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## Citation

McKay JL, Ting LH. Functional muscle synergies constrain force production during postural tasks. J Biomech. 2008;41(2):299-306. PUBMED

## 10 Word Summary

Muscle synergies add constraints to possible endpoint force production.

## Abstract

We recently demonstrated that a set of five functional muscle synergies were sufficient to characterize both hindlimb muscle activity and active forces during automatic postural responses in cats standing at multiple postural configurations. This characterization depended critically upon the assumption that the endpoint force vector (synergy force vector) produced by the activation of each muscle synergy rotated with the limb axis as the hindlimb posture varied in the sagittal plane. Here, we used a detailed, 3D static model of the hindlimb to confirm that this assumption is biomechanically plausible: as we varied the model posture, simulated synergy force vectors rotated monotonically with the limb axis in the parasagittal plane (r2=0.94+/-0.08). We then tested whether a neural strategy of using these five functional muscle synergies provides the same force-generating capability as controlling each of the 31 muscles individually. We compared feasible force sets (FFSs) from the model with and without a muscle synergy organization. FFS volumes were significantly reduced with the muscle synergy organization (F=1556.01, p<<0.01), and as posture varied, the synergy-limited FFSs changed in shape, consistent with changes in experimentally measured active forces. In contrast, nominal FFS shapes were invariant with posture, reinforcing prior findings that postural forces cannot be predicted by hindlimb biomechanics alone. We propose that an internal model for postural force generation may coordinate functional muscle synergies that are invariant in intrinsic limb coordinates, and this reduced-dimension control scheme reduces the set of forces available for postural control.

## Notes

• Aims of the paper were:
• Verify that rotating the synergy force vectors was biomechanically feasible.
• Determine how synergies affect the ability to create end-point forces.
• $\bar{F}_c = \left( J(\bar{q})^T \right)^+R(\bar{q})F_o F_{AFL}(\bar{q})W\bar{c}$
• Fc - endpoint forces and moments
• JT+ - pseudo-jacobian relating endpoint force and joint moments
• R - muscle moment arms
• Fo - maximum muscle force
• FAFL - active muscle force based on muscle length
• W - matrix of muscle synergies
• c - activation of synergies
• Feasible force set (FFS) the smallest convex polygon that encompasses all possible forces generated by the above equation.
• Certain forces that correspond to a particular synergy change direction as AP stance-width changes in cats.  Other forces stay nominally the same.
• Different muscle synergies produce similar "synergy force directions".
• The total FFS unconstrained by synergies produces similar results across different AP stance-widths.  However, the synergy constrained FFS rotates and changes shape with different AP stance-widths.
• Conclusions of this paper:
• Simulated synergy force vectors rotate monotonically with the limb axis in the sagittal plane as configuration varies.
• Synergies constrain the size of the FFS