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Musculoskeletal (MS) models should be able to integrate patient-specific MS architecture and undergo thorough validation prior to their introduction into clinical practice. We present a methodology to develop subject-specific models able to simultaneously predict muscle, ligament, and knee joint contact forces along with secondary knee kinematics. The MS architecture of a generic cadaver-based model was scaled using an advanced morphing technique to the subject-specific morphology of a patient implanted with an instrumented total knee arthroplasty (TKA) available in the fifth "grand challenge competition to predict in vivo knee loads" dataset. We implemented two separate knee models, one employing traditional hinge constraints, which was solved using an inverse dynamics technique, and another one using an 11-degree-of-freedom (DOF) representation of the tibiofemoral (TF) and patellofemoral (PF) joints, which was solved using a combined inverse dynamic and quasi-static analysis, called force-dependent kinematics (FDK). TF joint forces for one gait and one right-turn trial and secondary knee kinematics for one unloaded leg-swing trial were predicted and evaluated using experimental data available in the grand challenge dataset. Total compressive TF contact forces were predicted by both hinge and FDK knee models with a root-mean-square error (RMSE) and a coefficient of determination (R2) smaller than 0.3 body weight (BW) and equal to 0.9 in the gait trial simulation and smaller than 0.4 BW and larger than 0.8 in the right-turn trial simulation, respectively. Total, medial, and lateral TF joint contact force predictions were highly similar, regardless of the type of knee model used. Medial (respectively lateral) TF forces were over- (respectively, under-) predicted with a magnitude error of M < 0.2 (respectively > -0.4) in the gait trial, and under- (respectively, over-) predicted with a magnitude error of M > -0.4 (respectively < 0.3) in the right-turn trial. Secondary knee kinematics from the unloaded leg-swing trial were overall better approximated using the FDK model (average Sprague and Geers' combined error C = 0.06) than when using a hinged knee model (C = 0.34). The proposed modeling approach allows detailed subject-specific scaling and personalization and does not contain any nonphysiological parameters. This modeling framework has potential applications in aiding the clinical decision-making in orthopedics procedures and as a tool for virtual implant design.

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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.

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.

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.

We propose and analyze the properties of a simple, computationally efficient pair potential for nonpolar molecules based on the contact function for ellipsoidal cores. We discuss the relation of this potential to the Gaussian overlap potential and show that the present potential gives the correct extension of the ideas of the Gaussian overlap potential to mixtures. We show that this potential obeys a form of the principle of corresponding states and derive an expression for the second virial coefficient. As this potential has an incorrect symmetry at large separations, we derive another contact potential that behaves isotropically at infinite separation. Unfortunately, this potential does not have the good computational features of the one investigated here.