Visuo-manual tracking: does intermittent control with aperiodic sampling explain linear power and non-linear remnant without sensorimotor noise?

KEY POINTS: A human controlling an external system is described most easily and conventionally as linearly and continuously translating sensory input to motor output, with the inevitable output remnant, non-linearly related to the input, attributed to sensorimotor noise. Recent experiments show sustained manual tracking involves repeated refractoriness (insensitivity to sensory information for a certain duration), with the temporary 200-500 ms periods of irresponsiveness to sensory input making the control process intrinsically non-linear. This evidence calls for re-examination of the extent to which random sensorimotor noise is required to explain the non-linear remnant. This investigation of manual tracking shows how the full motor output (linear component and remnant) can be explained mechanistically by aperiodic sampling triggered by prediction error thresholds. Whereas broadband physiological noise is general to all processes, aperiodic sampling is associated with sensorimotor decision making within specific frontal, striatal and parietal networks; we conclude that manual tracking utilises such slow serial decision making pathways up to several times per second. ABSTRACT: The human operator is described adequately by linear translation of sensory input to motor output. Motor output also always includes a non-linear remnant resulting from random sensorimotor noise from multiple sources, and non-linear input transformations, for example thresholds or refractory periods. Recent evidence showed that manual tracking incurs substantial, serial, refractoriness (insensitivity to sensory information of 350 and 550 ms for 1st and 2nd order systems respectively). Our two questions are: (i) What are the comparative merits of explaining the non-linear remnant using noise or non-linear transformations? (ii) Can non-linear transformations represent serial motor decision making within the sensorimotor feedback loop intrinsic to tracking? Twelve participants (instructed to act in three prescribed ways) manually controlled two systems (1st and 2nd order) subject to a periodic multi-sine disturbance. Joystick power was analysed using three models, continuous-linear-control (CC), continuous-linear-control with calculated noise spectrum (CCN), and intermittent control with aperiodic sampling triggered by prediction error thresholds (IC). Unlike the linear mechanism, the intermittent control mechanism explained the majority of total power (linear and remnant) (77-87% vs. 8-48%, IC vs. CC). Between conditions, IC used thresholds and distributions of open loop intervals consistent with, respectively, instructions and previous measured, model independent values; whereas CCN required changes in noise spectrum deviating from broadband, signal dependent noise. We conclude that manual tracking uses open loop predictive control with aperiodic sampling. Because aperiodic sampling is inherent to serial decision making within previously identified, specific frontal, striatal and parietal networks we suggest that these structures are intimately involved in visuo-manual tracking.

Complexity and dynamics of switched human balance control during quiet standing.

In this paper, we use a combination of numerical simulations, time series analysis, and complexity measures to investigate the dynamics of switched systems with noise, which are often used as models of human balance control during quiet standing. We link the results with complexity measures found in experimental data of human sway motion during quiet standing. The control model ensuring balance, which we use, is based on an act-and-wait control concept, that is, a human controller is switched on when a certain sway angle is reached. Otherwise, there is no active control present. Given a time series data, we determine how does it look a typical pattern of control strategy in our model system. We detect the switched nonlinearity in the system using a frequency analysis method in the absence of noise. We also analyse the effect of time delay on the existence of limit cycles in the system in the absence of noise. We perform the entropy and detrended fluctuation analyses in view of linking the switchings (and the dead zone) with the occurrences of complexity in the model system in the presence of noise. Finally, we perform the entropy and detrended fluctuation analyses on experimental data and link the results with numerical findings in our model example.

Refractoriness in sustained visuo-manual control: is the refractory duration intrinsic or does it depend on external system properties?

Researchers have previously adopted the double stimulus paradigm to study refractoriness in human neuromotor control. Currently, refractoriness, such as the Psychological Refractory Period (PRP) has only been quantified in discrete movement conditions. Whether refractoriness and the associated serial ballistic hypothesis generalises to sustained control tasks has remained open for more than sixty years. Recently, a method of analysis has been presented that quantifies refractoriness in sustained control tasks and discriminates intermittent (serial ballistic) from continuous control. Following our recent demonstration that continuous control of an unstable second order system (i.e. balancing a 'virtual' inverted pendulum through a joystick interface) is unnecessary, we ask whether refractoriness of substantial duration (~200 ms) is evident in sustained visual-manual control of external systems. We ask whether the refractory duration (i) is physiologically intrinsic, (ii) depends upon system properties like the order (0, 1(st), and 2(nd)) or stability, (iii) depends upon target jump direction (reversal, same direction). Thirteen participants used discrete movements (zero order system) as well as more sustained control activity (1(st) and 2(nd) order systems) to track unpredictable step-sequence targets. Results show a substantial refractory duration that depends upon system order (250, 350 and 550 ms for 0, 1(st) and 2(nd) order respectively, n=13, p<0.05), but not stability. In sustained control refractoriness was only found when the target reverses direction. In the presence of time varying actuators, systems and constraints, we propose that central refractoriness is an appropriate control mechanism for accommodating online optimization delays within the neural circuitry including the more variable processing times of higher order (complex) input-output relations.

Does the motor system need intermittent control?

Explanation of motor control is dominated by continuous neurophysiological pathways (e.g., transcortical, spinal) and the continuous control paradigm. Using new theoretical development, methodology, and evidence, we propose intermittent control, which incorporates a serial ballistic process within the main feedback loop, provides a more general and more accurate paradigm necessary to explain attributes highly advantageous for competitive survival and performance.

Intermittent control models of human standing: similarities and differences.

Two architectures of intermittent control are compared and contrasted in the context of the single inverted pendulum model often used for describing standing in humans. The architectures are similar insofar as they use periods of open-loop control punctuated by switching events when crossing a switching surface to keep the system state trajectories close to trajectories leading to equilibrium. The architectures differ in two significant ways. Firstly, in one case, the open-loop control trajectory is generated by a system-matched hold, and in the other case, the open-loop control signal is zero. Secondly, prediction is used in one case but not the other. The former difference is examined in this paper. The zero control alternative leads to periodic oscillations associated with limit cycles; whereas the system-matched control alternative gives trajectories (including homoclinic orbits) which contain the equilibrium point and do not have oscillatory behaviour. Despite this difference in behaviour, it is further shown that behaviour can appear similar when either the system is perturbed by additive noise or the system-matched trajectory generation is perturbed. The purpose of the research is to come to a common approach for understanding the theoretical properties of the two alternatives with the twin aims of choosing which provides the best explanation of current experimental data (which may not, by itself, distinguish between the two alternatives) and suggesting future experiments to distinguish between the two alternatives.

Auto-regressive moving average analysis of linear and discontinuous models of human balance during quiet standing.

Linear Time Invariant (LTI) processes can be modelled by means of Auto-Regressive Moving Average (ARMA) model systems. In this paper, we examine whether an ARMA model can be fitted to a process characterised by switched nonlinearities. In particular, we conduct the following test: we generate data from known LTI and nonlinear (threshold/dead-zone) models of human balance and analyse the output using ARMA. We show that both these known systems can be fitted, according to standard criteria, with low order ARMA models. To check if there are some obvious effects of the dead-zone, we compare the power spectra of both systems with the power spectra of their ARMA models. We then examine spectral properties of three posturographic data sets and their ARMA models and compare them with the power spectra of our model systems. Finally, we examine the dynamics of our model systems in the absence of noise to determine what is the effect of the switching threshold (dead-zone) on the asymptotic dynamics.

Postural threat differentially affects the feedforward and feedback components of the vestibular-evoked balance response.

Circumstances may render the consequence of falling quite severe, thus maximising the motivation to control postural sway. This commonly occurs when exposed to height and may result from the interaction of many factors, including fear, arousal, sensory information and perception. Here, we examined human vestibular-evoked balance responses during exposure to a highly threatening postural context. Nine subjects stood with eyes closed on a narrow walkway elevated 3.85 m above ground level. This evoked an altered psycho-physiological state, demonstrated by a twofold increase in skin conductance. Balance responses were then evoked by galvanic vestibular stimulation. The sway response, which comprised a whole-body lean in the direction of the edge of the walkway, was significantly and substantially attenuated after ~800 ms. This demonstrates that a strong reason to modify the balance control strategy was created and subjects were highly motivated to minimise sway. Despite this, the initial response remained unchanged. This suggests little effect on the feedforward settings of the nervous system responsible for coupling pure vestibular input to functional motor output. The much stronger, later effect can be attributed to an integration of balance-relevant sensory feedback once the body was in motion. These results demonstrate that the feedforward and feedback components of a vestibular-evoked balance response are differently affected by postural threat. Although a fear of falling has previously been linked with instability and even falling itself, our findings suggest that this relationship is not attributable to changes in the feedforward vestibular control of balance.

Cautious gait in relation to knowledge and vision of height: is altered visual information the dominant influence?

For some people, visual exposure creates difficulty with movement and balance, yet the mechanisms causing this are poorly understood. The altered visual environment is an obvious possible cause of degraded balance. We studied locomotion in normal healthy adults along a 22-cm-wide walkway at ground level and at a height of 3.5 m. This produced substantial changes in gait progression (velocity reduced by 0.34 ms(-1), P <0.01), proportion of time spent in double support more than doubled (P <0.01), and galvanic skin conductance, a measure of physiological arousal, increased significantly (P <0.01). Since increasing visual distance is known to destabilize balance, our primary question was whether the disturbing effects of height could be eliminated by replacing sight of the drop with a visual surround comparable to ground level while retaining the danger and knowledge of the risk. Removing visual exposure did not significantly change the gait progression (P = 0.65) or double support duration (P = 0.58) but produced a small, significant reduction in physiological arousal (P = 0.04). In response to postural threat, knowledge of danger rather than current visual environment was the dominant cause of cautious gait and elevated physiological arousal in response to postural threat. We conclude that the mechanisms disturbing locomotion, balance, and autonomic response occur at a high task level which integrates cognition and prior experience with sensory input.

Recruitment of motor units in the medial gastrocnemius muscle during human quiet standing: is recruitment intermittent? What triggers recruitment?

The recruitment and the rate of discharge of motor units are determinants of muscle force. Within a motoneuron pool, recruitment and rate coding of individual motor units might be controlled independently, depending on the circumstances. In this study, we tested whether, during human quiet standing, the force of the medial gastrocnemius (MG) muscle is predominantly controlled by recruitment or rate coding. If MG control during standing was mainly due to recruitment, then we further asked what the trigger mechanism is. Is it determined internally, or is it related to body kinematics? While seven healthy subjects stood quietly, intramuscular electromyograms were recorded from the MG muscle with three pairs of wire electrodes. The number of active motor units and their mean discharge rate were compared for different sway velocities and positions. Motor unit discharges occurred more frequently when the body swayed faster and forward (Pearson R = 0.63; P < 0.0001). This higher likelihood of observing motor unit potentials was explained chiefly by the recruitment of additional units. During forward body shifts, the median number of units detected increased from 3 to 11 (P < 0.0001), whereas the discharge rate changed from 8 ± 1.1 (mean ± SD) to 10 ± 0.9 pulses/s (P = 0.001). Strikingly, motor units did not discharge continuously throughout standing. They were recruited within individual, forward sways and intermittently, with a modal rate of two recruitments per second. This modal rate is consistent with previous circumstantial evidence relating the control of standing to an intrinsic, higher level planning process.

Frequency-domain identification of the human controller.

System identification techniques applied to experimental human-in-the-loop data provide an objective test of three alternative control-theoretical models of the human control system: non-predictive control, predictive control, and intermittent predictive control. A two-stage approach to the identification of a single-input single-output control system is used: first, the closed-loop frequency response is derived using the periodic property of the experimental data, followed by the fitting of a parametric model. While this approach is well-established for non-predictive and predictive control, it is here used for the first time with intermittent predictive control. This technique is applied to data from experiments with human volunteers who use one of two control strategies, focusing either on position or on velocity, to manually control a virtual, unstable load which requires sustained feedback to maintain position or low velocity. The results show firstly that the non-predictive controller does not fit the data as well as the other two models, and secondly that the predictive and intermittent predictive controllers provide equally good models which cannot be distinguished using this approach. Importantly, the second observation implies that sustained visual manual control is compatible with intermittent control, and that previous results suggesting a continuous control model for the human control system do not rule out intermittent control as an alternative hypothesis. Thirdly, the parameters identified reflect the control strategy adopted by the human controller.

What is the contribution of voluntary and reflex processes to sensorimotor control of balance?

The contribution to balance of spinal and transcortical processes including the long-latency reflex is well known. The control of balance has been modelled previously as a continuous, state feedback controller representing, long-latency reflexes. However, the contribution of slower, variable delay processes has not been quantified. Compared with fixed delay processes (spinal, transcortical), we hypothesize that variable delay processes provide the largest contribution to balance and are sensitive to historical context as well as current states. Twenty-two healthy participants used a myoelectric control signal from their leg muscles to maintain balance of their own body while strapped to an actuated, inverted pendulum. We study the myoelectric control signal (u) in relation to the independent disturbance (d) comprising paired, discrete perturbations of varying inter-stimulus-interval (ISI). We fit the closed loop response, u from d, using one linear and two non-linear non-parametric (many parameter) models. Model M1 (ARX) is a generalized, high-order linear-time-invariant (LTI) process with fixed delay. Model M1 is equivalent to any parametric, closed-loop, continuous, linear-time-invariant (LTI), state feedback model. Model M2, a single non-linear process (fixed delay, time-varying amplitude), adds an optimized response amplitude to each stimulus. Model M3, two non-linear processes (one fixed delay, one variable delay, each of time-varying amplitude), add a second process of optimized delay and optimized response amplitude to each stimulus. At short ISI, the myoelectric control signals deviated systematically both from the fixed delay LTI process (M1), and also from the fixed delay, time-varying amplitude process (M2) and not from the two-process model (M3). Analysis of M3 (all fixed delay and variable delay response amplitudes) showed the variable (compared with fixed) delay process 1) made the largest contribution to the response, 2) exhibited refractoriness (increased delay related to short ISI) and 3) was sensitive to stimulus history (stimulus direction 2 relative to stimulus 1). For this whole-body balance task and for these impulsive stimuli, non-linear processes at variable delay are central to control of balance. Compared with fixed delay processes (spinal, transcortical), variable delay processes provided the largest contribution to balance and were sensitive to historical context as well as current states.

Is Intermittent Control the Source of the Non-Linear Oscillatory Component (0.2-2Hz) in Human Balance Control?

OBJECTIVE: To explain the 0.2-2Hz oscillation in human balance. MOTIVATION: Oscillation (0.2-2 Hz) in the control signal (ankle moment) is sustained independently of external disturbances and exaggerated in Parkinson's disease. Does resonance or limit cycles in the neurophysiological feedback loop cause this oscillation? We investigate two linear (non-predictive, predictive) and one non-linear (intermittent-predictive) control model (NPC, PC, IPC). METHODS: Fourteen healthy participants, strapped to an actuated single segment robot with dynamics of upright standing, used natural haptic-visual feedback and myoelectric control signals from lower leg muscles to maintain balance. An input disturbance applied stepwise changes in external force. A linear time invariant model (ARX) extracted the delayed component of the control signal related linearly to the disturbance, leaving the remaining, larger, oscillatory non-linear component. We optimized model parameters and noise (observation, motor) to replicate concurrently (i) estimated-delay, (ii) time-series of the linear component, and (iii) magnitude-frequency spectrum and transient magnitude response of the non-linear component. Results (mean±S.D., p<0.05): NPC produced estimated delays (0.116±0.03s) significantly lower than experiment (0.145±0.04s). Overall fit (i)-(iii) was (79±7%, 83±7%, 84±6% for NPC, PC, IPC). IPC required little or no noise. Mean frequency of experimental oscillation (0.99±0.16 Hz) correlated trial by trial with closed loop resonant frequency (fres), not limit cycles, nor sampling rate. NPC (0.36±0.08Hz) and PC (0.86±0.4Hz) showed fres significantly lower than IPC (0.98±0.2Hz). CONCLUSION: Human balance control requires short-term prediction. SIGNIFICANCE: IPC mechanisms (prediction error, threshold related sampling, sequential re-initialization of open-loop predictive control) explain resonant gain without uncontrolled oscillation for healthy balance.

Human control of an inverted pendulum: is continuous control necessary? Is intermittent control effective? Is intermittent control physiological?

Human motor control is often explained in terms of engineering 'servo' theory. Recently, continuous, optimal control using internal models has emerged as a leading paradigm for voluntary movement. However, these engineering paradigms are designed for high band-width, inflexible, consistent systems whereas human control is low bandwidth and flexible using noisy sensors and actuators. By contrast, engineering intermittent control was designed for bandwidth-limited applications. Our general interest is whether intermittent rather than continuous control is generic to human motor control. Currently, it would be assumed that continuous control is the superior and physiologically natural choice for controlling unstable loads, for example as required for maintaining human balance. Using visuo-manual tracking of an unstable load, we show that control using gentle, intermittent taps is entirely natural and effective. The gentle tapping method resulted in slightly superior position control and velocity minimisation, a reduced feedback time delay, greater robustness to changing actuator gain and equal or greater linearity with respect to the external disturbance. Control was possible with a median contact rate of 0.8±0.3 s(-1). However, when optimising position or velocity regulation, a modal contact rate of 2 s(-1) was observed. This modal rate was consistent with insignificant disturbance-joystick coherence beyond 1-2 Hz in both tapping and continuous contact methods. For this load, these results demonstrate a motor control process of serial ballistic trajectories limited to an optimum rate of 2 s(-1). Consistent with theoretical reasoning, our results suggest that intermittent open loop action is a natural consequence of human physiology.

Postural activation of the human medial gastrocnemius muscle: are the muscle units spatially localised?

In cat medial gastrocnemius (MG), fibres supplied by individual motoneurones (muscle units) distribute extensively along the muscle longitudinal axis. In the human MG, the size of motor unit territory is unknown. It is uncertain if the absolute size of muscle unit territory or the size relative to the whole muscle is most comparable with the cat. By comparing intramuscular and surface electromyograms we tested whether muscle units extend narrowly or widely along the human MG muscle. Due to the pennation of the MG, if individual motoneurones supply fibres scattered along the muscle, then action potentials of single motor units are expected to appear sparsely on the surface of the skin. In nine healthy subjects, pairs of wire electrodes were inserted in three locations along the MG muscle (MG60%, MG75% and MG90%). A longitudinal array of 16 surface electrodes was positioned alongside the intramuscular electrodes. While subjects stood quietly, 55 motor units were identified, of which, significantly more units were detected in the most distal sites. The surface action potentials had maximum amplitude at 4.40 ±1.67 (mean±S.D.), 8.02±2.16 and 11.63±2.09 cm (P <0.001) from the most proximal surface electrode, for motor units in the MG60%, MG75% and MG90% locations, respectively. Single motor unit potentials were recorded by five consecutive surface electrodes, at most, indicating that muscle units extend shortly along the MG longitudinal axis. It is concluded that relative to the whole muscle, and compared with the cat, muscle units in human MG are localised. The localisation of muscle units might have implications for the regional control of muscle activity.

A semi-automated programme for tracking myoblast migration following mechanical damage: manipulation by chemical inhibitors.

BACKGROUND: Potential roles for undifferentiated skeletal muscle stem cells or satellite cells in muscle hypertrophy and repair have been reported, however, the capacity, the mode and the mechanisms underpinning migration have not been investigated. We hypothesised that damaged skeletal myoblasts would elicit a mesenchymal-like migratory response, which could be precisely tracked and subsequently manipulated. METHODS: We therefore established a model of mechanical damage and developed a MATLAB(TM) tool to measure the migratory capacity of myoblasts in a non-subjective manner. RESULTS: Basal migration following damage was highly directional, with total migration distances of 948µm ± 239µm being recorded (average 0-24 hour distances: 491µm ± 113µm and 24-48 hour distances: 460µm ± 218µm). Pharmacological inhibition of MEK or PI3-K using PD98059 (20µM) or LY294002 (5µm), resulted in significant reduction of overall cell migration distances of 38% (p<0.001) and 39.5% (p<0.0004), respectively. Using the semi-automated cell tracking using MATLAB(TM) program we validated that not only was migration distance reduced as a consequence of reduced cell velocity, but critically also as a result of altered directionality of migration. CONCLUSION: These studies demonstrate that murine myoblasts in culture migrate and provide a good model for studying responsiveness to damage in vitro. They illustrate for the first time the powerful tool that MATLAB(TM) provides in determining that both velocity and directional capacity influence the migratory potential of cellular movement with obvious implications for homing and for metastases.

Intermittent control: a computational theory of human control.

The paradigm of continuous control using internal models has advanced understanding of human motor control. However, this paradigm ignores some aspects of human control, including intermittent feedback, serial ballistic control, triggered responses and refractory periods. It is shown that event-driven intermittent control provides a framework to explain the behaviour of the human operator under a wider range of conditions than continuous control. Continuous control is included as a special case, but sampling, system matched hold, an intermittent predictor and an event trigger allow serial open-loop trajectories using intermittent feedback. The implementation here may be described as "continuous observation, intermittent action". Beyond explaining unimodal regulation distributions in common with continuous control, these features naturally explain refractoriness and bimodal stabilisation distributions observed in double stimulus tracking experiments and quiet standing, respectively. Moreover, given that human control systems contain significant time delays, a biological-cybernetic rationale favours intermittent over continuous control: intermittent predictive control is computationally less demanding than continuous predictive control. A standard continuous-time predictive control model of the human operator is used as the underlying design method for an event-driven intermittent controller. It is shown that when event thresholds are small and sampling is regular, the intermittent controller can masquerade as the underlying continuous-time controller and thus, under these conditions, the continuous-time and intermittent controller cannot be distinguished. This explains why the intermittent control hypothesis is consistent with the continuous control hypothesis for certain experimental conditions.

Force accuracy rather than high stiffness is associated with faster learning and reduced falls in human balance.

Balance requires the centre of mass to be maintained within the base of support. This can be achieved by minimising position sway (stiffness control: SC) or minimising force error (force accuracy control: FAC). Minimising sway reduces exploration of system properties, whereas minimising force error maximizes accurate mapping of the force vs position. We hypothesise that (i) FAC is associated with faster learning and fewer falls whereas (ii) SC is not. Fifteen participants used myoelectric signals from their legs to maintain balance of an actuated, inverted pendulum, to which they were strapped. Using challenging perturbations, participants were trained to maintain balance without falling within five sessions and tested before (PRE) and after (POST) training. We quantified FAC as 'change (POST-PRE) in correlation of force with position' and SC as 'change in sway'. PRE training, five measures (sway, acceleration, co-contraction, effort, falls) showed no correlation with either FAC or SC. POST training, reduced fall rate, effort and acceleration correlated with FAC metric. SC correlated only with reduced sway. Unlike sway minimisation, development of force accuracy was associated with learning and reduced falls. These results support that accurate force estimation allowing movement is more relevant than stiffness to improve balance and prevent falls.

Estimation of absolute states of human skeletal muscle via standard B-mode ultrasound imaging and deep convolutional neural networks.

The objective is to test automated in vivo estimation of active and passive skeletal muscle states using ultrasonic imaging. Current technology (electromyography, dynamometry, shear wave imaging) provides no general, non-invasive method for online estimation of skeletal muscle states. Ultrasound (US) allows non-invasive imaging of muscle, yet current computational approaches have never achieved simultaneous extraction or generalization of independently varying active and passive states. We use deep learning to investigate the generalizable content of two-dimensional (2D) US muscle images. US data synchronized with electromyography of the calf muscles, with measures of joint moment/angle, were recorded from 32 healthy participants (seven female; ages: 27.5, 19-65). We extracted a region of interest of medial gastrocnemius and soleus using our prior developed accurate segmentation algorithm. From the segmented images, a deep convolutional neural network was trained to predict three absolute, drift-free components of the neurobiomechanical state (activity, joint angle, joint moment) during experimentally designed, simultaneous independent variation of passive (joint angle) and active (electromyography) inputs. For all 32 held-out participants (16-fold cross-validation) the ankle joint angle, electromyography and joint moment were estimated to accuracy 55 ± 8%, 57 ± 11% and 46 ± 9%, respectively. With 2D US imaging, deep neural networks can encode, in generalizable form, the activity-length-tension state relationship of these muscles. Observation-only, low-power 2D US imaging can provide a new category of technology for non-invasive estimation of neural output, length and tension in skeletal muscle. This proof of principle has value for personalized muscle assessment in pain, injury, neurological conditions, neuropathies, myopathies and ageing.