Non-rigid response of the trunk to dynamic axial loading: an evaluation of current modelling assumptions

Abstract

Most biomechanical models of the trunk and limb system represent the segments as rigid links joined with pins. The implication of this simplifying assumption is that dynamic loads applied to the body are instantaneously transmitted through the linkage with no distortion of the applied force-time waveform. The purpose of this study was to determine whether this assumption was justifiable for loads applied to the hands or shoulders and transmitted through the trunk to the bottom of the pelvis. If not, the intent was to find a transfer function relating load inputs applied to the top of the trunk and outputs measured at the bottom of the trunk. Loads were manually applied to a force transducer attached to a shoulder yoke or to a hand-held loading pan mounted on three subjects. The subjects sat both erect and slouched and also varied the trunk stiffness by voluntarily changing trunk muscle activation. Subjects sat on a rigid steel stool mounted on a force plate from which force outputs were recorded. In addition, a few case studies were performed; some trials utilized light impacts by a hammer to the transducer mounted on the crown of the bare head and in other trials the body was in a standing (lifting) posture. The results indicated that the mechanical response is indeed time dependent. For applied forces with a rise time less than 20 ms (hammer impact) the trunk system reduced the magnitude of the force peaks by up to 40%. However, for applied loads with rise times from about 30 to 300 ms the peak output force was larger than the applied force peak. This was due to inertial effects of the upper body mass as it ‘rebounded’ from the applied load. During these conditions of biologically generated applied forces, the output could be reasonably reconstructed by processing the input signal through a Butterworth second order low pass filter with a cutoff frequency of 7·5 Hz, a gain and in some cases, a shift in time up to 20 ms. The assumption of rigid body segments in these experiments appeared reasonably justified when the rise time of the applied force was greater than approximately 300 ms. However, for input signals that had a shorter rise time the trunk did not behave rigidly.