Spectral Estimation of Mechanical Impedance of Hemiplegic Arms

Patients with stroke who had robotic therapy using a performance-based, progressive protocol experienced a marked change in tone – a muscle’s resistance to passive elongation or stretch. Although clinicians judge muscle tone subjectively, an objective measure would provide valuable insight about the effect of stroke on a hemiplegic limb and better characterize the effect of rehabilitation therapy. Robots such as MIT-MANUS or InMotion2 (Interactive Motion Technologies, Inc.) are able to deliver forces to a patient’s limb and measure the position, velocity, and interaction forces between the robot and that limb. Therefore, these robots are well suited to measure motion of the human arm resulting from applied forces, i.e., mechanical admittance (inverse of mechanical impedance), and thereby objectively quantify at least one aspect of patient tone.

During the robotic measurement, patients were instructed to “simply relax and allow the robot to shake their arm.” One difficulty that often arises with stroke patients that usually doesn’t arise with unimpaired subjects is their inability to relax at a given position. The hemiplegic arms of patients exhibiting hypertonicity may curl towards the fetal position because their flexors contract more than their extensors. Therefore, a Proportional-Derivative (PD) controller was used to keep the hemiplegic arm close to the central target location used during their therapy. Simultaneously, a force perturbation was applied to the patient’s arm for 50 seconds. Perturbation commands were generated at a sampling rate of 500 Hz by filtering a set of uniformly distributed random numbers with an eighth-order Butterworth filter that had a cut-off frequency of 15 Hz (selected to exceed the natural frequency of the human arm, ~2 to 3 Hz).

Studies depict the force perturbation inputs (as measured by an ATI 6-axis force transducer) and the resulting displacements of the robot end effector over the first 2 seconds of a trial. Results of the spectral analysis for this trial, namely, the transfer function matrix from the perturbation forces to the resulting displacements are observed. This transfer function matrix is commonly termed the compliance matrix and is simply the inverse of the stiffness matrix. Although this method is currently being used to assess patient muscle tone during therapy, more patients need to complete the therapy protocol before its effectiveness can be determined.