The dynamic response of the cat ankle joint during load-moving contractions

The dynamic response of the cat´s ankle joint during load-moving activation of the medial gastrocnemius was determined. Sinusoidal-input oscillations of ankle plantar flexion were performed by the muscle at frequencies ranging from 0.4 to 5 Hz against a 10-N load acting via a cable through a pulley with a 2 cm radius. This was followed by sinusoidal muscle length changes against the same load while excluding the joint. The frequency responses of the two conditions were compared and decomposed in terms of their relative phase and gain, and best-fit pole-zero models to yield the dynamic model of the joint isolated from the muscle properties. The muscle displacement transfer function M(jω) was characterized as two sets of double poles at 2.1 and 3.2 Hz, with a pair of zeros at 0.92 and 20 Hz, and pure time delay of 8 ms. The joint model J(jω) was obtained by adding a pole at 5 Hz and a zero at 13 Hz. It was concluded that the ankle joint acts as a lag system, introducing significant increase in the phase lag between stimulus input and mechanical output without affecting the frequency-dependent attenuation of gain. Average harmonic distortion was less than 5% in all cases. This particular finding reveals that, despite its inherently nonlinear mechanical characteristics, the joint introduces no degradation in the simplified linear behavior of the muscle-joint system. This model is useful in the design of systems employing electrical stimulation to restore movement to limbs paralyzed by spinal cord injury or stroke. In this application, it is suggested that a linear systems approach may be reasonable, but that the joint´s dynamic response decreases the control system design stability margins of the muscle-joint unit. The joint model J(jω), albeit obtained from a condition in which only one muscle was activated, could be used in complex conditions where several muscles are cocontracting independently as agonists or antagonists to modify the - - torque, angle, or stiffness of the joint.