Davide Piovesan

Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

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 arms 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 techniques 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.

Comparative Analysis of Methods for Estimating Arm Segment Parameters and Joint Torques From Inverse Dynamics

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.

Experimental measure of arm stiffness during single reaching movements with a time-frequency analysis.

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 arms 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.

A new time-frequency approach to estimate single joint upper limb impedance

This paper proposes a new technique to estimate single joint impedance during postural tasks. The method is based on a reassigned spectrogram and can track the frequency modulation of biomechanical system after perturbations. Compared to the existing techniques, this procedure successfully estimated rapidly time varying impedance parameters in a faster and equally accurate way. For this reason it can be an optimum tool to easily estimate limb impedance of stroke patients, before, during, and after robot therapy sessions, without interfering with the delivered treatment.

Multijoint arm stiffness during movements following stroke: Implications for robot therapy

Impaired arm movements in stroke appear as a set of stereotypical kinematic patterns, characterized by abnormal joint coupling, which have a direct consequence on arm mechanics and can be quantified by the net arm stiffness at the hand. The current available measures of arm stiffness during functional tasks have limited clinical use, since they require several repetitions of the same test movement in many directions. Such procedure is difficult to obtain in stroke survivors who have lower fatigue threshold and increased variability compared to unimpaired individuals. The present study proposes a novel, fast quantitative measure of arm stiffness during movements by means of a Time-Frequency technique and the use of a reassigned spectrogram, applied on a trial-by-trial basis with a single perturbation. We tested the technique feasibility during robot mediated therapy, where a robot helped stroke survivors to regain arm mobility by providing assistive forces during a hitting task to 13 targets covering the entire reachable workspace. The endpoint stiffness of the paretic arm was estimated at the end of each hitting movements by suddenly switching of the assistive forces and observing the ensuing recoil movements. In addition, we considered how assistive forces influence stiffness. This method will provide therapists with improved tools to target the treatment to the individuals specific impairment and to verify the effects of the proposed exercises.

On force regulation strategies in predictable environments

This paper is focused on investigating force regulation strategies employed by human central nervous system (CNS). The mechanism responsible for force control is extremely important in peoples lives, but not yet well understood. We formulate the general model of force regulation and identify several possible control strategies. An experimental approach is used to determine which of the force control strategies could actually be used by the CNS. Obtained results suggest that the force regulation process involves not only the pure force controller, but also a coupled motion controller, relying on the internal model of the environment.

Critical damping conditions for third order muscle models: implications for force control.

Experimental results presented in the literature suggest that humans use a position control strategy to indirectly control force rather than direct force control. Modeling the muscle-tendon system as a third-order linear model, we provide an explanation of why an indirect force control strategy is preferred. We analyzed a third-order muscle system and verified that it is required for a faithful representation of muscle-tendon mechanics, especially when investigating critical damping conditions. We provided numerical examples using biomechanical properties of muscles and tendons reported in the literature. We demonstrated that at maximum isotonic contraction, for muscle and tendon stiffness within physiologically compatible ranges, a third-order muscle-tendon system can be under-damped. Over-damping occurs for values of the damping coefficient included within a finite interval defined by two separate critical limits (such interval is a semi-infinite region in second-order models). An increase in damping beyond the larger critical value would lead the system to mechanical instability. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved; thus resulting in an oscillatory free response of the system, independently of the value of the damping. Under such condition, combined with high muscle activation, oscillation of the system can be compensated only by active control.

THIRD-ORDER MUSCLE MODELS: THE ROLE OF OSCILLATORY BEHAVIOR IN FORCE CONTROL

This paper presents the analysis of a third-order linear differential equation representing a muscle-tendon system, including the identification of critical damping conditions. We analytically verified that this model is required for a faithful representation of muscle-skeletal muscles and provided numerical examples using the biomechanical properties of muscles and tendon reported in the literature. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved, thus resulting in an oscillatory free response of the system, independently of the value of the damping. Oscillation of the limb can be compensated only by active control, which requires creating an internal model of the limb mechanics. We demonstrated that, when admissible, over-damping of the muscle-tendon system occurs for damping values included within a finite interval between two separate critical limits. The same interval is a semi-infinite region in second-order models. Moreover, an increase in damping beyond the second critical point rapidly brings the system to mechanical instability.

Development of an Open-Source, Discrete Element Knee Model

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.

Lower Limb Stiffness Estimation during Running: The Effect of Using Kinematic Constraints in Muscle Force Optimization Algorithms

The focus of this paper is on the effect of muscle force optimization algorithms on the human lower limb stiffness estimation. By using a forward dynamic neuromusculoskeletal model coupled with a muscle short-range stiffness model we computed the human joint stiffness of the lower limb during running. The joint stiffness values are calculated using two different muscle force optimization procedures, namely: Toque-based and Torque/Kinematic-based algorithm. A comparison between the processed EMG signal and the corresponding estimated muscle forces with the two optimization algorithms is provided. We found that the two stiffness estimates are strongly influenced by the adopted algorithm. We observed different magnitude and timing of both the estimated muscle forces and joint stiffness time profile with respect to each gait phase, as function of the optimization algorithm used.