A mechanical analysis of force distribution between redundant, multiple degree-of-freedom actuators in the human: Implications for the central nervous system

This paper is a mechanical analysis of the apparent redundancy of muscles in the human body. Because differentiation of motor commands appears to occur at the motor unit level, the analysis examines possible distributions of motor unit activation levels for a given motor task. The transformation from these motor commands to movement is defined mathematically. Each motor unit, regardless of how many joints it crosses, produces a single action, a vector describing multi-joint motor tasks including control of position and/or force. These individual actions, even for apparently antagonistic muscles, are summed to produce overall movement. Because there are many possible combinations of motor unit actions which produce a desired net action, it is hypothesized that the central nervous system uses some consistent criteria for selecting favored combinations. Modeling these criteria with optimization cost functions, it is shown that the potential cost for producing movement decreases with increasing numbers of actuators, distributed in a variety of configurations. This approach is compatible with self-organizing topographic feature maps, which demonstrate how the central nervous system may perform the described transformations.