Postural instability via a loss of intermittent control in elderly and patients with Parkinson's disease: A model-based and data-driven approach

How the brain can be trained to achieve an intermittent control strategy for stabilizing quiet stance by means of reinforcement learning

The stabilization of human quiet stance is achieved by a combination of the intrinsic elastic properties of ankle muscles and an active closed-loop activation of the ankle muscles, driven by the delayed feedback of the ongoing sway angle and the corresponding angular velocity in a way of a delayed proportional (P) and derivative (D) feedback controller. It has been shown that the active component of the stabilization process is likely to operate in an intermittent manner rather than as a continuous controller: the switching policy is defined in the phase-plane, which is divided in dangerous and safe regions, separated by appropriate switching boundaries. When the state enters a dangerous region, the delayed PD control is activated, and it is switched off when it enters a safe region, leaving the system to evolve freely. In comparison with continuous feedback control, the intermittent mechanism is more robust and capable to better reproduce postural sway patterns in healthy people. However, the superior performance of the intermittent control paradigm as well as its biological plausibility, suggested by experimental evidence of the intermittent activation of the ankle muscles, leaves open the quest of a feasible learning process, by which the brain can identify the appropriate state-dependent switching policy and tune accordingly the P and D parameters. In this work, it is shown how such a goal can be achieved with a reinforcement motor learning paradigm, building upon the evidence that, in general, the basal ganglia are known to play a central role in reinforcement learning for action selection and, in particular, were found to be specifically involved in postural stabilization.

A comprehensive multivariate analysis of the center of pressure during quiet standing in patients with Parkinson's disease

BACKGROUND

We hypothesized that postural instability observed in individuals with Parkinson's disease (PD) can be classified as distinct subtypes based on comprehensive analyses of various evaluated parameters obtained from time-series of center of pressure (CoP) data during quiet standing. The aim of this study was to characterize the postural control patterns in PD patients by performing an exploratory factor analysis and subsequent cluster analysis using CoP time-series data during quiet standing.

METHODS

127 PD patients, 47 aged 65 years or older healthy older adults, and 71 healthy young adults participated in this study. Subjects maintain quiet standing for 30 s on a force platform and 23 variables were calculated from the measured CoP time-series data. Exploratory factor analysis and cluster analysis with a Gaussian mixture model using factors were performed on each variable to classify subgroups based on differences in characteristics of postural instability in PD.

RESULTS

The factor analysis identified five factors (magnitude of sway, medio-lateral frequency, anterio-posterior frequency, component of high frequency, and closed-loop control). Based on the five extracted factors, six distinct subtypes were identified, which can be considered as subtypes of distinct manifestations of postural disorders in PD patients. Factor loading scores for the clinical classifications (younger, older, and PD severity) overlapped, but the cluster classification scores were clearly separated.

CONCLUSIONS

The cluster categorization clearly identifies symptom-dependent differences in the characteristics of the CoP, suggesting that the detected clusters can be regarded as subtypes of distinct manifestations of postural disorders in patients with PD.

A neuromechanical model characterizing the motor planning and posture control in the voluntary lean in Parkinson's disease

Parkinson's disease targets patients' cognitive and motor abilities, including postural control. Many studies have been carried out to introduce mathematical models for a better understanding of postural control in such patients and the relation between the model parameters and the clinical assessments. So far, these studies have addressed this connection merely in static tests, such as quiet stance. The aim of this study is to develop a model for voluntary lean, and as such, identify the model parameters for both PD patients and healthy subjects from experimental data. The proposed model comprises planning and control sections. The model parameters for the planning section were extracted from the time response characteristics. Parameters for the control section were identified based on the spatial characteristics of the center-of-pressure (COP) response using an optimization process. 24 PD patients along with 24 matched healthy subjects participated in the study. The results showed a significant difference between the two groups in terms of temporal parameters for the planning section. This difference emphasizes bradykinesia as an essential symptom of PD. Also, differences were found for the postural control section. In all directions, the proportional gain of the feedback controller was significantly larger in PD patients; however, the gain of the feedforward controller was significantly smaller in PD patients. Furthermore, the control gains were strongly correlated with the clinical scales (Functional Reach Test and Unified Parkinson's Disease Rating Scale) in certain directions. In conclusion, the new model helps to better understand and quantify some PD symptoms in voluntary lean tasks.

An improved intermittent control model of postural sway during quiet standing implemented by a data driven approach

This paper proposes a new intermittent control model during human quiet standing, which is consisted of postulated "regular intervention" and "imminent intervention". The regular intervention is within the main control loop, and its trigger condition is equivalent to the switching frequency of center of pressure (COP) data calculated by wavelet transform. The imminent intervention will only be triggered after the postural sway angle exceeds a certain threshold. In order to prove the effectiveness of the new model, the simulation results of the new model and the model proposed by Asai et al. (2009) are compared with the experimental data. The setting parameters of both models are retrieved by Bayesian regression from the experimental data. The results show that the new model not only could exhibit two power law scaling regimes of power spectral density (PSD) of COP, but also show that indices of the probability density function distance, root mean square (RMS), Total Sway Path, displacement Range, 50% power frequency of center of mass (COP) between the simulation results and the experimental data are closer compared to the existing model. Moreover, the limit cycle oscillations (LCOs) obtained from the simulation results of the new model have a higher degree of matching with those retrieved from the experimental data.

Analysis of abnormal posture in patients with Parkinson's disease using a computational model considering muscle tones

Patients with Parkinson's disease (PD) exhibit distinct abnormal postures, including neck-down, stooped postures, and Pisa syndrome, collectively termed "abnormal posture" henceforth. In the previous study, when assuming an upright stance, patients with PD exhibit heightened instability in contrast to healthy individuals with disturbance, implying that abnormal postures serve as compensatory mechanisms to mitigate sway during static standing. However, limited studies have explored the relationship between abnormal posture and sway in the context of static standing. Increased muscle tone (i.e., constant muscle activity against the gravity) has been proposed as an underlying reason for abnormal postures. Therefore, this study aimed to investigate the following hypothesis: abnormal posture with increased muscle tone leads to a smaller sway compared with that in other postures, including normal upright standing, under the sway minimization criterion. To investigate the hypothesis, we assessed the sway in multiple postures, which is determined by joint angles, including cases with bended hip joints. Our approach involved conducting forward dynamics simulations using a computational model comprising a musculoskeletal model and a neural controller model. The neural controller model proposed integrates two types of control mechanisms: feedforward control (representing muscle tone as a vector) and feedback control using proprioceptive and vestibular sensory information. An optimization was performed to determine the posture of the musculoskeletal model and the accompanied parameters of the neural controller model for each of the given muscle tone vector to minimize sway. The optimized postures to minimize sway for the optimal muscle tone vector of patients with PD were compared to the actual postures observed in these patients. The results revealed that on average, the joint-angle differences between these postures was <4°, which was less than one-tenth of the typical joint range of motion. These results suggest that patients with PD exhibit less sway in the abnormal posture than in other postures. Thus, adopting an abnormal posture with increased muscle tone can potentially serve as a valid strategy for minimizing sway in patients with PD.

Discrete cortical control during quiet stance revealed by desynchronization and rebound of beta oscillations

Postural sway during quiet stance often exhibits a repetition of micro-fall and the subsequent micro-recovery. The classical view -that the quiet bipedal stance is stabilized by the ankle joint stiffness- has been challenged by paradoxical non-spring-like behaviors of calf muscles: gastrocnemius muscles are shortened and then lengthened, respectively, during the micro-fall and the micro-recovery. Here, we examined EEG based brain activity during quiet stance, and identified desynchronization and synchronization of beta oscillations that were associated, respectively, with the micro-fall and the micro-recovery. Based on a widely accepted scenario for beta-band desynchronization during movement and post-movement rebound in the control of discrete voluntary movement, our results reveal that the beta rebound can be considered as a manifestation of stop command to punctuate the motor control for every fall-recovery cycle. Namely, cortical interventions to the automatic postural control are discrete, rather than continuous modulations. The finding is highly compatible with the intermittent control model, rather than the stiffness control model.

Analysis of the Relationship Between Muscle Tones and Abnormal Postures in a Computational Model

Patients with Parkinson's disease (PD), a neurodegenerative disorder, exhibit a characteristic posture known as a forward flexed posture. Increased muscle tone is suggested as a possible cause of this abnormal posture. For further analysis, it is necessary to measure muscle tone, but the experimental measurement of muscle tone during standing is challenging. The aim of this study was to examine the hypothesis that "In patients with PD, abnormal postures are those with a small sway at increased muscle tones" using a computational model. The muscle tones of various magnitudes were estimated using the computational model and standing data of patients with PD. The postures with small sway at the estimated muscle tones were then calculated through an optimization method. The postures and sway calculated using the computational model were compared to those of patients with PD. The results showed that the differences in posture and sway between the simulation and experimental results were small at higher muscle tones compared to those considered plausible in healthy subjects by the simulations. This simulation result indicates that the reproduced sway at high muscle tones is similar to that of actual patients with PD and that the reproduced postures with small sway locally at high muscle tones in the simulations are similar to those of patients with PD. The result is consistent with the hypothesis, reinforcing the hypothesis.Clinical relevance- This study implies that improving the increased muscle tone in patients with PD may lead to an improved abnormal posture.

Characterization of Postural Control in Post-Stroke Patients by Musculoskeletal Simulation

An association is observed between the standing sway posture and falls in patients with stroke; hence, it is important to study their standing balance. Although there are studies on the standing balance in stroke patients, differences in control have not been adequately investigated. This study aims to propose a method to characterize the postural sway in standing stroke patients using a mathematical model. A musculoskeletal model and neural controller model were used to simulate ten stroke patients (five patients with cerebral hemorrhages and five patients with cerebral infarctions) and eight young healthy participants, and their data were monitored during quiet standing. The model parameters were adjusted by focusing on the maximum-minimum difference in sway, which was considered important in a previous study, and sway speed, which is frequently used in the analysis. The adjusted model parameters were subjected to dimension reduction using non-negative matrix factorization. Consequently, the sway characteristics of stroke patients were expressed as the magnitude of gain parameters related to the extension of the entire body. The results of this study demonstrated the possibility of representing the characteristics of postural sway as model parameters in stroke patients using a mathematical model. This characterization could lead to the design of individualized rehabilitation systems in the future.

Predictor feedback models for stick balancing with delay mismatch and sensory dead zones

Human stick balancing is investigated in terms of reaction time delay and sensory dead zones for position and velocity perception using a special combination of delayed state feedback and mismatched predictor feedback as a control model. The corresponding mathematical model is a delay-differential equation with event-driven switching in the control action. Due to the sensory dead zones, initial conditions of the actual state cannot always be provided for an internal-model-based prediction, which indicates that (1) perfect prediction is not possible and (2) the delay in the switching condition cannot be compensated. The imperfection of the predictor is described by the delay mismatch, which is treated as a lumped parameter that creates a transition between perfect predictor feedback (zero delay mismatch) and delayed state feedback (mismatch equal to switching delay). The maximum admissible switching delay (critical delay) is determined numerically based on a practical stabilizability concept. This critical delay is compared to a realistic reference value of 230 ms in order to assess the possible regions of the threshold values for position and velocity perception. The ratio of the angular position and angular velocity for 44 successful balancing trials by 8 human subjects was used to validate the numerical results. Comparison of actual human stick balancing data and numerical simulations based on the mismatched predictor feedback model provided a plausible range of parameters: position detection threshold 1°, velocity detection threshold between 4.24 and 9.35°/s, and delay mismatch around 100-150 ms.

Center of pressure plausibility for the double-link human stance model under the intermittent control paradigm

Despite human balance maintenance in quiet conditions could seem a trivial motor task, it is not. Recently, the human stance was described through a double link inverted pendulum (DIP) actively controlled at the ankle with an intermittent proportional (P) and derivative (D) control actions based on the sway of a virtual inverted pendulum (VIP) that links the ankle joint with the DIP center of mass. Such description, encompassing both the mechanical model and the intermittent control policy, was referred as the DIP/VIP human stance model, and it showed physiologically plausible kinematic patterns. In this study a mathematical formalization of the Center of pressure (COP) for a DIP structure was developed. Then, it was used in conjunction with an intermittently controlled DIP/VIP model to assess its kinetic plausibility. Three descriptors commonly employed in posturography were selected among six based on their capability to discriminate between young (Y) and elderly (O) adults groups. Then, they were applied to assess whether variations of the P-D parameters affect the synthetic COP. The results showed that DIP/VIP model can reproduce COP trajectories, showing characteristics similar to the Y and O groups. Moreover, it was observed that both P and D parameters increased passing from Y to O, indicating that the COP obtained from the DIP/VIP model is able to highlight differences in balance control between groups. The study hence promote the use of DIP/VIP in posturography, where inferential techniques can be applied to characterize neural control.

Introduction to Focus Issue: Dynamical disease: A translational approach

The concept of Dynamical Diseases provides a framework to understand physiological control systems in pathological states due to their operating in an abnormal range of control parameters: this allows for the possibility of a return to normal condition by a redress of the values of the governing parameters. The analogy with bifurcations in dynamical systems opens the possibility of mathematically modeling clinical conditions and investigating possible parameter changes that lead to avoidance of their pathological states. Since its introduction, this concept has been applied to a number of physiological systems, most notably cardiac, hematological, and neurological. A quarter century after the inaugural meeting on dynamical diseases held in Mont Tremblant, Québec [Bélair et al., Dynamical Diseases: Mathematical Analysis of Human Illness (American Institute of Physics, Woodbury, NY, 1995)], this Focus Issue offers an opportunity to reflect on the evolution of the field in traditional areas as well as contemporary data-based methods.

Long-Lasting Event-Related Beta Synchronizations of Electroencephalographic Activity in Response to Support-Surface Perturbations During Upright Stance: A Pilot Study Associating Beta Rebound and Active Monitoring in the Intermittent Postural Control

Movement related beta band cortical oscillations, including beta rebound after execution and/or suppression of movement, have drawn attention in upper extremity motor control literature. However, fewer studies focused on beta band oscillations during postural control in upright stance. In this preliminary study, we examined beta rebound and other components of electroencephalogram (EEG) activity during perturbed upright stance to investigate supraspinal contributions to postural stabilization. Particularly, we aimed to clarify the timing and duration of beta rebound within a non-sustained, but long-lasting postural recovery process that occurs more slowly compared to upper extremities. To this end, EEG signals were acquired from nine healthy young adults in response to a brief support-surface perturbation, together with the center of pressure, the center of mass and electromyogram (EMG) activities of ankle muscles. Event-related potentials (ERPs) and event-related spectral perturbations were computed from EEG data using the perturbation-onset as a triggering event. After short-latency (<0.3 s) ERPs, our results showed a decrease in high-beta band oscillations (event-related desynchronization), which was followed by a significant increase (event-related synchronization) in the same band, as well as a decrease in theta band oscillations. Unlike during upper extremity motor tasks, the beta rebound in this case was initiated before the postural recovery was completed, and sustained for as long as 3 s with small EMG responses for the first half period, followed by no excessive EMG activities for the second half period. We speculate that those novel characteristics of beta rebound might be caused by slow postural dynamics along a stable manifold of the unstable saddle-type upright equilibrium of the postural control system without active feedback control, but with active monitoring of the postural state, in the framework of the intermittent control.

Idiosyncratic Characteristics of Postural Sway in Normal and Perturbed Standing

Objective

Are people with a characteristically large physiological sway rendered particularly unstable when standing on a moving surface? Is postural sway in standing individuals idiosyncratic? In this study, we examine postural sway in individuals standing normally, and when subtle continuous sinusoidal disturbances are applied to their support platform. We calculate consistency between conditions to verify if sway can be considered characteristic of each individual. We also correlate two different aspects of participants’ responses to disturbance; their sway velocity and their regulation of body orientation.

Methods

Nineteen healthy adults (age 29.2 ± 3.2 years) stood freely on footplates coaxially aligned with their ankles and attached to a motorized platform. They had their eyes closed, and hips and knees locked with a light wooden board attached to their body. Participants either stood quietly on a fixed platform or on a slowly tilting platform (0.1 Hz sinusoid; 0.2 and 0.4 deg). Postural sway size was separated into two entities: (1) the spontaneous sway velocity component (natural random relatively rapid postural adjustments, RMS body angular velocity) and (2) the evoked tilt gain component (much slower 0.1 Hz synchronous tilt induced by the movement of the platform, measured as peak-to-peak (p-p) gain, ratio of body angle to applied footplate rotation).

Results

There was no correlation between the velocity of an individual’s sway and their evoked tilt gain (r = 0.34, p = 0.15 and r = 0.30, p = 0.22). However, when considered separately, each of the two measurements showed fair to good absolute agreement within conditions. Spontaneous sway velocity consistently increased as participants were subjected to increasing disturbance. Participants who swayed more (or less) did so across all conditions [ICC_(3,k) = 0.95]. Evoked tilt gain also showed consistency between conditions [ICC_(3,k) = 0.79], but decreased from least to most disturbed conditions.

Conclusion

The two measurements remain consistent between conditions. Consistency between conditions of two very distinct unrelated measurements reflects the idiosyncratic nature of postural sway. However, sway velocity and tilt gain are not related, which supports the idea that the short-term regulation of stability and the longer-term regulation of orientation are controlled by different processes.

The assessment of center of mass and center of pressure during quiet stance: Current applications and future directions

This perspective article provides a brief review of our understanding of how center of pressure (CoP) and center of mass (CoM) are traditionally utilized to measure quiet standing and how technological advancements are allowing for measurements to be derived outside the confines of a laboratory setting. Furthermore, this viewpoint provides descriptions of what CoP and CoM outcomes may reflect, a discussion of recent developments in selected balance outcomes, the importance of measuring instantaneous balance outcomes, and directions for future questions/research. Considering the enormous number and cost of falls annually, conclusions drawn from this perspective underscore the need for more cohesive efforts to advance our understanding of balance performance. As we refine the technology and algorithms used to portably assess postural stability, the question of which measurement (i.e. CoP or CoM) to utilize seems to be highly dependent on the question being asked. Further, the complexity of the question appears to span multiple disciplines and cultivate exploration of the intrinsic mechanisms of stability. Recently developed multi-dimensional methods for assessing balance performance may provide additional insight into balance, improving our ability to predict balance impairments and falls outside the laboratory and in the clinic. However, additional work will be necessary to understand the clinical significance and predictive capacity of these outcomes in various fall-prone populations.

The effects of sensory quantization and control torque saturation on human balance control

The effect of reaction delay, temporal sampling, sensory quantization, and control torque saturation is investigated numerically for a single-degree-of-freedom model of postural sway with respect to stability, stabilizability, and control effort. It is known that reaction delay has a destabilizing effect on the balancing process: the later one reacts to a perturbation, the larger the possibility of falling. If the delay is larger than a critical value, then stabilization is not even possible. In contrast, numerical analysis showed that quantization and control torque saturation have a stabilizing effect: the region of stabilizing control gains is greater than that of the linear model. Control torque saturation allows the application of larger control gains without overcontrol while sensory quantization plays a role of a kind of filter when sensory noise is present. These beneficial effects are reflected in the energy demand of the control process. On the other hand, neither control torque saturation nor sensory quantization improves stabilizability properties. In particular, the critical delay cannot be increased by adding saturation and/or sensory quantization.