A process account of the uncontrolled manifold structure of joint space variance in pointing movements

In many situations, the human movement system has more degrees of freedom than needed to achieve a given movement task. Martin et al. (Neural Comput 21(5):1371-1414, 2009) accounted for signatures of such redundancy like self-motion and motor equivalence in a process model in which a neural oscillator generated timed end-effector virtual trajectories that a neural dynamics transformed into joint virtual trajectories while decoupling task-relevant and task-irrelevant combinations of joint angles. Neural control of muscle activation and the biomechanical dynamics of the arm were taken into account. The model did not address the main signature of redundancy, however, the UCM structure of variance: Many experimental studies have shown that across repetitions, variance of joint configuration trajectories is structured. Combinations of joint angles that affect task variables (lying in the uncontrolled manifold, UCM) are much more variable than combinations of joint angles that do not. This finding has been robust across movement systems, age, and tasks and is often preserved in clinical populations as well. Here, we provide an account for the UCM structure of variance by adding four types of noise sources to the model of Martin et al. (Neural Comput 21(5):1371-1414, 2009). Comparing the model to human pointing movements and systematically examining the role of each noise source and mechanism, we identify three causes of the UCM effect, all of which, we argue, contribute: (1) the decoupling of motor commands across the task-relevant and task-irrelevant subspaces together with "neural" noise at the level of these motor commands; (2) "muscle noise" combined with imperfect control of the limb; (3) back-coupling of sensed joint configurations into the motor commands which then yield to the sensed joint configuration within the UCM.