Visualization techniques for analyzing control of human movement: Affine mappings between multidimensional spaces

摘要

Control of human movement is difficult to study in part due to the number of muscles, joints, and degrees-of-freedom about the joints. Interpreting the commands generated by the central nervous system or the resultant motion generated by muscles is not possible without a method for reducing the number of variables examined.;The goal of this dissertation is to develop and apply a method for understanding control of movement through visualization. This is made possible by examining the possible outputs of a system in terms of vectors composed of achievable accelerations and forces. The effect of many variables can then be seen in the final output, which is the summation of intermediate transformations. The visualization is predicated on a mathematical characteristic of the equations of motion, that they describe affine mappings.;A theory of muscle function in terms of output vectors was developed and applied to the study of the action of muscles that cross more than one joint, a topic of contemporary interest in the biomechanics community. It was found that each muscle can be described in terms of its resultant output vector. Any presumed special qualities are due to the muscle's unique location rather than the number of joints it crosses, as had been previously thought.;The theory of muscle function was also extended to encompass the set of all possible outputs. This set is useful to study when the actual command inputs or muscle forces are unknown, as is often the case in human movement. Movements made in response to postural perturbations were examined in light of the constraints acting upon this set. The constraints were found to greatly restrict the choices available to the central nervous system when forming a control. Sensitivity studies indicated that strengthening certain muscles can effect changes on the possible outputs. Finally, given the limited choices available, a model for central nervous system control showed that simple stability criteria are sufficient to approximate human behavior.