Simultaneous characterizations of reflex and nonreflex dynamic and static changes in spastic hemiparesis

Abstract

This study characterizes tonic and phasic stretch reflex and stiffness and viscosity changes associated with spastic hemiparesis. Perturbations were applied to the ankle of 27 hemiparetic and 36 healthy subjects under relaxed or active contracting conditions. A nonlinear delay differential equation model characterized phasic and tonic stretch reflex gains, elastic stiffness, and viscous damping. Tendon reflex was characterized with reflex gain and threshold. Reflexively, tonic reflex gain was increased in spastic ankles at rest (P < 0.038) and was not regulated with muscle contraction, indicating impaired tonic stretch reflex. Phasic-reflex gain in spastic plantar flexors was higher and increased faster with plantar flexor contraction (P < 0.012) than controls (P < 0.023) and higher in dorsi-flexors at lower torques (P < 0.038), primarily because of its increase at rest (P = 0.045), indicating exaggerated phasic stretch reflex especially in more spastic plantar flexors, which showed higher phasic stretch reflex gain than dorsi-flexors (P < 0.032). Spasticity was associated with increased tendon reflex gain (P = 0.002) and decreased threshold (P < 0.001). Mechanically, stiffness in spastic ankles was higher than that in controls across plantar flexion/dorsi-flexion torque levels (P < 0.032), and the more spastic plantar flexors were stiffer than dorsi-flexors at comparable torques (P < 0.031). Increased stiffness in spastic ankles was mainly due to passive stiffness increase (P < 0.001), indicating increased connective tissues/shortened fascicles. Viscous damping in spastic ankles was increased across the plantar flexion torque levels and at lower dorsi-flexion torques, reflecting increased passive viscous damping (P = 0.033). The more spastic plantar flexors showed higher viscous damping than dorsi-flexors at comparable torque levels (P < 0.047). Simultaneous characterizations of reflex and nonreflex changes in spastic hemiparesis may help to evaluate and treat them more effectively.

Keywords: reflexes; rehabilitation; spasticity; stiffness; stroke.

Fig. 1.

Experimental setup: the seat is adjusted in 4 degrees of freedom to align the ankle flexion axis with the motor shaft. In addition to other protective measures, the safety screws are used as mechanical stops to restrict the motor range of motion during the perturbation. The foot is fixed to the attachment through a clamp, and the foot attachment can be adjusted and locked in 4 degrees of freedom to achieve appropriate alignment. A 6-axis force sensor is mounted between the foot attachment and the motor shaft. The leg and thigh are strapped to the leg support and seat, respectively.

Fig. 2.

Representative mechanical and EMG signals during small-amplitude random perturbations. Each column corresponds to a trial. Left and right: trials during which the subject maintained steady dorsi-flexion and plantar flexion background muscle torques, respectively. Center: trial during which the subject was relaxed. First row: ankle dorsi-flexion (DF) torque with dorsi-flexor muscle contraction generating positive torque. Second row: ankle dorsi-flexion angle. Third and fourth rows: ankle plantar flexor (soleus) and dorsi-flexor [tibialis anterior (TA)] EMG signals (normalized to maximum values during experiment), respectively.

Fig. 3.

Nonlinear delay differential equation model represented by physical components of spring [with elastic stiffness K(λ)], dashpot [with coefficient of viscous damping B(λ)], mass (m), dynamic (phasic) stretch reflex gain B_d(λ,t_d1), and static (tonic) stretch reflex gain K_d(λ,t_d1). When the cart is pulled horizontally, the resistance force F(t) is generated by all 5 components, K, B, m, B_d, and K_d. In the corresponding rotational case, K(λ), B(λ), and m correspond to joint elastic stiffness, joint viscous damping, and foot inertia, respectively. The lower part represents the reflex feedback properties of the ankle joint and muscles crossing it. λ represents the system operating state and t_d1 the reflex-loop delay. Different from the nonreflex muscle-joint properties, the two reflex parameters, B_d(λ,t_d1) and K_d(λ,t_d1), characterize stretch reflex actions that are caused by the angular perturbation that occurred t_d1 seconds ago. Note that B_d(λ,t_d1) corresponds to unidirectional velocity of muscle stretching.

Fig. 4.

Measured (solid line) and simulated (dashed line) ankle plantar flexion torques. The simulation was based on the model in Eq. 1. Data were from a male stroke patient with severe plantar flexor spasticity.

Fig. 5.

Reflex and nonreflex properties of a representative healthy subject. Top left: joint elastic stiffness K as a function of the background muscle contraction. x-Axis represents the background muscle torque, and its positive direction corresponds to plantar flexor contraction. Each “+” corresponds to parameters estimated from a trial in which the subject maintained a steady level of contraction. Top right: joint viscous damping coefficient B as a function of the background muscle contraction. Bottom left: dynamic stretch reflex gain B_d as a function of the background muscle contraction. Bottom right: static stretch reflex gain K_d as a function of the background muscle contraction.

Fig. 6.

Reflex (C and D) and nonreflex (A and B) properties in 36 normal subjects and 27 spastic hemiparetic patients. A: joint elastic stiffness K as a function of the background muscle contraction. x-Axis represents the background muscle torque, and its positive and negative directions correspond to plantar flexor and dorsi-flexor muscle contractions, respectively. Vertical lines give the SE of the mean across subjects in each group. △ and * correspond to spastic hemiparetic and healthy subjects, respectively. B: joint viscosity B as a function of the background muscle contraction. C: dynamic stretch reflex gain B_d as a function of the background muscle contraction. D: static stretch reflex gain K_d as a function of the background muscle contraction.

Fig. 7.

Achilles tendon tapping results from a male stroke patient's spastic ankle (left) and from a normal male subject's ankle (right). The reflex threshold and tendon reflex gain for the stroke patient were 11.0 N and 12.8 cm, respectively. They were 16.8 N and 1.2 cm, respectively, for the normal subject. From top to bottom, tendon tapping force, soleus muscle EMG signal, and reflex-mediated plantar flexor ankle joint torque are shown. Subjects were asked to relax during the tapping trials. The ankle was fixed isometrically at 0° plantar flexion. Means ± SD over the different taps (25 taps for the spastic hemiparetic patient and 30 taps for the normal subject) are shown for each signal. The initial spike in the reflex torque signal (at ∼80 ms) was due to the mechanical impact to the torque sensor caused by the tapping.