Time-varying mechanical behavior of multijointed arm in man

Abstract

1. The aim of this study was to describe the time-varying changes in the mechanical parameters of a multijointed limb. The parameters we considered are the coefficients of stiffness, viscosity, and inertia. Continuous pseudorandom perturbations were applied at the elbow joint during a catching task. A modified version of an ensemble technique was used for the identification of time-varying parameters. Torques at the elbow and wrist joints were then modeled with a linear combination of the changes in angular position and velocity weighed by the matrix of angular stiffness and the matrix of angular viscosity, respectively. Control experiments were also performed that involved the stationary maintenance of a given limb posture by resisting actively the applied perturbations. Different limb postures were examined in each such experiment to investigate the dependence of the mechanical parameters on limb geometry. 2. The technique for the identification of limb mechanical parameters proved adequate. The input perturbations applied at the elbow joint elicited angular oscillations at the wrist essentially uncorrelated with those produced at the elbow. The frequency of oscillation is much higher at the wrist than at the elbow, mainly because of the smaller inertia. The variance accounted for by the model was ≃80% under both stationary and time-varying conditions in the latter case the value did not vary significantly throughout the task. In addition, the model predicted values of the inertial parameters that were close to the anthropometric measures, and it reproduced the stepwise increase in limb inertia that occurs at the time the hall is held in the hand. 3. The values of angular stiffness and viscosity estimated under stationary conditions did not vary significantly with joint angle, in agreement with previous results obtained under quasistatic postural conditions. The matrix of the coefficients of angular stiffness was not symmetrical, indicating a prominent role for nonautogenic reflex feedbacks with unequal gains for elbow and wrist muscles. 4. A complex temporal modulation of angular stiffness and viscosity was observed during the catching task. The changes in the direct coefficients of angular stiffness tended to covary with those in the coupling coefficients from trial start up to ≃30 ms before impact time. Around impact time, however, there was a complete dissociation; the direct terms peaked, whereas the coupling terms dropped. The direct terms of angular viscosity also increased before impact, whereas the viscosity coupling terms remained close to zero throughout. 5. Neural correlates of the changes in angular impedance were found by considering the time course of the changes in net electromyographic activity and stretch reflexes during catching. Anticipatory muscle activity started 100-200 ms before impact and correlated qualitatively with anticipatory changes in angular stiffness. The peaks of the direct terms of stiffness and viscosity around impact could be accounted by the transient reversal of the direction of short-latency stretch reflex responses. The decrease of the coupling terms of stiffness around impact could be explained by a transient decrease of the gain of heteronymous stretch reflexes. 6. The matrices of the coefficients expressing stiffness and viscosity in the Cartesian coordinates of the limb endpoint were also computed. From such matrices, the components corresponding to the vectors of resistance offered by the hand to a virtual vertical displacement were extracted. We found that the hand resistance is accurately modulated relative to the impact time. The magnitude of hand resistance vectors increased consistently before impact, although with a different time course for hand stiffness and viscosity. Also before impact, the direction of viscous resistance vectors rotated closer to the vertical, indicating that a larger component of reactive force is exerted in the direction of the expected perturbation. 7. The orientation of the vectors of hand viscosity was variably correlated with the orientation of the vectors of hand inertia during catching. This result suggests the existence of a parallel neural control of different components of hand impedance, that is inertia, stiffness, and viscosity. This parallel control is predicated on the availability of accurate internal models of the limb mechanical properties.