Reflex Torque Response to Movement of the Spastic Elbow: Theoretical Analyses and Implications for Quantification of Spasticity BRIAN D. SCHMIT, 1 YASIN DHAHER, 1 JULIUS P. A. DEWALD, 1,2 and W. ZEV RYMER 1,3 1 Department of Physical Medicine and Rehabilitation, 2 Programs in Physical Therapy, 3 Department of Biomedical Engineering, Northwestern University, and Sensory Motor Performance Program, Rehabilitation Institute of Chicago, 345 East Superior Street, Room 1406, Chicago, IL (Received 1 February 1999; accepted 1 September 1999) Abstract—A parametric model of the human reflex torque response to a large-amplitude, constant angular velocity elbow extension was developed in order to help quantify spasticity in hemiparetic stroke patients, and to better understand its patho- physiology. The model accounted for the routinely observed leveling of torque i.e., a plateau at a mean angular increment of 51°10° s.d. ( n =98) after the initial rise. This torque ‘‘pla- teau’’ was observed in all eight subjects, and in 98 of 125 trials across 25 experimental sessions. The occurrence of this plateau cannot be explained by decreases in elbow flexor moment arms during elbow extension. Rather, the plateau is attributable to a consistent leveling in muscle activation as confirmed both qualitatively from recordings of rectified, smoothed elec- tromyograph EMG activity, and quantitatively using an EMG coefficient model. A parametric model was developed in which the pattern of muscle activation in the stretch reflex response of elbow flexors was described as a cumulative normal distribu- tion with respect to joint angle. Two activation functions, one related to biceps and the other to brachioradialis/brachialis, were incorporated into the model in order to account for ob- servations of a bimodal angular stiffness profile. The resulting model yielded biologically plausible parameters of the stretch reflex response which may prove useful for quantifying spas- ticity. In addition, the model parameters had clear pathophysi- ological analogs, which may help us understand the nature of the stretch reflex response in spastic muscles. © 1999 Bio- medical Engineering Society. S0090-69649901206-0 Keywords—Spasticity, Stretch reflex, Biomechanics, Stroke, Hemiparesis. INTRODUCTION The torque response to constant velocity angular de- flections of the elbow can be used to quantify spasticity in brain-injured patients. Spasticity, defined clinically as a velocity-dependent resistance to passive stretch, 30 is quantitatively related to the magnitude of this torque response. 29 However, the specific parameters of the re- sponse that best describes the important clinical features of spasticity have not been identified. Based on earlier work from our laboratories, two specific parameters of the reflex response have been suggested to reflect signifi- cant aspects of the underlying pathophysiology. These parameters are the ‘‘angular threshold’’ of the stretch reflex and the ‘‘reflex stiffness’’. Physiologically, the an- gular threshold is defined as that angle at which an ini- tially passive muscle first shows evidence of motoneuron activation, and it primarily reflects the baseline level of excitability of the motoneurons. Alternatively, reflex stiffness, which is estimated from the slope of the joint torque–angle relation, has been associated with reflex loop ‘‘gain,’’ which relates motoneuronal discharge and the associated force output of muscles to the level of afferent input. 39,40 Identification of both the stretch reflex angular thresh- old and stiffness is often based on the assumption that an angular threshold is followed by a linearly increasing torque in response to a constant velocity ramp stretch. For example, Powers et al. noted that once the threshold for reflex activation of spastic muscles is reached, con- tinued angular extension produces a broadly linear in- crease in torque. 40 Stiffness was then calculated as the slope of the linear regression of the torque versus joint angle, and threshold was calculated from the ordinate angular intercept. These data confirmed the similarity of the spastic stretch reflex in man to the stretch reflex response observed in the decerebrate cat model, in which a linear force/length relation is generally recorded, after the initial exponential relation at the onset of the reflex. 33 It is worth acknowledging, however, that earlier studies in brain-injured humans, including those in our own laboratories, have relied on limited displacement ampli- tudes, generally 30° 18,46 to 60°. 40,47 These moderate am- plitude perturbations do not necessarily provide an ad- equate range for assessing the assumption of constant reflex stiffness. In the present study, we measured the reflex torque response to joint motion using large-amplitude 90°– 100°, constant-velocity angular extensions of spastic el- Address correspondence to Brian D. Schmit, Sensory Motor Per- formance Program, Rehabilitation Institute of Chicago, 345 E. Superior Street, Room 1406, Chicago, IL 60611. Electronic mail: bschmit@nwu.edu Annals of Biomedical Engineering, Vol. 27, pp. 815–829, 1999 0090-6964/99/276/815/15/$15.00 Printed in the USA. All rights reserved. Copyright © 1999 Biomedical Engineering Society 815