(A commentary on "A test of torque-control and equilibrium-point models of motor control" by G.L. Gottlieb)

E-mail: jaric@niwl.se

The paper by Gottlieb describes results of a series of experiments in which the subjects performed very fast movements against unexpectedly changed inertial loads. Based on the data, Gottlieb presents arguments against conclusions drawn in our recent publication based on a similar experiment (Jaric et al., 1999). Although the data set presented in our previous paper might not have been perfect (see later in this note), we cannot agree with the final conclusion by Gottlieb that "the results are consistent with the torque-control hypothesis and with neither version of the equilibrium-point hypothesis". We stick to our original opinion not solely because of being stubborn, but based on several methodological, statistical, and logical considerations that, as we think, speak in favor of our study and conclusions.

The two studies differ in a number of ways. Some of the differences are not easy to interpret, for example those related to how trials when the expected load differed from the actual one were presented. However, one difference may be of a major importance. In our study, the subjects were very well trained to move against loads that could vary within a rather small range. We purposefully limited the range of variation of the inertial load to decrease the possibility of subjects reacting to changes in the load, thus leading to a change in their motor command and making results poorly interpretable. All our predictions were predicated on an assumption that the subjects used unchanged motor command (no corrections) when the load changed unexpectedly in a trial.

In the study of Gottlieb, both very large and negative inertial loads were used. On the one hand, increasing the range of load changes increases chances of detecting a relation between expected load and a particular performance variable. However, when one gets to very large loads, movement time becomes also large and allows ample time for possible movement corrections even before the peak velocity is achieved. For example, movements against the 0.9 kgm² load over 56° were performed with the peak velocity of between 150 °/s and 200 °/s. Gottlieb does not present movement times in the paper, but according to his previous publication (Fig. 3 in Gottlieb et al., 1989), such movements were likely to take over 500 ms. On the other side of the spectrum, negative inertial loads make movements rather unstable so that subjects were likely to generate corrections at a rather short delay even when they were instructed not to do so. These corrections can significantly affect a range of kinematic variables (Milanovic et al., 2000).

The main finding of Gottlieb that is claimed to be incompatible with the equilibrium-point hypothesis is a change in movement peak velocity with expected load in addition to the well documented change with actual load (Benecke et al., 1985; Gottlieb et al., 1989). In other words, when a subject moves against a standard load, peak velocity is claimed to depend on whether he or she is expecting the actual load, a smaller load, or a bigger load. Figure 1 in Gottlieb's paper shows datapoints that significantly deviate off the 45° line suggesting non-zero additional effects of expected load.

Let us remind, however, predictions made by Jaric et al (1999). Two versions of the equilibrium-point hypothesis were considered. One predicted no changes in peak velocity with expected load, the other predicted a modest effect of the order of 10%. Torque-control hypotheses predicted changes of the order of 30% to 50%. Gottlieb cites these numbers and does not argue with them. So, we assume that our assessments are acceptable for him. In his statistical analysis, Gottlieb compares the data to the null-hypothesis that assumes no effects of expected load on peak velocity and shows that there are significant effects. However, he has never compared the data statistically to the predictions of the other version of the equilibrium-point hypothesis (an effect of 10%). The only quantitative statement made in the paper is that 17 out of 21 data points were outside the ±10% range; this is not an acceptable statistical proof, particularly because the same can be said about the ranges ±(30% to 50%).

The slopes of the two regression lines for the data in Fig. 1 are close to 1.17 and 0.81. The 95% confidence interval for the first line is (1.08 to 1.26); it includes 1.1 but does not include 1.3 or any larger numbers. For the second line, the 95% confidence interval is (0.77 to 0.86); it includes neither 0.9 nor 0.7. So, even if one ignores the first point related to the methodological problems of Gottlieb's study, his data are better statistically compatible with the second version of the equilibrium-point hypothesis than with torque-control predictions. This result is in a striking contradiction to the last phrase of the Gottlieb paper.

Gottlieb addressed one of the predictions made in Jaric et al. (1999), but has been silent with respect to other predictions. Note that the data in Jaric et al. (1999) were shown to be incompatible with torque-control models and compatible with the equilibrium-point hypothesis on more than one count. In particular, the Gottlieb version of torque-control predicted a large increase in movement time and a large drop in the symmetry ratio (acceleration time divided by deceleration time) when the expected load was smaller than the actual one, and opposite effects of the same magnitude when the expected load was larger than the actual one. Both predictions were not supported by our data. Unfortunately, Gottlieb in his paper does not present findings on movement time and symmetry ratio to challenge these issues.

Gottlieb states in his paper that a number of previously published Figures showed considerably different peak velocities when subjects expected a different load while moving against the same actual load. However, we believe that these Figures have been misrepresented in Gottlieb’s paper. In particular, Figure 2 in Latash (1994) shows considerable differences between peak velocities when the actual loads were different and only small differences (under 10%) when only the expected loads were different. Figures 4 and 5 in Gottlieb (1996) show changes in peak velocity when the subjects expected the same load but moved against different actual ones, i.e. actual rather than expected loads were different. Figure 2 in Gottlieb (1994) also shows data for different actual loads, and, in addition, velocity traces are not presented there at all. So, all the mentioned Figures in Gottlieb’s papers say nothing about potential changes in peak velocity with load expectation when the actual load is the same, while the Figure in Latash (1994) is more compatible with the second version of the equilibrium-point hypothesis than with Gottlieb’s torque-control model. Only Fig. 10A in Gottlieb (1996) compares the effects of actual and expected loads; however, there is no statistical analysis of the data that would show effects larger than 10%.

There may be a problem with our understanding of Gottlieb’s model, but its basic principles seem inconsistent. On the one hand, as mentioned in his paper, control signals represent patterns of muscle activation that generate appropriate torque patterns. On the other hand, Gottlieb also seems to agree that some kind of equilibrium-point control is necessary at the final position, when the muscles are quiescent, to provide position stability (Jaric et al., 1994; Gottlieb 1996; Ilic et al., 1996). However, a shift in the equilibrium point in a system with spring-like elements (muscles) by itself leads to the generation of joint torques. Does the system compute required torques, subtract what is expected from the shift in the equilibrium point, and generate muscle activation patterns to produce the residual? This sounds rather cumbersome.

Let us start with accepting some of the blame: Based on the data in our study, we cannot rule out modest effects of expected load on velocity. Although our data did not reach statistical significance (F_(1,5) = 2.6; 0.1 < p < 0.15), the small number of subjects makes the study prone to making a type 1 error. We do not think, however, that increasing the range of load changes (as it was done in Gottlieb's study) is a way to address the issue because of the mentioned methodological problems. An increase in the number of subjects seems to be the way to go while taking all the precautions that the subjects do not react to unexpected changes in the load.

To conclude, at least one version of the equilibrium-point hypothesis is able to handle modest changes in peak velocity with expected load. The data presented by Gottlieb can be handled by this hypothesis at least as well as by Gottlieb's own hypothesis, possibly better. Moreover, two additional predictions in Jaric et al. (1999), which speak in favor the equilibrium-point hypothesis, have not been addressed by Gottlieb. So, we would like to assure the readers that the equilibrium-point hypothesis is still alive and healthy and wishes all other hypotheses in the area of motor control a happy third millenium.

Benecke, R., Meinck, H.M., Conrad, B. (1985) Rapid goal-directed elbow flexion movements: Limitations of speed control system due to neural constraints. Experimental Brain Research 59: 470-477

Gottlieb, G.L. (1994) The generation of the efferent command and the importance of joint compliance in fast elbow movements. Experimental Brain Research 97: 545-550.

Gottlieb, G.L. (1996) On the voluntary movement of compliant inertial-viscoelastic loads by parcellated control mechanisms. Journal of Neurophysiology 76: 3207-3229.

Gottlieb, G.L., Corcos, D.M., Agarwal, G.C. (1989) Organizing principles for single joint movements. I: A speed-insensitive strategy. Journal of Neurophysiology 62: 342-357.

Ilic, D.B., Corcos, D.M., Gottlieb, G.L., Latash, M.L., Jaric, S. (1996) The effects of practice on movement reproduction: Implications for models of motor control. Human Movement Science 15: 101-114.

Jaric, S., Corcos, D.M., Gottlieb, G.L., Ilic, D.B., Latash, M.L. (1994) The effects of practice on movement distance and final position reproduction: Implications for the equilibrium-point control of movements. Experimental Brain Research 100: 353-359.

Jaric, S., Milanovic, S., Blesic, S., Latash, M.L. (1999) Changes in movement kinematics during single-joint movements against expectedly and unexpectedly changed inertial loads. Human Movement Science 18: 49-66.

Latash, M.L. (1994) Control of fast elbow movement: A study of electromyographic patterns during movements against unexpectedly decreased inertial load. Experimental Brain Research 98: 145-152.

Milanovic, S., Blesic, S., Jaric, S. (2000) Changes in movement variables associated with the transient overshoot of the final position. Journal of Motor Behavior, 32:115-120.