides better estimates than the SVD-LS method for the thigh during majority of the stance phase and provides comparable estimates for the shank during the entire gait cycle. For knee angle estimates, the PCT-PT method provides equivalent results as the SVD-LS method.

Comparison of a Scaled Cadaver-Based Musculoskeletal Model With a Clinical Upper Extremity Model

Reliably and accurately estimating joint/segmental kinematics from optical motion capture data has remained challenging. Studies objectively characterizing human movement patterns have typically involved inverse kinematics and inverse dynamics techniques. Subsequent research has included scaled cadaver-based musculoskeletal (MSK) modeling for noninvasively estimating joint and muscle loads. As one of the ways to enhance confidence in the validity of MSK model predictions, the kinematics from the preceding step that drives such a model needs to be checked for agreement or compared with established/widely used models. This study rigorously compares the upper extremity (UE) joint kinematics calculated by the Dutch Shoulder Model implemented in the AnyBody Managed Model Repository (involving multibody kinematics optimization (MKO)) with those estimated by the Vicon Plug-in Gait model (involving single-body kinematics optimization (SKO)). Ten subjects performed three trials of (different types of) reaching tasks in a three-dimensional marker-based optical motion capture laboratory setting. Joint angles, processed marker trajectories, and reconstruction residuals corresponding to both models were compared. Scatter plots and Bland-Altman plots were used to assess the agreement between the two model outputs. Results showed the largest differences between the two models for shoulder, followed by elbow and wrist, with all root-mean-squared differences less than 10 deg (although this limit might be unacceptable for clinical use). Strong-to-excellent Spearman's rank correlation coefficients were found between the two model outputs. The Bland-Altman plots showed a good agreement between most of the outputs. In conclusion, results indicate that these two models with different kinematic algorithms broadly agree with each other, albeit with few key differences.

Kinetics influence of multibody kinematics optimisation for soft tissue artefact compensation

Soft tissue artefact (STA) remains a major source of error in human movement analysis. The multibody kinematics optimisation (MKO) approach is widely stated as a solution to reduce the effects of STA. This study aimed at assessing the influence of the MKO STA-compensation on the errors of estimation of the knee intersegment moments. Experimental data were issued from the CAMS-Knee dataset where six participants with instrumented total knee arthroplasty performed five activities of daily living: gait, downhill walking, stair descent, squat, and sit-to-stand. Kinematics was measured both on the basis of skin markers and a mobile mono-plane fluoroscope, used to obtain the STA-free bone movement. For four different lower limb models and one corresponding to a single-body kinematics optimization (SKO), knee intersegmental moments (estimated using model-derived kinematics and ground reaction force) were compared with an estimate based on the fluoroscope. Considering all participants and activities, mean root mean square differences were the largest along the adduction/abduction axis: of 3.22Nm with a SKO approach, 3.49Nm with the three-DoF knee model, and 7.66Nm, 8.52Nm, and 8.54Nm with the one-DoF knee models. Results showed that adding joint kinematics constraints can increase the estimation errors of the intersegmental moment. These errors came directly from the errors in the estimation of the position of the knee joint centre induced by the constraints. When using a MKO approach, we recommend to analyse carefully joint centre position estimates that do not remain close to the one obtained with a SKO approach.

Evaluating Lower Limb Kinematics Using Microsoft's Kinect: A Simple, Novel Method

Purpose: Our aim was to evaluate the Microsoft Kinect sensor (MKS) as a markerless system for motion capture and analysis of lower limb motion, compare it with a state-of-the-art marker-based system (MBS), and investigate its accuracy in simultaneously capturing several lower limb joint movements on several planes while participants walked freely. Method: Participants were asked to walk while gait data were simultaneously recorded by both the MKS and the MBS. Software for analysing the Kinect data stream was developed using Microsoft Visual Studio and Kinect for Windows software development kits. Visual three-dimensional (3D) C-Motion software was used to calculate 3D joint angles of the MBS. Deviation of the joint angles calculated by the two systems was calculated using root-mean-square error (RMSE) on the basis of a designated formula. Results: The calculated RMSE average was <5° between the two systems, a level of difference that has practically no clinical significance. Conclusions: Quantitative measurements of the joint angles of the knee and hip can be acquired using one MKS with some accuracy. The system can be advantageous for clinical use, at the pre- and post-treatment stages of rehabilitation, at significantly lower costs. Further evaluation of the MKS should be performed with larger study populations.

A Novel Kinematic Model of the Tibiofemoral Joint Based on a Parallel Mechanism

This paper presents a complete kinematic model of the tibiofemoral joint (TFJ) based on a RRPP + 4-SPS parallel mechanism, where R, P, and S stand for revolute, prismatic, and spherical joints, respectively. The model accounts for the contact between tibia and femur, and the four major ligaments: anterior cruciate, posterior cruciate, medial collateral, and lateral collateral, with anatomical significance in their length variations. An experimental flexion passive motion task is performed, and the kinematic model is tested to determine its capability to reproduce the workspace of the motion task. In addition, an optimization process is performed to simulate prescribed ligament length variations during the motion task. The proposed kinematic model is capable to reproduce with high accuracy an experimental three-dimensional workspace, and at the same time, to simulate prescribed ligament length variation during the spatial flexion task. Prescribed ligament length variations are achieved through an optimization process of the ligament insertion points. This model can be used to improve the multibody kinematic optimization (MKO) process during gait analysis, and also in the design of rehabilitation devices as well as trajectories to accelerate the recovery of injured ligaments. The model shows potential to predict ligament length variations during different motion tasks, and can serve as a basis to develop complex models for kinetostatic and dynamic analyses without dealing with computationally expensive models.

Measuring three-dimensional tibiofemoral kinematics using dual-slice real-time magnetic resonance imaging

PURPOSE

The purpose of this study is to propose and evaluate a slice-to-volume registration (SVR) method integrating an advanced dual-slice real-time magnetic resonance image (MRI) and three-dimensional (3D) MRI volume of the tibiofemoral joint for determining their 3D kinematics.

METHODS

The real-time and 3D MRI of the knee were collected from 12 healthy adults at 5 static flexion positions and during dynamic flexion/extension movement. The 3D positions and orientations of the femur and tibia were obtained by registering their volumetric models constructed from the 3D MRI to dual-slice real-time MRI using an optimization process. The proposed method was quantitatively evaluated for its performance in terms of the robustness and measurement accuracy, and compared to those of a single-slice SVR method. Its repeatability in measuring knee kinematics during flexion/extension movement was also determined.

RESULTS

In comparison to the single-slice SVR method, the dual-slice method was significantly superior, giving a successful registration rate > 95%, a bias less than 0.5 mm in translations and 0.6° in rotations and a precision <0.7 mm in translations and 0.9° in rotations for determining the 3D tibiofemoral poses. For repeatability of the dual-slice SVR in measuring tibiofemoral kinematics during dynamic flexion/extension, the means of the time-averaged standard deviations were <0.9° for joint angles and 0.5 mm for joint translations.

CONCLUSION

A dual-slice SVR method in conjunction with real-time MRI has been developed and evaluated for its performance in measuring 3D kinematics of the tibiofemoral joint in 12 young adults in terms of the accuracy, robustness, and repeatability. The proposed MRI-based 3D measurement method provides a noninvasive and ionizing radiation-free approach for 3D kinematic measurement of the tibiofemoral joint, which will be helpful for future academic and clinical applications.

Multibody Kinematics Optimization for the Estimation of Upper and Lower Limb Human Joint Kinematics: A Systematized Methodological Review

Multibody kinematics optimization (MKO) aims to reduce soft tissue artefact (STA) and is a key step in musculoskeletal modeling. The objective of this review was to identify the numerical methods, their validation and performance for the estimation of the human joint kinematics using MKO. Seventy-four papers were extracted from a systematized search in five databases and cross-referencing. Model-derived kinematics were obtained using either constrained optimization or Kalman filtering to minimize the difference between measured (i.e., by skin markers, electromagnetic or inertial sensors) and model-derived positions and/or orientations. While hinge, universal, and spherical joints prevail, advanced models (e.g., parallel and four-bar mechanisms, elastic joint) have been introduced, mainly for the knee and shoulder joints. Models and methods were evaluated using: (i) simulated data based, however, on oversimplified STA and joint models; (ii) reconstruction residual errors, ranging from 4 mm to 40 mm; (iii) sensitivity analyses which highlighted the effect (up to 36 deg and 12 mm) of model geometrical parameters, joint models, and computational methods; (iv) comparison with other approaches (i.e., single body kinematics optimization and nonoptimized kinematics); (v) repeatability studies that showed low intra- and inter-observer variability; and (vi) validation against ground-truth bone kinematics (with errors between 1 deg and 22 deg for tibiofemoral rotations and between 3 deg and 10 deg for glenohumeral rotations). Moreover, MKO was applied to various movements (e.g., walking, running, arm elevation). Additional validations, especially for the upper limb, should be undertaken and we recommend a more systematic approach for the evaluation of MKO. In addition, further model development, scaling, and personalization methods are required to better estimate the secondary degrees-of-freedom (DoF).

Standardization proposal of soft tissue artefact description for data sharing in human motion measurements

Soft tissue artefact (STA) represents one of the main obstacles for obtaining accurate and reliable skeletal kinematics from motion capture. Many studies have addressed this issue, yet there is no consensus on the best available bone pose estimator and the expected errors associated with relevant results. Furthermore, results obtained by different authors are difficult to compare due to the high variability and specificity of the phenomenon and the different metrics used to represent these data. Therefore, the aim of this study was twofold: firstly, to propose standards for description of STA; and secondly, to provide illustrative STA data samples for body segments in the upper and lower extremities and for a range of motor tasks specifically, level walking, stair ascent, sit-to-stand, hip- and knee-joint functional movements, cutting motion, running, hopping, arm elevation and functional upper-limb movements. The STA dataset includes motion of the skin markers measured in vivo and ex vivo using stereophotogrammetry as well as motion of the underlying bones measured using invasive or bio-imaging techniques (i.e., X-ray fluoroscopy or MRI). The data are accompanied by a detailed description of the methods used for their acquisition, with information given about their quality as well as characterization of the STA using the proposed standards. The availability of open-access and standard-format STA data will be useful for the evaluation and development of bone pose estimators thus contributing to the advancement of three-dimensional human movement analysis and its translation into the clinical practice and other applications.

Knee Kinematics Estimation Using Multi-Body Optimisation Embedding a Knee Joint Stiffness Matrix: A Feasibility Study

The use of multi-body optimisation (MBO) to estimate joint kinematics from stereophotogrammetric data while compensating for soft tissue artefact is still open to debate. Presently used joint models embedded in MBO, such as mechanical linkages, constitute a considerable simplification of joint function, preventing a detailed understanding of it. The present study proposes a knee joint model where femur and tibia are represented as rigid bodies connected through an elastic element the behaviour of which is described by a single stiffness matrix. The deformation energy, computed from the stiffness matrix and joint angles and displacements, is minimised within the MBO. Implemented as a "soft" constraint using a penalty-based method, this elastic joint description challenges the strictness of "hard" constraints. In this study, estimates of knee kinematics obtained using MBO embedding four different knee joint models (i.e., no constraints, spherical joint, parallel mechanism, and elastic joint) were compared against reference kinematics measured using bi-planar fluoroscopy on two healthy subjects ascending stairs. Bland-Altman analysis and sensitivity analysis investigating the influence of variations in the stiffness matrix terms on the estimated kinematics substantiate the conclusions. The difference between the reference knee joint angles and displacements and the corresponding estimates obtained using MBO embedding the stiffness matrix showed an average bias and standard deviation for kinematics of 0.9±3.2° and 1.6±2.3 mm. These values were lower than when no joint constraints (1.1±3.8°, 2.4±4.1 mm) or a parallel mechanism (7.7±3.6°, 1.6±1.7 mm) were used and were comparable to the values obtained with a spherical joint (1.0±3.2°, 1.3±1.9 mm). The study demonstrated the feasibility of substituting an elastic joint for more classic joint constraints in MBO.

A model of the soft tissue artefact rigid component

When using stereophotogrammetry and skin-markers, the reconstruction of skeletal movement is affected by soft-tissue artefact (STA). This may be described by considering a marker-cluster as a deformable shape undergoing a geometric transformation formed by a non-rigid (change in size and shape) and a rigid component (translation and rotation displacements). A modal decomposition of the STA, relative to an appropriately identified basis, allows the separation of these components. This study proposes a mathematical model of the STA that embeds only its rigid component and estimates the relevant six mode amplitudes as linear functions of selected proximal and distal joint rotations during the analysed task. This model was successfully calibrated for thigh and shank using simultaneously recorded pin- and skin-marker data of running volunteers. The root mean square difference between measured and model-estimated STA rigid component was 1.1(0.8)mm (median (inter-quartile range) over 3 subjects × 5 trials × 33 markers coordinates), and it was mostly due to the wobbling not included in the model. Knee joint kinematics was estimated using reference pin-marker data and skin-marker data, both raw and compensated with the model-estimated STA. STA compensation decreased inaccuracy on average from 6% to 1% for flexion/extension, from 43% to 18% for the other two rotations, and from 69% to 25% for the linear displacements. Thus, the proposed mathematical model provides an STA estimate which can be effectively used within optimal bone pose and joint kinematics estimators for artefact compensation, and for simulations aimed at their comparative assessments.

Can optimal marker weightings improve thoracohumeral kinematics accuracy?

Local and global optimization algorithms have been developed to estimate joint kinematics to reducing soft movement artifact (STA). Such algorithms can include weightings to account for different STA occur at each marker. The objective was to quantify the benefit of optimal weighting and determine if optimal marker weightings can improve humerus kinematics accuracy. A pin with five reflective markers was inserted into the humerus of four subjects. Seven markers were put on the skin of the arm. Subjects performed 38 different tasks including arm elevation, rotation, daily-living tasks, and sport activities. In each movement, mean and peak errors in skin- vs. pins-orientation were reported. Then, optimal marker weightings were found to best match skin- and pin-based orientation. Without weighting, the error of the arm orientation ranged from 1.9° to 17.9°. With weighting, 100% of the trials were improved and the average error was halved. The mid-arm markers weights were close to 0 for three subjects. Weights of a subject applied to the others for a given movement, and weights of a movement applied to others for a given subject did not systematically increased accuracy of arm orientation. Without weighting, a redundant set of marker and least square algorithm improved accuracy to estimate arm orientation compared to data of the literature using electromagnetic sensor. Weightings were subject- and movement-specific, which reinforces that STA are subject- and movement-specific. However, markers on the deltoid insertion and on lateral and medial epicondyles may be preferred if a limited number of markers is used.

Non-invasive assessment of soft-tissue artefacts in hip joint kinematics using motion capture data and ultrasound depth measurements

In human movement analysis, the hip joint centre can be estimated using a functional method based on the relative motion of the femur to the pelvis measured using reflective markers attached to the skin surface by an optical motion capture system. The principal source of errors in estimating the hip joint centre location using functional methods is soft tissue artefacts due to the relative motion between the markers and bone; one of the main objectives in human movement analysis is the assessment of soft tissue artefact. Various studies have described the movement of soft tissue artefact and compensated for it invasively; examples include: intra-cortical pins, external fixators, percutaneous skeletal trackers, and Roentgen photogrammetry. The goal of this study is to present a non-invasive method to assess soft tissue artefact using optical motion capture data and tissue thickness from ultrasound measurements during flexion and abduction (both with the knee extended) of the hip joint. Results showed that the skin marker displacements caused by the artefact are non-linear and larger in areas closer to the hip joint. It was also found that the marker displacements are dependent on the movement type and relatively larger in abduction movement.

Effect of calibration error on bone tracking accuracy with fluoroscopy

Model-based 3D-fluoroscopy can quantify joint kinematics with 1 mm and 1 deg accuracy level. A calibration based on the acquisition of devices of known geometry is usually applied to size the system. This study aimed at quantifying the sensitivity of the fluoroscopic pose estimation accuracy specifically to errors in the calibration process, excluding other sources of error. X-ray focus calibration error was quantified for different calibration setups, and its propagation to the pose estimation was characterized in-silico. Focus reference position influenced the calibration error dispersion, while calibration cage pose affected its bias. In the worst-case scenario, the estimation error of the principal point and of the focus distance was lower than 1 mm and 2 mm, respectively. The consequent estimation of joint angles was scarcely influenced by calibration errors. A linear trend was highlighted for joint translations, with a sensitivity proportional to the distance between the model and the image plane, resulting in a submillimeter error for realistic calibration errors. The biased component of the error is compensated when computing relative joint kinematics between two segments.

Sensitivity of joint kinematics and kinetics to different pose estimation algorithms and joint constraints in the elderly

The purpose of this research was to study the sensitivity of lower limb joint kinematics and kinetics, calculated during different functional tasks (walking, stair descent and stair ascent) in a sample of older adults, to different pose estimation algorithms and models' joint constraints. Three models were developed and optimized differently: in one model, each segment had 6 degrees of freedom (segment optimization, SO), while in the other two, global optimization (GO) was used, with different joint constraints: (1) GO, allowing all joint rotations; (2) GOR, allowing three rotations at the hip, one at the knee (flexion/extension) and two at the ankle (dorsi/plantar flexion and eversion/inversion). The results showed that joint angles are more sensitive to the model's constraints than joint moments and, the more restrictive the model, the higher the differences between models, especially for the frontal and transverse planes (max. RMS difference during gait: 11.7 degrees (64%) vs 0.12 N·m/kg (35.4%). In addition, except for knee abduction/adduction angle, differences between SO and GO models were relatively low. Since GO avoids the nonanatomical dislocations sometimes observed in SO, choosing this model seems to be reasonable for future studies with a similar sample and study design.

Validity and reliability of the Kinect within functional assessment activities: comparison with standard stereophotogrammetry

The recent availability of the Kinect™ sensor, a cost-effective markerless motion capture system (MLS), offers interesting possibilities in clinical functional analysis and rehabilitation. However, neither validity nor reproducibility of this device is known yet. These two parameters were evaluated in this study. Forty-eight volunteers performed shoulder abduction, elbow flexion, hip abduction and knee flexion motions; the same protocol was repeated one week later to evaluate reproducibility. Movements were simultaneously recorded by the Kinect (with Microsoft Kinect SDK v.1.5) MLS and a traditional marker-based stereophotogrammetry system (MBS). Considering the MBS as reference, discrepancies between MLS and MBS were evaluated by comparing the range of motion (ROM) between both systems. MLS reproducibility was found to be statistically similar to MBS results for the four exercises. Measured ROMs however were found different between the systems.

Can the effect of soft tissue artifact be eliminated in upper-arm internal-external rotation?

The purpose of this study was to quantify the effect of soft tissue artifact during three-dimensional motion capture and assess the effectiveness of an optimization method to reduce this effect. Four subjects were captured performing upper-arm internal-external rotation with retro-reflective marker sets attached to their upper extremities. A mechanical arm, with the same marker set attached, replicated the tasks human subjects performed. Artificial sinusoidal noise was then added to the recorded mechanical arm data to simulate soft tissue artifact. All data were processed by an optimization model. The result from both human and mechanical arm kinematic data demonstrates that soft tissue artifact can be reduced by an optimization model, although this error cannot be successfully eliminated. The soft tissue artifact from human subjects and the simulated soft tissue artifact from artificial sinusoidal noise were demonstrated to be considerably different. It was therefore concluded that the kinematic noise caused by skin movement artifact during upper-arm internal-external rotation does not follow a sinusoidal pattern and cannot be effectively eliminated by an optimization model.

The weighted optimal common shape technique improves identification of the hip joint center of rotation in vivo

Functional methods present a promising approach for the identification of skeletal kinematics, but their accuracy is limited by soft tissue artifacts (STAs). We hypothesized that consideration of the nonuniform distribution of STAs across the segment can lead to a significant improvement in the determination of the center of rotation at the hip. Twenty-four total hip arthroplasty (THA) patients performed repetitions of a star-arc movement. The location of the hip centers of rotation (CoRs) were estimated from the motion data using the Symmetrical Center of Rotation Estimation (SCoRE), both with and without procedures to minimize the effect of STAs. The precision of the CoR estimations was evaluated using the SCoRE residual, a measure of joint precision. Application of the newly developed weighted Optimal Common Shape Technique (wOCST) achieved the best CoR estimations with a precision of better than 3 mm, while the precision using raw data alone was up to seven times worse. Furthermore, consideration of the nonuniform distribution of STA across the surface of the skin using the wOCST produced an improvement of ∼24% over kinematics data processed using the standard OCST. Functional determination of the CoR at the hip using the newly developed wOCST can now identify the joint CoR with a precision of millimeters. Such approaches therefore offer improved precision in the assessment of skeletal kinematics and may aid in evaluating clinical treatment success and differentiating between therapy outcomes.

Double calibration: an accurate, reliable and easy-to-use method for 3D scapular motion analysis

The most recent non-invasive methods for the recording of scapular motion are based on an acromion marker (AM) set and a single calibration (SC) of the scapula in a resting position. However, this method fails to accurately measure scapular kinematics above 90° of arm elevation, due to soft tissue artifacts of the skin and muscles covering the acromion. The aim of this study was to evaluate the accuracy, and inter-trial and inter-session repeatability of a double calibration method (DC) in comparison with SC. The SC and DC data were measured with an optoelectronic system during arm flexion and abduction at different angles of elevation (0-180°). They were compared with palpation of the scapula using a scapula locator. DC data was not significantly different from palpation for 5/6 axes of rotation tested (Y, X, and Z in abduction and flexion), where as SC showed significant differences for 5/6 axes. The root mean square errors ranged from 2.96° to 4.48° for DC and from 6° to 9.19° for SC. The inter-trial repeatability was good to excellent for SC and DC. The inter-session repeatability was moderate to excellent for SC and moderate to good for DC. Coupling AM and DC is an easy-to-use method, which yields accurate and reliable measurements of scapular kinematics for the complete range of arm motion. It can be applied to the measurement of shoulder motion in many fields (sports, orthopaedics, and rehabilitation), especially when large ranges of arm motion are required.

Quantification of soft tissue artifact in lower limb human motion analysis: a systematic review

This systematic review critically evaluates the quantification of soft tissue artifact (STA) in lower limb human motion analysis. It has a specific focus on assessing the quality of previous studies and comparing quantitative results. A specific search strategy identified 20 published articles or abstracts that fulfilled the selection criteria. The quality of the articles was evaluated using a customised critical appraisal tool. Data extraction tools were used to identify key aspects reported in the articles. Most studies had small sample sizes of mostly young, slim participants. Eleven of the reviewed articles used physically invasive techniques to assess STA. STA was found to reach magnitudes of greater than 30 mm on the thigh segment, and up to 15 mm on the tibia. The range of soft tissue artifact reached greater than 25 mm in some cases when comparing the results of reviewed studies.