Our recent work showed for the first time the in vivo movements of gastrocnemius and soleus during quiet stance (Loram et al. 2005a,b). The observational data that we presented, including cross correlations (Loram et al. 2005a, Figs 3A and B and 4), frequency domain relationships (Loram et al. 2005a, Fig. 5A, B, D and E; Loram et al. 2005b, Fig. 2), power spectra (Loram et al. 2005b, Fig. 3) and time locked averaging (Loram et al. 2005b, Figs 5–9) show unequivocally the relationships between muscle length, CoM angle and EMG in standing. These facts do not depend on any closed versus open loop assumptions. The criticism solely concerns our interpretation and conclusions.
Actually, mechanical considerations show that the criticism is irrelevant. We consistently observe low frequency paradoxical muscle movements during standing. This fact demands that the series elastic stiffness (s.e.c. tendon and foot) is less than the load stiffness (mgh) of the body. If the s.e.c. is stiffer than mgh then it is impossible to produce low frequency paradoxical muscle movements during normal standing. Thus, no amount of neural system dynamics or muscle contraction dynamics or closed loop feedback can account for balancing with low frequency paradoxical movements. Moreover, no amount of closed loop feedback can obscure the fact that the nervous system requires anticipation to overcome the 100–200 ms muscle contraction delay between changes in EMG and changes in muscle length. The critic has simply misunderstood, thinking erroneously that we were claiming to measure the dynamics of the neural feedback path rather than the delay inherent in the ‘motors’ of the body. Impulsive is an apt adjective to describe the mechanical effect of small, short duration changes in muscle length, tension and activity that are associated with changes in velocity rather than changes in position of the centre of mass. Ballistic is an appropriate description given that the nervous system is producing temporally compressed patterns of neural output several hundred milliseconds in advance of the current state of bodily motion.
We agree there are issues when analysing closed loop systems. We consider the critics have overstated their case and have actually misapplied the clear, illuminating analysis of van der Kooij et al. (2005). Analysis of a closed loop system is not erroneous per se. For the system we are analysing which is a mechanically determined plant, with no output disturbances, driven by noisy feedback, the methods we have used are entirely appropriate (Sinha & Kuszta, 1983). As we show in the appendix (online Supplemental Material), the analysis of van der Kooij et al. demonstrates the basis and validity of our methods. Other theorists would defend the advantages that closed loop analysis has to offer (Sinha & Kuszta, 1983). It is the only way to obtain signals recording the natural unperturbed activity, rather than something else. This is important. Humans are not machines with invariant mechanisms. Neural activation patterns and responsivity change readily with circumstance and intention. The nervous system has more information about self initiated postural sway than it has about sway driven by less predictable disturbances. Even the mechanical properties of the calf muscles change beyond the short range stiffness that operates over approximately one degree of ankle rotation.
Perturbation studies are essential. However, just like closed loop analysis, opened loop analysis also rests on assumptions. Perturbations always involve distortion of the system and the introduction of further assumptions including the obvious speculation that the response to perturbation follows the same rules as the natural activity. Kooij et al. assume that the feedback is time invariant. Their methods will average out a control process that may be variable in time or discontinuous. If that is the control mechanism they will miss the story.