Guiding functional reorganization of motor redundancy using a body-machine interface

Abstract

Background: Body-machine interfaces map movements onto commands to external devices. Redundant motion signals derived from inertial sensors are mapped onto lower-dimensional device commands. Then, the device users face two problems, a) the structural problem of understanding the operation of the interface and b) the performance problem of controlling the external device with high efficiency. We hypothesize that these problems, while being distinct are connected in that aligning the space of body movements with the space encoded by the interface, i.e. solving the structural problem, facilitates redundancy resolution towards increasing efficiency, i.e. solving the performance problem.

Methods: Twenty unimpaired volunteers practiced controlling the movement of a computer cursor by moving their arms. Eight signals from four inertial sensors were mapped onto the two cursor's coordinates on a screen. The mapping matrix was initialized by asking each user to perform free-form spontaneous upper-limb motions and deriving the two main principal components of the motion signals. Participants engaged in a reaching task for 18 min, followed by a tracking task. One group of 10 participants practiced with the same mapping throughout the experiment, while the other 10 with an adaptive mapping that was iteratively updated by recalculating the principal components based on ongoing movements.

Results: Participants quickly reduced reaching time while also learning to distribute most movement variance over two dimensions. Participants with the fixed mapping distributed movement variance over a subspace that did not match the potent subspace defined by the interface map. In contrast, participant with the adaptive map reduced the difference between the two subspaces, resulting in a smaller amount of arm motions distributed over the null space of the interface map. This, in turn, enhanced movement efficiency without impairing generalization from reaching to tracking.

Conclusions: Aligning the potent subspace encoded by the interface map to the user's movement subspace guides redundancy resolution towards increasing movement efficiency, with implications for controlling assistive devices. In contrast, in the pursuit of rehabilitative goals, results would suggest that the interface must change to drive the statistics of user's motions away from the established pattern and toward the engagement of movements to be recovered.

Trial registration: ClinicalTrials.gov, NCT01608438, Registered 16 April 2012.

Keywords: Body-machine interface; Forward model; Motor redundancy; Sensorimotor learning.

Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Fig. 1

Experimental Setup and Protocol. Panel a – participants set in a chair with the sensors strapped around the arms and forearms as depicted, two per side, and were free to move their arms in a comfortable range. A screen positioned in front of the subjects displayed the cursor position, the current target position and a score in the top right corner. Panel b – target locations for the reaching task (top panel), and trajectory followed by the moving target during tracking (bottom panel). Panel c – summary of the experimental protocol for the Constant map group (top) and Adaptive map group (bottom). H0 stands for the BoMI map obtained after calibration, which is used by the Constant group throughout the session. Hi is the map updated iteratively during reaching in the Adaptive map group, and HK is the final map after adaptation

Fig. 2

Summary of performance in the trained task. Panel a – average reaching time in the first and last 20 trials of reaching practice with full visual feedback of the cursor. Panel b – average Reaching Error during the first and last 20 trials with full visual feedback of the cursor. Panel c – Average Reaching Error in the first and last 10 trials in the blind condition. Black bars and red bars refer to Constant map and Adaptive map group respectively. The vertical error is the standard deviation, asterisks denote significant comparisons according to a t-test

Fig. 3

Participants grouping according to skill level. Panel a – Reaching Time for each trial through practice time for participants in the Constant (C - black lines) and Adaptive (A - red lines) map groups classified according to their initial performance in the reaching task. Panel b – average time constant estimated by fitting an exponential function to the Reaching Time over experiment time data in panel a. Panel c – average cumulative score across all blocks of reaching practice for good and poor performers, Adaptive map in red and Constant map in black. The vertical error is the standard deviation, asterisks denote significant comparisons according to a t-test ** for p < 0.001

Fig. 4

Learning dynamics. Panel a – average Reaching Time for the participants in the Constant group averaged in bins of 3 trials; Panel b – average Planarity Index of movement computed on bins of 3 trials. Shaded areas represent the 90% confidence interval around the mean. In black/red the result of fitting a single exponential model to the data of Constant/Adaptive map group using a non-linear mixed effect model; panel c – comparison of the time constants estimated by the model fitted on performance and on planarity for each individual in the two groups

Fig. 5

Movement distribution during reaching. Panel a - Variance Accounted for by the body-machine interface map in the first and last minute of reaching practice. Panel b – Subspace Angle between the subspace of reaching movements and BoMI subspace in the first and last minute of reaching. Constant map group is in black, adaptive map group in red. * represents significant differences after a paired t-test with p < 0.05. Panel c – Subspace angle between the two subspaces of reaching movements computed over the first and the last minute of reaching. Constant map group is in black, adaptive map group in red. Panel d – The X-axis represents the Variance Accounted for by the BoMI subspace in the last minute of reaching (as in panel A) for the participants of the Constant map group, while the Y-axis represents the percent change in movement variance during the last minute of reaching relative to the movement variance during calibration. The red line shows the linear model fit of the data. Panel e – Example of projection of the movement distribution during the last minute of reaching over the calibration subspace and over the subspace computed by taking the first two principal components of movement variance. The top figures show the projection in 3D using the 3rd principal component with variance λ3 as z-dimension, the bottom figures show the projection onto the first two principal components

Fig. 6

Effect of task on movement distribution. Panel a – Planarity Index computed across tasks: Cal – calibration, Reach = last minute of reaching, Track = tracking task. Constant map group is in black, Adaptive map group in red. * indicate significant differences with p < 0.05. Panel b – Subspace Angle between the subspace of tracking movements and the subspace spanned by reaching movements during the last minute of training, C = Constant map group, A = Adaptive Map group. Panel c – distance between tracking subspace and reaching subspace and the tracking subspace and the BoMI subspace in terms of Subspace Angle. The reaching subspace is computed during the last minute of training. Black dots are individual subjects in the Constant map group, Red crosses are individual subjects in the Adaptive map group. Panel d – example of tracking movement projected onto the subspace obtained from the last 60″ of reaching data in the space of the first 3 principal components (top view) and in the hyperplane of the first two