Objective: Biomechanical modeling is an important tool in that it can provide estimates of forces that cannot easily be measured (e.g., soft tissue loads). The goal of this study was to develop a discrete element model of the knee that is open source to allow for utilization of modeling by a wider audience of researchers. Methods: A six degree-of-freedom tibiofemoral and one degree-of-freedom patellofemoral joint were created in OpenSim. Eighteen ligament bundles and tibiofemoral contact were included in the model. Results: During a passive flexion movement, maximum deviation of the model from the literature occurred at the most flexed angle with deviations of 2° adduction, 7° internal rotation, 1-mm posterior translation, 12-mm inferior translation, and 4-mm lateral translation. Similarly, the overall elongation of the ligaments agreed with literature values with strains of less than 13%. Conclusion: These results provide validation of the physiological relevance of the model. Significance: This model is one of the few open source, discrete element knee models to date, and has many potential applications, one being for use in an open-source cosimulation framework.

We tested an innovative method to estimate joint stiffness and damping during multijoint unfettered arm movements. The technique employs impulsive perturbations and a time-frequency analysis to estimate the arm's mechanical properties along a reaching trajectory. Each single impulsive perturbation provides a continuous estimation on a single-reach basis, making our method ideal to investigate motor adaptation in the presence of force fields and to study the control of movement in impaired individuals with limited kinematic repeatability. In contrast with previous dynamic stiffness studies, we found that stiffness varies during movement, achieving levels higher than during static postural control. High stiffness was associated with elevated reflexive activity. We observed a decrease in stiffness and a marked reduction in long-latency reflexes around the reaching movement velocity peak. This pattern could partly explain the difference between the high stiffness reported in postural studies and the low stiffness measured in dynamic estimation studies, where perturbations are typically applied near the peak velocity point.

This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.

Spasticity and muscular hypertonus are frequently found in stroke survivors and may have a significant effect on functional impairment. These abnormal neuro-muscular properties, which are quantifiable by the net impedance of the hand, have a direct consequence on arm mechanics and are likely to produce anomalous motor paths. Literature studies quantifying limb impedance in stroke survivors have focused on multijoint static tasks and single joint movements. Despite this research, little is known about the role of sensory motor integration in post-stroke impedance modulation. The present study elucidates this role by integrating an evaluation of arm impedance into a robotically mediated therapy protocol. Our analysis had three specific objectives: 1) obtaining a reliable measure for the mechanical proprieties of the upper limb during robotic therapy; 2) investigating the effects of robot-assisted training and visual feedback on arm stiffness and viscosity; 3) determining if the stiffness measure and its relationship with either training or visual feedback depend on arm position, speed, and level of assistance. This work demonstrates that the performance improvements produced by minimally assistive robot training are associated with decreased viscosity and stiffness in stroke survivors' paretic arm and that these mechanical impedance components are partially modulated by visual feedback.

It is well documented that neurological deficits after stroke can disrupt motor control processes that affect the smoothness of reaching movements. The smoothness of hand trajectories during multi-joint reaching depends on shoulder and elbow joint angular velocities and their successive derivatives as well as on the instantaneous arm configuration and its rate of change. Right-handed survivors of unilateral hemiparetic stroke and neurologically-intact control participants held the handle of a two-joint robot and made horizontal planar reaching movements. We decomposed endpoint jerk into components related to shoulder and elbow joint angular velocity, acceleration, and jerk. We observed an abnormal decomposition pattern in the most severely impaired stroke survivors consistent with deficits of inter-joint coordination. We then used numerical simulations of reaching movements to test whether the specific pattern of inter-joint coordination deficits observed experimentally could be explained by either a general increase in motor noise related to weakness or by an impaired ability to compensate for multi-joint interaction torque. Simulation results suggest that observed deficits in movement smoothness after stroke more likely reflect an impaired ability to compensate for multi-joint interaction torques rather than the mere presence of elevated motor noise.

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.