Postural feedback scaling deficits in Parkinson's disease

Abstract

Many differences in postural responses have been associated with age and Parkinson's disease (PD), but until now there has been no quantitative model to explain these differences. We developed a feedback control model of body dynamics that could reproduce the postural responses of young subjects, elderly subjects, and subjects with PD, and we investigated whether the postural impairments of subjects with PD can be described as an abnormal scaling of postural feedback gain. Feedback gains quantify how the nervous system generates compensatory joint torques based on kinematic responses. Seven subjects in each group experienced forward postural perturbations to seven different backward support surface translations ranging from 3- to 15-cm amplitudes and with a constant duration of 275 ms. Ground reaction forces and joint kinematics were measured to obtain joint torques from inverse dynamics. A full-state feedback controller with a two-segment body dynamic model was used to simulate joint kinematics and kinetics in response to perturbations. Results showed that all three subject groups gradually scaled postural feedback gains as a function of perturbation amplitudes, and the scaling started even before the maximum allowable ankle torque was reached. This result implies that the nervous system takes body dynamics into account and adjusts postural feedback gains to accommodate biomechanical constraints. PD subjects showed significantly smaller than normal ankle feedback gain with low scaling and larger hip feedback gain, which led to an early violation of the flat-foot constraint and unusually small (bradykinetic) postural responses. Our postural feedback control model quantitatively described the postural abnormality of the patients with PD as abnormal feedback gains and reduced ability to modify postural feedback gain with changes in postural challenge.

Fig. 1.

A: schematic model of long-loop human postural control by the CNS. Sensory information of body states are measured by vision, the vestibular organ and muscle spindles, and then sent to the CNS to be processed. Based on an estimate of body kinematics, appropriate control plans are selected and then corresponding motor commands are produced as joint torques. B: the feedback control of the body posture can be modeled by a feedback control system. Plant represents the musculoskeletal system, sensor describes the multisensory system, and the controller represents the CNS.

Fig. 2.

Joint angle and joint torque data and model simulation with regression gain (A and B) and optimized feedback gain (C and D). Empirical data of the ankle (black) and hip (gray) joint are shown with dashed lines, and the model simulation is displayed with solid lines. Regression gain, which was obtained by the least-squares method from the torque and the joint kinematics, gives unstable closed-loop eigen values and makes the simulation diverge from the data with time.

Fig. 3.

Averaged joint angle (A–C) and joint torque (D–E) trajectories of the young (A and D), elderly (B and E), and Parkinson's disease (PD) subjects (C and F). Joint angles were defined from subjects' preferred upright posture with a positive sign for extension in the sagittal plane. Net joint torque of the ankle and hip were normalized for each subject's weight multiplied by height for intersubject averaging. Scaled kinematic and kinetic trajectories illustrate the responses to the increased perturbations of magnitudes from 3–15 cm for the young, 3–12 cm for the elderly, and 3–9 cm for the PD subjects. Arrows in A and D show the direction of change during balance recovery. Arrows in B and E show increasing responses with increasing perturbation magnitudes.

Fig. 4.

Peak amplitudes of ankle joint angles (A), hip joint angles (B), normalized ankle joint torques (C), and hip joint torques (D) of the young (■), elderly (), and subjects with PD () in response to each perturbation magnitude. Error bars indicate SDs. *, statistical significance is P < 0.05.

Fig. 5.

Representative time trajectories of ankle (black) and hip (gray) joint angle (A–C) and corresponding normalized joint torque (D–E) of the empirical data (dashed line) and model simulation (solid line) of the young (A and D), the elderly (B and E), and the PD subjects (C and F). R² values comparing data with simulations for each group were 0.86, 0.88, and 0.79, respectively.

Fig. 6.

Averaged feedback gain components of the young (●), elderly (), and PD (○) groups obtained from optimization that minimizes the fitting error between the data and the model simulation. Gradual scaling was observed in most of the gains with statistical significance for the gain parameters of k₁₁, k₁₂, k₁₃, k₂₁, k₂₄ in the young, k₁₁, k₁₂, k₁₃, k₂₄ in the elderly, and k₁₁, k₁₂, k₂₁, k₂₃, k₂₄ in the PD. Error bars indicate SE.

Fig. 7.

Simulation of the change of peak ankle joint (A) angle and hip joint (B) angle as a function of feedback gains and upper body mass of the young and elderly groups. Increased upper body mass slightly increases the magnitude of ankle joint motion, while feedback gain of the elderly significantly reduces the ankle joint angle. In contrast, the body parameters and the gain of the elderly increase peak hip joint angle. Missing mesh grids indicate that the system becomes unstable.