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## Citation

Tresch MC, Saltiel P, Bizzi E. The construction of movement by the spinal cord. Nat Neurosci. 1999 Feb;2(2):162-7. Pubmed

## 10 Word Summary

NMF decomposition of EMGs suggests hierarchical structure to muscle activity.

## Abstract

We used a computational analysis to identify the basic elements with which the vertebrate spinal cord constructs one complex behavior. This analysis extracted a small set of muscle synergies from the range of muscle activations generated by cutaneous stimulation of the frog hindlimb. The flexible combination of these synergies was able to account for the large number of different motor patterns produced by different animals. These results therefore demonstrate one strategy used by the vertebrate nervous system to produce movement in a computationally simple manner.

## Notes

• Stimulation of different locations on the frog leg produced different patterns of coordinated muscle activation.
• Goal was to determine if these varied patterns in muscle activation were composed of distinct sets of muscles working in concert.
• Figure 1 shows how recorded EMG changes based on location of stimulus.
• The muscle activation was examined using the following formula
• $m^{obs}_{j} = \overset{N}{\underset{i=1}{\sum}} c_{ij}w_{i}$
• m_j - the jth observed pattern of muscle activation
• c_ij - positive weight of the ith synergy for the jth muscle pattern
• w_i - the ith muscle synergy
• N - the total number of muscle synergies
• Coefficients were found using non-negative least-squares minimization of the function:
• $\Delta w_{i} = \sum \mu \left( m^{obs}_j - m^{pre}_j \right) c_{ig} g^\prime \left( w_{i} \right)$
• g'(x) = d/dt( exp(x) )
• µ = 0.005
• For another way to solve the above equation see Lee and Seung 1999
• Figure 2 shows an example of EMG response from 1 site multiple times.
• 1st response appears different than the rest.
• 4 synergies appear to recreate the responses pretty well.
• Synergies were similar across different animals, but location of stimulation eliciting synergy changed between individuals (p164)
• Figure 3 compares synergy weighting across three individuals.  Similar patterns are observed, but the weightings show a difference in location of stimulation eliciting the same synergy.
• Synergies could explain 80% of the behavior, but not ALL behavior.
• Tresch mentions that other pathways (other than spinal cord) might be using the synergies.  He suggests that this might account for the variation.
• Does he say why he only picked 4 synergies?  Did PCA came up with 4 components to explain 90% of the variance.
• Would more synergies explain more behavior? Adding another synergy only explained an additional 3% in variance.
• Synergies, hierarchical control and spinal cord unit burst generator all share similar elements of neural control philosophy.
• Linear combinations work.  Unknown as to why...but very cool!
• Figure 4 shows how synergies derived from a limited set of responses explains behavior of the total set of observed behavior.  Not surprisingly, the behavior further away from the data set used to make the synergies has the most difficulty reconstructing measured results.