Models of ensemble firing of muscle spindle afferents recorded during normal locomotion in cats

Abstract

In spite of many years of research there is still much uncertainty regarding the nature of proprioceptive signals and the role of these signals in kinaesthesia and movement control. The uncertainty mainly concerns the firing characteristics of the most numerous proprioceptors, the muscle spindles. From many studies in anaesthetized animals it is known that mammalian muscle spindle afferents respond to muscle displacement and velocity and that these responses are strongly modulated by ã_fusimotor activity emanating from the central nervous system. Fusimotor action not only increases the firing rate of spindle afferents at a given muscle length ('bias'), it also controls the sensitivity of the afferents to changes in muscle length ('gain'). Just how the mammalian nervous system controls fusimotor action in daily life remains the subject of controversy (for review, see Prochazka, 1996). The firing rate of muscle spindles can also be affected by mechanical factors such as tendon strain, changes in pennation angle, Journal of Physiology (1998) 1. The aim of this work was to compare the ability of several mathematical models to predict the firing characteristics of muscle spindle primary afferents recorded chronically during normal stepping in cats. 2. Ensemble firing profiles of nine hamstring spindle primary (presumed group Ia) afferents were compiled from stored data from 132 step cycles. Three sets of profiles corresponding to slow, medium and fast steps were generated by averaging groups of step cycles aligned to peak muscle length in each cycle. 3. Five models obtained from the literature were compared. Each of these models was used to predict the spindle firing profiles from the averaged muscle length signals. The models were also used in the reverse direction, namely to predict muscle length from the firing profiles. A sixth model incorporating some key aspects of the other models was also included in the comparisons. 4. Five of the models predicted spindle firing well, with root mean square (r.m.s.) errors lower than 14% of the modulation depth of the target profiles. The key variable in achieving good predictions was muscle velocity, the best fits being obtained with power-law functions of velocity, with an exponent of 0·5 or 0·6 (i.e. spindle firing rate is approximately proportional to the square root of muscle velocity). The fits were slightly improved by adding small components of EMG signal to mimic fusimotor action linked to muscle activation. The modest relative size of EMG-linked fusimotor action may be related to the fact that hamstring muscles are not strongly recruited in stepping. 5. Length was predicted very accurately from firing profiles with the inverse of the above models, indicating that the nervous system could in principle process spindle firing in a relatively simple way to give accurate information on muscle length. 6. The responses of the models to standard ramp-and-hold displacements at 10 mm s¢ were also studied (i.e. velocities that were an order of magnitude lower than that during ...

Ensemble firing of muscle afferents recorded during normal locomotion in cats

“…The issue here was the same as that in Fig. 2 of the previous paper (Prochazka & Gorassini, 1998), namely whether the relatively simple predictions of spindle primary firing from velocity and displacement alone could be enhanced by adding EMG-linked components of spindle firing. Figure 2A shows the prediction of the best model from the previous paper (f = 4·3v 0·6 + 2d + mean rate).…”

“…The recordings were obtained from thirty-four freely moving adult cats. All of the surgical and recording techniques used have been described in detail elsewhere and were summarized in the previous paper (Prochazka & Gorassini, 1998). Ensemble firing profiles of spindle primary and secondary and tendon organ afferents are presented.…”

“…6 is the inclusion of length profiles predicted from afferent firing profiles by inverse models (see Fig. 5 in Prochazka & Gorassini, 1998). For spindle primary afferents we used the inverse of the hybrid power-law model used in A, in this case, the Poppele & Bowman transfer function gave a very good fit.…”

“…Finally, we used the Houk & Simon (1967) transfer function describing tendon organ afferents. As in the previous paper (Prochazka & Gorassini, 1998), the ensembles were built up from the raw data using DASA2, a custom data analysis program. Matlab 4.2c and Simulink 1.3c software (Mathworks Inc., Natick, MA, USA) were used to implement the models in graphical form (see Appendix of previous paper).…”

“…Although some mathematical modelling of ensemble firing profiles has been performed for the purpose of estimating changes in spindle afferent stretch sensitivity (Prochazka & Hulliger, 1983;Gorassini, Prochazka & Taylor, 1993), so far this approach has never been applied to estimating the strength of á_linked components of fusimotor action in ensemble spindle afferent data. In this and the previous paper (Prochazka & Gorassini, 1998), we have derived such estimates from the discrepancies between the recorded firing rate profile and those estimated from muscle length signals with mathematical models. A larger data base of chronic recordings from muscle afferents recorded during locomotion has now been collected.…”