The validation of new phase-dependent gait stability measures:A modelling approach

Identification of individuals at risk of falling is important when designing fall prevention methods. Current measures that estimate gait stability and robustness appear limited in predicting falls in older adults. Inspired by recent findings on changes in phase-dependent local stability within a gait cycle, we devised several phase-dependent stability measures and tested for their usefulness to predict gait robustness in compass walker models. These measures are closely related to the often-employed maximum finite-time Lyapunov exponent and maximum Floquet multiplier that both assess a system's response to infinitesimal perturbations. As such, they entail linearizing the system, but this is realized in a rotating hypersurface orthogonal to the period-one solution followed by estimating the trajectory-normal divergence rate of the swing phases and the foot strikes. We correlated the measures with gait robustness, i.e. the largest perturbation a walker can handle, in two compass walker models with either point or circular feet to estimate their prediction accuracy. To also test for the dependence of the measures under state space transform, we represented the point feet walker in both Euler-Lagrange and Hamiltonian canonical form. Our simulations revealed that for most of the measures their correlation with gait robustness differs between models and between different state space forms. In particular, the latter may jeopardize many stability measures' predictive capacity for gait robustness. The only exception that consistently displayed strong correlations is the divergence of foot strike. Our results admit challenges of using phase-dependent stability measures as objective means to estimate the risk of falling

In Vivo Dynamics of the Musculoskeletal System Cannot Be Adequately Described Using a Stiffness-Damping-Inertia Model

Background: Visco-elastic properties of the (neuro-)musculoskeletal system play a fundamental role in the control of posture and movement. Often, these properties are described and identified using stiffness-damping-inertia (KBI) models. In such an approach, perturbations are applied to the (neuro-)musculoskeletal system and subsequently KBI-model parameters are optimized to obtain a best fit between simulated and experimentally observed responses. Problems with this approach may arise because a KBI-model neglects critical aspects of the real musculoskeletal system. Methodology/Principal Findings: The purpose of this study was to analyze the relation between the musculoskeletal properties and the stiffness and damping estimated using a KBI-model, to analyze how this relation is affected by the nature of the perturbation and to assess the sensitivity of the estimated stiffness and damping to measurement errors. Our analyses show that the estimated stiffness and damping using KBI-models do not resemble any of the dynamical parameters of the underlying system, not even when the responses are very accurately fitted by the KBI-model. Furthermore, the stiffness and damping depend non-linearly on all the dynamical parameters of the underlying system, influenced by the nature of the perturbation and the time interval over which the KBI-model is optimized. Moreover, our analyses predict a very high sensitivity of estimated parameters to measurement errors. Conclusions/Significance: The results of this study suggest that the usage of stiffness-damping-inertia models t

Conclusions on motor control depend on the type of model used to represent the periphery

Within the field of motor control, there is no consensus on which kinematic and kinetic aspects of movements are planned or controlled. Perturbing goal-directed movements is a frequently used tool to answer this question. To be able to draw conclusions about motor control from kinematic responses to perturbations, a model of the periphery (i.e., the skeleton, muscle-tendon complexes, and spinal reflex circuitry) is required. The purpose of the present study was to determine to what extent such conclusions depend on the level of simplification with which the dynamical properties of the periphery are modeled. For this purpose, we simulated fast goal-directed single-joint movement with four existing types of models. We tested how three types of perturbations affected movement trajectory if motor commands remained unchanged. We found that the four types of models of the periphery showed different robustness to the perturbations, leading to different predictions on how accurate motor commands need to be, i.e., how accurate the knowledge of external conditions needs to be. This means that when interpreting kinematic responses obtained in perturbation experiments the level of error correction attributed to adaptation of motor commands depends on the type of model used to describe the periphery

A model of open-loop control of equilibrium position and stiffness of the human elbow joint

According to the equilibrium point theory, the control of posture and movement involves the setting of equilibrium joint positions (EP) and the independent modulation of stiffness. One model of EP control, the α-model, posits that stable EPs and stiffness are set open-loop, i.e. without the aid of feedback. The purpose of the present study was to explore for the elbow joint the range over which stable EPs can be set open-loop and to investigate the effect of co-contraction on intrinsic low-frequency elbow joint stiffness (

An agonist-antagonist pitch production model

Prosody is a phenomenon that is crucial for numerous fields of speech research, accenting the importance of having a robust prosody model. A class of intonation models based on the physiology of pitch pro- duction are especially attractive for their inherent multilingual support. These models rely on an accurate model of muscle activation. Tradi- tionally they have used the 2nd order spring-damper-mass (SDM) mus- cle model. However, recent research has shown that the SDM model is not sufficient for adequate modelling of the muscle dynamics. The 3rd order Hill type model offers a more accurate representation of mus- cle dynamics, but it has been shown to be underdamped when using physiologically plausible muscle parameters. In this paper we propose an agonist-antagonist pitch production (A2P2) model that both validates and gives insight behind the improved results of using higher-order crit- ically damped system models in intonation modelling

Do we use a priori knowledge of gravity when making elbow rotations?

In this study, we aim to investigate whether motor commands, emanating from movement planning, are customized to movement orientation relative to gravity from the first trial on. Participants made fast point-to-point elbow flexions and extensions in the transverse plane. We compared movements that had been practiced in reclined orientation either against or with gravity with the same movement relative to the body axis made in the upright orientation (neutral compared to gravity). For each movement type, five rotations from reclined to upright orientation were made. For each rotation, we analyzed the first trial in upright orientation and the directly preceding trial in reclined orientation. Additionally, we analyzed the last five trials of a 30-trial block in upright position and compared these trials with the first trials in upright orientation. Although participants moved fast, gravitational torques were substantial. The change in body orientation affected movement planning: we found a decrease in peak angular velocity and a decrease in amplitude for the first trials made in the upright orientation, regardless of whether the previous movements in reclined orientation were made against or with gravity. We found that these decreases disappeared after participants familiarized themselves with moving in upright position in a 30-trial block. These results indicate that participants used a general strategy, corresponding to the strategy observed in situations with unreliable or limited information on external conditions. From this, we conclude that during movement planning, a priori knowledge of gravity was not used to specifically customize motor commands for the neutral gravity condition

Supramolecularly directed rotary motion in a photoresponsive receptor

Stimuli-controlled motion at the molecular level has fascinated chemists already for several decades. Taking inspiration from the myriad of dynamic and machine-like functions in nature, a number of strategies have been developed to control motion in purely synthetic systems. Unidirectional rotary motion, such as is observed in ATP synthase and other motor proteins, remains highly challenging to achieve. Current artificial molecular motor systems rely on intrinsic asymmetry or a specific sequence of chemical transformations. Here, we present an alternative design in which the rotation is directed by a chiral guest molecule, which is able to bind non-covalently to a light-responsive receptor. It is demonstrated that the rotary direction is governed by the guest chirality and hence, can be selected and changed at will. This feature offers unique control of directional rotation and will prove highly important in the further development of molecular machinery

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 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