Comparative assessment of knee joint models used in multi-body kinematics optimisation for soft tissue artefact compensation

Estimating joint kinematics from skin-marker trajectories recorded using stereophotogrammetry is complicated by soft tissue artefact (STA), an inexorable source of error. One solution is to use a bone pose estimator based on multi-body kinematics optimisation (MKO) embedding joint constraints to compensate for STA. However, there is some debate over the effectiveness of this method. The present study aimed to quantitatively assess the degree of agreement between reference (i.e., artefact-free) knee joint kinematics and the same kinematics estimated using MKO embedding six different knee joint models. The following motor tasks were assessed: level walking, hopping, cutting, running, sit-to-stand, and step-up. Reference knee kinematics was taken from pin-marker or biplane fluoroscopic data acquired concurrently with skin-marker data, made available by the respective authors. For each motor task, Bland-Altman analysis revealed that the performance of MKO varied according to the joint model used, with a wide discrepancy in results across degrees of freedom (DoFs), models and motor tasks (with a bias between −10.2° and 13.2° and between −10.2 mm and 7.2 mm, and with a confidence interval up to ±14.8° and ±11.1 mm, for rotation and displacement, respectively). It can be concluded that, while MKO might occasionally improve kinematics estimation, as implemented to date it does not represent a reliable solution to the STA issue.     

Soft tissue displacement over pelvic anatomical landmarks during 3-D hip movements

The position, in a pelvis-embedded anatomical coordinate system, of skin points located over the following anatomical landmarks (AL) was determined while the hip assumed different spatial postures: right and left anterior superior and posterior superior iliac spines, and the sacrum. Postures were selected as occurring during walking and during a flexion–extension and circumduction movement, as used to determine the hip joint centre position (star-arc movement). Five volunteers, characterised by a wide range of body mass indices (22–37), were investigated. Subject-specific MRI pelvis digital bone models were obtained. For each posture, the pose of the pelvis-embedded anatomical coordinate system was determined by registering this bone model with points digitised over bony prominences of the pelvis, using a wand carrying a marker-cluster and stereophotogrammetry. The knowledge of how the position of the skin points varies as a function of the hip posture provided information regarding the soft tissue artefact (STA) that would affect skin markers located over those points during stereophotogrammetric movement analysis. The STA was described in terms of amplitude (relative to the position of the AL during an orthostatic posture), diameter (distance between the positions of the AL which were farthest away from each other), and pelvis orientation. The STA amplitude, exhibited, over all postures, a median [inter-quartile] value of 9[6] and 16[11] mm, for normal and overweight volunteers, respectively. STA diameters were larger for the star-arc than for the walking postures, and the direction was predominantly upwards. Consequent errors in pelvic orientation were in the range 1–9 and 4–11 degrees, for the two groups respectively.     

Evaluation of knee functional calibration with and without the effect of soft tissue artefact

Functional calibration methods were devised to improve repeatability and accuracy of the knee flexion–extension axis, which is used to define the medio-lateral axis of the femur coordinate system in gait analysis. Repeatability of functional calibration methods has been studied extensively in healthy individuals, but not accuracy in the absence of a benchmark knee axis. We captured bi-plane fluoroscopy data of the knee joint in 17 subjects with unilateral total knee arthroplasty during treadmill walking. The prosthesis provided a benchmark knee axis to evaluate the functional calibration methods. Stereo-photogrammetry data of thigh and shank marker clusters were captured simultaneously to investigate the effect of soft tissue artefact (STA). Three methods were tested, the Axis Transformation Technique (ATT) finds the best single fixed axis of rotation, 2DofKnee finds the axis that minimises knee varus–valgus and trajAJC finds the axis perpendicular to the trajectory, in the transverse plane of the femur, of a point located on the longitudinal axis of the tibia. Using fluoroscopy data, functional axes formed an angle of less than 2° in the transverse plane with the benchmark axis. True internal–external range of movement was correlated with decreased accuracy for ATT, while varus–valgus range of movement was correlated with decreased accuracy for 2DofKnee and trajAJC. STA had negative impact on accuracy and variability. Using stereo-photogrammetry data, the accuracy of 2DofKnee was 1.7°(SD: 5.1°), smaller than ATT 2.9°(SD: 5.1°) but not to trajAJC 1.7°(SD: 5.2°). Our results confirm that of previous studies, which utilised the femur condylar axis as reference.     

Effect of various upper limb multibody models on soft tissue artefact correction: A case study

Soft tissue artefacts (STA) introduce errors in joint kinematics when using cutaneous markers, especially on the scapula. Both segmental optimisation and multibody kinematics optimisation (MKO) algorithms have been developed to improve kinematics estimates. MKO based on a chain model with joint constraints avoids apparent joint dislocation but is sensitive to the biofidelity of chosen joint constraints. Since no recommendation exists for the scapula, our objective was to determine the best models to accurately estimate its kinematics. One participant was equipped with skin markers and with an intracortical pin screwed in the scapula. Segmental optimisation and MKO for 24-chain models (including four variations of the scapulothoracic joint) were compared against the pin-derived kinematics using root mean square error (RMSE) on Cardan angles. Segmental optimisation led to an accurate scapula kinematics (1.1° ≤ RMSE ≤ 3.3°) even for high arm elevation angles. When MKO was applied, no clinically significant difference was found between the different scapulothoracic models (0.9° ≤ RMSE ≤ 4.1°) except when a free scapulothoracic joint was modelled (1.9° ≤ RMSE ≤ 9.6°). To conclude, using MKO as a STA correction method was not more accurate than segmental optimisation for estimating scapula kinematics.     

Bone orientation and position estimation errors using Cosserat point elements and least squares methods: Application to gait

The aim of this study was to analyze the accuracy of bone pose estimation based on sub-clusters of three skin-markers characterized by triangular Cosserat point elements (TCPEs) and to evaluate the capability of four instantaneous physical parameters, which can be measured non-invasively in vivo, to identify the most accurate TCPEs. Moreover, TCPE pose estimations were compared with the estimations of two least squares minimization methods applied to the cluster of all markers, using rigid body (RBLS) and homogeneous deformation (HDLS) assumptions. Analysis was performed on previously collected in vivo treadmill gait data composed of simultaneous measurements of the gold-standard bone pose by bi-plane fluoroscopy tracking the subjects' knee prosthesis and a stereophotogrammetric system tracking skin-markers affected by soft tissue artifact. Femur orientation and position errors estimated from skin-marker clusters were computed for 18 subjects using clusters of up to 35 markers. Results based on gold-standard data revealed that instantaneous subsets of TCPEs exist which estimate the femur pose with reasonable accuracy (median root mean square error during stance/swing: 1.4/2.8 deg for orientation, 1.5/4.2 mm for position). A non-invasive and instantaneous criteria to select accurate TCPEs for pose estimation (4.8/7.3 deg, 5.8/12.3 mm), was compared with RBLS (4.3/6.6 deg, 6.9/16.6 mm) and HDLS (4.6/7.6 deg, 6.7/12.5 mm). Accounting for homogeneous deformation, using HDLS or selected TCPEs, yielded more accurate position estimations than RBLS method, which, conversely, yielded more accurate orientation estimations. Further investigation is required to devise effective criteria for cluster selection that could represent a significant improvement in bone pose estimation accuracy.     

Assessment of the lower limb soft tissue artefact at marker-cluster level with a high-density marker set during walking

The estimation of joint kinematics from skin markers is hindered by the soft tissue artefact (STA), a well-known phenomenon although not fully characterized. While most assessments of the STA have been performed based on the individual skin markers displacements, recent assessments were based on the marker-cluster geometrical transformations using, e.g., principal component or modal analysis. However, these marker-clusters were generally made of 4–6 markers and the current findings on the STA could have been biased by the limited number of skin makers analysed. The objective of the present study was therefore to confirm them with a high-density marker set, i.e. 40 markers placed on the segments.A larger number of modes than found in the literature was required to describe the STA. Nevertheless, translations and rotations of the marker-cluster remained the main STA modes, archetypally the translation along the proximal-distal and anterior-posterior axes for the shank and the translation along the proximal-distal axis and the rotation about the medial-lateral axis for the thigh. High correlations were also found between the knee flexion angle and the amplitude of these modes for the thigh whereas moderate ones were found for the shank.These findings support the current re-orientation of the STA compensation methods, from bone pose estimators which typically address the non-rigid components of the marker-cluster to kinematic-driven rigid-component STA models.     

CAT & MAUS: A novel system for true dynamic motion measurement of underlying bony structures with compensation for soft tissue movement

Optoelectronic motion capture systems are widely employed to measure the movement of human joints. However, there can be a significant discrepancy between the data obtained by a motion capture system (MCS) and the actual movement of underlying bony structures, which is attributed to soft tissue artefact. In this paper, a computer-aided tracking and motion analysis with ultrasound (CAT & MAUS) system with an augmented globally optimal registration algorithm is presented to dynamically track the underlying bony structure during movement. The augmented registration part of CAT & MAUS was validated with a high system accuracy of 80%. The Euclidean distance between the marker-based bony landmark and the bony landmark tracked by CAT & MAUS was calculated to quantify the measurement error of an MCS caused by soft tissue artefact during movement. The average Euclidean distance between the target bony landmark measured by each of the CAT & MAUS system and the MCS alone varied from 8.32 mm to 16.87 mm in gait. This indicates the discrepancy between the MCS measured bony landmark and the actual underlying bony landmark. Moreover, Procrustes analysis was applied to demonstrate that CAT & MAUS reduces the deformation of the body segment shape modeled by markers during motion. The augmented CAT & MAUS system shows its potential to dynamically detect and locate actual underlying bony landmarks, which reduces the MCS measurement error caused by soft tissue artefact during movement.     

Bayesian inverse kinematics vs. least-squares inverse kinematics in estimates of planar postures and rotations in the absence of soft tissue artifact

A variety of inverse kinematics (IK) algorithms exist for estimating postures and displacements from a set of noisy marker positions, typically aiming to minimize IK errors by distributing errors amongst all markers in a least-squares (LS) sense. This paper describes how Bayesian inference can contrastingly be used to maximize the probability that a given stochastic kinematic model would produce the observed marker positions. We developed Bayesian IK for two planar IK applications: (1) kinematic chain posture estimates using an explicit forward kinematics model, and (2) rigid body rotation estimates using implicit kinematic modeling through marker displacements. We then tested and compared Bayesian IK results to LS results in Monte Carlo simulations in which random marker error was introduced using Gaussian noise amplitudes ranging uniformly between 0.2 mm and 2.0 mm. Results showed that Bayesian IK was more accurate than LS-IK in over 92% of simulations, with the exception of one center-of-rotation coordinate planar rotation, for which Bayesian IK was more accurate in only 68% of simulations. Moreover, while LS errors increased with marker noise, Bayesian errors were comparatively unaffected by noise amplitude. Nevertheless, whereas the LS solutions required average computational durations of less than 0.5 s, average Bayesian IK durations ranged from 11.6 s for planar rotation to over 2000 s for kinematic chain postures. These results suggest that Bayesian IK can yield order-of-magnitude IK improvements for simple planar IK, but also that its computational demands may make it impractical for some applications.     

Proximal placement of lateral thigh skin markers reduces soft tissue artefact during normal gait using the Conventional Gait Model

A primary source of measurement error in gait analysis is soft-tissue artefact. Hip and knee angle measurements, regularly used in clinical decision-making, are particularly prone to pervasive soft tissue on the femur. However, despite several studies of thigh marker artefact it remains unclear how lateral thigh marker height affects results using variants of the Conventional Gait Model. We compared Vicon Plug-in Gait hip and knee angle estimates during gait using a proximal and distal thigh marker placement for ten healthy subjects. Knee axes were estimated by optimizing thigh rotation offsets to minimize knee varus-valgus range during gait. Relative to the distal marker, the proximal marker produced 37% less varus-valgus range and 50% less hip rotation range (p < 0.001), suggesting that it produced less soft-tissue artefact in knee axis estimates. The thigh markers also produced different secondary effects on the knee centre estimate. Using whole gait cycle optimization, the distal marker showed greater minimum and maximum knee flexion (by 6° and 2° respectively) resulting in a 4° reduction in range. Mid-stance optimization reduced distal marker knee flexion by 5° throughout, but proximal marker results were negligibly affected. Based on an analysis of the Plug-in Gait knee axis definition, we show that the proximal marker reduced sensitivity to soft-tissue artefact by decreasing collinearity between the points defining the femoral frontal plane and reducing anteroposterior movement between the knee and thigh markers. This study suggests that a proximal thigh marker may be preferable when performing gait analysis using the Plug-in Gait model.     

Joint kinematics estimation using a multi-body kinematics optimisation and an extended Kalman filter,and embedding a soft tissue artefact model

To reduce the impact of the soft tissue artefact (STA) on the estimate of skeletal movement using stereophotogrammetric and skin-marker data, multi-body kinematics optimisation (MKO) and extended Kalman filters (EKF) have been proposed. This paper assessed the feasibility and efficiency of these methods when they embed a mathematical model of the STA and simultaneously estimate the ankle, knee and hip joint kinematics and the model parameters. A STA model was used that provides an estimate of the STA affecting the marker-cluster located on a body segment as a function of the kinematics of the adjacent joints. The MKO and the EKF were implemented with and without the STA model. To assess these methods, intra-cortical pin and skin markers located on the thigh, shank, and foot of three subjects and tracked during the stance phase of running were used. Embedding the STA model in MKO and EKF reduced the average RMS of marker tracking from 12.6 to 1.6 mm and from 4.3 to 1.9 mm, respectively, showing that a STA model trial-specific calibration is feasible. Nevertheless, with the STA model embedded in MKO, the RMS difference between the estimated and the reference joint kinematics determined from the pin markers slightly increased (from 2.0 to 2.1 deg) On the contrary, when the STA model was embedded in the EKF, this RMS difference was slightly reduced (from 2.0 to 1.7 deg) thus showing a better potentiality of this method to attenuate STA effects and improve the accuracy of joint kinematics estimate.     

Surgical resection,intraoperative radiotherapy and immediate plastic reconstruction: A good option for the treatment of distal extremity soft tissue sarcomas

AimTo show three patients with soft tissue sarcomas of distal extremities conservatively treated after tumor-board discussion, involving margin-free surgery, exclusive intraoperative radiotherapy, and immediate reconstruction.BackgroundCurrent guidelines show clear and robust recommendations regarding the composition of the treatment of sarcomas of extremities. However, little evidence exists regarding the application of these treatments depending on the location of the primary neoplasia. Tumors that affect the distal extremities present different challenges and make multidisciplinary discussions desirable.Methods/ResultsWe reported 3 patients who were approached with a conservative intention, after tumor board recomendation. The goals from the treatment performed were aesthetic and functional preservation, while enruring locoregional control. We had wound healing complications in 2 of the cases, requiring additional reconstruction measures. Patients are followed up for 24, 20 and 10 months; local control is 100%, and functional preservation is 100%.ConclusionsDespite being a small series, it was sufficient to illustrate successful multidisciplinary planning, generating a therapeutic result with improved quality of life for patients who had an initial indication for extremity amputation.     

Kalman smoothing improves the estimation of joint kinematics and kinetics in marker-based human gait analysis

We developed a Kalman smoothing algorithm to improve estimates of joint kinematics from measured marker trajectories during motion analysis. Kalman smoothing estimates are based on complete marker trajectories. This is an improvement over other techniques, such as the global optimisation method (GOM), Kalman filtering, and local marker estimation (LME), where the estimate at each time instant is only based on part of the marker trajectories. We applied GOM, Kalman filtering, LME, and Kalman smoothing to marker trajectories from both simulated and experimental gait motion, to estimate the joint kinematics of a ten segment biomechanical model, with 21 degrees of freedom. Three simulated marker trajectories were studied: without errors, with instrumental errors, and with soft tissue artefacts (STA). Two modelling errors were studied: increased thigh length and hip centre dislocation. We calculated estimation errors from the known joint kinematics in the simulation study. Compared with other techniques, Kalman smoothing reduced the estimation errors for the joint positions, by more than 50% for the simulated marker trajectories without errors and with instrumental errors. Compared with GOM, Kalman smoothing reduced the estimation errors for the joint moments by more than 35%. Compared with Kalman filtering and LME, Kalman smoothing reduced the estimation errors for the joint accelerations by at least 50%. Our simulation results show that the use of Kalman smoothing substantially improves the estimates of joint kinematics and kinetics compared with previously proposed techniques (GOM, Kalman filtering, and LME) for both simulated, with and without modelling errors, and experimentally measured gait motion.     

Propagation of soft tissue artifacts to the center of rotation: A model for the correction of functional calibration techniques

This paper presents a mathematical model for the propagation of errors in body segment kinematics to the location of the center of rotation. Three functional calibration techniques, usually employed for the gleno-humeral joint, are studied: the methods based on the pivot of the instantaneous helical axis (PIHA) or the finite helical axis (PFHA), and the “symmetrical center of rotation estimation” (SCoRE). A procedure for correcting the effect of soft tissue artifacts is also proposed, based on the equations of those techniques and a model of the artifact, like the one that can be obtained by double calibration. An experiment with a mechanical analog was performed to validate the procedure and compare the performance of each technique. The raw error (between 57 and 68 mm) was reduced by a proportion of between 1:6 and less than 1:15, depending on the artifact model and the mathematical method. The best corrections were obtained by the SCoRE method. Some recommendations about the experimental setup for functional calibration techniques and the choice of a mathematical method are derived from theoretical considerations about the formulas and the results of the experiment.     

Estimating joint kinematics from skin motion observation: modelling and validation

Modelling of soft tissue motion is required in many areas, such as computer animation, surgical simulation, 3D motion analysis and gait analysis. In this paper, we will focus on the use of modelling of skin deformation during 3D motion analysis. The most frequently used method in 3D human motion analysis involves placing markers on the skin of the analysed segment which is composed of the rigid bone and the surrounding soft tissues. Skin and soft tissue deformations introduce a significant artefact which strongly influences the resulting bone position, orientation and joint kinematics. For this study, we used a statistical solid dynamics approach which is a combination of several previously reported tools: the point cluster technique (PCT) and a Kalman filter which was added to the PCT. The methods were tested and evaluated on controlled human-arm motions, using an optical motion capture system (Vicon^TM).

The addition of a Kalman filter to the PCT for rigid body motion estimation results in a smoother signal that better represents the joint motion. Calculations indicate less signal distortion than when using a digital low-pass filter. Furthermore, adding a Kalman filter to the PCT substantially reduces the dispersion of the maximal and minimal instantaneous frequencies. For controlled human movements, the result indicated that adding a Kalman filter to the PCT produced a more accurate signal. However, it could not be concluded that the proposed Kalman filter is better than a low-pass filter for estimation of the motion. We suggest that implementation of a Kalman filter with a better biomechanical motion model will be more likely to improve the results.     

Effect of rocker shoes and running speed on lower limb mechanics and soft tissue vibrations

Previous studies have shown a possible effect of running speed and the sole material of footwear on lower-limb mechanics and soft tissue vibrations, while little information has been offered concerning the influence of the shape of the footwear’s sole. The purpose of this study is to assess the effect of running speed and rocker shoes on muscular activity, ground reaction force, and soft tissue vibrations. Twenty participants performed heel-toe running with two shoes, differentiated only by their sole shape (i.e. rocker and non-rocker), at four running speeds. Ground reaction force and electromyograms of the gastrocnemius medialis and vastus lateralis were measured, and soft tissue accelerations of the same muscles were recorded with tri-axial accelerometers. A continuous wavelet transform was applied to the accelerometer’s signals to analyse them in the time-frequency domain. The rocker of the shoes did not change the muscular activations, ground reaction force, nor power of soft tissue vibrations. In opposite, increased running speed led to an augmentation of all of the measured parameters. Interestingly, running speed augmentation led to a greater increase in high frequencies component of soft tissue vibrations (25–50 Hz, 242%) than lower ones (8–25 Hz, 111%). Consequently, we indicated a 10% increase in the relative part of the high frequencies of the total power. In conclusion, although rocker shoes have shown an effect on lower-limb kinetics in some studies, no influence on soft tissue vibration is denoted. By contrast, soft tissue vibrations may be modulated by changing running speed.     

A finite nonlinear hyper-viscoelastic model for soft biological tissues

Soft tissues exhibit highly nonlinear rate and time-dependent stress-strain behaviour. Strain and strain rate dependencies are often modelled using a hyperelastic model and a discrete (standard linear solid) or continuous spectrum (quasi-linear) viscoelastic model, respectively. However, these models are unable to properly capture the materials characteristics because hyperelastic models are unsuited for time-dependent events, whereas the common viscoelastic models are insufficient for the nonlinear and finite strain viscoelastic tissue responses. The convolution integral based models can demonstrate a finite viscoelastic response; however, their derivations are not consistent with the laws of thermodynamics. The aim of this work was to develop a three-dimensional finite hyper-viscoelastic model for soft tissues using a thermodynamically consistent approach. In addition, a nonlinear function, dependent on strain and strain rate, was adopted to capture the nonlinear variation of viscosity during a loading process. To demonstrate the efficacy and versatility of this approach, the model was used to recreate the experimental results performed on different types of soft tissues. In all the cases, the simulation results were well matched ($R^2⩾0.99$) with the experimental data.