Structured variability of muscle activations supports the minimal intervention principle of motor control

Abstract

Numerous observations of structured motor variability indicate that the sensorimotor system preferentially controls task-relevant parameters while allowing task-irrelevant ones to fluctuate. Optimality models show that controlling a redundant musculo-skeletal system in this manner meets task demands while minimizing control effort. Although this line of inquiry has been very productive, the data are mostly behavioral with no direct physiological evidence on the level of muscle or neural activity. Furthermore, biomechanical coupling, signal-dependent noise, and alternative causes of trial-to-trial variability confound behavioral studies. Here we address those confounds and present evidence that the nervous system preferentially controls task-relevant parameters on the muscle level. We asked subjects to produce vertical fingertip force vectors of prescribed constant or time-varying magnitudes while maintaining a constant finger posture. We recorded intramuscular electromyograms (EMGs) simultaneously from all seven index finger muscles during this task. The experiment design and selective fine-wire muscle recordings allowed us to account for a median of 91% of the variance of fingertip forces given the EMG signals. By analyzing muscle coordination in the seven-dimensional EMG signal space, we find that variance-per-dimension is consistently smaller in the task-relevant subspace than in the task-irrelevant subspace. This first direct physiological evidence on the muscle level for preferential control of task-relevant parameters strongly suggest the use of a neural control strategy compatible with the principle of minimal intervention. Additionally, variance is nonnegligible in all seven dimensions, which is at odds with the view that muscle activation patterns are composed from a small number of synergies.

FIG. 1.

A: experimental paradigm. As in Venkadesan and Valero-Cuevas (2008), the subject grasped a metallic dowel fixed to ground with their thumb, middle, ring, and little finger and placed the fingertip of the index finger on the center of the recording surface of the rigidly held force sensor, with the distal phalanx in a vertical orientation. Defining the location of the hand and fingertip in 3 dimension (3D), plus the orientation of the distal phalanx, in this way suffices to replicate the posture of the fingers across trials in this isometric task. B: measured fingertip forces (thick, red), predicted forces from the linear normalized muscle tension-to-force model (dotted, black), and instructed normal force (thin, blue) for a typical trial. Each trial started with a brief preloading phase which is not shown (and is not used in the analyses). C: processed normalized muscle tensions for the 7 muscles acting on the index finger, for the same trial shown in subplot B. FDP, flexor digitorum profundus (slip to the index finger); FDS, flexor digitorum superficialis (slip to the index finger); EIP, extensor indicis proprius; EDC, extensor digitorum communis (slip to the index finger); LUM, 1st lumbrical; DI, 1st dorsal interosseous; and PI, 1st palmar interosseous.

FIG. 2.

A: ratio of task-relevant to -irrelevant variance indices, computed from the full covariance (full, P), diagonal covariance (diag, D), and signal-dependent noise covariance (SDN, S) in the constant phase (last 10 s of each trial). The bars show the grand means ± SE computed from the means from the 8 individual subjects. Black, significantly different from 1 (t-test, P < 0.01); gray, not significantly different from 1. B: variance accounted for by each principal component. Principal-component analysis (PCA) is applied to the full covariance matrix averaged over all trials for the constant phase. C: loadings of the 1st principal component on all muscles () for the constant phase. Note that all values are positive, indicating positive correlation among muscles or “coactivation.” •, the loadings of the 1st independent component, extracted via independent-component analysis (ICA) from the pooled data (all trials, constant phase). Trial-specific means were subtracted before pooling the data. D–F: same as in subplots A–C but for the time-varying phase of each trial (1st 10 s after the constant preloading phase).

FIG. 3.

Loadings of the 2nd through 7th principal component for constant (A) and time-varying (B) phases. This figure shows the strong similarity in the percent variance explained and the loadings obtained for both phases despite the assumptions made for the time-varying analysis.

FIG. 4.

Histogram and cumulative histogram of the ratio of task-relevant to -irrelevant variance for both constant and time-varying phases for the Full covariance matrix. Note that 80% of the trials have a ratio <1, in support of our hypothesis.

FIG. 5.

Projection of the normalized muscle tension variance onto the task-relevant (top 3 red traces) vs. task-irrelevant (bottom 4 traces) subspaces. The data are for the same trial as shown in Fig. 1. Note that this figure highlights the fact that the multidimensional interactions across muscles is a complex phenomenon that is not readily detectable by studying individual muscle signals or, more importantly, when one records only from a subset of muscles as was done in prior studies. An important motivation for this study is that, to our knowledge, this is the first time this analysis is performed on electromyographic signals collected simultaneously from all muscles of a musculoskeletal system, in this case a finger.