Michael Skipper Andersen

Do kinematic models reduce the effects of soft tissue artefacts in skin marker-based motion analysis? An in vivo study of knee kinematics

We investigated the effects of including kinematic constraints in the analysis of knee kinematics from skin markers and compared the result to simultaneously recorded trajectories of bone pin markers during gait of six healthy subjects. The constraint equations that were considered for the knee were spherical and revolute joints, which have been frequently used in musculoskeletal modelling. In the models, the joint centres and joint axes of rotations were optimised from the skin marker trajectories over the trial. It was found that the introduction of kinematic constraints did not reduce the error associated with soft tissue artefacts. The inclusion of a revolute joint constraint showed a statistically significant increase in the mean flexion/extension joint angle error and no statistically significant change for the two other mean joint angle errors. The inclusion of a spherical joint showed a statistically significant increase in the mean flexion/extension and abduction/adduction errors. In addition, when a spherical joint was included, a statistically significant increase in the sum of squared differences between measured marker trajectories and the trajectories of the pin markers in the models was seen. From this, it was concluded that both more advanced knee models as well as models of soft tissue artefacts should be developed before accurate knee kinematics can be calculated from skin markers.

Kinematic analysis of over-determinate biomechanical systems

In this paper, we introduce a new general method for kinematic analysis of rigid multi body systems subject to holonomic constraints. The method extends the standard analysis of kinematically determinate rigid multi body systems to the over-determinate case. This is accomplished by introducing a constrained optimisation problem with the objective function given as a function of the set of system equations that are allowed to be violated while the remaining equations define the feasible set. We show that exact velocity and acceleration analysis can also be performed by solving linear sets of equations, originating from differentiation of the Karush–Kuhn–Tucker optimality conditions. The method is applied to the analysis of an 18 degrees-of-freedom gait model where the kinematical drivers are prescribed with data from a motion capture experiment. The results show that significant differences are obtained between applying standard kinematic analysis or minimising the least-square errors on the two fully equivalent 3D gait models with only the way the experimental data is processed being different.

A computationally efficient optimisation-based method for parameter identification of kinematically determinate and over-determinate biomechanical systems

This paper introduces a general optimisation-based method for identification of biomechanically relevant parameters in kinematically determinate and over-determinate systems from a given motion. The method is designed to find a set of parameters that is constant over the time frame of interest as well as the time-varying system coordinates, and it is particularly relevant for biomechanical motion analysis where the system parameters can be difficult to accurately determine by direct measurements. Although the parameter identification problem results in a large-scale optimisation problem, we show that, due to a special structure in the linearised Karush–Kuhn–Tucker optimality conditions, the solution can be found very efficiently. The method is applied to a set of test problems relevant for gait analysis. These involve determining the local coordinates of markers placed on the model, segment lengths and joint axes of rotation from both gait and range of motion experiments.

On validation of multibody musculoskeletal models

We review the opportunities to validate multibody musculoskeletal models in view of the current transition of musculoskeletal modelling from a research topic to a practical simulation tool in product design, healthcare and other important applications. This transition creates a new need for justification that the models are adequate representations of the systems they simulate. The need for a consistent terminology and established standards is identified and knowledge from fields with a more progressed state-of-the-art in verification and validation is introduced. A number of practical steps for improvement of the validation of multibody musculoskeletal models are pointed out and directions for future research in the field are proposed. It is hoped that a more structured approach to model validation can help to improve the credibility of musculoskeletal models.

A linear soft tissue artefact model for human movement analysis: Proof of concept using in vivo data

We investigated the accuracy of a linear soft tissue artefact (STA) model in human movement analysis. Simultaneously recorded bone-mounted pin and skin marker data for the thigh and shank during walking, cutting and hopping were used to measure and model the motion of the skin marker clusters within anatomical reference frames (ARFs). This linear model allows skin marker movements relative to the underlying bone contrary to a rigid-body assumption. The linear model parameters were computed through a principal component analysis, which revealed that 95% of the variance of the STA motion for the thigh was contained in the first four principal components for all three tasks and all subjects. For the shank, 95% of the variance was contained in the first four principal components during walking and cutting and first five during hopping. For the thigh, the maximum residual artefact was reduced from 27.0mm to 5.1mm (walking), 22.7 mm to 3.0mm (cutting) and 16.2mm to 3.5mm (hopping) compared to a rigid-body assumption. Similar reductions were observed for the shank: 24.2mm to 1.9 mm (walking), 20.3mm to 1.9 mm (cutting) and 14.7 mm to 1.8mm (hopping). A geometric analysis of the first four principal components revealed that, within the ARFs, marker cluster STA is governed by rigid-body translations and rotations rather than deformations. The challenge remains, however, in finding the linear model parameters without bone pin data, but this investigation shows that relatively few parameters in a linear model are required to model the vast majority of the STA movements.

A musculoskeletal foot model for clinical gait analysis

Several full body musculoskeletal models have been developed for research applications and these models may potentially be developed into useful clinical tools to assess gait pathologies. Existing full-body musculoskeletal models treat the foot as a single segment and ignore the motions of the intrinsic joints of the foot. This assumption limits the use of such models in clinical cases with significant foot deformities. Therefore, a three-segment musculoskeletal model of the foot was developed to match the segmentation of a recently developed multi-segment kinematic foot model. All the muscles and ligaments of the foot spanning the modeled joints were included. Muscle pathways were adjusted with an optimization routine to minimize the difference between the muscle flexion-extension moment arms from the model and moment arms reported in literature. The model was driven by walking data from five normal pediatric subjects (aged 10.6+/-1.57 years) and muscle forces and activation levels required to produce joint motions were calculated using an inverse dynamic analysis approach. Due to the close proximity of markers on the foot, small marker placement error during motion data collection may lead to significant differences in musculoskeletal model outcomes. Therefore, an optimization routine was developed to enforce joint constraints, optimally scale each segment length and adjust marker positions. To evaluate the model outcomes, the muscle activation patterns during walking were compared with electromyography (EMG) activation patterns reported in the literature. Model-generated muscle activation patterns were observed to be similar to the EMG activation patterns.

Prediction of ground reaction forces and moments during various activities of daily living

Inverse dynamics based simulations on musculoskeletal models is a commonly used method for the analysis of human movement. Due to inaccuracies in the kinematic and force plate data, and a mismatch between the model and the subject, the equations of motion are violated when solving the inverse dynamics problem. As a result, dynamic inconsistency will exist and lead to residual forces and moments. In this study, we present and evaluate a computational method to perform inverse dynamics-based simulations without force plates, which both improves the dynamic consistency as well as removes the model׳s dependency on measured external forces. Using the equations of motion and a scaled musculoskeletal model, the ground reaction forces and moments (GRF&Ms) are derived from three-dimensional full-body motion. The method entails a dynamic contact model and optimization techniques to solve the indeterminacy problem during a double contact phase and, in contrast to previously proposed techniques, does not require training or empirical data. The method was applied to nine healthy subjects performing several Activities of Daily Living (ADLs) and evaluated with simultaneously measured force plate data. Except for the transverse ground reaction moment, no significant differences (P>0.05) were found between the mean predicted and measured GRF&Ms for almost all ADLs. The mean residual forces and moments, however, were significantly reduced (P>0.05) in almost all ADLs using our method compared to conventional inverse dynamic simulations. Hence, the proposed method may be used instead of raw force plate data in human movement analysis using inverse dynamics.

Scaling of musculoskeletal models from static and dynamic trials

Subject-specific scaling of cadaver-based musculoskeletal models is important for accurate musculoskeletal analysis within multiple areas such as ergonomics, orthopaedics and occupational health. We present two procedures to scale ‘generic’ musculoskeletal models to match segment lengths and joint parameters to a specific subject and compare the results to a simpler approach based on linear, segment-wise scaling. By incorporating data from functional and standing reference trials, the new scaling approaches reduce the model sensitivity to assumed model marker positions. For validation, we applied all three scaling methods to an inverse dynamics-based musculoskeletal model and compared predicted knee joint contact forces to those measured with an instrumented prosthesis during gait. Additionally, a Monte Carlo study was used to investigate the sensitivity of the knee joint contact force to random adjustments of the assumed model marker positions (+/− one marker diameter). The model based on linear scaling showed the highest variation in the knee joint contact force of 1.44 body weight (BW) around contra-lateral heel strike, and a variation in root mean square deviation (RMSD) of 0.36 BW. The proposed methods reduced the variation to 1.0 BW (RMSD 0.26 BW) for the anatomical landmark based method and 0.47 BW (RMSD 0.06 BW) for the functional based method. Variation in model predictions due to uncertainty in marker positions is a trait of all marker-based musculoskeletal modelling approaches. The presented methods solve part of this problem and rely less on manual identification of anatomical landmarks in the model. The work represents a step towards a more consistent methodology in musculoskeletal modelling.

Individual motion patterns during gait and sit-to-stand contribute to edge-loading risk in metal-on-metal hip resurfacing

The occurrence of pseudotumours (soft tissue masses relating to the hip joint) following metal-on-metal hip resurfacing arthroplasty has been associated with higher than normal bearing wear and high serum metal ion levels although both these findings do not necessarily coexist. The purpose of this study was to examine patient activity patterns and their influence on acetabular component edge loading in a group of subjects with known serum metal ion levels. Fifteen subjects with metal-on-metal hip resurfacing arthroplasty (eight males and seven females) were recruited for motion analysis followed by computed tomography scans. They were divided into three groups based on their serum metal ion levels and the orientation of their acetabular component: well-positioned acetabular component with low metal ions, mal-positioned acetabular component with low metal ions and mal-positioned acetabular component with high ions. A combination of motion analysis, subject-specific modelling (AnyBody Modeling System, Aalborg, Denmark) and computed tomography measurements was used to calculate dynamically the contact patch-to-rim distance for each subject during gait and sit-to-stand. The contact-pitch-to-rim distance for the high ion group was significantly lower (p<0.001) than for the two low ion groups (well-positioned and mal-positioned) during the stance phase of gait (0%–60%) and loading phase of sit-to-stand (20%–80%). The results of this study, in particular, the significant difference between the two mal-positioned groups, suggest that wear of metal-on-metal hip resurfacing arthroplasty is not only affected by acetabular cup orientation but also influenced by individual patient activity patterns.

Estimation of Ground Reaction Forces and Moments During Gait Using Only Inertial Motion Capture

Ground reaction forces and moments (GRF&M) are important measures used as input in biomechanical analysis to estimate joint kinetics, which often are used to infer information for many musculoskeletal diseases. Their assessment is conventionally achieved using laboratory-based equipment that cannot be applied in daily life monitoring. In this study, we propose a method to predict GRF&M during walking, using exclusively kinematic information from fully-ambulatory inertial motion capture (IMC). From the equations of motion, we derive the total external forces and moments. Then, we solve the indeterminacy problem during double stance using a distribution algorithm based on a smooth transition assumption. The agreement between the IMC-predicted and reference GRF&M was categorized over normal walking speed as excellent for the vertical (ρ = 0.992, rRMSE = 5.3%), anterior (ρ = 0.965, rRMSE = 9.4%) and sagittal (ρ = 0.933, rRMSE = 12.4%) GRF&M components and as strong for the lateral (ρ = 0.862, rRMSE = 13.1%), frontal (ρ = 0.710, rRMSE = 29.6%), and transverse GRF&M (ρ = 0.826, rRMSE = 18.2%). Sensitivity analysis was performed on the effect of the cut-off frequency used in the filtering of the input kinematics, as well as the threshold velocities for the gait event detection algorithm. This study was the first to use only inertial motion capture to estimate 3D GRF&M during gait, providing comparable accuracy with optical motion capture prediction. This approach enables applications that require estimation of the kinetics during walking outside the gait laboratory.