Shifting Frames of Reference but the Same Old Point of View

A commentary on the target article by Feldman and Levin

Gerald L. Gottlieb, NeuroMuscular Research Center, Boston University
19 Deerfield St., Boston MA 02215
(617) 358-0719 glg@bu.edu

Abstract:

Commentary:

Feldman and his colleagues have, over the last 30 years, progressively developed and elaborated a model for posture and movement for which "the central idea [is] that the CNS organizes positional frames of reference or systems of coordinates for the motor apparatus and produces active movement by shifting the frames in space" and where "MN threshold properties and proprioceptive feedback may be the cardinal components of the mechanism which define such frames of reference" (p 4). While they have shown how this mechanism could be consistent with kinematic and EMG patterns associated with a limited set of voluntary movements, the model offers no compelling reasons to believe that this is true and remains seriously incomplete and inaccurate in many of its predictions.

It fails to confront the two primary functions of models of this sort: First, it does not give us insight into how the CNS will specify its CVs in order to perform various purposeful tasks such as moving different distances at different speeds with different external loads. While remaining dogmatically rigid about one aspect of its control scheme (namely the behavior of R, its shifting reference frame), it has proven to be simultaneously flexible, extensible and vague about others (C1, C2, µ) that are no less important. Second, it does not provide a unified interpretation of EMG patterns and experimentally observed kinematics although that is one of its fundamental claims.

One of the most serious errors of the lambda-model is reversal of causality in its attempt to explain EMG patterns in terms of observed kinematics. Kinematic patterns are the consequence of the interaction of muscle activation (which we suggest is mostly centrally driven) and muscle and load compliance. The nonutility of the lambda-model is illustrated by the following experimental fragment. The figure shows three "fast and accurate" elbow flexion series by one subject using all the usual protocols (Gottlieb, 1994) . The dashed line movements are inertially loaded (M). A viscous load (M+B) has been added by a torque motor for the solid line and an elastic load (M+K) has been added for the dotted line. We have proposed that the CNS adjusts the CVs (described in terms of excitation pulses and steps) to the expected load based upon its knowledge, acquired through practice, of task dynamics (Gottlieb, 1993; Gottlieb, Corcos, & Agarwal, 1992) . According to this model, the differences in EMG patterns are primarily consequences of this "educated" motor controller. Kinematics are an "emergent" property of this central control pattern and of muscle, reflex and load dynamics.

Average of 10 movements over 54° with known inertial, viscous and elastic loads. Similar kinematic traces on the left are produced by very different muscle forces that emerge from different muscle activation patterns as revealed by the EMGs. Net muscle torque is equal and opposite to sum of the motor and inertial (limb plus manipulandum) torque components. It is well correlated with the EMG patterns. Neither muscle torque nor EMG patterns can be determined from the kinematics alone without reference to the dynamics of the load moved by the limb.

Kinematic, force and EMG variables are illustrated as functions of time on the left and as functions of joint angle on the right. The instructions to the subject were only to be "fast and accurate" and it was in retrospect that the similarity of the movement trajectories (particularly with M and B+M loads) was noticed. In general, changes in load alter the trajectory but the degree to which they do so is strongly dependent on the type of load, its magnitude and the strength of the subject. This figure may be considered from two points of view. One is that EMG patterns are mostly proprioceptively driven consequences of kinematics. The other is that EMG patterns are mostly consequences of centrally specified patterns (CVs). The choice is left as an exercise for the reader.

Our interpretation of this figure in terms of the lambda-model is that all three loads are initially moved by the same R command that rises at a fixed rate for 100 ms or less, producing initially identical EMG and torque patterns. The final value of R for the K load is greater and is reached later than for the other two loads to accomodate the static load of the external spring. Subsequent differences in muscle activation and force arise from proprioceptively driven differences in kinematics and presumably by different C and µ commands but the lambda-model offers little guidance as to how these parameters will be specified.

With two (actually at least three) free control variables, one might expect that the lambda-model can do the job but it cannot. To take one specific example, the lambda-model does not correctly predict at even a qualitative level, the antagonist EMG patterns illustrated. Kinematic feedback alone will not produce the largest, earliest antagonist EMG burst (and the shortest agonist burst) for the slowest movement (M load). The latency of the antagonist burst monotonically increases with increases in inertial or viscous loads or distance or decreases in intended speed. Of all these task variations, only increases in inertial load will increase the area of the antagonist burst (Gottlieb, Corcos, & Agarwal, 1989) . Increases in viscous load decrease the antagonist burst, as do decreases in intended speed. The only thing figure 13 of the target article gets right is the decrease in antagonist area. The lambda-model makes similar errors simulating movements of different distances.

In retrospect we discovered that the kinematics of the inertially and viscously loaded series were virtually identical although the torque and EMG patterns differed considerably (as they must in order to produce similar movements with different external loads). On the right are plotted velocity, net muscle torque and the EMGs with angle as the independent variable. Phase-plane plots have sometimes been employed to show how proprioceptive information may be used by the lambda-model (velocity scaled by µ) to generate muscle activation patterns that are load adaptive (e.g. figure 12B of the target article). I am skeptical that the different torque and EMG patterns shown in the lower panels can be explained by the kinematic differences between the phase plane trajectories (The difference towards the end of the elastically loaded movement is due to a different CV). In that case, as in our own model, the central commands must be adapted to load dynamics by an "educated" central controller. Whether this is best described in terms of a complex shift of reference frame (Latash & Goodman, 1994) and auxilliary CVs or in more explicit terms of forces as we have suggested is an issue we have previously addressed in this forum (Gottlieb, 1992) .

The lambda-models' hallmarks are elastic invariant characteristics mediated by reflex mechanisms. Only lip service has been given to intrinsic muscle properties (they are absent from their own simulations (St-Onge, Haiming, & Feldman, 1993) ). After 30 years, there is hardly any published data to support the contention that spring-like reflex mechanisms provide any explanatory power about the initiation of a fast, voluntary movement. Neither observations of movements against known inertial or elastic loads nor simulations have provided such data. A class of experiments that has been more revealing has used unexpected load changes imposed during voluntary movements. The affirmative conclusion in (Levin, Feldman, Milner, & Lamarre, 1992) rests more on computational methodology than data. (Smeets, Erkelens, & Denier van der Gon, 1990) , (Gottlieb, 1994) (Gottlieb, submitted; Gottlieb, 1995; Latash, 1994) ) and others show data that does not support the lambda-model (although Latash's interpretation is more generous, see following)

Equilibrium point models, even rephrased in terms of shifting reference frames and auxilliary control variables, are at best conceptual tools for understanding posture and slow or quasi-static movement. As general descriptions of the control of voluntary movement, even at the single joint, they provide little predictive utility or insight.

REFERENCES CITED