Muscle Synergies Heavily Influence the Neural Control of Arm Endpoint Stiffness and Energy Consumption
Fig 5
Visualization of mechanical and energetic constraints.
A. Consider a limb with one rotational joint driven by 3 muscles. We show the parameters and variables needed to implement Eq 14. B. As described elsewhere in detail [34–36, 41, 42], the set of all physiologically feasible neural commands to a limb that can be visualized as a positive hypercube of as many dimensions as there are independently controllable muscles (3 in this case). Each constraint that defines the mechanical task reduces the set of feasible neural commands to a subset of that hypercube. Therefore, the feasible activation set for a task is the intersection of those constraints that lie within the hypercube. If the constraints are linear functions of activation, they reduce the subset of feasible neural commands to a hyperplane. We see this for the linear constraints defining the size, shape (i.e., eccentricity) and orientation of the desired endpoint stiffness ellipse (blue plane); and enforcing static equilibrium with zero endpoint force (green plane). Their intersections with the hypercube are shown schematically as triangular polygons. The feasible activation set that meets both constraints, if it exists, is the black line—which naturally contains infinitely many points (i.e., muscle redundancy). The individual solution with the minimal energetic cost is given by the point where the line is tangential to the smallest spherical manifold defined by the quadratic cost function in Eq 11. C. A muscle synergy can similarly be visualized as a constraint that ties the activations of several muscles in an obligatory way, which in this 3-dimensional example reduces the set of all physiologically feasible neural commands from a cube to a plane. This reduction in independently controllable muscle actions has the inevitable consequence of reducing—or even annihilating—the ability to meet multiple endpoint stiffness and energetic constrains as shown in our results.