John Rasmussen

Analysis of Musculoskeletal Systems in the AnyBody Modeling System

This paper reviews the simulation software the AnyBody Modeling System, which was originally developed by the authors. AnyBody is capable of analyzing the musculoskeletal system of humans or other creatures as rigid-body systems. The paper introduces the main features of the system; in particular, the inverse dynamic analysis that resolves the fundamental indeterminacy of the muscle configuration. In addition to the musculoskeletal system, a model can comprise external objects, loads, and motion specifications, thereby providing a complete set of the boundary conditions for a given task. The paper also describes the basic ideas of structured model development in AnyBody. 2006 Elsevier B.V. All rights reserved.

Muscle recruitment by the min/max criterion — a comparative numerical study

This paper introduces the min/max criterion for simulation of muscle recruitment in multiple muscle systems. The criterion is introduced and justified by comparison to two known criterion types: the polynomial criterion and the soft saturation criterion. The comparison is performed on a planar three-muscle elbow model performing a dumbbell curl. A generalized form of the soft saturation criterion is introduced, and it is shown that the min/max criterion can be interpreted as the limit of the classical criteria when the exponents in their mathematical expressions approach infinity. We finally show how the min/max criterion can be cast into a form that allows for efficient and robust numerical solution by linear programming. It is concluded that the min/max criterion possesses a number of attractive physiological as well as algorithmic advantages.

Anatomy and biomechanics of the back muscles in the lumbar spine with reference to biomechanical modeling.

Study Design. This article describes the development of a musculoskeletal model of the human lumbar spine with focus on back muscles. It includes data from literature in a structured form. Objective. To review the anatomy and biomechanics of the back muscles related to the lumbar spine with relevance for biomechanical modeling. Summary of Background Data. To reduce complexity, muscle units have been incorporated in an abridged manner, reducing their actions more or less to a single force equivalent. In early models of the lumbar spine, this may have been a necessary step to reduce complexity and, thereby, calculation time. The muscles of the spine are well described in the literature, but mainly qualitatively. Most of the literature provides a description of the structures without precise data of fiber length, muscle length, cross-sectional areas, moment arms, forces, etc. The predicted output of musculoskeletal models is very much dependent on the input parameters. The information needed to improve models consists of better approximations of the attachments to the vertebrae, and more precise data. Method. Review of literature. Results. The predicted output of musculoskeletal models is very much dependent on the input parameters. Moderate changes in the assumed muscle line-of-action (i.e., moment arm) could substantially alter the magnitudes of predicted muscle and spinal forces, while the choice of optimization formulation is less sensitive. Conclusions. Input parameters, moment arms, as well as physiologic cross-sectional areas have a profound effect on the predicted muscle forces. Therefore, it is important to choose the values for moment arm and physiologic cross-sectional area carefully because they are essential input parameters to biomechanical models.

A Method of “Exact” Numerical Differentiation for Error Elimination in Finite-Element-Based Semi-Analytical Shape Sensitivity Analyses

ABSTRACT The traditional, simple numerical differentiation of finite-element stiffness matrices by a forward difference scheme is the source of severe error problems that have been reported recently for certain problems of finite-element-based, semi-analytical shape design sensitivity analysis. In order to develop a method for elimination of such errors, without a sacrifice of the simple numerical differentiation and other main advantages of the semi-analytical method, the common mathematical structure of a broad range of finite-element stiffness matrices is studied in this paper. This study leads to the result that element stiffness matrices can generally be expressed in terms of a class of special scalar functions and a class of matrix functions of shape design variables that are defined such that the members of the classes admit “exact” numerical differentiation (exact up to round-off error) by means of very simple correction factors to upgrade standard computationally inexpensive first-order finite di...

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.

Validation of a musculoskeletal model of wheelchair propulsion and its application to minimizing shoulder joint forces

The majority of manual wheelchair users (MWUs) will inevitably develop some degree of shoulder pain over time. Previous research has suggested a link between the shoulder joint forces associated with the repetition of wheelchair (WC) propulsion and pain. The objective of this work is to present and validate a rigid-body musculoskeletal model of the upper limb for calculation of shoulder joint forces throughout WC propulsion. It is anticipated that when prescribing a WC, the use of a patient-specific computational model will aide in determining an axle placement in which shoulder joint forces are at a minimum, thus potentially delaying or reducing the shoulder pain that so many MWUs experience. During the validation experiment, 3 subjects (2 individuals with paraplegia and one able-bodied individual) propelled a WC at a self-selected speed, during which, kinematics, kinetics, and electromyography (EMG) activity were measured for the contact phase of 10 consecutive push strokes. The measured forces at the push rim and the 3-D propulsion kinematics drove the model, and the computationally calculated muscle activities were compared with the experimental muscle activities, resulting in an average mean absolute error (MAE) of 0.165. Further investigation of the shoulder joint forces throughout propulsion demonstrate the effect of axle placement on the magnitude of these forces. The present work serves to validate the patient-specific upper limb model for use as a prescriptive tool for fitting a subject to their WC. Minimizing joint forces from injury onset may prolong a MWUs pain-free way of life.

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.

Study of inaccuracy in semi-analytical sensitivity analysis — a model problem

The semi-analytical method of sensitivity analysis (Zienkiewicz and Campbell 1973; Esping 1983; Cheng and Liu 1987) of finite element discretized structures is attractive due to the balance between computational cost and ease of implementation (Cheng and Liu 1987; Haftka and Adelman 1989), but unfortunately the method may exhibit serious inaccuracies when applied in shape optimization of structures modelled by beam, plate, shell and Hermite elements (Cheng and Liu 1987; Haftka and Adelman 1989; Barthelemyet al. 1988; Barthelemy and Haftka 1988; Choi and Twu 1991, Pedersenet al. 1989; Chenget al. 1989).In the present paper, we perform an exact analysis of the error of sensitivity for a simple model problem which has earlier been considered by Barthelemyet al. (1988), Barthelemy and Haftka (1988), Pedersenet al. (1989). The analysis gives a deep insight into the nature of the general inaccuracy problem and enables us to devise methods by which the severe error of the sensitivity can be substantially reduced or removed for the model problem. The results of the paper are illustrated via an example.A method of error elimination for an extended class of semianalytical analysis problems is developed and presented in a companion paper (Olhoff and Rasmussen 1991).