A Test of Torque-Control and Equilibrium-Point Models of Motor Control

ABSTRACT

Based upon predictions of equilibrium point models of motor control, a recent article by Jaric et al. (1999), reported that the peak velocity of an inertially loaded single degree-of-freedom elbow movement was not altered to a statistically distinguishable degree by the accuracy of the subject’s expectation about the size of the load. They concluded that their results confirmed their equilibrium point models and were incompatible with what they described as torque control models. A review of the literature and analysis of a more extensive set of data does not support that conclusion. To the contrary, if the actual load is heavier (or lighter) than expected, it is moved more slowly (or faster) than it would have been, had expectation matched reality. Torque-control models predict those consequences, equilibrium point models do not.

INTRODUCTION

A recent paper by Jaric et al. (1999) describes a series of experiments on elbow flexion movements in which inertial loads are intermittently changed without the subjects' knowledge. It is generally found that movements are slower with heavier than with lighter loads. At issue is whether subject's expectation about the size of the load is also a factor. They analyze the movements in terms of two versions of the equilibrium point (EP) hypotheses (Latash 1993; Feldman and Levin 1995). According to Jaric et al. (1999), whether a subject expects a light load or a heavy load, "movement velocity is supposed to reach approximately the same level in both cases" (page 53) in Feldman's version of the EP hypothesis. In Latash's version "peak velocity may be expected to drop slightly [if the subject encounters a heavier than expected load]… the difference may be expected to be about 10%" (page 55). They contrast this prediction with what they term "torque-control hypotheses" (Atkeson 1989; Bock 1990; Gottlieb 1996) that they suggest predict substantial (as much as 30-50%) decreases in peak velocity with loads that are heavier than expected. Jaric et al. (1999) find, for six subjects, no statistically significant effects of expectation on peak velocity. They conclude (page 64) that "Gottlieb's [torque-control] hypothesis is wrong in 2 of four predictions…[while] Both versions of the EP-hypothesis make qualitatively similar predictions which all happen to be correct."

Given such clearly stated differences, it seems appropriate to examine our own model of motor control as well as those that seem to be confirmed by Jaric et al. (1999). A clear, unambiguously negative finding for any theory's predictions provides a strong rational basis for rejecting it. We will only examine the effects of expectation on peak velocity because it is a variable that can be measured unambiguously and is also the variable of clearest disagreement.

METHODS

Subjects made 54° elbow flexions, as "fast and accurately" as possible, using a manipulandum that allowed rotation about the elbow in the horizontal plane. The right upper arm was abducted 90° and the elbow started from 60° of flexion from a straight arm. A digital computer sampled joint angle and tangential acceleration at 1000/s using a 12-bit A/D converter. A torque motor that could vary its torque using acceleration feedback controlled the effective inertia of the manipulandum. All subjects gave informed consent according to Rush Medical Center procedures before participating.

Subjects made movements under two conditions. Under known conditions they practiced with a fixed inertial load and then 11-15 movements were recorded. Under uncertain conditions, they made 30-60 movements. For most movements, the actual moment of inertia of a typical arm plus manipulandum ( about 0.18 kg m²) was the total load. Infrequently (1/3 to 1/6 of the time) the torque motor added an additional load. It could take 1 to 3 different values over a range of —0.13 kg m² to +0.9 kg m². Loads were intermixed in a pseudo-randomized order. We assumed that under uncertain conditions, the subjects expected the most likely load and planned accordingly. Hence, they experienced actual loads that were either equal to expected (A=X), heavier than expected (A>X) or lighter than expected (A<X). In our analysis, we compare peak movement velocity under known conditions with the velocity under uncertain conditions for the same load.

RESULTS

TABLE 1: A test of the hypothesis that Peak Velocity (PV) under uncertain load conditions is the same under known load conditions using Student's t-test. In row 1 the actual load was equal to the expected (i.e. the most likely) load. In row 2 the actual load was greater than expected. In row 3 the actual load was less than expected.

These results show a three-fold variation in peak velocity with load and across subjects. Subjects moved at the same velocity under known conditions as they did under uncertain conditions if the actual load equaled the expected one (A=X). The slope of linear regression through the origin is 1.003 (1.041-0.965 are the 95% confidence limits), r²=0.97. Similar velocities were not found if the actual load was greater or less than expected. For any actual load, subjects moved significantly more slowly if it was heavier than expected and significantly faster if it was lighter. The slope of linear regression for A<X is 1.171 (1.262-1.080), r²=0.83 and for A>X is 0.807 (0.859-0.766) r²=0.81.

DISCUSSION