Dynamic Determinants of the Uncontrolled Manifold during Human Quiet Stance.

Human postural sway during stance arises from coordinated multi-joint movements. Thus, a sway trajectory represented by a time-varying postural vector in the multiple-joint-angle-space tends to be constrained to a low-dimensional subspace. It has been proposed that the subspace corresponds to a manifold defined by a kinematic constraint, such that the position of the center of mass (CoM) of the whole body is constant in time, referred to as the kinematic uncontrolled manifold (kinematic-UCM). A control strategy related to this hypothesis (CoM-control-strategy) claims that the central nervous system (CNS) aims to keep the posture close to the kinematic-UCM using a continuous feedback controller, leading to sway patterns that mostly occur within the kinematic-UCM, where no corrective control is exerted. An alternative strategy proposed by the authors (intermittent control-strategy) claims that the CNS stabilizes posture by intermittently suspending the active feedback controller, in such a way to allow the CNS to exploit a stable manifold of the saddle-type upright equilibrium in the state-space of the system, referred to as the dynamic-UCM, when the state point is on or near the manifold. Although the mathematical definitions of the kinematic- and dynamic-UCM are completely different, both UCMs play similar roles in the stabilization of multi-joint upright posture. The purpose of this study was to compare the dynamic performance of the two control strategies. In particular, we considered a double-inverted-pendulum-model of postural control, and analyzed the two UCMs defined above. We first showed that the geometric configurations of the two UCMs are almost identical. We then investigated whether the UCM-component of experimental sway could be considered as passive dynamics with no active control, and showed that such UCM-component mainly consists of high frequency oscillations above 1 Hz, corresponding to anti-phase coordination between the ankle and hip. We also showed that this result can be better characterized by an eigenfrequency associated with the dynamic-UCM. In summary, our analysis highlights the close relationship between the two control strategies, namely their ability to simultaneously establish small CoM variations and postural stability, but also make it clear that the intermittent control hypothesis better explains the spectral characteristics of sway.

Robot therapy for stroke survivors: proprioceptive training and regulation of assistance.

Robot therapy seems promising with stroke survivors, but it is unclear which exercises are most effective, and whether other pathologies may benefit from this technique. In general, exercises should exploit the adaptive nature of the nervous system, even in chronic patients. Ideally, exercise should involve multiple sensory modalities and, to promote active subject participation, the level of assistance should be kept to a minimum. Moreover, exercises should be tailored to the different degrees of impairment, and should adapt to changing performance. To this end, we designed three tasks: (i) a hitting task, aimed at improving the ability to perform extension movements; (ii) a tracking task, aimed at improving visuo-motor control; and (iii) a bimanual task, aimed at fostering inter-limb coordination. All exercises are conducted on a planar manipulandum with two degrees of freedom, and involve alternating blocks of exercises performed with and without vision. The degree of assistance is kept to a minimum, and adjusted to the changing subject's performance. All three exercises were tested on chronic stroke survivors with different levels of impairment. During the course of each exercise, movements became faster, smoother, more precise, and required decreasing levels of assistive force. These results point to the potential benefit of that assist-as-needed training with a proprioceptive component in a variety of clinical conditions.

Braccio di Ferro: a new haptic workstation for neuromotor rehabilitation.

This technical note describes a new robotic workstation for neurological rehabilitation, shortly named Braccio di Ferro. It has been designed by having in mind the range of forces and the frequency bandwidth that characterize the interaction between a patient and a physical therapist, as well as a number of requirements that we think are essential for allowing a natural haptic interaction: back-driveability, very low friction and inertia, mechanical robustness, the possibility to operate in different planes, and an open software environment, which allows the operator to add new functionalities and design personalized rehabilitation protocols. Braccio di Ferro is an open system and, in the spirit of open source design, is intended to foster the dissemination of robot therapy. Moreover, its combination of features is not present in commercially available systems.

Body sway during quiet standing: is it the residual chattering of an intermittent stabilization process?

This paper reviews different approaches for explaining body sway while quiet standing that directly address the instability of the human inverted pendulum. We argue that both stiffness control [Winter, D. A., Patla, A. E., Riedtyk, S., & Ishac, M. (2001). Ankle muscle stiffness in the control of balance during quiet standing. Journal of Neurophysiology, 85, 2630-2633] and continuous feedback control by means of a PID (Proportional, Integral, Derivative) mechanism [Peterka, R. J. (2000). Postural control model interpretation of stabilogram diffusion analysis. Biological Cybernetics, 83, 335-343.] can guarantee asymptotic stability of controlled posture at the expense of unrealistic assumptions: the level of intrinsic muscle stiffness in the former case, and the level of background noise in the latter, which also determines an unrealistic level of jerkiness in the sway. We show that the decomposition of the control action into a slow and a fast component (rambling and trembling, respectively, as proposed by [Zatsiorsky, V. M., & Duarte, M. (1999). Instant equilibrium point and its migration in standing tasks: Rambling and trembling components of the stabilogram. Motor Control, 4, 185-200; Zatsiorsky, V. M., & Duarte, M. (2000). Rambling and trembling in quiet standing. Motor Control, 4, 185-200.]) is useful but must be modified in order to take into account that rambling is not a stable equilibrium trajectory. We address the possibility of a form of stability weaker than asymptotic stability in light of the intermittent stabilization mechanism outlined by [Loram, I. D., & Lakie, M. (2002a). Human balancing of an inverted pendulum: position control by small, ballistic-like, throw and catch movements. Journal of Physiology, 540, 1111-1124.], and propose an indicator of intermittent stabilization that is related to the phase portrait of the human inverted pendulum. This indicator provides a further argument against the plausibility of PID-like control mechanisms. Finally, we draw attention to the sliding mode control theory that provides a useful theoretical framework for formulating realistic intermittent, stabilization models.

Direct measurement of ankle stiffness during quiet standing: implications for control modelling and clinical application.

In this study, we describe a device for the direct measurement of intrinsic ankle stiffness in quiet standing. It consists of a motorised footplate mounted on a force platform. By generating random sequences of step-like disturbances (1 degrees amplitude, 150 ms duration) and measuring the corresponding displacements of the center of pressure in the antero-posterior direction, we obtained torque-rotation patterns after aligning, averaging, and scaling the postural responses. Such patterns were used for estimating the value of the ankle stiffness, which was normalized as a fraction of the critical value. In order to be confident that the measurements addressed the intrinsic ankle stiffness and were not affected in a significant way by the reflex activation of the muscles in response to the test disturbances, we performed the estimates in different ways: least squares estimates with time windows of different widths and an instantaneous estimate at the time in which the angular acceleration vanishes. The statistical analysis showed that there is no significant difference among the different methods of estimate and the inspection of the electromyographic activity in response to the perturbations showed that at least two of the estimates were certainly outside the possible influence of reflex patterns. The intrinsic ankle stiffness was evaluated to be 64+/-8% of the critical stiffness for test disturbances of the order of 1 degrees. We argue that this figure identifies the lower bound of the range of values which characterise normal sway in quiet standing, whereas the upper bound is given by the estimates performed with much smaller test disturbances [1] which yield a higher value: 91+/-23%. The two estimation paradigms (with very small and very large test disturbances, respectively) are complementary also because they behave in a different way as regards the sensitivity to a bias torque: it is close to zero in the Loram & Lakie's paradigm, whereas it is significant in our paradigm. Thus, as the bias grows, it appears that the range of stiffness values is narrowed and is pushed towards the upper bound. There is a clear potential for the clinical application of these methods, in the sense that the identification of the range of stiffness values used by a patient is a measurable index of motor organisation/reorganisation.

Spot check and recalibration of stabilometric platforms.

The purpose of this paper is to describe a system for the rapid spot check of the accuracy of stabilometric platforms used in clinical posturography and, if needed, for estimating a recalibration matrix. It is based on a simple mechanical device which can be applied to any stabilometric platform; it consists of a ballast and a rotating mass which can generate a spiral-shaped training set of posturographic data. A software package has been developed whose purpose is to estimate a calibration matrix and to provide a figure of merit for the calibrated system. The data analysis is organized into two phases: a preliminary global phase, which uses the covariance matrix of the training set, and a refinement, iterative phase, which exploits the equation of the spiral. The characteristic features of the proposed system are: 1) it uses dynamic, not static loading, 2) loading is not applied manually, 3) it uses distributed, not point loads, 4) there is no need to bolt the system to the platform. Although these features are found, separately, in different prototypes described in the literature, their combination can only be found in the proposed system. Moreover, while most systems in the literature are intended for gait analysis, the proposed one is specifically designed for posturography.

The sway-density curve and the underlying postural stabilization process.

The sway-density curve (SDC) is computed by counting, for each time instant, the number of consecutive samples of the statokinesigram falling inside a circle of small radius R. The authors evaluated the sensitivity of the curve to the variation of R and found that in the range 3-5 mm the sensitivity was low, indicating that SDC is a robust descriptor of posturographic patterns. In addition, they investigated the relationship between SDC and the underlying postural stabilization process by decomposing the total ankle torque into three components: a tonic component (over 69 & of the total torque), an elastic torque caused by ankle stiffness (about 19 &), and an anticipatory active torque (about 12 &). The last component, although the smallest in size, is the most critical for the overall stability of the standing posture and appears to be correlated with the SDC curve.

Cerebellar ataxia: quantitative assessment and cybernetic interpretation.

To assess neuromotor disorders clinicians often rely on rating scales. Unfortunately, these scales lack the sensitivity and accuracy needed to detect the small changes in motor coordination that reflect the clinical progression of the disease on the basis of which treatment programmes can be adjusted. As a contribution to this topic, the present paper proposes a straightforward kinematic and kinetic analysis of reaching movements of patients with cerebellar ataxia in conjunction with a cybernetic interpretation of the data. The aim of the approach is to capture key deficits in the underlying motor control processes. We suggest that cerebellar ataxia may be characterized by defective feedforward control.

Ankle muscle stiffness alone cannot stabilize balance during quiet standing.

This communication addresses again the hypothesis that the stabilization of balance during quiet standing is achieved by the stiffness of ankle muscles without anticipatory active control. It is shown that a recently proposed method of estimating ankle stiffness directly from the analysis of the posturographic data is incorrect because it ignores the modulation of motoneuronal activity and grossly overestimates the real range of values in relation with the critical value of stiffness. Moreover, a new simulation study with a realistic model of ankle muscles demonstrates the mechanical instability of the system when there is no anticipatory control input. However, the simulations also suggest that in normal subjects the active stiffness mechanisms of stabilization have similar weights in determining the restoring forces that are necessary for preventing the body from falling.

A new look at posturographic analysis in the clinical context: sway-density versus other parameterization techniques.

In order to identify useful guidelines for the clinical practitioner as regards the use of static posturographic analysis, we collected a set of posturograms from 3 groups of participants (normal participants, Parkinsonian patients, and osteo-porotic patients), according to the Romberg test. From each posturogram, we extracted global parameters (in the time domain and frequency domain) and structural parameters (based on diffusion plots and sway-density plots), with a total of 38 parameters. The discriminative power of each parameter was evaluated by means of statistical analysis in relation to the condition effect (open vs. closed eyes) and the pathology effect (normal participants vs. patients). The initial set of 38 parameters was reduced to 24 by identifying clear redundancies, and then to 18 by eliminating the parameters that did not pass the condition effect with normal participants. These parameters were analyzed for reliability and discriminative power in the general framework of a biomechanic model of postural stabilization. At the end of this analysis, we suggested that a set of 4 parameters is particularly valuable in the clinical practice: 2 global parameters (sway-path and frequency band of the posturogram) and 2 structural parameters (mean value of peaks and mean inter-peak distance in the sway-density plots).

Coordinate-free sensorimotor processing: computing with population codes.

The purpose of the study is to outline a computational architecture for the intelligent processing of sensorimotor patterns. The focus is on the nature of the internal representations of the outside world which are necessary for planning and other goal-oriented functions. A model of cortical map dynamics and self-organization is proposed that integrates a number of concepts and methods partly explored in the field. The novelty and the biological plausibility is related to the global architecture which allows one to deal with sensorimotor patterns in a coordinate-free way, using population codes as distributed internal representations of external variables and the coupled dynamics of cortical maps as a general tool of trajectory formation. The basic computational features of the model are demonstrated in the case of articulatory speech synthesis and some of the metric properties are evaluated by means of simple simulation studies.