Quantization of continuous arm movements in humans with brain injury

Abstract

Segmentation of apparently continuous movement has been reported for over a century by human movement researchers, but the existence of primitive submovements has never been proved. In 20 patients recovering from a single cerebral vascular accident (stroke), we identified the apparent submovements that composed a continuous arm motion in an unloaded task. Kinematic analysis demonstrated a submovement speed profile that was invariant across patients with different brain lesions and provided experimental verification of the detailed shape of primitive submovements. The submovement shape was unaffected by its peak speed, and to test further the invariance of shape with speed, we analyzed movement behavior in a patient with myoclonus. This patient occasionally made involuntary shock-like arm movements, which occurred near the maximum capacity of the neuromuscular system, exhibited speed profiles that were comparable to those identified in stroke patients, and were also independent of speed.

Figure 1

(A) Patient A drawing clockwise single circles starting and ending at the 9:00 position. Patients wear a hand-holder that connects their palm to the robot end-effector and an elbow support. Patients were instructed to draw a smooth circle, while their hand was in view. No explicit feedback was provided. (B) Unimpaired subject drawing clockwise single circle starting and ending at the 9:00 position. Subject grasped the robot handle with the palm and was instructed to draw a smooth circle, while the hand was in view. No explicit feedback was provided.

Figure 2

Kinematic data of patient A in a point-to-point movement without time constraint. (Left) The hand displacement in the horizontal plane. (Right) Hand speed.

Figure 3

Examples of normalized β-density function for different values of r and s. The figure shows that the proper choice of parameters leads to a wide variety of shapes, e.g., symmetric, skewed, unimodal, bimodal.

Figure 4

Normalized β-density function parameters for the stroke patients. The Insets show the parameters (mean p and standard deviation ps) for the β-density function, which were estimated from the first two recorded movements for each point-to-point task from the stroke patients. The figure shows the ensemble best-fit β-function superimposed on each of the 38 individual β-functions, as well as a Gaussian with standard deviation equal to half the width of the ensemble β-function at 0.67 and a minimum-jerk curve with the same normalized displacement and duration. The peaks of all curves are centered at the same point.

Figure 5

Assessment of the ensemble best-fit β-function. (Upper) An example of an individual speed profile (solid line) compared with the ensemble best-fit β-function (dashed line). (Lower Left) The histogram of the slope of the principal eigenvector of the covariance matrix between the individual speed profiles and the ensemble best-fit β-function. The histogram on the Lower Right shows the correlation coefficient between the individual speed profiles and the ensemble best-fit β-function.

Figure 6

Histogram of the individual speed profiles for stroke and myoclonus patients. The stroke patients’ movements were typically slow (left distribution), whereas the myoclonus patient’s involuntary shock-like movements were fast (right distribution), near the maximum capacity of the neuromuscular system.

Figure 7

Normalized β-density function parameters for the myoclonus shock-like movements. The Insets show the parameters (mean p and standard deviation ps) for the β-density function, which were estimated from recorded movements from the myoclonus patient during point-to-point task. The figure shows the ensemble best-fit β-function superimposed on each of the 14 individual β-functions, as well as a Gaussian with standard deviation equal to half the width of the ensemble β-function at 0.67 and a minimum-jerk curve with the same normalized displacement and duration. The peaks of all curves are centered at the same point.