Stretch reflex gain in cat triceps surae muscles with compliant loads

Abstract

The triceps surae (TS) stretch reflex was measured in decerebrate cats during crossed extensor stimulation (tonic contractions) and after spinalization during rhythmic locomotor activity. The TS reflex force in response to a short pulse stretch measured during tonic contractions at low level of background activity was greater than when more background activity was present at the time of application of stretch. In contrast, the reflex force measured during rhythmic contractions was very small at low level of background force (flexion phase) and increased at moderate and high levels of background activity (extension phase). Thus, even in reduced preparations, a task modulation of the stretch reflex occurs. Throughout the experimental procedure, the torque motor used to stretch the muscles behaved like a spring of a preset compliance (from isometric to very compliant). A reflex model was used to simulate the responses obtained experimentally. The gain of the stretch reflex loop was estimated for each load condition and both behavioural tasks. The reflex loop gain was significantly larger as the compliance of the external load increased for both tonic and rhythmic contractions, although to a lesser extent in the phasically activated muscles. During rhythmic locomotor contractions the gain was less than 1, assuring stability of the system. In contrast, during tonic contractions against a compliant load the gain exceeded 1, consistent with the instability (oscillations, clonus) seen at times under these load conditions. However, the high gain and instability was only transient, since repeated stretch reduced the gain. Thus, non-linearities in the system assured vigorous responses at the onset of perturbations, but then weaker responses to ongoing perturbations to reduce the chance of feedback instability (clonus).

Figure 1. Reflexes during tonic and phasic contractions

A, reflex responses to pulse stretches before and during contractions produced by contralateral CP nerve stimulation (vertical arrow marks onset of stimulation) in a decerebrate cat. Only the beginning of the tonic contraction is shown. From top to bottom the traces are, respectively: TS length, force and EMG. Data recorded with an isometric load. B, reflex responses to pulse stretches during locomotion in a spinal cat. Same formats as in A.

Figure 2. Typical reflex responses to pulse stretch during tonic and phasic contractions

A, averaged length trace representing a pulse stretch in isometric condition. B, averaged total force and reflex force in response to a pulse stretch in isometric condition, for low (left panel) and high (right panel) levels of background force, in tonically active TS muscles (decerebrate). Remember that the reflex force is obtained by subtracting the averaged force recorded after deafferentation (dotted line) from the averaged force obtained with intact dorsal roots (continuous line, see also Fig. 1). Arrows indicate the reflex force measurement. C, averaged total force and reflex force in response to pulse stretch in isometric conditions, for low (left panel) and high (right panel) levels of background force, in phasically active TS muscles (spinal walking). Same formats as in B.

Figure 3. Normalized reflex responses across background force levels

Reflex force was plotted against background force levels across tasks, after normalization. The data for all cats are grouped in three distinct levels of background force (low, moderate and high). Each point represents the mean ± standard error for data from seven cats.

Figure 4. Examples of effect of a compliant load on the reflex response to a pulse stretch

Length (left panel) and force (right panel) responses to a pulse stretch for isometric and compliant loads (0.2, 0.5 and 1.5 mm N⁻¹). Note the increase in muscle shortening with a more compliant load accompanied by a decrease in reflex force.

Figure 5. Examples of experimental and simulated data across tasks

Simulated responses to a pulse stretch superimposed to the averaged length (left panel) and force (right panel) traces obtained experimentally during a tonic contraction, and in a resting and walking spinal cat. The numbers in brackets indicate the proportion of the variance accounted for (VAF) by the fit, calculated for verification of goodness of fit. Experimental data is from one cat with a load compliance of 0.2 mm N⁻¹.

Figure 6. Reflex loop gain magnitude and phase across stretch frequencies for non-isometric loading

Reflex gain magnitude (top graphs) and phase (bottom graphs) estimated for tonic and phasic contractions, for compliant loads of 0.2, 0.5 and 1.5 mm N⁻¹, plotted against the sinusoidal stretch frequency. Sinusoidal inputs of 1, 2, 5, 7, 10, 14 and 20 Hz were used in the reflex model described in Appendix. Horizontal dashed lines help indicate the frequency at which the phase lag reaches 180 deg for each load, each task. Note that at this specific frequency the gain magnitude is well below 1 for all loads during phasic contractions. Each point represents the mean ± standard error for simulation data from five cats.

Figure 7. Gain magnitude for both tasks across load compliance

Reflex gain magnitude estimated for sinusoidal stretch of 5 Hz, during low level of tonic and phasic contractions for each load compliance. The gain was also estimated for an extremely compliant load (free to move). Each point represents the mean ± standard error for simulation data from five cats.

Figure 8. Schematic diagrams of the reflex loop model

A, schematic representation of the Hill-type muscle model used to simulate the experimental data. B, detailed block diagram of the muscle, load and muscle spindle showing the feedback loop and where the loop was cut open (indicated by **) to estimate the open-loop gain. See Appendix for details.