A telescopic inverted-pendulum model of the musculo-skeletal system and its use for the analysis of the sit-to-stand motor task

Abstract

For field applicability of biomechanical methodologies aiming at assessing motor ability in disabled, or at risk of disablement (e.g. elderly), subjects, measurements must be carried out using a least perceivable to the subject and essential experimental apparatus. Since data thus obtained do not necessarily lend themselves to straightforward interpretation, they should be fed to a model of the portion of the musculo-skeletal system involved that already embodies the invariant aspects of both the modelled system and the motor task. Through such a minimum measured-input model, richer, physiology-related, and thus easier to interpret, information may be expected. In this framework, the present study investigated the sit-to-stand motor task using information obtained only from a force plate located under seat and subject's feet, a seat uniaxial load-cell and basic anthropometric parameters. Data were collected in a sample of 12 able-bodied subjects while executing the motor task at different speeds. The musculo-skeletal system was modelled as a telescopic inverted pendulum (TIP) that could vary its length (shortening or elongation) by effect of a force actuator and its orientation in space by effect of two couple actuators that were looked upon as muscle equivalent effectors. The TIP model output consisted in the kinematics and dynamics of these actuators. It allowed the identification of four functional phases in which the seat-to-stand motor task could be divided, and a detailed description of the relevant mechanics in terms of balance control and centre of mass elevation. Motor strategy modifications associated with speed variation could also be identified. For a global evaluation of the motor act it showed to be no less informative than more demanding multi-segment models. Although it is true that specific musculo-articular functions can only be inferred, the more compact information yielded by the TIP model is expected to facilitate subject and/or disability classification.