Michael Damsgaard

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.

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.

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.

Computational method for muscle-path representation in musculoskeletal models.

Abstract. This paper presents a new and efficient method to calculate the line-of-action of a muscle as it wraps over bones and other tissues on its way from origin to insertion. The muscle is assumed to be a one-dimensional, massless, taut string, and the surfaces of bones that the muscle may wrap around are approximated by cross-sectional boundaries obtained by slicing geometrical models of bones. Each cross-sectional boundary is approximated by a series of connected line segments. Thus, the muscle path to be calculated is piecewise linear with vertices being the contact points on the cross-sectional boundaries of the bones. Any level of geometric accuracy can be obtained by increasing the number of cross sections and the number of line segments in each cross section. The algorithm is computationally efficient even for large numbers of cross sections.

TLEM 2.0 - A comprehensive musculoskeletal geometry dataset for subject-specific modeling of lower extremity

When analyzing complex biomechanical problems such as predicting the effects of orthopedic surgery, subject-specific musculoskeletal models are essential to achieve reliable predictions. The aim of this paper is to present the Twente Lower Extremity Model 2.0, a new comprehensive dataset of the musculoskeletal geometry of the lower extremity, which is based on medical imaging data and dissection performed on the right lower extremity of a fresh male cadaver. Bone, muscle and subcutaneous fat (including skin) volumes were segmented from computed tomography and magnetic resonance images scans. Inertial parameters were estimated from the image-based segmented volumes. A complete cadaver dissection was performed, in which bony landmarks, attachments sites and lines-of-action of 55 muscle actuators and 12 ligaments, bony wrapping surfaces, and joint geometry were measured. The obtained musculoskeletal geometry dataset was finally implemented in the AnyBody Modeling System (AnyBody Technology A/S, Aalborg, Denmark), resulting in a model consisting of 12 segments, 11 joints and 21 degrees of freedom, and including 166 muscle-tendon elements for each leg. The new TLEM 2.0 dataset was purposely built to be easily combined with novel image-based scaling techniques, such as bone surface morphing, muscle volume registration and muscle-tendon path identification, in order to obtain subject-specific musculoskeletal models in a quick and accurate way. The complete dataset, including CT and MRI scans and segmented volume and surfaces, is made available at http://www.utwente.nl/ctw/bw/research/projects/TLEMsafe for the biomechanical community, in order to accelerate the development and adoption of subject-specific models on large scale. TLEM 2.0 is freely shared for non-commercial use only, under acceptance of the TLEMsafe Research License Agreement.

Introduction to Force-dependent Kinematics: Theory and Application to Mandible Modeling

Knowledge of the muscle, ligament, and joint forces is important when planning orthopedic surgeries. Since these quantities cannot be measured in vivo under normal circumstances, the best alternative is to estimate them using musculoskeletal models. These models typically assume idealized joints, which are sufficient for general investigations but insufficient if the joint in focus is far from an idealized joint. The purpose of this study was to provide the mathematical details of a novel musculoskeletal modeling approach, called force-dependent kinematics (FDK), capable of simultaneously computing muscle, ligament, and joint forces as well as internal joint displacements governed by contact surfaces and ligament structures. The method was implemented into the anybody modeling system and used to develop a subject-specific mandible model, which was compared to a point-on-plane (POP) model and validated against joint kinematics measured with a custom-built brace during unloaded emulated chewing, open and close, and protrusion movements. Generally, both joint models estimated the joint kinematics well with the POP model performing slightly better (root-mean-square-deviation (RMSD) of less than 0.75 mm for the POP model and 1.7 mm for the FDK model). However, substantial differences were observed when comparing the estimated joint forces (RMSD up to 24.7 N), demonstrating the dependency on the joint model. Although the presented mandible model still contains room for improvements, this study shows the capabilities of the FDK methodology for creating joint models that take the geometry and joint elasticity into account.

How Good is Good Enough? Lessons in Musculoskeletal Model Validation With the Anybody Modeling System

In the last two decades a steady evolution has taken place in the realm of musculoskeletal simulation, which is now taking an increasingly central role in guiding ergonomics evaluations, influencing medical device design, and informing clinical decisions. Musculoskeletal simulation holds tremendous promise to help bring safer, more innovative products to market more quickly and to drive optimized, patient-specific care. But, to effectively deliver on these challenging goals, both the software and the models created from it must meet high expectations for verification and validation so that critical choices influenced by simulation can be made with confidence. Verification is the job of the software developer, but due to the breadth of modeling applications, the task of validation falls to the user. Rigorous model validation is time consuming and often technically difficult. And so, the question arises, in the context of both verification and validation, “How good is good enough?” The goal of this paper is to offer a response to that question. The discussion will be complemented by relevant validation examples from the open literature pertaining to one commercial musculoskeletal simulation software, the AnyBody Modeling System (AMS).Copyright